title: Kid Pix

text: Hickman sent a copy of the application to Broderbund Software in the Summer of 1990 on the encouragement of friends, and having been given details for a contact within the company. He did not anticipate the application being adopted, but received a call within a week indicating that Broderbund would like to publish it. Broderbund's release of "Kid Pix" was demonstrated during the MacWorld keynote in 1991 and "Kid Pix 1.0" was released in March 1991 to very positive feedback. By this point Broderbund had also begun developing a version of "Kid Pix" for MS-DOS. "Kid Pix 1.0" received several industry awards, including the 1991 MacUser Eddi for best Children's Program, the 1991 Software Publishers Association Awards for Best User Interface in a New Program and Best Early Learning Program, and the MacWorld World-Class award for Best Education Program.


title: Kid Pix

text: The latest Mac and Windows versions of the product were developed by the current owner and publisher of "Kid Pix", Software MacKiev, who had been involved in development of the Macintosh version of "Kid Pix Deluxe 3" and has been the sole developer of the "Kid Pix" series since the initial release of "Kid Pix Deluxe 3X" prior to acquiring the brand from Houghton Mifflin Harcourt in October 2011. Hickman had no involvement with the development of "Kid Pix" from 1996 until late 2011 when he began consulting with Software MacKiev on the development of future editions.


title: Kid Pix

text: "Kid Pix 2" added new features to the original. These features were originally available in an add-on known as "Kid Pix Companion".


title: Kid Pix

text: "SlideShow" is a program allowing the creation of a slide show of "Kid Pix" images with transitions and custom recorded sounds. By setting the time delay between slides to the lowest possible setting animations can be created using multiple "Kid Pix" images acting as each of the frames of animation.


title: Kid Pix

text: The "Wacky TV" allows the user to watch video clips in common media formats such as MOV or AVI. The picture can then be distorted using various buttons. The CD came with various sample clips to watch. If a movie contained sound, there was also an option to speed up the audio by 50%, or play it in reverse.


title: Kid Pix

text: "Kid Pix Studio" offered a complement of programs to the original "Kid Pix". It opened up the ability for children to create not only static images but animated creations as well.


title: Kid Pix

text: SlideShow was extended to allow the use of any "Kid Pix", Moopie, Stampimator and Digital Puppet files in the slide show.


title: Kid Pix

text: "Moopies" is very similar to the standard "Kid Pix" program except with a reduced canvas size and the ability to add several animated rubber stamps and wacky brush items. Music and sounds can also be chosen to play in the background of the "moopie."


title: Kid Pix

text: "Stampimator" is again similar to the standard "Kid Pix" program and "Moopies", except the animated rubber stamps can be dragged across the canvas recording a path which they would then repetitively follow.


title: Kid Pix

text: Several pre-made computer puppets are provided in this program. The user can animate them like a real puppet including choosing facial expressions by hitting various keys on the keyboard. Sound and music, and a background can be added to go along with the movement of the puppet.


title: Kid Pix

text: The "Moopies," "Digital Puppets," "Stampimator" and "Slideshow" creations can be saved as a standalone executable that enables them to be viewed by others regardless of them owning a copy of "Kid Pix Studio". "Slideshows" also have the added possibility of being exported to a video file, although this functionality is limited to slide shows that contain only "Kid Pix" drawings.


title: Kid Pix

text: The "Wacky TV" feature allowed users to watch movies and animations made in Moopies, and Slideshow, and even any movies the user may have on their computer. Several buttons are available for use in this feature, which allows users to watch the movies in several different ways, like in reverse or flipped screen. This was also available on the previous version of "Kid Pix".


title: Kid Pix

text: A later version, titled "Kid Pix Studio Deluxe", featured an updated picker screen and allowed editing text items after they have been placed down, which was not possible in prior versions of "Kid Pix". It was also possible in this version to have the computer read the text aloud, and, exclusive to the Macintosh version, add some music to play in the background during a SlideShow.


title: Kid Pix

text: "Kid Pix" received a significant makeover with "Kid Pix Deluxe 3". It was updated with a new 3D looking interface and new sound effects which makes it almost unrecognizable from the older versions. The only surviving new feature inherited from "Kid Pix Studio" was the SlideShow. This is possibly because the others were rendered unnecessary with the addition of clip art pictures and animations to the basic "Kid Pix" program.


title: Kid Pix

text: "Kid Pix Deluxe 4" was released in 2004 and saw several improvements over "Kid Pix Deluxe 3", including an updated interface whose layout is more faithful to the original "Kid Pix" (thus causing the canvas to be larger), the Text tool having a WYSIWYG font menu, the Idea Machine being accessible from the user interface instead of simply from the program's menu, a leaner and more organized Background library, a bilingual Undo Guy that can yap out both English and Spanish phrases, and video tutorials on how to use the program and each of its individual tools. For Macintosh users, this was the first version of "Kid Pix" to be compatible with Mac OS X, the last version to be compatible with the "Classic" Mac OS (in this case, Mac OS 8 and 9), and the only version to utilize Apple's Carbon API.


title: Kid Pix

text: A new version of "Kid Pix Deluxe 3", which was initially released in 2004, featured Mac OS X compatibility, increased canvas size and integration with applications from the Apple's iLife application suite, such as iMovie, iTunes, iPhoto and GarageBand. Also, it features export of "Kid Pix" projects to iPod video format, giving kids a head start in creating their own podcasts. Further, the exploding screen eraser from the previous "Kid Pix Deluxe 3" Edition was replaced with a fire hose, which was less destructive and noisy.


title: Kid Pix

text: A significant upgrade from "Kid Pix Deluxe 3X", the 3D edition was published for the Mac by Software MacKiev in October 2010 and for Windows in October 2011. While retaining the features of the previous "3X" edition, "Kid Pix Deluxe 3D" emphasizes digital storytelling with video narration and export to YouTube. The "3D" part of the name comes from the newly added 3D animations and backgrounds, and an export to 3D feature that creates anaglyph video images that can be viewed using red/blue 3D glasses (included in the package).


title: Kid Pix

text: "Kid Pix 5: The S.T.E.A.M. Edition" is the newest version of Kid Pix by Software MacKiev, available for Mac, Windows, and iPad. It is the first version to have iPad support and 64-bit compatibility, and has a new Steam age interface. Currently, it is only available as an upgrade or for educational institutions.


title: Kid Pix

text: The canvas occupies most of the available screen face, and the entire canvas is visible at all times. The drawing tools available to the user are placed in a column of buttons down the left edge of the screen. Instead of using menus to access the different options that each tool has, they are displayed in a row of icons along the bottom of the screen. Selecting a new tool presents a new set of options, such as different styles for the "Wacky Brush". The color palette is situated below the list of tools and consists of a collection of colored squares for each of the available colors. Files with the KPX extension can be converted to the more accessible PCX format by renaming the extension.


title: Kid Pix

text: "Kid Pix" includes a selection of tools that go beyond drawing simple lines and shapes. These include:


title: Kid Pix

text: "KidPix" was given a blue chip award at the 1994 Oppenheim Toy Portfolio Awards. The judges described it as "a fun-filled multimedia art exploration program with a sense of humor" and "chockful of clever goodies that invite computer and artistic exploration", however they noted that the DOS and Mac versions were superior to the Windows version. "KidPix Companion" was reviewed in the Oppenheim Guide Book where it was described as a program that "make[s] a good thing better", alongside a review for "KidCuts" which was described as "a 21st-century evolution of an old kids' favorite" and "a springboard for off-line creative play".


title: Ricci flow

text: In the mathematical fields of differential geometry and geometric analysis, the Ricci flow ( , ), sometimes also referred to as Hamilton's Ricci flow, is a certain partial differential equation for a Riemannian metric. It is often said to be analogous to the diffusion of heat and the heat equation, due to formal similarities in the mathematical structure of the equation. However, it is nonlinear and exhibits many phenomena not present in the study of the heat equation.


