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Einstein Gravity as an emergent phenomenon ; In this essay we marshal evidence suggesting that Einstein gravity may be an emergent phenomenon, one that is not fundamental'' but rather is an almost automatic lowenergy longdistance consequence of a wide class of theories. Specifically, the emergence of a curved spacetime effective Lorentzian geometry'' is a common generic result of linearizing a classical scalar field theory around some nontrivial background. This explains why so many different analog models'' of general relativity have recently been developed based on condensed matter physics; there is something more fundamental going on. Upon quantizing the linearized fluctuations around this background geometry, the oneloop effective action is guaranteed to contain a term proportional to the EinsteinHilbert action of general relativity, suggesting that while classical physics is responsible for generating an effective geometry'', quantum physics can be argued to induce an effective dynamics''. This physical picture suggests that Einstein gravity is an emergent lowenergy longdistance phenomenon that is insensitive to the details of the highenergy shortdistance physics.

Lectures on Quantum Cosmology ; The problems encountered in trying to quantize the various cosmological models, are brought forward by means of a concrete example. The Automorphism groups are revealed as the key element through which G.C.T.'s can be used for a general treatment of these problems. At the classical level, the time dependent automorphisms lead to significant simplifications of the line element for the generic spatially homogeneous geometry, without loss of generality. At the quantum level, the ''frozen'' automorphisms entail an important reduction of the configuration space spanned by the 6 components of the scale factor matrix on which the WheelerDeWitt equation, is to be based. In this spirit the canonical quantization of the most general minisuperspace actions i.e. with all six scale factor as well as the lapse function and the shift vector present describing the vacuum type II, I geometries, is considered. The reduction to the corresponding physical degrees of freedom is achieved through the usage of the linear constraints as well as the quantum version of the entire set of all classical integrals of motion.

Quantum suppression of the generic chaotic behavior close to cosmological singularities ; In classical general relativity, the generic approach to the initial singularity is very complicated as exemplified by the chaos of the Bianchi IX model which displays the generic local evolution close to a singularity. Quantum gravity effects can potentially change the behavior and lead to a simpler initial state. This is verified here in the context of loop quantum gravity, using methods of loop quantum cosmology the chaotic behavior stops once quantum effects become important. This is consistent with the discrete structure of space predicted by loop quantum gravity.

Local covariant quantum field theory over spectral geometries ; A framework which combines ideas from Connes' noncommutative geometry, or spectral geometry, with recent ideas on generally covariant quantum field theory, is proposed in the present work. A certain type of spectral geometries modelling possibly noncommutative globally hyperbolic spacetimes is introduced in terms of socalled globally hyperbolic spectral triples. The concept is further generalized to a category of globally hyperbolic spectral geometries whose morphisms describe the generalization of isometric embeddings. Then a local generally covariant quantum field theory is introduced as a covariant functor between such a category of globally hyperbolic spectral geometries and the category of involutive algebras or algebras. Thus, a local covariant quantum field theory over spectral geometries assigns quantum fields not just to a single noncommutative geometry or noncommutative spacetime, but simultaneously to all'' spectral geometries, while respecting the covariance principle demanding that quantum field theories over isomorphic spectral geometries should also be isomorphic. It is suggested that in a quantum theory of gravity a particular class of globally hyperbolic spectral geometries is selected through a dynamical coupling of geometry and matter compatible with the covariance principle.

Causal structure of acoustic spacetimes ; The socalled analogue models of general relativity'' provide a number of specific physical systems, well outside the traditional realm of general relativity, that nevertheless are welldescribed by the differential geometry of curved spacetime. Specifically, the propagation of acoustic disturbances in moving fluids are described by effective metrics'' that carry with them notions of causal structure'' as determined by an exchange of sound signals. These acoustic causal structures serve as specific examples of what can be done in the presence of a Lorentzian metric without having recourse to the Einstein equations of general relativity. After all, the underlying fluid mechanics is governed by the equations of traditional hydrodynamics, not by the Einstein equations. In this article we take a careful look at what can be said about the causal structure of acoustic spacetimes, focusing on those containing sonic points or horizons, both with a view to seeing what is different from standard general relativity, and to seeing what the similarities might be.

New Models of General Relativistic Static Thick Disks ; New families of exact general relativistic thick disks are constructed using the displace, cut, fill and reflect'' method. A class of functions used to fill'' the disks is derived imposing conditions on the first and second derivatives to generate physically acceptable disks. The analysis of the function's curvature further restrict the ranges of the free parameters that allow phisically acceptable disks. Then this class of functions together with the Schwarzschild metric is employed to construct thick disks in isotropic, Weyl and Schwarzschild canonical coordinates. In these last coordinates an additional function must be added to one of the metric coefficients to generate exact disks. Disks in isotropic and Weyl coordinates satisfy all energy conditions, but those in Schwarzschild canonical coordinates do not satisfy the dominant energy condition.

Spin Gauge Theory of Gravity in Clifford Space A Realization of KaluzaKlein Theory in 4Dimensional Spacetime ; A theory in which 4dimensional spacetime is generalized to a larger space, namely a 16dimensional Clifford space Cspace is investigated. Curved Clifford space can provide a realization of KaluzaKlein theory. A covariant Dirac equation in curved Cspace is explored. The generalized Dirac field is assumed to be a polyvectorvalued object a Clifford number which can be written as a superposition of four independent spinors, each spanning a different left ideal of Clifford algebra. The general transformations of a polyvector can act from the left andor from the right, and form a large gauge group which may contain the group U1xSU2xSU3 of the standard model. The generalized spin connection in Cspace has the properties of YangMills gauge fields. It contains the ordinary spin connection related to gravity with torsion, and extra parts describing additional interactions, including those described by the antisymmetric KalbRamond fields.

Clifford and RiemannFinsler Structures in Geometric Mechanics and Gravity ; The book contains a collection of works on RiemannCartan and metricaffine manifolds provided with nonlinear connection structure and on generalized FinslerLagrange and CartanHamilton geometries and Clifford structures modelled on such manifolds. The choice of material presented has evolved from various applications in modern gravity and geometric mechanics and certain generalizations to noncommutative RiemannFinsler geometry. The authors develop and use the method of anholonomic frames with associated nonlinear connection structure and apply it to a number of concrete problems constructing of generic offdiagonal exact solutions, in general, with nontrivial torsion and nonmetricity, possessing noncommutative symmetries and describing black ellipsoidtorus configurations, locally anisotropic wormholes, gravitational solitons and warped factors and investigation of stability of such solutions; classification of Lagrange Finsler affine spaces; definition of nonholonomic Dirac operators and their applications in commutative and noncommutative Finsler geometry.

Singularities and Quantum Gravity ; Although there is general agreement that a removal of classical gravitational singularities is not only a crucial conceptual test of any approach to quantum gravity but also a prerequisite for any fundamental theory, the precise criteria for nonsingular behavior are often unclear or controversial. Often, only special types of singularities such as the curvature singularities found in isotropic cosmological models are discussed and it is far from clear what this implies for the very general singularities that arise according to the singularity theorems of general relativity. In these lectures we present an overview of the current status of singularities in classical and quantum gravity, starting with a review and interpretation of the classical singularity theorems. This suggests possible routes for quantum gravity to evade the devastating conclusion of the theorems by different means, including modified dynamics or modified geometrical structures underlying quantum gravity. The latter is most clearly present in canonical quantizations which are discussed in more detail. Finally, the results are used to propose a general scheme of singularity removal, quantum hyperbolicity, to show cases where it is realized and to derive intuitive semiclassical pictures of cosmological bounces.

GaugeCoupling Unification and the Minimal SUSY Model A Fourth Generation Below the Top ; We explore the possibility of a fourth generation in the gaugecouplingunified, minimal supersymmetric MSSM framework. We find that a sequential fourth generation with a heavy neutrino nu' can still fit, surviving all present experimental constraints, provided lambdabMUlambdatauMU Yukawa unification is relaxed. For the theory to remain perturbative up to MU, the new leptonic generation must lie within reach of LEPII and the new b',t' must have masses within the reach of the Tevatron. For example, for mt150gev we find mnu',mtau' 86gev, mt'178, and mb'156gev. Experiments at Fermilab are already sensitive to the latter mass regions; we comment on direct b' searches and on the mt'simeq mt case in light of new CDF data. Discovery may involve novel decay signatures; however, CDF and LEPII will confirm or exclude an MSSM fourth generation in the near future.

GIM Violation and New Dynamics of the Third Generation ; In strong dynamical schemes for electroweak symmetry breaking the third generation must be treated in a special manner, owing to the heavy top quark. This potentially leads to new flavor physics involving the members of the third generation in concert with the adjoining generations, with potential novel effects in beauty and charm physics. We give a general discussion and formulation of this kind of physics, abstracted largely from Topcolor models which we elaborate in detail. We identify sensitive channels for such new physics accessible to current and future experiments.

Electroweak Origin of Cosmological Magnetic Fields ; Magnetic fields may have been generated in the electroweak phase transition through spontaneous symmetry breaking or through the subsequent dynamical evolution of semiclassical field configurations. Here I demonstrate explicitly how magnetic fields emerge spontaneously in the phase transition also when no gradients of the Higgs field are present. Using a simple model, I show that no magnetic fields are generated, at least initially, from classical twobubble collisions in a firstorder phase transition. An improved gaugeinvariant definition of the electromagnetic field is advocated which is more appropriate in the sense that it never allows electrically neutral fields to serve as sources for the electromagnetic field. In particular, semiclassical configurations of the Z field alone do not generate magnetic fields. The possible generation of magnetic fields in the decay of unstable Zstrings is discussed.