title: Ricci flow

text: The Ricci flow, so named for the presence of the Ricci tensor in its definition, was introduced by Richard Hamilton, who used it through the 1980s to prove striking new results in Riemannian geometry. Later extensions of Hamilton's methods by various authors resulted in new applications to geometry, including the resolution of the differentiable sphere conjecture by Simon Brendle and Richard Schoen.


title: Ricci flow

text: Following Shing-Tung Yau's suggestion that the singularities of solutions of the Ricci flow could identify the topological data predicted by William Thurston's geometrization conjecture, Hamilton produced a number of results in the 1990s which were directed towards the conjecture's resolution. In 2002 and 2003, Grigori Perelman presented a number of fundamental new results about the Ricci flow, including a novel variant of some technical aspects of Hamilton's program. Hamilton and Perelman's works are now widely regarded as forming a proof of the Thurston conjecture, including as a special case the Poincaré conjecture, which had been a well-known open problem in the field of geometric topology since 1904. Their results are considered as a milestone in the fields of geometry and topology.


title: Ricci flow

text: On a smooth manifold , a smooth Riemannian metric automatically determines the Ricci tensor . For each element of , by definition is a positive-definite inner product on the tangent space at . If given a one-parameter family of Riemannian metrics , one may then consider the derivative , which then assigns to each particular value of and a symmetric bilinear form on . Since the Ricci tensor of a Riemannian metric also assigns to each a symmetric bilinear form on , the following definition is meaningful.


title: Ricci flow

text: The Ricci tensor is often thought of as an average value of the sectional curvatures, or as an algebraic trace of the Riemann curvature tensor. However, for the analysis of existence and uniqueness of Ricci flows, it is extremely significant that the Ricci tensor can be defined, in local coordinates, by a formula involving the first and second derivatives of the metric tensor. This makes the Ricci flow into a geometrically-defined partial differential equation. The analysis of the ellipticity of the local coordinate formula provides the foundation for the existence of Ricci flows; see the following section for the corresponding result.


title: Ricci flow

text: Let be a nonzero number. Given a Ricci flow on an interval , consider for between and . Then . So, with this very trivial change of parameters, the number −2 appearing in the definition of the Ricci flow could be replaced by any other nonzero number. For this reason, the use of −2 can be regarded as an arbitrary convention, albeit one which essentially every paper and exposition on Ricci flow follows. The only significant difference is that if −2 were replaced by a positive number, then the existence theorem discussed in the following section would become a theorem which produces a Ricci flow that moves backwards (rather than forwards) in parameter values from initial data.


title: Ricci flow

text: The parameter is usually called , although this is only as part of standard informal terminology in the mathematical field of partial differential equations. It is not physically meaningful terminology. In fact, in the standard quantum field theoretic interpretation of the Ricci flow in terms of the renormalization group, the parameter corresponds to length or energy, rather than time.


title: Ricci flow

text: Suppose that is a compact smooth manifold, and let be a Ricci flow for in the interval . Define so that each of the Riemannian metrics has volume 1; this is possible since is compact. (More generally, it would be possible if each Riemannian metric had finite volume.) Then define to be the antiderivative of which vanishes at . Since is positive-valued, is a bijection onto its image . Now the Riemannian metrics , defined for parameters , satisfy


title: Ricci flow

text: Here denotes scalar curvature. This is called the normalized Ricci flow equation. Thus, with an explicitly defined change of scale and a reparametrization of the parameter values, a Ricci flow can be converted into a normalized Ricci flow. The converse also holds, by reversing the above calculations.


title: Ricci flow

text: The primary reason for considering the normalized Ricci flow is that it allows a convenient statement of the major convergence theorems for Ricci flow. However, it is not essential to do so, and for virtually all purposes it suffices to consider Ricci flow in its standard form. Moreover, the normalized Ricci flow is not generally meaningful on noncompact manifolds.


title: Ricci flow

text: Let formula_2 be a smooth closed manifold, and let "g" be any smooth Riemannian metric on formula_2. Making use of the Nash–Moser implicit function theorem, showed the following existence theorem:


title: Ricci flow

text: The existence theorem provides a one-parameter family of smooth Riemannian metrics. In fact, any such one-parameter family also depends smoothly on the parameter. Precisely, this says that relative to any smooth coordinate chart ("U","φ") on "M", the function formula_8 is smooth for any "i","j" = 1...,"n".


title: Ricci flow

text: Dennis DeTurck subsequently gave a proof of the above results which uses the Banach implicit function theorem instead. His work is essentially a simpler Riemannian version of Yvonne Choquet-Bruhat's well-known proof and interpretation of well-posedness for the Einstein equations in Lorentzian geometry.


title: Ricci flow

text: As a consequence of Hamilton's existence and uniqueness theorem, when given the data ("M","g"), one may speak unambiguously of "the" Ricci flow on "M" with initial data "g", and one may select "T" to take on its maximal possible value, which could be infinite. The principle behind virtually all major applications of Ricci flow, in particular in the proof of the Poincaré conjecture and geometrization conjecture, is that, as "t" approaches this maximal value, the behavior of the metrics "g" can reveal and reflect deep information about "M".


title: Ricci flow

text: The three-dimensional result is due to . Hamilton's proof, inspired by and loosely modeled upon James Eells and Joseph Sampson's epochal 1964 paper on convergence of the harmonic map heat flow, included many novel features, such as an extension of the maximum principle to the setting of symmetric 2-tensors. His paper (together with that of Eells−Sampson) is among the most widely cited in the field of differential geometry. There is an exposition of his result in .


title: Ricci flow

text: In terms of the proof, the two-dimensional case is properly viewed as a collection of three different results, one for each of the cases in which the Euler characteristic of is positive, zero, or negative. As demonstrated by , the negative case is handled by the maximum principle, while the zero case is handled by integral estimates; the positive case is more subtle, and Hamilton dealt with the subcase in which has positive curvature by combining a straightforward adaptation of Peter Li and Shing-Tung Yau's gradient estimate to the Ricci flow together with an innovative "entropy estimate". The full positive case was demonstrated by Bennett , in an extension of Hamilton's techniques. Since any Ricci flow on a two-dimensional manifold is confined to a single conformal class, it can be recast as a partial differential equation for a scalar function on the fixed Riemannian manifold . As such, the Ricci flow in this setting can also be studied by purely analytic methods; correspondingly, there are alternative non-geometric proofs of the two-dimensional convergence theorem.


title: Ricci flow

text: The higher-dimensional case has a longer history. Soon after Hamilton's breakthrough result, Gerhard Huisken extended his methods to higher dimensions, showing that if almost has constant positive curvature (in the sense of smallness of certain components of the Ricci decomposition), then the normalized Ricci flow converges smoothly to constant curvature. found a novel formulation of the maximum principle in terms of trapping by convex sets, which led to a general criterion relating convergence of the Ricci flow of positively curved metrics to the existence of "pinching sets" for a certain multidimensional ordinary differential equation. As a consequence, he was able to settle the case in which is four-dimensional and has positive curvature operator. Twenty years later, Christoph Böhm and Burkhard Wilking found a new algebraic method of constructing "pinching sets," thereby removing the assumption of four-dimensionality from Hamilton's result (). Simon Brendle and Richard Schoen showed that positivity of the isotropic curvature is preserved by the Ricci flow on a closed manifold; by applying Böhm and Wilking's method, they were able to derive a new Ricci flow convergence theorem (). Their convergence theorem included as a special case the resolution of the differentiable sphere theorem, which at the time had been a long-standing conjecture. The convergence theorem given above is due to , which subsumes the earlier higher-dimensional convergence results of Huisken, Hamilton, Böhm & Wilking, and Brendle & Schoen.


title: Ricci flow

text: The results in dimensions three and higher show that any smooth closed manifold which admits a metric of the given type must be a space form of positive curvature. Since these space forms are largely understood by work of Élie Cartan and others, one may draw corollaries such as


title: Ricci flow

text: So if one could show directly that any smooth closed simply-connected 3-dimensional manifold admits a smooth Riemannian metric of positive Ricci curvature, then the Poincaré conjecture would immediately follow. However, as matters are understood at present, this result is only known as a (trivial) corollary of the Poincaré conjecture, rather than vice versa.


title: Ricci flow

text: Given any larger than two, there exist many closed -dimensional smooth manifolds which do not have any smooth Riemannian metrics of constant curvature. So one cannot hope to be able to simply drop the curvature conditions from the above convergence theorems. It could be possible to replace the curvature conditions by some alternatives, but the existence of compact manifolds such as complex projective space, which has a metric of nonnegative curvature operator (the Fubini-Study metric) but no metric of constant curvature, makes it unclear how much these conditions could be pushed. Likewise, the possibility of formulating analogous convergence results for negatively curved Riemannian metrics is complicated by the existence of closed Riemannian manifolds whose curvature is arbitrarily close to constant and yet admit no metrics of constant curvature.


title: Ricci flow

text: Making use of a technique pioneered by Peter Li and Shing-Tung Yau for parabolic differential equations on Riemannian manifolds, proved the following "Li–Yau inequality."


title: Ricci flow

text: Both of these remarkable inequalities are of profound importance for the proof of the Poincaré conjecture and geometrization conjecture. The terms on the right hand side of Perelman's Li–Yau inequality motivates the definition of his "reduced length" functional, the analysis of which leads to his "noncollapsing theorem." The noncollapsing theorem allows application of Hamilton's compactness theorem (Hamilton 1995) to construct "singularity models," which are Ricci flows on new three-dimensional manifolds. Owing to the Hamilton–Ivey estimate, these new Ricci flows have nonnegative curvature. Hamilton's Li–Yau inequality can then be applied to see that the scalar curvature is, at each point, a nondecreasing (nonnegative) function of time. This is a powerful result that allows many further arguments to go through. In the end, Perelman shows that any of his singularity models is asymptotically like a complete gradient shrinking Ricci soliton, which are completely classified; see the previous section.


title: Ricci flow

text: See for details on Hamilton's Li–Yau inequality; the books and contain expositions of both inequalities above.


title: Ricci flow

text: Let ("M","g") be a Riemannian manifold which is Einstein, meaning that there is a number "λ" such that Ric = "λg". Then "g" = (1 − 2"λt")"g" is a Ricci flow with "g" = "g", since then


title: Ricci flow

text: If "M" is closed, then according to Hamilton's uniqueness theorem above, this is the only Ricci flow with initial data "g". One sees, in particular, that:


title: Ricci flow

text: In each case, since the Riemannian metrics assigned to different values of "t" differ only by a constant scale factor, one can see that the normalized Ricci flow "G" exists for all time and is constant in "s"; in particular, it converges smoothly (to its constant value) as "s"→∞.


title: Ricci flow

text: The Einstein condition has as a special case that of constant curvature; hence the particular examples of the sphere (with its standard metric) and hyperbolic space appear as special cases of the above.


title: Ricci flow

text: A gradient shrinking Ricci soliton consists of a smooth Riemannian manifold ("M","g") and "f" ∈ "C"("M") such that


title: Ricci flow

text: One of the major achievements of was to show that, if "M" is a closed three-dimensional smooth manifold, then finite-time singularities of the Ricci flow on "M" are modeled on complete gradient shrinking Ricci solitons (possibly on underlying manifolds distinct from "M"). In 2008, Huai-Dong Cao, Bing-Long Chen, and Xi-Ping Zhu completed the classification of these solitons, showing:


title: Ricci flow

text: Hamilton's first work on Ricci flow was published at the same time as William Thurston's geometrization conjecture, which concerns the topological classification of three-dimensional smooth manifolds. Hamilton's idea was to define a kind of nonlinear diffusion equation which would tend to smooth out irregularities in the metric. Suitable canonical forms had already been identified by Thurston; the possibilities, called Thurston model geometries, include the three-sphere S, three-dimensional Euclidean space E, three-dimensional hyperbolic space H, which are homogeneous and isotropic, and five slightly more exotic Riemannian manifolds, which are homogeneous but not isotropic. (This list is closely related to, but not identical with, the Bianchi classification of the three-dimensional real Lie algebras into nine classes.)


title: Ricci flow

text: Hamilton succeeded in proving that any smooth closed three-manifold which admits a metric of "positive" Ricci curvature also admits a unique Thurston geometry, namely a spherical metric, which does indeed act like an attracting fixed point under the Ricci flow, renormalized to preserve volume. (Under the unrenormalized Ricci flow, the manifold collapses to a point in finite time.) However, this doesn't prove the full geometrization conjecture, because of the restrictive assumption on curvature.


title: Ricci flow

text: Indeed, a triumph of nineteenth-century geometry was the proof of the uniformization theorem, the analogous topological classification of smooth two-manifolds, where Hamilton showed that the Ricci flow does indeed evolve a negatively curved two-manifold into a two-dimensional multi-holed torus which is locally isometric to the hyperbolic plane. This topic is closely related to important topics in analysis, number theory, dynamical systems, mathematical physics, and even cosmology.


title: Ricci flow

text: Note that the term "uniformization" suggests a kind of smoothing away of irregularities in the geometry, while the term "geometrization" suggests placing a geometry on a smooth manifold. "Geometry" is being used here in a precise manner akin to Klein's notion of geometry (see Geometrization conjecture for further details). In particular, the result of geometrization may be a geometry that is not isotropic. In most cases including the cases of constant curvature, the geometry is unique. An important theme in this area is the interplay between real and complex formulations. In particular, many discussions of uniformization speak of complex curves rather than real two-manifolds.


title: Ricci flow

text: Hamilton showed that a compact Riemannian manifold always admits a short-time Ricci flow solution. Later Shi generalized the short-time existence result to complete manifolds of bounded curvature. In general, however, due to the highly non-linear nature of the Ricci flow equation, singularities form in finite time. These singularities are curvature singularities, which means that as one approaches the singular time the norm of the curvature tensor formula_18 blows up to infinity in the region of the singularity. A fundamental problem in Ricci flow is to understand all the possible geometries of singularities. When successful, this can lead to insights into the topology of manifolds. For instance, analyzing the geometry of singular regions that may develop in 3d Ricci flow, is the crucial ingredient in Perelman's proof the Poincare and Geometrization Conjectures.


title: Ricci flow

text: To study the formation of singularities it is useful, as in the study of other non-linear differential equations, to consider blow-ups limits. Intuitively speaking, one zooms into the singular region of the Ricci flow by rescaling time and space. Under certain assumptions, the zoomed in flow tends to a limiting Ricci flow formula_19, called a singularity model. Singularity models are ancient Ricci flows, i.e. they can be extended infinitely into the past. Understanding the possible singularity models in Ricci flow is an active research endeavor.


title: Ricci flow

text: Below, we sketch the blow-up procedure in more detail: Let formula_20 be a Ricci flow that develops a singularity as formula_21. Let formula_22 be a sequence of points in spacetime such that


title: Ricci flow

text: Due to the symmetry of the Ricci flow equation under parabolic dilations, the metrics formula_26 are also solutions to the Ricci flow equation. In the case that


title: Ricci flow

text: i.e. up to time formula_28 the maximum of the curvature is attained at formula_29, then the pointed sequence of Ricci flows formula_30 subsequentially converges smoothly to a limiting ancient Ricci flow formula_31. Note that in general formula_32 is not diffeomorphic to formula_2.