Thermal and NonThermal Production of Gravitinos in the Early Universe ; The excessive production of gravitinos in the early universe destroys the successful predictions of nucleosynthesis. The thermal generation of gravitinos after inflation leads to the bound on the reheating temperature, TRH 109 GeV. However, it has been recently realized that the nonthermal generation of gravitinos in the early universe can be extremely efficient and overcome the thermal production by several orders of magnitude, leading to much tighter constraints on the reheating temperature. In this paper, we first investigate some aspects of the thermal production of gravitinos, taking into account that in fact reheating is not instantaneous and inflation is likely to be followed by a prolonged stage of coherent oscillations of the inflaton field. We then proceed by further investigating the nonthermal generation of gravitinos, providing the necessary tools to study this process in a generic timedependent background with any number of superfields. We also present the first numerical results regarding the nonthermal generation of gravitinos in particular supersymmetric models.

Charge Asymmetry in the Brane World and Formation of Charged Black Holes ; In theories with an infinite extra dimension, free particles localized on the brane can leak out to the extra space. We argue that if there were color confinement in the bulk, electrons would be more able to escape than quarks and than protons which are composed states. Thus, this process generates an electric charge asymmetry on brane matter densities. A primordial charge asymmetry during Big Bang Nucleosynthesis era is predicted. We use current bounds on this and on electron disappearance to constrain the parameter space of these models. Although the generated asymmetry is generically small, it could be particularly enhanced on large densities as in astrophysical objects, like massive stars. We suggest the possibility that such accumulation of charge may be linked, upon supernova collapse, to the formation of a charged Black Hole and the generation of GammaRay Bursts.

Generalized Spin Systems and Models ; A generalization of the SU2spin systems on a lattice and their continuum limit to an arbitrary compact group G is discussed. The continuum limits are, in general, nonrelativistic sigmamodel type field theories targeted on a homogeneous space GH, where H contains the maximal torus of G. In the ferromagnetic case the equations of motion derived from our continuum Lagrangian generalize the LandauLifshitz equations with quadratic dispersion relation for small wave vectors. In the antiferromagnetic case the dispersion law is always linear in the long wavelength limit. The models become relativistic only when GH is a symmetric space. Also discussed are a generalization of the HolsteinPrimakoff representation of the SUN algebra, the topological term and the existence of the instanton type solutions in the continuum limit of the antiferromagnetic systems.

Generalized TwoDimensional QCD ; We study twodimensional gauge theories with fundamental fermions and a general first order gaugefield Lagrangian. For the case of U1 we show how standard bosonization of the Schwinger model generalizes to give mesons interacting through a general LandauGinzburg potential. We then show how for a subclass of SUN theories, 't Hooft's solution of large N twodimensional QCD can be generalized in a consistent and natural manner. We finally point out the possible relevance of studying these theories to the string formulation of twodimensional QCD as well as to understanding QCD in higher dimensions.

Loop Equations as a Generalized Virasoro Constraints ; The loop equations in the UN lattice gauge theory are represented in the form of constraints imposed on a generating functional for the Wilson loop correlators. These constraints form a closed algebra with respect to commutation. This algebra generalizes the Virasoro one, which is known to appear in onematrix models in the same way. The realization of this algebra in terms of the infinitesimal changes of generators of the loop space is given. The representations on the tensor fields on the loop space, generalizing the integer spin conformal fields, are constructed. The structure constants of the algebra under consideration being independent of the coupling constants, almost all the results are valid in the continuum.

Coset Realization of Unifying WAlgebras ; We construct several quantum coset Walgebras, e.g. sl2,RU1 and sl2,Rsl2,R sl2,R, and argue that they are finitely nonfreely generated. Furthermore, we discuss in detail their role as unifying Walgebras of Casimir Walgebras. We show that it is possible to give coset realizations of various types of unifying Walgebras, e.g. the diagonal cosets based on the symplectic Lie algebras sp2n realize the unifying Walgebras which have previously been introduced as WDn'. In addition, minimal models of WDn are studied. The coset realizations provide a generalization of levelrankduality of dual coset pairs. As further examples of finitely nonfreely generated quantum Walgebras we discuss orbifolding of Walgebras which on the quantum level has different properties than in the classical case. We demonstrate in some examples that the classical limit according to Bowcock and Watts of these nonfreely finitely generated quantum Walgebras probably yields infinitely nonfreely generated classical Walgebras.

General Rotating Black Holes in String Theory Greybody Factors and Event Horizons ; We derive the wave equation for a minimally coupled scalar field in the background of a general rotating fivedimensional black hole. It is written in a form that involves two types of thermodynamic variables, defined at the inner and outer event horizon, respectively. We model the microscopic structure as an effective string theory, with the thermodynamic properties of the left and right moving excitations related to those of the horizons. Previously known solutions to the wave equation are generalized to the rotating case, and their regime of validity is sharpened. We calculate the greybody factors and interpret the resulting Hawking emission spectrum microscopically in several limits. We find a Uduality invariant expression for the effective string length that does not assume a hierarchy between the charges. It accounts for the universal lowenergy absorption crosssection in the general nonextremal case.

Generating branes via sigmamodels ; Starting with the Ddimensional Einsteindilatonantisymmetric form equations and assuming a blockdiagonal form of a metric we derive a Dddimensional sigmamodel with the target space SLd,RSOd times SL2,RSO2 times R or its noncompact form. Various solutiongenerating techniques are developed and applied to construct some known and some new pbrane solutions. It is shown that the Harrison transformation belonging to the SL2,R subgroup generates black pbranes from the seed Schwarzschild solution. A fluxbrane generalizing the BonnorMelvinGibbonsMaeda solution is constructed as well as a nonlinear superposition of the fluxbrane and a spherical black hole. A new simple way to endow branes with additional internal structure such as plane waves is suggested. Applying the harmonic maps technique we generate new solutions with a nontrivial shell structure in the transverse space matrioshka' pbranes. It is shown that the pbrane intersection rules have a simple geometric interpretation as conditions ensuring the symmetric space property of the target space. Finally, a Bonnortype symmetry is used to construct a new magnetic 6brane with a dipole moment in the tendimensional IIA theory.

A holographic formulation of quantum general relativity ; We show that there is a sector of quantum general relativity which may be expressed in a completely holographic formulation in terms of states and operators defined on a finite boundary. The space of boundary states is built out of the conformal blocks of SU2L SU2R, WZW field theory on the npunctured sphere, where n is related to the area of the boundary. The Bekenstein bound is explicitly satisfied. These results are based on a new lagrangian and hamiltonian formulation of general relativity based on a constrained Sp4 topological field theory. The hamiltonian formalism is polynomial, and also leftright symmetric. The quantization uses balanced SU2L SU2R spin networks and so justifies the state sum model of Barrett and Crane. By extending the formalism to Osp4N a holographic formulation of extended supergravity is obtained, as will be described in detail in a subsequent paper.

A crucial ingredient of inflation ; Nonminimal coupling of the inflaton field to the Ricci curvature of spacetime is generally unavoidable, and the paradigm of inflation should be generalized by including the corresponding term in the Lagrangian of the inflationary theory. This paper reports on the status of the programme of generalizing inflation. First, the problem of finding the correct value or set of values of the coupling constant is analyzed; the result has important consequences for the success or failure of inflationary scenarios. Then, the slowroll approximation to generalized inflation is studied. Both the unperturbed inflating universe models and scalartensor perturbations are discussed, and open problems are pointed out.

General TwoDimensional Supergravity from Poisson Superalgebras ; We provide the geometric actions for most general N1 supergravity in two spacetime dimensions. Our construction implies an extension to arbitrary N. This provides a supersymmetrization of any generalized dilaton gravity theory or of any theory with an action being an essentially arbitrary function of curvature and torsion. Technically we proceed as follows The bosonic part of any of these theories may be characterized by a generically nonlinear Poisson bracket on a threedimensional target space. In analogy to a given ordinary Lie algebra, we derive all possible N1 extensions of any of the given Poisson or W algebras. Using the concept of graded Poisson Sigma Models, any extension of the algebra yields a possible supergravity extension of the original theory, local Lorentz and superdiffeomorphism invariance follow by construction. Our procedure automatically restricts the fermionic extension to the minimal one; thus local supersymmetry is realized onshell. By avoiding a superfield approach we are also able to circumvent in this way the introduction of constraints and their solution. For many wellknown dilaton theories different supergravity extensions are derived. In generic cases their field equations are solved explicitly.

Geometrical Origin of Fermion Families in SU2xU1 Gauge Theory ; A spontaneously broken SU2xU1 gauge theory with just one primordial generation of fermions is formulated in the context of generally covariant theory which contains two measures of integration in the action the standard sqrtgd4x and a new Phi d4x, where Phi is a density built out of degrees of freedom independent of the metric. Such type of models are known to produce a satisfactory answer to the cosmological constant problem. Global scale invariance is implemented. After SSB of scale invariance and gauge symmetry it is found that with the conditions appropriate to laboratory particle physics experiments, to each primordial fermion field corresponds three physical fermionic states. Two of them correspond to particles with constant masses and they are identified with the first two generations of the electroweak theory. The third fermionic states at the classical level get nonpolynomial interactions which indicate the existence of fermionic condensate and fermionic mass generation.

Open String BRST Cohomology for Generalized Complex Branes ; It has been shown recently that the geometry of Dbranes in general topologically twisted 2,2 sigmamodels can be described in the language of generalized complex structures. On general grounds such Dbranes called generalized complex GC branes must form a category. We compute the BRST cohomology of open strings with both ends on the same GC brane. In mathematical terms, we determine spaces of endomorphisms in the category of GC branes. We find that the BRST cohomology can be expressed as the cohomology of a Lie algebroid canonically associated to any GC brane. In the special case of Bbranes, this leads to an apparently new way to compute Ext groups of holomorphic line bundles supported on complex submanifolds while the usual method leads to a spectral sequence converging to the Ext, our approach expresses the Ext group as the cohomology of a certain differential acting on the space of smooth sections of a graded vector bundle on the submanifold. In the case of coisotropic Abranes, our computation confirms a proposal of D. Orlov and one of the authors A.K..