title: Ricci flow

text: Hamilton distinguishes between Type I and Type II singularities in Ricci flow. In particular, one says a Ricci flow formula_34, encountering a singularity a time formula_35 is of Type I if


title: Ricci flow

text: Otherwise the singularity is of Type II. It is known that the blow-up limits of Type I singularities are gradient shrinking Ricci solitons. In the Type II case it is an open question whether the singularity model must be a steady Ricci soliton—so far all known examples are.


title: Ricci flow

text: In 3d the possible blow-up limits of Ricci flow singularities are well-understood. By Hamilton, Perelman and recent work by Brendle, blowing up at points of maximum curvature leads to one of the following three singularity models:


title: Ricci flow

text: The first two singularity models arise from Type I singularities, whereas the last one arises from a Type II singularity.


title: Ricci flow

text: In four dimensions very little is known about the possible singularities, other than that the possibilities are far more numerous than in three dimensions. To date the following singularity models are known


title: Ricci flow

text: Note that the first three examples are generalizations of 3d singularity models. The FIK shrinker models the collapse of an embedded sphere with self-intersection number −1.


title: Ricci flow

text: To see why the evolution equation defining the Ricci flow is indeed a kind of nonlinear diffusion equation, we can consider the special case of (real) two-manifolds in more detail. Any metric tensor on a two-manifold can be written with respect to an exponential isothermal coordinate chart in the form


title: Ricci flow

text: The easiest way to compute the Ricci tensor and Laplace-Beltrami operator for our Riemannian two-manifold is to use the differential forms method of Élie Cartan. Take the coframe field


title: Ricci flow

text: To compute the curvature tensor, we take the exterior derivative of the covector fields making up our coframe:


title: Ricci flow

text: where we have taken advantage of the anti-symmetric property of the connection (formula_54). Take another exterior derivative


title: Ricci flow

text: The reader may object that the heat equation is of course a linear partial differential equation—where is the promised "nonlinearity" in the p.d.e. defining the Ricci flow?


title: Ricci flow

text: The answer is that nonlinearity enters because the Laplace-Beltrami operator depends upon the same function p which we used to define the metric. But notice that the flat Euclidean plane is given by taking formula_65. So if formula_66 is small in magnitude, we can consider it to define small deviations from the geometry of a flat plane, and if we retain only first order terms in computing the exponential, the Ricci flow on our two-dimensional almost flat Riemannian manifold becomes the usual two dimensional heat equation. This computation suggests that, just as (according to the heat equation) an irregular temperature distribution in a hot plate tends to become more homogeneous over time, so too (according to the Ricci flow) an almost flat Riemannian manifold will tend to flatten out the same way that heat can be carried off "to infinity" in an infinite flat plate. But if our hot plate is finite in size, and has no boundary where heat can be carried off, we can expect to "homogenize" the temperature, but clearly we cannot expect to reduce it to zero. In the same way, we expect that the Ricci flow, applied to a distorted round sphere, will tend to round out the geometry over time, but not to turn it into a flat Euclidean geometry.


title: Ricci flow

text: The Ricci flow has been intensively studied since 1981. Some recent work has focused on the question of precisely how higher-dimensional Riemannian manifolds evolve under the Ricci flow, and in particular, what types of parametric singularities may form. For instance, a certain class of solutions to the Ricci flow demonstrates that neckpinch singularities will form on an evolving "n"-dimensional metric Riemannian manifold having a certain topological property (positive Euler characteristic), as the flow approaches some characteristic time formula_67. In certain cases, such neckpinches will produce manifolds called Ricci solitons.


title: Ricci flow

text: For a 3-dimensional manifold, Perelman showed how to continue past the singularities using surgery on the manifold.


title: Ricci flow

text: Kähler metrics remain Kähler under Ricci flow, and so Ricci flow has also been studied in this setting, where it is called Kähler–Ricci flow.


title: Siquijor

text: Siquijor ( , ), officially the Province of Siquijor (; ), is an island province in the Philippines located in the Central Visayas region. Its capital is the municipality also named Siquijor. To the north of Siquijor is Cebu, to the west is Negros, northeast is Bohol, and to the south, across the Bohol Sea, is Mindanao.


title: Siquijor

text: During the Spanish colonial period of the Philippines, the Spaniards called the island (Island of Fire). Siquijor is commonly associated with mystic traditions that the island's growing tourism industry capitalizes on.


title: Siquijor

text: A Siquijor legend tells of a great storm which once engulfed the region. Then there came a strong earthquake that shook the earth and sea. Amidst the lightning and thunder arose an island from the depths of the ocean's womb which came to be known as the island. Despite being a legend, modern times highland farmers have unraveled giant shell casings under farm plots, supporting the theory that Siquijor is indeed an island that rose from the sea.


title: Siquijor

text: Prior to colonization, the island polity was home to the Kingdom (Kedatuan) of Katugasan, from tugas, the molave trees that cover the hills, which abounded the island along with fireflies.


title: Siquijor

text: The "tugas" or molave trees were used by the ancient dwellers of the island in making posts or "haligi" of their houses because of its strength and durability that could withstand and struggle against strong typhoons and "habagat" and was proven by the house of "Totang" built near the artesian well of Cang-igdot. Most of the patriarchs of the island made the "tugas" trees to a wooden plow or "tukod" to cultivate the rocky soil for farming using mainly "toro" or male cattle to pull it through the sticky and hard rocky soil. However, before the discovery of making "tugas" as the foundations of their house, the primitive Siquijodnons dwelt in the caves as evidenced by the pottery and old tools like stone grinder or "liligsan" excavated by Mitring from the three caves of Sam-ang.


title: Siquijor

text: During this time, the people of the kingdom was already in contact with Chinese traders, as seen through archaeological evidence including Chinese ceramics and other objects. The art of traditional healing and traditional witchcraft belief systems also developed within this period. During the arrival of the Spanish, the monarch of the island was Datu Kihod, as recorded in Legazpi's chronicles.


title: Siquijor

text: The island was first sighted by the Spaniards in 1565 during Miguel López de Legazpi's expedition. The Spaniards called the island ("Island of Fire"), because the island gave off an eerie glow, from the great swarms of fireflies that lived in the numerous molave trees on the island. Esteban Rodríguez of the Legazpi expedition led the first Spaniards to discover the island. He was captain of a small party that left Legazpi's camp in Bohol to explore the nearby islands which are now called Pamilican, Siquijor, and Negros.


title: Siquijor

text: The island, along with the rest of the archipelago, was subsequently annexed to the Spanish Empire. Founded in 1783 under the administration of secular clergymen, Siquijor became the first municipality as well as the first parish to be established on the island. Siquijor was, from the beginning, administered by the Diocese of Cebu. As for civil administration, Siquijor was under Bohol since the province had its own governor. The first Augustinian Recollect priest arrived in Siquijor in 1794. Several years later, a priest of the same order founded the parishes of Larena (initially called ), Lazi (formerly Tigbawan), San Juan (Makalipay), and Maria (). With the exception of Enrique Villanueva, the other five municipalities were established as parishes in 1877. From 1854 to 1892, Siquijor was administered by the politico-military province of Bohol. Later in 1892, it was transferred to Negros Oriental and became its sub-province in 1901.


title: Siquijor

text: At the turn of the century, Spain ceded the Philippines to the United States of America with the Treaty of Paris that ended the Spanish–American War. Siquijor island felt the presence of American rule when a unit of the American Cavalry Division came and stayed for sometime. The American Military Governor in Manila appointed James Fugate, a scout with the California Volunteers of the U.S. Infantry, to oversee and to implement the organization and development programs in Siquijor Island. Governor Fugate stayed for 16 years as lieutenant governor of Siquijor.