Fermion generations, masses and mixings in a 6D brane model ; We study the motion of higher dimensional fermions in a nonsingular 6D brane background with an increasing warp factor. This background acts as a potential well trapping fermions and fields of other spins near a 31 dimensional brane. By adjusting the shape of this potential well it is possible to obtain three normalizable zero mass modes giving a possible higher dimensional solution to the fermion generation puzzle. The three different zero mass modes correspond to the different angular momentum eigenvalues for rotations around the brane. This bulk angular momentum acts as the family or generation number. The three normalizable zero modes have different profiles with respect to the bulk, thus by coupling the higher dimensional fermion field to a higher dimensional scalar field it is possible to generate both a realistic mass hierarchy and realistic mixings between the different families.

Generalized SerreTate Ordinary Theory ; We study a generalization of SerreTate theory of ordinary abelian varieties and their deformation spaces. This generalization deals with abelian varieties equipped with additional structures. The additional structures can be not only an action of a semisimple algebra and a polarization, but more generally the data given by some crystalline Hodge cycles'' a padic version of a Hodge cycle in the sense of motives. Compared to SerreTate ordinary theory, new phenomena appear in this generalized context. We give an application of this theory to the existence of good'' integral models of those Shimura varieties whose adjoints are products of simple, adjoint Shimura varieties of Dlbf H type with lge 4.

On the Generation of Hyperpowersets for the DSmT ; The recent theory of plausible and paradoxical reasoning DSmT for short, or DezertSmarandache Theory, developed by the authors, appears to be a nice promising theoretical tools to solve many information fusion problems for example in military defense, medicine, etc., where the Shafer's model cannot be used due to the intrinsic paradoxical nature of the elements of the frame of discernment and where a strong internal conflict between sources arises. The main idea of DSmT is to work on the hyperpowerset of the frame of discernment of the problem under consideration. Although the definition of hyperpowerset is well established, the major difficulty in practice is to generate such hyperpowersets in order to implement DSmT fusion rule on computers. We present in this paper a simple algorithm for generating hyperpowersets and discuss the limitations of our actual computers to generate such hyperpowersets when the dimension of the problem increases.

Regular rapidly decreasing nonlinear generalized functions. Application to microlocal regularity ; We present new types of regularity for nonlinear generalized functions, based on the notion of regular growth with respect to the regularizing parameter of Colombeau's simplified model. This generalizes the notion of Ginfty regularity introduced by M. Oberguggenberger. A key point is that these regularities can be characterized, for compactly supported generalized functions, by a property of their Fourier transform. This opens the door to microanalysis of singularities of generalized functions, with respect to these regularities. We present a complete study of this topic, including properties of the Fourier transform exchange and regularity theorems and relationship with classical theory, via suitable results of embeddings.

Comment on formulating and generalizing Dirac's, Proca's, and Maxwell's equations with biquaternions or Clifford numbers ; Many difficulties of interpretation met by contemporary researchers attempting to recast or generalize Dirac's, Proca's, or Maxwell's theories using biquaternions or Clifford numbers have been encountered long ago by a number of physicists including Lanczos, Proca, and Einstein. In the modern approach initiated by Gursey, these difficulties are solved by recognizing that most generalizations lead to theories describing superpositions of particles of different intrinsic spin and isospin, so that the correct interpretation emerges from the requirement of full Poincare covariance, including space and time reversal, as well as of reversion and gauge invariance. For instance, the doubling of the number of solutions implied by the simplest generalization of Dirac's equation i.e., Lanczos's equation can be interpreted as isospin. In this approach, biquaternions and Clifford numbers become powerful opportunities to formulate the Standard Model of elementary particles, as well as many of its possible generalizations, in very elegant and compact ways.

Quantum Macrostatistical Theory of Nonequilibrium Steady States ; We provide a general macrostatistical formulation of nonequilibrium steady states of reservoir driven quantum systems. This formulation is centred on the large scale properties of the locally conserved hydrodynamical observables, and our basic assumptions comprise a a chaoticity hypothesis for the nonconserved currents carried by these observables, b an extension of Onsager's regression hypothesis to the fluctuations about nonequilibrium states, and c a certain mesoscopic local equilibrium hypothesis. On this basis we obtain a picture wherein the fluctuations of the hydrodynamical observables about a nonequilibrium steady state execute a Gaussian Markov process of a generalized OnsagerMachlup type, which is completely determined by the position dependent transport coefficients and the equilibrium entropy function of the system. This picture reveals that the transport coefficients satisfy a generalized form of the Onsager reciprocity relations in the nonequilibrium situation and that the spatial correlations of the hydrodynamical observables are generically of long range. This last result constitutes a modelindependent generalization of that obtained for special classical stochastic systems and marks a striking difference between the steady nonequilibrium and equilibrium states, since it is only at critical points that the latter carry long range correlations.

Generalized Benney Lattice and the Heavenly Equation ; We generalize the Benney lattice and show that the new system of equations can be reduced to a generalized Chaplygin gas as well as the heavenly equation. We construct two infinite sets of conserved charges and show that one of the sets can be obtained from the Lax function. The conserved densities are related to Legendre polynomials and we present closed form expressions for the generating functions for these densities which also determines the Riemann invariants of the problem. We prove that the system is biHamiltonian and that the conserved charges are in involution with respect to either of the Hamiltonian structures. We show that the associated generalized elastic medium equations are biHamiltonian as well. We also bring out various other interesting features of our model.

On generating functions in the AKNS hierarchy ; It is shown that the selfinduced transparency equations can be interpreted as a generating function for as positive so negative flows in the AKNS hierarchy. Mutual commutativity of these flows leads to other hierarchies of integrable equations. In particular, it is shown that stimulated Raman scattering equations generate the hierarchy of flows which include the Heisenberg model equations. This observation reveals some new relationships between known integrable equations and permits one to construct their new physically important combinations. Reductions of the AKNS hierarchy to ones with complex conjugate and real dependent variables are also discussed and the corresponding generating functions of positive and negative flows are found. Generating function of Whitham modulation equations in the AKNS hierarchy is obtained.

A Model of Classical and Quantum Measurement ; We take the view that physical quantities are values generated by processes in measurement, not preexistent objective quantities, and that a measurement result is strictly a product of the apparatus and the subject of the measurement. We habitually make an inaccurate statements when we speak of the measurement of a quantity by an apparatus. These statements can be formalised as a many valued logic with the structure of a vector space with a hermitian form in such a way as to generate probabilities in the results of measurement. The difference between this and classical probability theory is that we are not finding probabilities generated by unknown variables, but probabilities generated by unknown structure. We thus interpret quantum logic as the application of complex truth values to statements in an inaccurate language, and find that the properties of vector space hold for approximate measurement as well as for measurement of optimal accuracy, suggesting that Planck's constant governs the scale of the fundamental structures of matter.

Theory of sub10 fs Generation in Kerrlens Modelocked SolidState Lasers with a Coherent Semiconductor Absorber ; The results of the study of ultrashort pulse generation in continuouswave Kerrlens modelocked KLM solidstate lasers with semiconductor saturable absorbers are presented. The issues of extremely short pulse generation are addressed in the frames of the theory that accounts for the coherent nature of the absorberpulse interaction. We developed an analytical model that bases on the coupled generalized LandauGinzburg laser equation and Bloch equations for a coherent absorber. We showed, that in the absence of KLM semiconductor absorber produces 2pi nonsechpulses of selfinduced transparency, while the KLM provides an extremely short sechshaped pulse generation. 2pi and pisechshaped solutions and variablearea chirped pulses have been found. It was shown, that the presence of KLM removes the limitation on the minimal modulation depth in absorber. An automudulational stability and selfstarting ability were analyzed, too.

Laser Generated Magnetic Pulses Hot Electron Propagation in Conducting and Dielectric Material ; We report experimental evidence of electrostatic inhibition of fast electrons, generated in a highly resistive material upon irradiation with an intense ultrashort 1016 Wcm2, 100 fmsec laser pulse. The experiment involves measurement of temporal evolution of selfgenerated magnetic pulses using pumpprobe polarimetry. A comparison is made between the temporal behaviour of magnetic pulses generated with Aluminum and Glass targets. It is found that in contrast to Aluminium, selfgenerated magnetic pulse decays much faster in glass. This is attributed to the absence of return shielding currents in glass, which results in build up of electrostatic field, which in turn inhibits the movement of fast electrons. Fitting of experimental measurements using a one dimensional model, yields estimate of conductivity of Aluminium and glass, and penetration depth of hot electrons in these materials.

Terahertz generation in Czochralski grown periodically poled MgYLiNbO3 via optical rectification ; Using a canonical pumpprobe experimental technique, we studied the terahertz THz waves generation and detection via optical rectification and mixing in Czochralskigrown periodically poled MgYLiNbO3 PPLN crystals. THz waves with frequencies at 1.37 THz and 0.68 THz as well as 1.8 THz were obtained for PPLN with nonlinear grating periods of 0.03 and 0.06 mm, respectively. A general theoretical model was developed by considering the dispersion and damping of low frequency phononpolariton mode. Our results show that THz waves are generated in forward and backward directions via pumping pulse rectification. The generated THz waves depend on the spectral shape of the laser pulses, quasiphase mismatches and dispersion characteristics of a crystal.

Mathematical Structure of Rabi Oscillations in the Strong Coupling Regime ; In this paper we generalize the JaynesCummings Hamiltonian by making use of some operators based on Lie algebras su1,1 and su2, and study a mathematical structure of Rabi floppings of these models in the strong coupling regime. We show that Rabi frequencies are given by matrix elements of generalized coherent operators quantph0202081 under the rotatingwave approximation. In the first half we make a general review of coherent operators and generalized coherent ones based on Lie algebras su1,1 and su2. In the latter half we carry out a detailed examination of Frasca quantph0111134 and generalize his method, and moreover present some related problems. We also apply our results to the construction of controlled unitary gates in Quantum Computation. Lastly we make a brief comment on application to Holonomic Quantum Computation.