title: Siquijor

text: While it was not at the center of military action, Siquijor was not spared by World War II. Imperial Japanese detachments occupied the island between 1942 and 1943, announcing their arrival on the island with heavy shelling. At the outbreak of the war, Siquijor was a sub-province of Negros Oriental, headed by Lieutenant Governor Nicolas Parami. Refusing to pledge allegiance to the Japanese forces, Lt. Governor Parami was taken by Japanese soldiers from his residence at Poo, Lazi one evening and brought to the military headquarters in Larena. He was never heard from again. On November 10, 1942, Japanese warships started shelling Lazi from Cangabas Point. In Lazi, a garrison was established in the old Home Economics Building of the Central School. Filipino guerrillas engaged in sabotage and the interaction during this time caused havoc on the Japanese lives and properties.


title: Siquijor

text: During this period, Siquijor was briefly governed by Shunzo Suzuki, a Japanese civilian appointed by the Japanese forces until he was assassinated in October 1942 by the guerrilla forces led by Iluminado Jumawanin, of Caipilan, Siquijor. Mamor Fukuda took control of Siquijor from June 1943 until the Japanese forces abandoned the island when the liberation forces came in 1944. In 1943, the Japanese puppet government appointed Sebastian Monera of San Juan as Governor of Siquijor. His administration, however, was cut short when he was executed, presumably by Filipino guerrillas operating in the mountains of Siquijor.


title: Siquijor

text: On September 30, 1943, the United States submarine USS "Bowfin" (SS-287) delivered supplies to the people of Siquijor and evacuated people from the island.


title: Siquijor

text: On February 21, 1945, the destroyer USS "Renshaw" (DD-499), part of Task Unit 78.7.6, was escorting a convoy of about 50 various landing ships with 12 other escorts. At 10:59, "Renshaw" was attacked by a Japanese midget submarine off the coast of Siquijor, which caused extensive damage to the ship and killed 19 of the crew.


title: Siquijor

text: In mid-1945, local Filipino soldiers and officers under the 7th, 75th and 76th Infantry Division of the Philippine Commonwealth Army arrived, and alongside recognized guerrilla fighter groups, liberated Siquijor.


title: Siquijor

text: For a time Siquijor was a subprovince of Negros Oriental, but it became an independent province on September 17, 1971, by virtue of "Republic Act 6398". The move was supported by the people of Siquijor as they have a distinct culture from those of Negros Oriental, while Marcos used the movement as a means to secure support from the people of the island to pave martial law acceptance the following year. The capital, formerly Larena, was transferred to the municipality of Siquijor in 1972 by "Proclamation No. 1075", under martial law.


title: Siquijor

text: In 2006, the Lazi Church was added by the government as an extension to the Baroque Churches of the Philippines UNESCO World Heritage Site. The inscription of the church has been pending since.


title: Siquijor

text: Siquijor is an island province in Central Visayas. It lies southeast from Cebu and Negros across Cebu Strait (also called Bohol Strait) and southwest from Bohol. Panglao Island, which is part of Bohol province, has a similar composition of the soil which is found throughout the whole island of Siquijor.


title: Siquijor

text: With a land area of and a coastline long, Siquijor is the third smallest province of the Philippines, both in terms of population as well as land area: (after Camiguin and Batanes).


title: Siquijor

text: The island lies about east of the nearest point on southern Negros, southeast of Cebu, southwest of Bohol, and north of Zamboanga del Norte in Mindanao. It is predominantly hilly and in many places the hills reach the sea, producing precipitous cliffs. At the center, Mount Malabahoc (locally known as Mount Bandilaan) reaches about in elevation, the highest point on the island. Three marine terraces can be roughly traced especially in the vicinity of Tagibo on the southwestern part of the island, a barrio of San Juan municipality from the seacoast up into the central part.


title: Siquijor

text: Siquijor is a coralline island, and fossils of the giant clam "tridacna" are often encountered in the plowed inland fields. On the hilltops there are numerous shells of the molluscan species presently living in the seas around the island. Siquijor was probably formed quite recently, geologically speaking. The ocean depths between Siquijor and Bohol and Mindanao are in the neighborhood of .


title: Siquijor

text: Siquijor has two different climates, dominated by Am. All climate is within Coronas climate type IV, characterised by not very pronounced maximum rainfall with a short dry season from one to three months and a wet season of nine to ten months. The dry season starts in February and lasts through April sometimes extending to midMay.


title: Siquijor

text: Five of the municipalities have significant rainfall most months of the year, with a short dry season that has little effect. This location is classified as Am (tropical monsoon climate) by Köppen–Geiger climate classification system. The average annual temperature in Siquijor is , with variation throughout the year less than 2 degrees Celsius ( deg F). The precipitation about varies between the driest month and the wettest month, with the average rainfall or less.


title: Siquijor

text: The municipality Lazi has a significant amount of rainfall during the year. This is true even for the driest month. According to Köppen and Geiger, this climate is classified as Af (tropical rainforest climate). In a year, the average rainfall is .


title: Siquijor

text: Siquijor (province) comprises 6 municipalities. Siquijor (municipality) is the capital and most important port.


title: Siquijor

text: The Lone district of Siquijor is the representation of the province in various national legislatures. The current representative is Jake Vincent S. Villa.


title: Siquijor

text: According to the 2015 census, it has a population of 95,984. The average annual growth rate between 2000 and 2015 was , lower than the national growth rate of for the same period.


title: Siquijor

text: The main language spoken in the island province is Cebuano, with Tagalog and English often used as second languages. The former is understood and used as the national "lingua franca", but it is rarely used in everyday conversation among locals.


title: Siquijor

text: 95% of the island's residents belong to the Catholic Church, while the remainder belong to various other Christian churches. Despite the province's Catholic affinities, almost all of the residents continue to adhere to traditional practices that were used prior the 15th century, albeit these practices have also adopted Christian belief systems as well. Due to the ingrained and indispensable traditional belief systems, majority of residents have continued to possess a high respect for the natural environment which was revered by the ancestors of the people. Siquijor is known for its unique Philippine culture of blending Catholicism with traditional religious practices – a major part of its people's cultural heritage and identity.


title: Siquijor

text: The literacy rate of 92.5% is one of the highest in the country. The Siquijor State College located in Larena is the only state college in the province.


title: Siquijor

text: Siquijor's long-time reputation as a place of magic and sorcery both attracts and repulses visitors. Siquijor is also well known for its festivals that focus on healing rituals where incantations are sung while the old folks make potions out of herbs, roots, insects and tree barks.


title: Siquijor

text: Among the many attractions are the beaches, caves, waterfalls, Bandilaan natural park and butterfly sanctuary. The most popular of them are the Cambugahay Falls, Paliton Beach and the centuries-old Balete tree, both located in Lazi.


title: Siquijor

text: The coral reefs ringing the island offer some of the best diving in the Philippines for snorkelers and scuba divers. Dive courses are conducted by several dive operators on the island in version of PADI, CMAS* and NAUI. Siquijor was declared a marine visitor arrivals among the three provinces in Region VII.


title: Siquijor

text: The island of Siquijor has two seaports capable of servicing cargo and passenger sea crafts. Siquijor also has an airfield located near Siquijor capable of handling smaller and mostly airplanes.


title: L.A. Confidential

text: L.A. Confidential (1990) is a neo-noir novel by James Ellroy and the third of his L.A. Quartet series. It is dedicated to Mary Doherty Ellroy. The epigraph is "A glory that costs everything and means nothing"—Steve Erickson.


title: L.A. Confidential

text: The story is about several Los Angeles Police Department officers in the early 1950s who become embroiled in a mix of sex, corruption and murder following a massacre at the Nite Owl coffee shop. The story eventually encompasses organized crime, political corruption, heroin trafficking, pornography, prostitution and Hollywood. The title refers to the scandal magazine "Confidential", which is fictionalized as "Hush-Hush". It also deals with the real "Bloody Christmas" scandal.


title: L.A. Confidential

text: The three protagonists are LAPD officers. Edmund Exley, the son of prestigious detective Preston Exley, is a "straight arrow" who informs on other officers in a police brutality scandal. He is first and foremost a politician and a ladder climber. This earns the enmity of Wendell "Bud" White, an intimidating enforcer with a fixation on men who abuse women. Between the two of them is Jack Vincennes, who acts as more of a celebrity than a cop, who is a technical advisor on a police television show called "Badge of Honor" (similar to the real-life show "Dragnet") and provides tips to a scandal magazine. The three of them must set their differences aside to unravel the conspiracy linking the novel's events.


title: L.A. Confidential

text: The "Chicago Tribune" said, "Ellroy is a master at juggling plot lines, using a stripped, spare noir style that hits like a cleaver but is honed like a scalpel".


title: L.A. Confidential

text: "The Los Angeles Times" gave a critical review, calling the novel "incontinent mayhem" with a plot "faster than a stray bullet and equally random."


title: L.A. Confidential

text: Kirkus Reviews described "LA Confidential" as "energetic, sprawling, and often stylistically irritating."


title: L.A. Confidential

text: "The New York Times" wrote that "the plotting becomes so tortuous and the narrative style so burdened by repetitive scenes of atrocious violence that the author compromises the truthfulness of his own vision."


title: L.A. Confidential

text: The book was adapted for a 1997 film of the same name, directed and co-written by Curtis Hanson and starring Kevin Spacey, Russell Crowe, Guy Pearce, James Cromwell, Kim Basinger, David Strathairn and Danny DeVito. The film was universally acclaimed. It was nominated for nine Academy Awards; Kim Basinger won both a Golden Globe and an Academy Award for Best Supporting Actress for her performance in the film, while Curtis Hanson and Brian Helgeland won the Oscar for Best Adapted Screenplay.


title: L.A. Confidential

text: In 2003, a television pilot of "L.A. Confidential" was aired. However, the pilot was not picked up as a running series. The show's main actors would have been Kiefer Sutherland, Josh Hopkins, David Conrad, Pruitt Taylor Vince, Melissa George, Tom Nowicki, and Eric Roberts. The pilot is a special feature on the two-disc DVD and the Blu-ray releases of the film.


title: L.A. Confidential

text: In 2018, CBS ordered a new pilot based on the novel. The pilot would star Walton Goggins as Vincennes, Mark Webber as White, Brian J. Smith as Exley, Sarah Jones as Lynn, Alana Arenas as June, and Shea Whigham as Dick Stensland. In May 2018, it was announced that the pilot would not be moving forward.


title: Contact angle

text: The contact angle is the angle, conventionally measured through the liquid, where a liquid–vapor interface meets a solid surface. It quantifies the wettability of a solid surface by a liquid via the Young equation. A given system of solid, liquid, and vapor at a given temperature and pressure has a unique equilibrium contact angle. However, in practice a dynamic phenomenon of contact angle hysteresis is often observed, ranging from the advancing (maximal) contact angle to the receding (minimal) contact angle. The equilibrium contact is within those values, and can be calculated from them. The equilibrium contact angle reflects the relative strength of the liquid, solid, and vapour molecular interaction.


title: Contact angle

text: The contact angle depends upon the medium above the free surface of the liquid, and the nature of the liquid and solid in contact. It is independent of the inclination of solid to the liquid surface. It changes with surface tension and hence with the temperature and purity of the liquid.


title: Contact angle

text: The shape of a liquid–vapor interface is determined by the Young–Dupré equation, with the contact angle playing the role of a boundary condition via the Young equation.


title: Contact angle

text: The theoretical description of contact arises from the consideration of a thermodynamic equilibrium between the three phases: the liquid phase (L), the solid phase (S), and the gas or vapor phase (G) (which could be a mixture of ambient atmosphere and an equilibrium concentration of the liquid vapor). (The "gaseous" phase could be replaced by another immiscible liquid phase.) If the solid–vapor interfacial energy is denoted by formula_1, the solid–liquid interfacial energy by formula_2, and the liquid–vapor interfacial energy (i.e. the surface tension) by formula_3, then the equilibrium contact angle formula_4 is determined from these quantities by the Young equation:


title: Contact angle

text: The earliest study on the relationship between contact angle and surface tensions for sessile droplets on flat surfaces was reported by Thomas Young in 1805. A century later Gibbs proposed a modification to Young’s equation to account for the volumetric dependence of the contact angle. Gibbs postulated the existence of a line tension, which acts at the three-phase boundary and accounts for the excess energy at the confluence of the solid-liquid-gas phase interface, and is given as:


title: Contact angle

text: where "κ"["N"] is the line tension and "a"["m"] is the droplet radius. Although experimental data validates an affine relationship between the cosine of the contact angle and the inverse line radius, it does not account for the correct sign of κ and overestimates its value by several orders of magnitude.


title: Contact angle

text: With improvements in measuring techniques such as atomic force microscopy, confocal microscopy, and scanning electron microscope, researchers were able to produce and image droplets at ever smaller scales. With the reduction in droplet size came new experimental observations of wetting. These observations confirmed that the modified Young’s equation does not hold at the micro-nano scales. Jasper proposed that including a "V" "dP" term in the variation of the free energy may be the key to solving the contact angle problem at such small scales. Given that the variation in free energy is zero at equilibrium:


title: Contact angle

text: The variation in the pressure at the free liquid-vapor boundary is due to Laplace pressure, which is proportional to the mean curvature. Solving the above equation for both convex and concave surfaces yields:


title: Contact angle

text: This equation relates the contact angle, a geometric property of a sessile droplet to the bulk thermodynamics, the energy at the three phase contact boundary, and the mean curvature of the droplet. For the special case of a sessile droplet on a flat surface formula_14:


title: Contact angle

text: In the above equation, the first two terms are the modified Young’s equation, while the third term is due to the Laplace pressure. This nonlinear equation correctly predicts the sign and magnitude of κ, the flattening of the contact angle at very small scales, and contact angle hysteresis.


title: Contact angle

text: A given substrate-liquid-vapor combination yields a continuous range of contact angle values in practice. The maximum contact angle is referred to as the advancing contact angle and the minimum contact angle is referred to as the receding contact angle. The advancing and receding contact angles are measured from dynamic experiments where droplets or liquid bridges are in movement. In contrast, the equilibrium contact angle described by the Young-Laplace equation is measured from a static state. Static measurements yield values in-between the advancing and receding contact angle depending on deposition parameters (e.g. velocity, angle, and drop size) and drop history (e.g. evaporation from time of deposition). Contact angle hysteresis is defined as formula_16although the term is also used to describe the expression formula_17. The static, advancing, or receding contact angle can be used in place of the equilibrium contact angle depending on the application. The overall effect can be seen as closely analogous to static friction, i.e., a minimal amount of work per unit distance is required to move the contact line.


title: Contact angle

text: The advancing contact angle can be described as a measure of the liquid-solid cohesion while the receding contact angle is a measure of liquid-solid adhesion. The advancing and receding contact angles can be measured directly using different methods and can also be calculated from other wetting measurements such as force tensiometery (aka Wilhemy-Plate method).


title: Contact angle

text: Advancing and receding contact angles can be measured directly from the same measurement if drops are moved linearly on a surface. For example, a drop of liquid will adopt a given contact angle when static, but when the surface is tilted the drop will initially deform so that the contact area between the drop and surface remains constant. The "downhill" side of the drop will adopt a higher contact angle while the "uphill" side of the drop will adopt a lower contact angle. As the tilt angle increases the contact angles will continue to change but the contact area between the drop and surface will remain constant. At a given surface tilt angle, the advancing and receding contact angles will be met and the drop will move on the surface. In practice, the measurement can be influenced by shear forces and momentum if the tilt velocity is high. The measurement method can also be challenging in practice for systems with high (>30 degrees) or low (<10 degrees) contact angle hysteresis.