Green functions for generalized point interactions in 1D A scattering approach ; Recently, general point interactions in one dimension has been used to model a large number of different phenomena in quantum mechanics. Such potentials, however, requires some sort of regularization to lead to meaningful results. The usual ways to do so rely on technicalities which may hide important physical aspects of the problem. In this work we present a new method to calculate the exact Green functions for general point interactions in 1D. Our approach differs from previous ones because it is based only on physical quantities, namely, the scattering coefficients, R and T, to construct G. Renormalization or particular mathematical prescriptions are not invoked. The simple formulation of the method makes it easy to extend to more general contexts, such as for lattices of N general point interactions; on a line; on a halfline; under periodic boundary conditions; and confined in a box.

Distillability and positivity of partial transposes in general quantum field systems ; Criteria for distillability, and the property of having a positive partial transpose, are introduced for states of general bipartite quantum systems. The framework is sufficiently general to include systems with an infinite number of degrees of freedom, including quantum fields. We show that a large number of states in relativistic quantum field theory, including the vacuum state and thermal equilibrium states, are distillable over subsystems separated by arbitrary spacelike distances. These results apply to any quantum field model. It will also be shown that these results can be generalized to quantum fields in curved spacetime, leading to the conclusion that there is a large number of quantum field states which are distillable over subsystems separated by an event horizon.

Direct versus measurement assisted bipartite entanglement in multiqubit systems and their dynamical generation in spin systems ; We consider multiqubit systems and relate quantitatively the problems of generating cluster states with high value of concurrence of assistance, and that of generating states with maximal bipartite entanglement. We prove an upper bound for the concurrence of assistance. We consider dynamics of spin12 systems that model qubits, with different couplings and possible presence of magnetic field to investigate the appearance of the discussed entanglement properties. We find that states with maximal bipartite entanglement can be generated by an XY Hamiltonian, and their generation can be controlled by the initial state of one of the spins. The same Hamiltonian is capable of creating states with high concurrence of assistance with suitably chosen initial state. We show that the production of graph states using the Ising Hamiltonian is controllable via a singlequbit rotation of one spin12 subsystem in the initial multiqubit state. We shown that the property of Ising dynamics to convert a product state basis into a special maximally entangled basis is temporally enhanced by the application of a suitable magnetic field. Similar basis transformations are found to be feasible in the case of isotropic XY couplings with magnetic field.

A Possible Generalization of Quantum Mechanics ; A minimal generalization of Quantum Mechanics is proposed, where the Lagrangian or the action functional is a mapping from the classical states of a system to the Lie algebra of a general compact Lie group, and the wave function takes values in the corresponding group algebra. This formalism admits a probability interpretation and a suitable dynamics, but has no obvious classical correspondence. Allowing the Lagrangian or the action functional to take values in a general Lie algebra instead of only the real number field actually the u1 algebra enlarges the extent of possible physical laws that can describe the real world. The generalized quantum dynamics of a point particle in a background gauge field is given as an example, which realizes the gauge invariance by a Wilson line structure and shows that some Schrodingerlike equation can be deduced within this formalism. Some possible developments of this formalism are also discussed.

The rise and fall of quantum and classical correlations in opensystem dynamics ; Interacting quantum systems evolving from an uncorrelated composite initial state generically develop quantum correlations entanglement. As a consequence, a local description of interacting quantum system is impossible as a rule. A unitarily evolving isolated quantum system generically develops extensive entanglement the magnitude of the generated entanglement will increase without bounds with the effective Hilbert space dimension of the system. It is conceivable, that coupling of the interacting subsystems to local dephasing environments will restrict the generation of entanglement to such extent, that the evolving composite system may be considered as approximately disentangled. This conjecture is addressed in the context of some common models of a bipartite system with linear and nonlinear interactions and local coupling to dephasing environments. Analytical and numerical results obtained imply that the conjecture is generally false. Open dynamics of the quantum correlations is compared to the corresponding evolution of the classical correlations and a qualitative difference is found.

On generalized entropy measures and pathways ; Product probability property, known in the literature as statistical independence, is examined first. Then generalized entropies are introduced, all of which give generalizations to Shannon entropy. It is shown that the nature of the recursivity postulate automatically determines the logarithmic functional form for Shannon entropy. Due to the logarithmic nature, Shannon entropy naturally gives rise to additivity, when applied to situations having product probability property. It is argued that the natural process is nonadditivity, important, for example, in statistical mechanics, even in product probability property situations and additivity can hold due to the involvement of a recursivity postulate leading to a logarithmic function. Generalizations, including Mathai's generalized entropy are introduced and some of the properties are examined. Situations are examined where Mathai's entropy leads to pathway models, exponential and power law behavior and related differential equations. Connection of Mathai's entropy to Kerridge's measure of inaccuracy is also explored.

Thirdorder cosmological perturbations of zeropressure multicomponent fluids Pure general relativistic nonlinear effects ; Present expansion stage of the universe is believed to be mainly governed by the cosmological constant, collisionless dark matter and baryonic matter. The latter two components are often modeled as zeropressure fluids. In our previous work we have shown that to the secondorder cosmological perturbations, the relativistic equations of the zeropressure, irrotational, multicomponent fluids in a spatially near flat background effectively coincide with the Newtonian equations. As the Newtonian equations only have quadratic order nonlinearity, it is practically interesting to derive the potential thirdorder perturbation terms in general relativistic treatment which correspond to pure general relativistic corrections. Here, we present pure general relativistic correction terms appearing in the thirdorder perturbations of the multicomponent zeropressure fluids. We show that, as in a single component situation, the thirdorder correction terms are quite small 5 x105 smaller compared with the relativisticNewtonian secondorder terms due to the weak level anisotropy of the cosmic microwave background radiation. Still, there do exist pure general relativistic correction terms in thirdorder perturbations which could potentially become important in future development of precision cosmology. We include the cosmological constant in all our analyses.

A general approach to fewcycle intense laser interactions with complex atoms ; A general it abinitio and nonperturbative method to solve the timedependent Schrodinger equation TDSE for the interaction of a strong attosecond laser pulse with a general atom, i.e., beyond the models of quasioneelectron or quasitwoelectron targets, is described. The fieldfree Hamiltonian and the dipole matrices are generated using a flexible Bspline Rmatrix method. This numerical implementation enables us to construct termdependent, nonorthogonal sets of oneelectron orbitals for the bound and continuum electrons. The solution of the TDSE is propagated in time using the ArnoldiLanczos method, which does not require the diagonalization of any large matrices. The method is illustrated by an application to the multiphoton excitation and ionization of Ne atoms. Good agreement with Rmatrix Floquet calculations for the generalized cross sections for twophoton ionization is achieved.

Theoretical studies of highharmonic generation Effects of symmetry, degeneracy and orientation ; Using a quantum mechanical threestep model we present numerical calculations on the highharmonic generation from four polyatomic molecules. Ethylene C2H4 serves as an example where orbital symmetry directly affects the harmonic yield. We treat the case of methane CH4 to address the highharmonic generation resulting from a molecule with degenerate orbitals. To this end we illustrate how the single orbital contributions show up in the total highharmonic signal. This example illustrates the importance of adding coherently amplitude contributions from the individual degenerate orbitals. Finally, we study the highharmonic generation from propane C3H8 and butane C4H10. These two molecules, being extended and far from spherical in structure, produce harmonics with nontrivial orientational dependencies. In particular, propane can be oriented so that very highfrequency harmonics are favorized, and thus the molecule contains prospects for the generation of UV attosecond pulses.

Double Lepton Polarization in b l l Decay in the Standard Model with Fourth Generations Scenario ; This study investigates the influence of the fourth generation quarks on the double lepton polarizations in Lambdab Lambda ell ell decay by taking Vastt'sVt'b 0.005,0.01,0.02,0.03 with phase 60circ,90circ,120circ. We will try to obtain a constrain on the mass of the 4th generation top like quark t', which is consistent with the b sellell rate . With the above mentioned parameters, we will try to show that the double leptonmuon, tau polarizations are quite sensitive to the existence of fourth generation. It can serve as a good tool to search for new physics effects, precisely, to search for the fourth generation quarkst', b' via its indirect manifestations in loop diagrams.

The Newtonian Limit of FR gravity ; A general analytic procedure is developed to deal with the Newtonian limit of fR gravity. A discussion comparing the Newtonian and the postNewtonian limit of these models is proposed in order to point out the differences between the two approaches. We calculate the postNewtonian parameters of such theories without any redefinition of the degrees of freedom, in particular, without adopting some scalar fields and without any change from Jordan to Einstein frame. Considering the Taylor expansion of a generic fR theory, it is possible to obtain general solutions in term of the metric coefficients up to the third order of approximation. In particular, the solution relative to the gtt component gives a gravitational potential always corrected with respect to the Newtonian one of the linear theory fRR. Furthermore, we show that the Birkhoff theorem is not a general result for fRgravity since timedependent evolution for spherically symmetric solutions can be achieved depending on the order of perturbations. Finally, we discuss the postMinkowskian limit and the emergence of massive gravitational wave solutions.

CEDAR tools for event generator tuning ; I describe the work of the CEDAR collaboration in developing tools for tuning and validating Monte Carlo event generator programs. The core CEDAR task is to interface the Durham HepData database of experimental measurements to event generator validation tools such as the UCL JetWeb system this has necessitated the migration of HepData to a new relational database system and a Javabased interaction model. The number crunching part of JetWeb is also being upgraded, from the Fortran HZTool library to the new C Rivet system and a generator interfacing layer named RivetGun. Finally, I describe how Rivet is already being used as a central part of a new generator tuning system, and summarise two other CEDAR activities, HepML and HepForge.

The general relativistic infinite plane ; Uniform fields are one of the simplest and most pedagogically useful examples in introductory courses on electrostatics or Newtonian gravity. In general relativity there have been several proposals as to what constitutes a uniform field. In this article we examine two metrics that can be considered the general relativistic version of the infinite plane with finite mass per unit area. The first metric is the 4D version of the 5D brane world models which are the starting point for many current research papers. The second case is the cosmological domain wall metric. We examine to what extent these different metrics match or deviate from our Newtonian intuition about the gravitational field of an infinite plane. These solutions provide the beginning student in general relativity both computational practice and conceptual insight into Einstein's field equations. In addition they do this by introducing the student to material that is at the forefront of current research.

Invariant conserved currents for gravity ; We develop a general approach, based on the LagrangeNoether machinery, to the definition of invariant conserved currents for gravity theories with general coordinate and local Lorentz symmetries. In this framework, every vector field xi on spacetime generates, in any dimension n, for any Lagrangian of gravitational plus matter fields and for any minimal or nonminimal type of interaction, a current Jxi with the following properties 1 the current n1form Jxi is constructed from the Lagrangian and the generalized field momenta, 2 it is conserved, d Jxi 0, when the field equations are satisfied, 3 Jxi dPixi on shell, 4 the current Jxi, the superpotential Pixi, and the charge Qxi int Jxi are invariant under diffeomorphisms and the local Lorentz group. We present a compact derivation of the Noether currents associated with diffeomorphisms and apply the general method to compute the total energy and angular momentum of exact solutions in several physically interesting gravitational models.

Primordial perturbations and nonGaussianities in DBI and general multifield inflation ; We study cosmological perturbations in general inflation models with multiple scalar fields and arbitrary kinetic terms, with special emphasis on the multifield extension of DiracBornInfeld DBI inflation. We compute the secondorder action governing the dynamics of linear perturbations in the most general case. Specializing to DBI, we show that the adiabatic and entropy modes propagate with a it common effective sound speed and are thus amplified at sound horizon crossing. In the small sound speed limit, we find that the amplitude of the entropy modes is much higher than that of the adiabatic modes. We also derive, in the general case, the thirdorder action which is useful for studying primordial nonGaussianities generated during inflation. In the DBI case, we compute the dominant contributions to nonGaussianities, which depend on both the adiabatic and entropy modes.

Discontinuous Superprocesses with Dependent Spatial Motion ; We construct a class of discontinuous superprocesses with dependent spatial motion and general branching mechanism. The process arises as the weak limit of critical interactingbranching particle systems where the spatial motions of the particles are not independent. The main work is to solve the martingale problem. When we turn to the uniqueness of the process, we generalize the localization method introduced by D.W. Stroock, Diffusion processes associated with Levy generators, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 321975 209244 to the measurevalued context. As for existence, we use particle system approximation and a perturbation method. This work generalizes the model introduced in D.A. Dawson, Z. Li, H. Wang, Superprocesses with dependent spatial motion and general branching densities, Electron. J. Probab. 62001, no.25, 33 pp. electronic where quadratic branching mechanism was considered. We also investigate some properties of the process.

Scalartensor cosmologies general relativity as a fixed point of the Jordan frame scalar field ; We study the evolution of homogeneous and isotropic, flat cosmological models within the general scalartensor theory of gravity with arbitrary coupling function and potential and scrutinize its limit to general relativity. Using the methods of dynamical systems for the decoupled equation of the Jordan frame scalar field we find the fixed points of flows in two cases potential domination and matter domination. We present the conditions on the mathematical form of the coupling function and potential which determine the nature of the fixed points attractor or other. There are two types of fixed points, both are characterized by cosmological evolution mimicking general relativity, but only one of the types is compatible with the Solar System PPN constraints.

N 2 worldsheet approach to Dbranes on generalized Kaehler geometries I. General formalism ; We present an N 2 worldsheet superspace description of Dbranes on bihermitian or generalized Kaehler manifolds. To accomplish this, Dbranes are considered as boundary conditions for a nonlinear sigmamodel in what we call N 2 boundary superspace. In this note the general formalism for such an approach is presented and the resulting classification sketched. This includes some remarks regarding target spaces whose parameterization includes semichiral superfields which have not appeared in the literature yet. In an accompanying note we turn to some examples and applications of the general setup presented here.

Bayesian Generalized Probability Calculus for Density Matrices ; One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions can be seen as a special case when the density matrix is restricted to be diagonal. We develop a probability calculus based on these more general distributions that includes definitions of joints, conditionals and formulas that relate these, including analogs of the Theorem of Total Probability and various Bayes rules for the calculation of posterior density matrices. The resulting calculus parallels the familiar conventional probability calculus and always retains the latter as a special case when all matrices are diagonal. We motivate both the conventional and the generalized Bayes rule with a minimum relative entropy principle, where the KullbachLeibler version gives the conventional Bayes rule and Umegaki's quantum relative entropy the new Bayes rule for density matrices. Whereas the conventional Bayesian methods maintain uncertainty about which model has the highest data likelihood, the generalization maintains uncertainty about which unit direction has the largest variance. Surprisingly the bounds also generalize as in the conventional setting we upper bound the negative log likelihood of the data by the negative log likelihood of the MAP estimator.

Solidsolid interaction in the two body problem ; We consider the solidsolid interactions in the two body problem. The relative equilibria have been previously studied analytically and general motions were numerically analyzed using some expansion of the gravitational potential up to the second order, but only when there are no direct interactions between the orientation of the bodies. Here we expand the potential up to the fourth order and we show that the secular problem obtained after averaging over fast angles, as for the precession model of Boue and Laskar Boue, G., Laskar, J., 2006. Icarus 185, 312330, is integrable, but not trivially. We describe the general features of the motions and we provide explicit analytical approximations for the solutions. We demonstrate that the general solution of the secular system can be decomposed as a uniform precession around the total angular momentum and a periodic symmetric orbit in the precessing frame. More generally, we show that for a general nbody system of rigid bodies in gravitational interaction, the regular quasiperiodic solutions can be decomposed into a uniform precession around the total angular momentum, and a quasiperiodic motion with one frequency less in the precessing frame.

Neutrino masses from higher than d5 effective operators ; We discuss the generation of small neutrino masses from effective operators higher than dimension five, which open new possibilities for low scale seesaw mechanisms. In order to forbid the radiative generation of neutrino mass by lower dimensional operators, extra fields are required, which are charged under a new symmetry. We discuss this mechanism in the framework of a two Higgs doublet model. We demonstrate that the tree level generation of neutrino mass from higher dimensional operators often leads to inverse seesaw scenarios in which small lepton number violating terms are naturally suppressed by the new physics scale. Furthermore, we systematically discuss tree level generalizations of the standard seesaw scenarios from higher dimensional operators. Finally, we point out that higher dimensional operators can also be generated at the loop level. In this case, we obtain the TeV scale as new physics scale even with order one couplings.

Singlegeneration Network Coding for Networks with Delay ; A singlesource network is said to be textitmemoryfree if all of the internal nodes those except the source and the sinks do not employ memory but merely send linear combinations of the incoming symbols received at their incoming edges on their outgoing edges. Memoryfree networks with delay using network coding are forced to do intergeneration network coding, as a result of which the problem of some or all sinks requiring a large amount of memory for decoding is faced. In this work, we address this problem by utilizing memory elements at the internal nodes of the network also, which results in the reduction of the number of memory elements used at the sinks. We give an algorithm which employs memory at the nodes to achieve singlegeneration network coding. For fixed latency, our algorithm reduces the total number of memory elements used in the network to achieve singlegeneration network coding. We also discuss the advantages of employing singlegeneration network coding together with convolutional networkerror correction codes CNECCs for networks with unitdelay and illustrate the performance gain of CNECCs by using memory at the intermediate nodes using simulations on an example network under a probabilistic network error model.

Stochastic background of gravitational waves generated by pregalactic black holes ; In this work, we consider the stochastic background of gravitational waves SBGWs produced by pregalactic stars, which form black holes in scenarios of structure formation. The calculation is performed in the framework of hierarchical structure formation using a PressSchechterlike formalism. Our model reproduces the observed star formation rate at redshifts z 6.5. The signal predicted in this work is below the sensitivity of the first generation of detectors but could be detectable by the next generation of groundbased interferometers. Specifically, correlating two coincident advanced LIGO detectors LIGO III interferometers, the expected signaltonoiseratio SN could be as high as 90 10 for stars forming at redshift z 20 with a Salpeter initial mass function with slope x0.35 1.35, and if the efficiency of generation of gravitational waves is close to the maximum value 7 x 104. However, the sensitivity of the future third generation of detectors as, for example, the European antenna EGO could be high enough to produce SN3 same with efficiency 2 x 105. We also discuss what astrophysical information could be derived from a positive or even negative detection of the SBGWs investigated here.

General spherically symmetric elastic stars in Relativity ; The relativistic theory of elasticity is reviewed within the spherically symmetric context with a view towards the modeling of star interiors possessing elastic properties such as theones expected in neutron stars. Emphasis is placed on generality in the main sections of the paper, and the results are then applied to specific examples. Along the way, a few general results for spacetimes admitting isometries are deduced, and their consequences are fully exploited in the case of spherical symmetry relating them next to the the case in which the material content of the spacetime is some elastic material. This paper extends and generalizes the pioneering work by Magli and Kijowski 1, Magli 2 and 3, and complements, in a sense, that by Karlovini and Samuelsson in their interesting series of papers 4, 5 and 6.