title: Contact angle

text: Advancing and receding contact angle measurements can be carried out by adding and removing liquid from a drop deposited on a surface. If a sufficiently small volume of liquid is added to a drop, the contact line will still be pinned, and the contact angle will increase. Similarly, if a small amount of liquid is removed from a drop, the contact angle will decrease.


title: Contact angle

text: The Young's equation assumes a homogeneous surface and does not account for surface texture or outside forces such as gravity. Real surfaces are not atomically smooth or chemically homogeneous so a drop will assume contact angle hysteresis. The equilibrium contact angle (formula_18) can be calculated from formula_19 and formula_20 as was shown theoretically by Tadmor and confirmed experimentally by Chibowski as,


title: Contact angle

text: On a surface that is rough or contaminated, there will also be contact angle hysteresis, but now the local equilibrium contact angle (the Young equation is now only locally valid) may vary from place to place on the surface. According to the Young–Dupré equation, this means that the adhesion energy varies locally – thus, the liquid has to overcome local energy barriers in order to wet the surface. One consequence of these barriers is contact angle hysteresis: the extent of wetting, and therefore the observed contact angle (averaged along the contact line), depends on whether the liquid is advancing or receding on the surface.


title: Contact angle

text: Because liquid advances over previously dry surface but recedes from previously wet surface, contact angle hysteresis can also arise if the solid has been altered due to its previous contact with the liquid (e.g., by a chemical reaction, or absorption). Such alterations, if slow, can also produce measurably time-dependent contact angles.


title: Contact angle

text: Surface roughness has a strong effect on the contact angle and wettability of a surface. The effect of roughness depends on if the droplet will wet the surface grooves or if air pockets will be left between the droplet and the surface.


title: Contact angle

text: If the surface is wetted homogeneously, the droplet is in Wenzel state. In Wenzel state, adding surface roughness will enhance the wettability caused by the chemistry of the surface. The Wenzel correlation can be written as


title: Contact angle

text: where "θ" is the measured contact angle, θ is the Young contact angle and r is the roughness ratio. The roughness ratio is defined as the ratio between the actual and projected solid surface area.


title: Contact angle

text: If the surface is wetted heterogeneously, the droplet is in Cassie-Baxter state. The most stable contact angle can be connected to the Young contact angle. The contact angles calculated from the Wenzel and Cassie-Baxter equations have been found to be good approximations of the most stable contact angles with real surfaces.


title: Contact angle

text: For liquid moving quickly over a surface, the contact angle can be altered from its value at rest. The advancing contact angle will increase with speed, and the receding contact angle will decrease. The discrepancies between static and dynamic contact angles are closely proportional to the capillary number, noted formula_24.


title: Contact angle

text: On the basis of interfacial energies, the profile of a surface droplet or a liquid bridge between two surfaces can be described by the Young–Laplace equation. This equation is applicable for three-dimensional axisymmetric conditions and is highly non-linear. This is due to the mean curvature term which includes products of first- and second-order derivatives of the drop shape function formula_25:


title: Contact angle

text: Solving this elliptic partial differential equation that governs the shape of a three-dimensional drop, in conjunction with appropriate boundary conditions, is complicated, and an alternate energy minimization approach to this is generally adopted. The shapes of three-dimensional sessile and pendant drops have been successfully predicted using this energy minimisation method.


title: Contact angle

text: Contact angles are extremely sensitive to contamination; values reproducible to better than a few degrees are generally only obtained under laboratory conditions with purified liquids and very clean solid surfaces. If the liquid molecules are strongly attracted to the solid molecules then the liquid drop will completely spread out on the solid surface, corresponding to a contact angle of 0°. This is often the case for water on bare metallic or ceramic surfaces, although the presence of an oxide layer or contaminants on the solid surface can significantly increase the contact angle. Generally, if the water contact angle is smaller than 90°, the solid surface is considered hydrophilic and if the water contact angle is larger than 90°, the solid surface is considered hydrophobic. Many polymers exhibit hydrophobic surfaces. Highly hydrophobic surfaces made of low surface energy (e.g. fluorinated) materials may have water contact angles as high as ≈ 120°. Some materials with highly rough surfaces may have a water contact angle even greater than 150°, due to the presence of air pockets under the liquid drop. These are called superhydrophobic surfaces.


title: Contact angle

text: If the contact angle is measured through the gas instead of through the liquid, then it should be replaced by 180° minus their given value. Contact angles are equally applicable to the interface of two liquids, though they are more commonly measured in solid products such as non-stick pans and waterproof fabrics.


title: Contact angle

text: Control of the wetting contact angle can often be achieved through the deposition or incorporation of various organic and inorganic molecules onto the surface. This is often achieved through the use of specialty silane chemicals which can form a SAM (self-assembled monolayers) layer. With the proper selection of the organic molecules with varying molecular structures and amounts of hydrocarbon and/or perfluoronated terminations, the contact angle of the surface can tune. The deposition of these specialty silanes can be achieved in the gas phase through the use of a specialized vacuum ovens or liquid-phase process. Molecules that can bind more perfluorinated terminations to the surface can results in lowering the surface energy (high water contact angle).


title: Contact angle

text: The sessile drop contact angle is measured by a contact angle goniometer using an optical subsystem to capture the profile of a pure liquid on a solid substrate. The angle formed between the liquid–solid interface and the liquid–vapor interface is the contact angle. Older systems used a microscope optical system with a back light. Current-generation systems employ high resolution cameras and software to capture and analyze the contact angle. Angles measured in such a way are often quite close to advancing contact angles. Equilibrium contact angles can be obtained through the application of well defined vibrations.


title: Contact angle

text: Measuring contact angles for pendant drops is much more complicated than for sessile drops due to the inherent unstable nature of inverted drops. This complexity is further amplified when one attempts to incline the surface. Experimental apparatus to measure pendant drop contact angles on inclined substrates has been developed recently. This method allows for the deposition of multiple microdrops on the underside of a textured substrate, which can be imaged using a high resolution CCD camera. An automated system allows for tilting the substrate and analysing the images for the calculation of advancing and receding contact angles.


title: Contact angle

text: The dynamic sessile drop is similar to the static sessile drop but requires the drop to be modified. A common type of dynamic sessile drop study determines the largest contact angle possible without increasing its solid–liquid interfacial area by adding volume dynamically. This maximum angle is the advancing angle. Volume is removed to produce the smallest possible angle, the receding angle. The difference between the advancing and receding angle is the contact angle hysteresis.


title: Contact angle

text: The dynamic Wilhelmy method is a method for calculating average advancing and receding contact angles on solids of uniform geometry. Both sides of the solid must have the same properties. Wetting force on the solid is measured as the solid is immersed in or withdrawn from a liquid of known surface tension. Also in that case it is possible to measure the equilibrium contact angle by applying a very controlled vibration. That methodology, called VIECA, can be implemented in a quite simple way on every Wilhelmy balance.


title: Contact angle

text: An optical variation of the single-fiber Wilhelmy method. Instead of measuring with a balance, the shape of the meniscus on the fiber is directly imaged using a high resolution camera. Automated meniscus shape fitting can then directly measure the static, advancing or receding contact angle on the fiber.


title: Contact angle

text: In case of a porous materials many issues have been raised both about the physical meaning of the calculated pore diameter and the real possibility to use this equation for the calculation of the contact angle of the solid, even if this method is often offered by much software as consolidated. Change of weight as a function of time is measured.


title: Los Lonely Boys

text: Los Lonely Boys are an American musical group from San Angelo, Texas. They play a style of music they call "Texican Rock n' Roll," combining elements of rock and roll, Texas blues, brown-eyed soul, country, and Tejano.