Implication of a Quasi Fixed Point with a Heavy Fourth Generation The emergence of a TeVscale physical cutoff ; It has been shown in a recent paper that the Higgs quartic and Yukawa sectors of the Standard Model SM with a heavy fourth generation exhibit at a twoloop level a quasi fixed point structure instead of the oneloop Landau singularity and which could be located in the TeV region, a scale which is denoted by LambdaFP in this paper. This provides the possibility of the existence of a TeVscale physical cutoff endowed with several implications. In the vicinity of this quasi fixed point bound states and Higgslike condensates made up of the 4th generation quarks and leptons get formed. It implies the possibility of a dynamical electroweak symmetry breaking generated by 4th generation condensates. The quasi fixed points also hint at at a possible restoration of scale symmetry at LambdaFP and above and the emergence of a theory which could be deeper than the SM.

Supersymmetric AdS4 black holes and attractors ; Using the general recipe given in arXiv0804.0009, where all timelike supersymmetric solutions of N2, D4 gauged supergravity coupled to abelian vector multiplets were classified, we construct the first examples of genuine supersymmetric black holes in AdS4 with nonconstant scalar fields. This is done for various choices of the prepotential, amongst others for the STU model. These solutions permit to study the BPS attractor flow in AdS. We also determine the most general supersymmetric static nearhorizon geometry and obtain the attractor equations in gauged supergravity. As a general feature we find the presence of flat directions in the black hole potential, i.e., generically the values of the moduli on the horizon are not completely specified by the charges. For one of the considered prepotentials, the resulting moduli space is determined explicitely. Still, in all cases, we find that the black hole entropy depends only on the charges, in agreement with the attractor mechanism.

Distributed control of reactive power flow in a radial distribution circuit with high photovoltaic penetration ; We show how distributed control of reactive power can serve to regulate voltage and minimize resistive losses in a distribution circuit that includes a significant level of photovoltaic PV generation. To demonstrate the technique, we consider a radial distribution circuit with a single branch consisting of sequentiallyarranged residentialscale loads that consume both real and reactive power. In parallel, some loads also have PV generation capability. We postulate that the inverters associated with each PV system are also capable of limited reactive power generation or consumption, and we seek to find the optimal dispatch of each inverter's reactive power to both maintain the voltage within an acceptable range and minimize the resistive losses over the entire circuit. We assume the complex impedance of the distribution circuit links and the instantaneous load and PV generation at each load are known. We compare the results of the optimal dispatch with a suboptimal local scheme that does not require any communication. On our model distribution circuit, we illustrate the feasibility of high levels of PV penetration and a significant 20 or higher reduction in losses.

Inverted Sparticle Hierarchies from Natural Particle Hierarchies ; A possible resolution of the flavor puzzle is that the fermion mass hierarchy can be dynamically generated through the coupling of the first two generation fields to a strongly coupled sector, which is approximately conformally invariant and leads to large anomalous dimensions for the first two generation fields over a large range of energies. We investigate the possibility of using the same sector to also break supersymmetry. We show that this automatically gives an inverted hierarchy in which the first two generation squarks and sleptons are much heavier than the other superpartners. Implementing this construction generically requires some finetuning in order to satisfy the constraints on flavorchanging neutral currents at the same time as solving the hierarchy problem. We show that this finetuning can be reduced to be milder than the percent level by making some technically natural assumptions about the form of the strongly coupled sector and its couplings to the standard model.

Highorder harmonic generation from polyatomic molecules including nuclear motion and a nuclear modes analysis ; We present a generic approach for treating the effect of nuclear motion in the highorder harmonic generation from polyatomic molecules. Our procedure relies on a separation of nuclear and electron dynamics where we account for the electronic part using the Lewenstein model and nuclear motion enters as a nuclear correlation function. We express the nuclear correlation function in terms of FranckCondon factors which allows us to decompose nuclear motion into modes and identify the modes that are dominant in the highorder harmonic generation process. We show results for the isotopes CH4 and CD4 and thereby provide direct theoretical support for a recent experiment Baker it et al., Science bf 312, 424 2006 that uses highorder harmonic generation to probe the ultrafast structural nuclear rearrangement of ionized methane.

Time Delay Interferometry for LISA with one arm dysfunctional ; In order to attain the requisite sensitivity for LISA a joint space mission of the ESA and NASA the laser frequency noise must be suppressed below the secondary noises such as the optical path noise, acceleration noise etc. By combining six appropriately timedelayed data streams containing fractional Doppler shifts a technique called time delay interferometry TDI the laser frequency noise may be adequately suppressed. We consider the general model of LISA where the armlengths vary with time, so that second generation TDI are relevant. However, we must envisage the possibility, that not all the optical links of LISA will be operating at all times, and therefore, we here consider the case of LISA operating with two arms only. As shown earlier in the literature, obtaining even approximate solutions of TDI to the general problem is very difficult. Since here only four optical links are relevant, the algebraic problem simplifies considerably. We are then able to exhibit a large number of solutions from mathematical point of view an infinite number and further present an algorithm to generate these solutions.

Expanding perfect fluid generalizations of the Cmetric ; We reexamine Petrov type D gravitational fields generated by a perfect fluid with spatially homogeneous energy density and in which the flow lines form a timelike nonshearing and nonrotating congruence. It is shown that the anisotropic such spacetimes, which comprise the vacuum Cmetric as a limit case, can have emphnonzero expansion, contrary to the conclusion in the original investigation by Barnes Gen. Rel. Grav. 4, 105 1973. This class consists of cosmological models with generically one and at most two Killing vectors. We construct their line element and discuss some important properties. The methods used in this investigation incite to deduce testable criteria regarding shearfree normality and staticity op Petrov type D spacetimes in general, which we add in an appendix.

General Gauge Mediation with Gauge Messengers ; We generalize the General Gauge Mediation formalism to allow for the possibility of gauge messengers. Gauge messengers occur when charged matter fields of the susybreaking sector have nonzero Fterms, which leads to treelevel, susybreaking mass splittings in the gauge fields. A classic example is that SU5 SU3 x SU2 x U1 gauge fields could be gauge messengers. We give a completely general, model independent, currentalgebra based analysis of gauge messenger mediation of susybreaking to the visible sector. Characteristic aspects of gauge messengers include enhanced contributions to gaugino masses, tachyonic sfermion masssquareds generated already at one loop, and also at two loops, and significant oneloop Aterms, already at the messenger scale.

Testing General Relativity with Current Cosmological Data ; Deviations from general relativity, such as could be responsible for the cosmic acceleration, would influence the growth of large scale structure and the deflection of light by that structure. We clarify the relations between several different model independent approaches to deviations from general relativity appearing in the literature, devising a translation table. We examine current constraints on such deviations, using weak gravitational lensing data of the CFHTLS and COSMOS surveys, cosmic microwave background radiation data of WMAP5, and supernova distance data of Union2. Markov Chain Monte Carlo likelihood analysis of the parameters over various redshift ranges yields consistency with general relativity at the 95 confidence level.

Fractional Dynamics from Einstein Gravity, General Solutions, and Black Holes ; We study the fractional gravity for spacetimes with noninteger dimensions. Our constructions are based on a geometric formalism with the fractional Caputo derivative and integral calculus adapted to nonolonomic distributions. This allows us to define a fractional spacetime geometry with fundamental geometricphysical objects and a generalized tensor calculus all being similar to respective integer dimension constructions. Such models of fractional gravity mimic the Einstein gravity theory and various LagrangeFinsler and HamiltonCartan generalizations in nonholonomic variables. The approach suggests a number of new implications for gravity and matter field theories with singular, stochastic, kinetic, fractal, memory etc processes. We prove that the fractional gravitational field equations can be integrated in very general forms following the anholonomic deformation method for constructing exact solutions. Finally, we study some examples of fractional black hole solutions, fractional ellipsoid gravitational configurations and imbedding of such objects in fractional solitonic backgrounds.

Derivatives and asymptotics of Whittaker functions ; Let F be a padic field, and Gn one of the groups GLn,F, GSO2n1,F, GSp2n,F, or GSO2n1,F. Using the mirabolic subgroup or analogues of it, and related derivative functors, we give an asymptotic expansion of functions in the Whittaker model of generic representations of Gn, with respect to a minimal set of characters of subgroups of the maximal torus. Denoting by Zn the center of Gn, and by Nn the unipotent radical of its standard Borel subgroup, we characterize generic representations occurring in L2ZnNnbackslash Gn in terms of these characters. This is related to a conjecture of Lapid and Mao for general split groups, asserting that the generic representations occurring in L2ZnNnbackslash Gn are the generic discrete series; we prove it for the group Gn.

MultiUser Cooperative Diversity through Network Coding Based on Classical Coding Theory ; In this work, we propose and analyze a generalized construction of distributed network codes for a network consisting of M users sending different information to a common base station through independent block fading channels. The aim is to increase the diversity order of the system without reducing its throughput. The proposed scheme, called generalized dynamicnetwork codes GDNC, is a generalization of the dynamicnetwork codes DNC recently proposed by Xiao and Skoglund. The design of the network codes that maximize the diversity order is recognized as equivalent to the design of linear block codes over a nonbinary finite field under the Hamming metric. We prove that adopting a systematic generator matrix of a maximum distance separable block code over a sufficiently large finite field as the network transfer matrix is a sufficient condition for full diversity order under link failure model. The proposed generalization offers a much better tradeoff between rate and diversity order compared to the DNC. An outage probability analysis showing the improved performance is carried out, and computer simulations results are shown to agree with the analytical results.

Large Nonlocal NonGaussianity from a Curvaton Brane ; We use a generalized delta N formalism to study the generation of the primordial curvature perturbation in the curvaton brane scenario inspired by stringy compactifications. We note that the nonGaussian features, especially the trispectra, crucially depend on the decay mechanism in a general curvaton scenario. Specifically, we study the bispectra and trispectra of the curvaton brane model in detail to illustrate the importance of curvaton decay in generating nonlinear fluctuations. When the curvaton brane moves nonrelativistically during inflation, the shape of nonGaussianity is local, but the corresponding size is different from that in the standard curvaton scenario. When the curvaton brane moves relativistically in inflationary stage, the shape of nonGaussianity is of equilateral type.

Derivatives and Asymptotics of Whittaker functions ; Let F be a padic field, and Gn one of the groups GLn, F, GSO2n1, F, GSp2n, F, or GSO2n 1, F. Using the mirabolic subgroup or analogues of it, and related derivative functors, we give an asymptotic expansion of functions in the Whittaker model of generic representations of Gn, with respect to a minimal set of characters of subgroups of the maximal torus. Denoting by Zn the center of Gn, and by Nn the unipotent radical of its standard Borel subgroup, we characterize generic representations occurring in L2ZnNnGn in terms of these characters. This is related to a conjecture of Lapid and Mao for general split groups, asserting that the generic representations occurring in L2ZnNnGn are the generic discrete series; we prove it for the group Gn.

Effective cosmological equations of induced fR gravity ; We expand the study of generalized brane cosmologies by allowing for an ftildecal R gravity term on the brane, with tildecal R the curvature scalar derived from the induced metric. We also include arbitrary matter components on the brane and in the fivedimensional bulk. At low energies, the effect of the bulk on the brane evolution can be described through a mirage component, termed generalized dark radiation, in the effective fourdimensional field equations. Using the covariant formalism, we derive the exact form of these equations. We also derive an effective conservation equation involving the brane matter and the generalized dark radiation. At low energies the coupled branebulk system has a purely fourdimensional description. The applications of the formalism include generalizations of the Starobinsky model and the DvaliGabadadzePorrati cosmology.

Semileptonic B to Scalar meson Decays in the Standard Model with Fourth Generation ; We study the effects of the fourth generation of quarks on the total branching ratio and the lepton polarizations in barB0rightarrow K0ast1430lll mu , tau decay. Taking fourth generation quark mass mtprime of about 400 to 600 GeV with the mixing angle VtprimebastVtprimes in the range 0.051.4times 102 and using the phase to be 80o, it is found that the branching ratio and lepton polarizations are quite sensitive to these fourth generation parameters. In future the experimental study of this decay will give us an opportunity to study new physics effects, precisely, to search for the fourth generation of quarks tprime,bprime in an indirect way.

Properties of neutrality tests based on allele frequency spectrum ; One of the main necessities for population geneticists is the availability of statistical tools that enable to accept or reject the neutral WrightFisher model with high power. A number of statistical tests have been developed to detect specific deviations from the null frequency spectrum in different directions i.e., Tajima's D, Fu and Li's F and D test, Fay and Wu's H. Recently, a general framework was proposed to generate all neutrality tests that are linear functions of the frequency spectrum. In this framework, a family of optimal tests was developed to have almost maximum power against a specific alternative evolutionary scenario. Following these developments, in this paper we provide a thorough discussion of linear and nonlinear neutrality tests. First, we present the general framework for linear tests and emphasize the importance of the property of scalability with the sample size that is, the results of the tests should not depend on the sample size, which, if missing, can guide to errors in data interpretation. The motivation and structure of linear optimal tests are discussed. In a further generalization, we develop a general framework for nonlinear neutrality tests and we derive nonlinear optimal tests for polynomials of any degree in the frequency spectrum.

A general solution to the SchrodingerPoission equation for charged hard wall Application to potential profile of an AlNGaN barrier structure ; A general, systemindependent formulation of the parabolic SchrodingerPoisson equation is presented for a charged hard wall in the limit of complete screening by the ground state. It is solved numerically using iteration and asymptoticboundary conditions. The solution gives a simple relation between the band bending and charge density at an interface. I further develop approximative analytical forms for the potential and wave function, based on properties of the exact solution. Specific tests of the validity of the assumptions leading to the general solution are made. The assumption of complete screening by the ground state is found be a limitation; however, the general solution still provides a fair approximate account of the potential when the bulk is doped. The general solution is further used in a simple model for the potential profile of an AlNGaN barrier, and gives an approximation which compares well with the solution of the full SchrodingerPoisson equation.

A Unified Approach to Variational Derivatives of Modified Gravitational Actions ; Our main aim in this paper is to promote the coframe variational method as a unified approach to derive field equations for any given gravitational action containing the algebraic functions of the scalars constructed from the Riemann curvature tensor and its contractions. We are able to derive a master equation which expresses the variational derivatives of the generalized gravitational actions in terms of the variational derivatives of its constituent curvature scalars. Using the Lagrange multiplier method relative to an orthonormal coframe, we investigate the variational procedures for modified gravitational Lagrangian densities in spacetime dimensions ngeqslant 3. We study wellknown gravitational actions such as those involving the GaussBonnet and Riccisquared, Kretchmann scalar, Weylsquared terms and their algebraic generalizations similar to generic fR theories and the algebraic generalization of sixth order gravitational Lagrangians. We put forth a new model involving the gravitational ChernSimons term and also give three dimensional New massive gravity equations in a new form in terms of the Cotton 2form.

No uniform density star in general relativity ; As per general relativity GR, there cannot be any superluminal propagation of energy. And thus, the sound speed in a continuous medium, cssqrtdpdrho, must be subluminal. However, if one would conceive of a em homogeneous fluid, one would have csinfty unless pressure too would be homogeneous. Thus it is universally accepted that the maiden GR interior solution obtained by Schwarzschild, involving a homogeneous fluid having a boundary, is unphysical. However no one has ever shown how this exact solution is in reality devoid of physical reality. Also, this solution is universally used for approximate modelling of general relativistic stars and compact objects. But here first we show that in order that the Kretschmann scalar is continuous, one should have rho0 for strictly homogeneous static stars. Further, by invoking the fact that in GR, given one time label t one can choose another time label tft em without any loss of generality, we obtain the same result that for a static homogeneous sphere rho0. Consequently, it is eventually found that the static homogeneous sphere having a boundary is just part of the vacuum where cs0 rather than infty. Therefore all general relativistic stars must be inhomogeneous.

Generalized Lyapunov Exponent and Transmission Statistics in Onedimensional Gaussian Correlated Potentials ; Distribution of the transmission coefficient T of a long system with a correlated Gaussian disorder is studied analytically and numerically in terms of the generalized Lyapunov exponent LE and the cumulants of lnT. The effect of the disorder correlations on these quantities is considered in weak, moderate and strong disorder for different models of correlation. Scaling relations between the cumulants of lnT are obtained. The cumulants are treated analytically within the semiclassical approximation in strong disorder, and numerically for an arbitrary strength of the disorder. A small correlation scale approximation is developed for calculation of the generalized LE in a general correlated disorder. An essential effect of the disorder correlations on the transmission statistics is found. In particular, obtained relations between the cumulants and between them and the generalized LE show that, beyond weak disorder, transmission fluctuations and deviation of their distribution from the lognormal form in a long but finite system are greatly enhanced due to the disorder correlations. Parametric dependence of these effects upon the correlation scale is presented.

Fourth Generation Bound States ; We investigate the spectrum and wave functions of bar q'q' bound states for heavy fourth generation quarks q' that have a very small mixing with the three observed generations of standard model quarks. Such bound states come with different color, spin and flavor quantum numbers. Since the fourth generation Yukawa coupling, lambdaq', is large we include all perturbative corrections to the potential between the heavy quark and antiquark of order lambdaq'2Nc16pi2 where Nc is the number of colors, as well as relativistic corrections suppressed by vc2. We find that the lightest fourth generation quark masses for which a bound state exists for color octet states. For the the color singlet states, which always have a bound state, we analyze the influence that the Higgs couplings have on the size and binding energy of the bound states.

Exact and Efficient Algorithm to Discover Extreme Stochastic Events in Wind Generation over Transmission Power Grids ; In this manuscript we continue the thread of M. Chertkov, F. Pan, M. Stepanov, Predicting Failures in Power Grids The Case of Static Overloads, IEEE Smart Grid 2011 and suggest a new algorithm discovering most probable extreme stochastic events in static power grids associated with intermittent generation of wind turbines. The algorithm becomes EXACT and EFFICIENT polynomial in the case of the proportional or other low parametric control of standard generation, and logconcave probability distribution of the renewable generation, assumed known from the wind forecast. We illustrate the algorithm's ability to discover problematic extreme events on the example of the IEEE RTS96 model of transmission with additions of 10, 20 and 30 of renewable generation. We observe that the probability of failure may grow but it may also decrease with increase in renewable penetration, if the latter is sufficiently diversified and distributed.

Neutrino dark matter candidate in fourth generation scenarios ; We overview the constraints on the 4thgeneration neutrino dark matter candidate and investigate a possible way to make it a viable dark matter candidate. Given the LEP constraints tell us that the 4thgeneration neutrino has to be rather heavy MZ2, in sharp contrast to the other three neutrinos, the underlying nature of the 4thgeneration neutrino is expected to be different. We suggest that an additional gauge symmetry B4L4 distinguishes it from the Standard Model's three lighter neutrinos and this also facilitates promotion of the 4thgeneration predominantly righthanded neutrino to a good cold dark matter candidate. It provides distinguishable predictions for the dark matter direct detection and the Large Hadron Collider experiments.

A Fourth Chiral Generation And Susy Breaking ; We revisit four generations within the context of supersymmetry. We compute the perturbativity limits for the fourth generation Yukawa couplings and show that if the masses of the fourth generation lie within reasonable limits of their present experimental lower bounds, it is possible to have perturbativity only up to scales around 1000 TeV, i.e. the current experimental bounds and perturbative unification are mutually exclusive. Such low scales are ideally suited to incorporate gauge mediated supersymmetry breaking, where the mediation scale can be as low as 1020 TeV. The minimal messenger model, however, is highly constrained. Lack of electroweak symmetry breaking rules out a large part of the parameter space, and in the remaining part, the fourth generation stau is tachyonic.

Generalizations of Wiener polarity index and terminal Wiener index ; In theoretical chemistry, distancebased molecular structure descriptors are used for modeling physical, pharmacologic, biological and other properties of chemical compounds. We introduce a generalized Wiener polarity index Wk G as the number of unordered pairs of vertices u, v of G such that the shortest distance d u, v between u and v is k this is actually the kth coefficient in the Wiener polynomial. For k 3, we get standard Wiener polarity index. Furthermore, we generalize the terminal Wiener index TWk G as the sum of distances between all pairs of vertices of degree k. For k 1, we get standard terminal Wiener index. In this paper we describe a linear time algorithm for computing these indices for trees and partial cubes, and characterize extremal trees maximizing the generalized Wiener polarity index and generalized terminal Wiener index among all trees of given order n.

A method for generating realistic correlation matrices ; Simulating sample correlation matrices is important in many areas of statistics. Approaches such as generating Gaussian data and finding their sample correlation matrix or generating random uniform 1,1 deviates as pairwise correlations both have drawbacks. We develop an algorithm for adding noise, in a highly controlled manner, to general correlation matrices. In many instances, our method yields results which are superior to those obtained by simply simulating Gaussian data. Moreover, we demonstrate how our general algorithm can be tailored to a number of different correlation models. Using our results with a few different applications, we show that simulating correlation matrices can help assess statistical methodology.

Multiorientable Group Field Theory ; Group Field Theories GFT are quantum field theories over group manifolds; they can be seen as a generalization of matrix models. GFT Feynman graphs are tensor graphs generalizing ribbon graphs or combinatorial maps; these graphs are dual not only to manifolds. In order to simplify the topological structure of these various singularities, colored GFT was recently introduced and intensively studied since. We propose here a different simplification of GFT, which we call multiorientable GFT. We study the relation between multiorientable GFT Feynman graphs and colorable graphs. We prove that tadfaces and some generalized tadpoles are absent. Some Feynman amplitude computations are performed. A few remarks on the renormalizability of both multiorientable and colorable GFT are made. A generalization from threedimensional to fourdimensional theories is also proposed.

Designing a CPU model from a pseudoformal document to fast code ; For validating low level embedded software, engineers use simulators that take the real binary as input. Like the real hardware, these fullsystem simulators are organized as a set of components. The main component is the CPU simulator ISS, because it is the usual bottleneck for the simulation speed, and its development is a long and repetitive task. Previous work showed that an ISS can be generated from an Architecture Description Language ADL. In the work reported in this paper, we generate a CPU simulator directly from the pseudoformal descriptions of the reference manual. For each instruction, we extract the information describing its behavior, its binary encoding, and its assembly syntax. Next, after automatically applying many optimizations on the extracted information, we generate a SystemCTLM ISS. We also generate tests for the decoder and a formal specification in Coq. Experiments show that the generated ISS is as fast and stable as our previous handwritten ISS.

Resonant magnetic fields from inflation ; We propose a novel scenario to generate primordial magnetic fields during inflation induced by an oscillating coupling of the electromagnetic field to the inflaton. This resonant mechanism has two key advantages over previous proposals. First of all, it generates a narrow band of magnetic fields at any required wavelength, thereby allaying the usual problem of a strongly blue spectrum and its associated backreaction. Secondly, it avoids the need for a strong coupling as the coupling is oscillating rather than growing or decaying exponentially. Despite these major advantages, we find that the backreaction is still far too large during inflation if the generated magnetic fields are required to have a strength of order 1015 Gauss today on observationally interesting scales. We provide a more general nogo argument, proving that this problem will apply to any model in which the magnetic fields are generated on subhorizon scales and freeze after horizon crossing.

Scalartensor cosmologies with dust matter in the general relativity limit ; We consider flat FriedmannLemaitreRobertsonWalker cosmological models in the framework of general scalartensor theories of gravity with arbitrary coupling functions, set in the Jordan frame, in the cosmological epoch when the energy density of the ordinary dust matter dominates over the energy density of the scalar potential. Motivated by cosmological observations, we apply an approximation scheme in the regime close to the socalled limit of general relativity. The ensuing nonlinear approximate equations for the scalar field and the Hubble parameter can be solved analytically in cosmological time. This allows us to distinguish the theories with solutions that asymptotically converge to general relativity and draw some implications about the cosmological dynamics near this limit.

Stochastic oscillations of general relativistic disks ; We analyze the general relativistic oscillations of thin accretion disks around compact astrophysical objects interacting with the surrounding medium through nongravitational forces. The interaction with the external medium a thermal bath is modeled via a friction force, and a random force, respectively. The general equations describing the stochastically perturbed disks are derived by considering the perturbations of trajectories of the test particles in equatorial orbits, assumed to move along the geodesic lines. By taking into account the presence of a viscous dissipation and of a stochastic force we show that the dynamics of the stochastically perturbed disks can be formulated in terms of a general relativistic Langevin equation. The stochastic energy transport equation is also obtained. The vertical oscillations of the disks in the Schwarzschild and Kerr geometries are considered in detail, and they are analyzed by numerically integrating the corresponding Langevin equations. The vertical displacements, velocities and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and the Kerr cases.

On logicallygeometric types of algebras ; The connection between classical model theoretical types MTtypes and logicallygeometrical types LGtypes introduced by B. Plotkin is considered. It is proved that MTtypes of two ntuples in two universal algebras coincide if and only if their LGtypes coincide. An algebra H is called logically perfect if for every two ntuples in H whose types coincide, one can be sent to another by means of an automorphism of this algebra. Some sufficient condition for logically perfectness of free finitely generated algebras is given which helps to prove that finitely generated free Abelian groups, finitely generated free nilpotent groups and finitely generated free semigroups are logically perfect. It is proved that if two Abelian groups have the same type and one of them is finitely generated and free then these groups are isomorphic.

Relativistic cosmological perturbation scheme on a general background scalar perturbations for irrotational dust ; In standard perturbation approaches and Nbody simulations, inhomogeneities are described to evolve on a predefined background cosmology, commonly taken as the homogeneousisotropic solutions of Einstein's field equations FriedmannLemaitreRobertsonWalker FLRW cosmologies. In order to make physical sense, this background cosmology must provide a reasonable description of the effective, i.e. spatially averaged, evolution of structure inhomogeneities also in the nonlinear regime. Guided by the insights that i the average over an inhomogeneous distribution of matter and geometry is in general not given by a homogeneous solution of general relativity, and that ii the class of FLRW cosmologies is not only locally but also globally gravitationally unstable in relevant cases, we here develop a perturbation approach that describes the evolution of inhomogeneities on a general background being defined by the spatially averaged evolution equations. This physical background interacts with the formation of structures. We derive and discuss the resulting perturbation scheme for the matter model irrotational dust' in the Lagrangian picture, restricting our attention to scalar perturbations.

Cosmology in the Newtonian limit ; Numerical Nbody simulations of large scale structure formation in the universe are based on Newtonian gravity. However, according to our current understanding, the most correct theory of gravity is general relativity. It is therefore important to understand which degrees of freedom and which features are lost when the relativistic universe is approximated, or rather replaced, by a Newtonian one. This is the main purpose of our investigation. We first define Newtonian cosmology and we give an overview on general relativity, both in its standard and covariant formulations. We show how the two theories deal with inhomogeneous cosmological models and we introduce the backreaction conjecture. Then we review on how Newtonian gravity and general relativity relate to each other in the fully nonlinear regime. For this purpose we discuss frame theory. We carry out the same investigation also in the weakfield, smallvelocity limit of general relativity, and we derive the Newtonian limit resorting to the framework of postNewtonian cosmology. Finally we remark that there are solutions of Newtonian gravity which do not have any relativistic counterpart.

Monomer Basis Representation Method For Calculating The Spectra Of Molecular Clusters I. The Method And Qualitative Models ; Firstly, a sequential symmetry adaptation procedure is derived for semidirect product groups. Then, this sequential symmetry adaptation procedure is used in the development of new method named Monomer Basis Representation MBR for calculating the vibrationrotationtunneling VRT spectra of molecular clusters. The method is based on generation of optimized bases for each monomer in the cluster as a linear combination of some primitive basis functions and then using the sequential symmetry adaptation procedure for generating a small symmetry adapted basis for the solution of the full problem. It is seen that given an optimized basis for each monomer the application of the sequential symmetry adaptation procedure leads to a generalized eigenvalue problem instead of a standard eigenvalue problem if the procedure is used as it is. In this paper, MBR method will be developed as a solution of that problem such that it leads to generation of an orthogonal optimized basis for the cluster being studied regardless of the nature of the primitive bases that are used in the generation of optimized bases of the monomers.

Entanglement generation in relativistic quantum fields ; We present a general, analytic recipe to compute the entanglement that is generated between arbitrary, discrete modes of bosonic quantum fields by Bogoliubov transformations. Our setup allows the complete characterization of the quantum correlations in all Gaussian field states. Additionally, it holds for all Bogoliubov transformations. These are commonly applied in quantum optics for the description of squeezing operations, relate the mode decompositions of observers in different regions of curved spacetimes, and describe observers moving along nonstationary trajectories. We focus on a quantum optical example in a cavity quantum electrodynamics setting an uncharged scalar field within a cavity provides a model for an optical resonator, in which entanglement is created by nonuniform acceleration. We show that the amount of generated entanglement can be magnified by initial singlemode squeezing, for which we provide an explicit formula. Applications to quantum fields in curved spacetimes, such as an expanding universe, are discussed.

On the nature of the fourth generation neutrino and its implications ; We consider the neutrino sector of a Standard Model with four generations. While the three light neutrinos can obtain their masses from a variety of mechanisms with or without new neutral fermions, fourthgeneration neutrinos need at least one new relatively light righthanded neutrino. If lepton number is not conserved this neutrino must have a Majorana mass term whose size depends on the underlying mechanism for lepton number violation. Majorana masses for the fourth generation neutrinos induce relative large twoloop contributions to the light neutrino masses which could be even larger than the cosmological bounds. This sets strong limits on the mass parameters and mixings of the fourth generation neutrinos.