title: Los Lonely Boys

text: The band consists of three brothers: Henry (guitar, vocals), Jojo (bass, vocals), and Ringo (drums, vocals) Garza. They follow the tradition of their father, Ringo Garza Sr., who formed a band with his brothers called the Falcones. The Falcones played conjunto music in South Texas during the 1970s and 1980s. The debut single by Los Lonely Boys, "Heaven", was a number-one hit on the "Billboard" adult contemporary chart and reached the top 40 on the "Billboard" Hot 100 in 2004. In 2009, they signed to an Austin-based indie label, Playing in Traffic Records, and released an EP, "1969" and three albums under their LonelyTone imprint, "Keep On Giving: Acoustic Live!", "Rockpango", and their newest release, "Revelation".


title: Los Lonely Boys

text: The three brothers were discovered by a local club owner, John R. Steele, who hired them as his house band. When they started to attract attention in San Angelo they hired Mr. Steele as a road manager and they went on the road, finally ending up in Nashville where they landed a recording contract in the 1990s. After moving back to their home state of Texas, they recorded an album in 2003 in Austin at Willie Nelson's Pedernales recording studio. The album was initially released by Or Music and later acquired by Epic Records for distribution in March 2004.


title: Los Lonely Boys

text: The group's first single, "Heaven", reached number one on the Adult Contemporary chart, and number 16 on the "Billboard" Hot 100, and number 11 at top 40. "Heaven" was featured in "". In 2005, the song won a Grammy Award for Best Pop Performance by a Duo or Group with Vocal. Other songs nominated for Grammys include "More Than Love" and "Onda," both in 2006.


title: Los Lonely Boys

text: In 2005, the group recorded "I Don't Wanna Lose Your Love" with Carlos Santana for the Santana album "All That I Am". In June of that year, the group appeared in an episode of CMT's "Crossroads" show with country music legend Ronnie Milsap. Their 2006 album, "Sacred", features the song "Outlaws". In a "closing of the circle", Enrique Garza Sr. sings the verse about the "missing outlaws, just like me". Willie Nelson, who is credited on the 2004 album, also provided a verse which makes reference to his hit "On the Road Again".


title: Los Lonely Boys

text: In 2007, Los Lonely Boys participated in Amnesty International's Make Some Noise project. Their cover of John Lennon's "Whatever Gets You thru the Night" is the second single from the "." The song was released on iTunes on April 17, with the entire album available on June 12 courtesy of Warner Bros. Records. "Whatever Gets You thru the Night" is noteworthy as John Lennon's only US number-one solo single while he was alive.


title: Los Lonely Boys

text: Their third studio album, "Forgiven", was released on July 1, 2008. The album was recorded at East Side Stages in Austin and was produced by Steve Jordan. On October 23, 2008, Los Lonely Boys sang the national anthem to open game two of the 2008 World Series in St. Petersburg, Florida.


title: Los Lonely Boys

text: In March 2009, Los Lonely Boys left Sony/Epic and signed with Austin-based Playing In Traffic Records. In March 2010, the group was awarded "Best Rock Band" in the Austin Music Awards.


title: Los Lonely Boys

text: The trio released a tribute EP titled "1969" on October 13, 2009, paying homage to the 40th anniversary of the titular year with covers of Santana's "Evil Ways", The Doors' "Roadhouse Blues", Blind Faith's version of Buddy Holly's "Well All Right", The Beatles' "She Came in Through the Bathroom Window", and Tony Joe White's "Polk Salad Annie". The EP was produced by Andy Johns and marked the first release on their new label.


title: Los Lonely Boys

text: Following their 2009-2010 tour, which included roughly 200 shows seen by over 350,000 fans, Los Lonely Boys headed back to the studio to complete their fourth full-length studio album. It was announced on January 14, 2011, that the new album, entitled "Rockpango" (a Spanglish word that means "rock party"), would be released on March 29. "Rockpango," which features 11 original tracks, marks the first full-length studio album released by the band on their LonelyTone imprint for Playing in Traffic Records. A deluxe edition of the album will include three bonus songs, a behind-the-scenes video, and a fold-out poster of the cover art.


title: Los Lonely Boys

text: In early 2014, Los Lonely Boys released their fifth studio album, "Revelation". The album represents new territory for the Boys, with the conjunto touches on "Blame It On Love" and the reggae groove of "Give A Little More", among many other new sonic elements.


title: Los Lonely Boys

text: In 2016, the band recorded a cover version of John Fogerty's "Born on the Bayou", to be included in the project "Quiero Creedence". This album, scheduled for July 2016 release, is a tribute to Creedence Clearwater Revival by various Latin recording artists.


title: Los Lonely Boys

text: In October 2019, Los Lonely Boys canceled all upcoming performances after Jojo Garza announced he was leaving the group, causing the band to take a temporary hiatus.


title: Los Lonely Boys

text: On April 21, 2022, with Jojo having allegedly changed his mind after two years, Los Lonely Boys announced they were joining The Who on some tour dates in Dallas, Houston, and Oklahoma City. They announced alongside it that they had officially reunited, with new music and additional shows coming soon.


title: Same-sex union legislation

text: Same-sex marriage is legal in the following countries: Argentina, Australia, Austria, Belgium, Brazil, Canada, Chile, Colombia, Costa Rica, Cuba, Denmark, Ecuador, Finland, France, Germany, Iceland, Ireland, Luxembourg, Malta, Mexico, the Netherlands, New Zealand, Norway, Portugal, Slovenia, South Africa, Spain, Sweden, Switzerland, Taiwan, the United Kingdom, the United States, and Uruguay. It will also soon be legal in Andorra.


title: Same-sex union legislation

text: Same-sex marriage is recognized, but not performed, in Israel. Furthermore, same-sex marriages performed in the Netherlands are recognized in Aruba, Curaçao and Sint Maarten. Whether same-sex couples should be allowed to marry has been and remains the topic of debate worldwide. 32 countries and four jurisdictions worldwide have passed constitutional amendments that explicitly prohibit the legal recognition of same-sex marriage and sometimes other forms of legal unions as well. Sixteen countries and 34 jurisdictions worldwide have authorized civil unions or unregistered cohabitation for same-sex couples as an alternative to marriage. The legal name of those unions as well as the number of rights that they provide can vary greatly.


title: Same-sex union legislation

text: The first legislation of unregistered cohabitation was introduced in the Netherlands in June 1979. However, the first substantial recognition of same-sex couples didn't occur before the introduction of a new legal form, that of registered partnerships, which was first enacted in Denmark in June 1989. Many countries have followed with similar legislation since then. Legislation of these forms of legal unions still occur with a variety of different names, even after the introduction of same sex marriage, although sometimes they are overwritten by subsequent legislation of same-sex marriage.


title: Same-sex union legislation

text: There are currently 13 countries that have an alternative form of legal recognition other than marriage on a national level. Those are Andorra, Croatia, Cyprus, the Czech Republic, Estonia, Greece, Hungary, Israel, Italy, Liechtenstein, Monaco, Montenegro and San Marino.


title: Same-sex union legislation

text: As of , legislation to allow an alternative form of legal recognition of same-sex couples other than marriage is pending, or has passed at least one legislative house on a national level in Lithuania and Thailand.


title: Same-sex union legislation

text: As of , same-sex marriage has been legal (nationwide or in some parts) in Argentina, Australia, Austria, Belgium, Brazil, Canada, Chile, Colombia, Costa Rica, Cuba, Denmark, Ecuador, Finland, France, Germany, Iceland, Ireland, Luxembourg, Malta, Mexico, the Netherlands, New Zealand, Norway, Portugal, Slovenia, South Africa, Spain, Sweden, Switzerland, Taiwan, the United Kingdom, the United States and Uruguay. It is also pending an effective date in Andorra.


title: Same-sex union legislation

text: As of , legislation to allow same-sex marriage is being considered in at least one legislative house on a national level in the Czech Republic, Greece, Liechtenstein and Thailand.


title: Same-sex union legislation

text: In countries with a federal system of governance, states and territories often may grant recognition to same-sex couples in their own jurisdictions, although unitary states with a level of devolution, such as Spain or the United Kingdom, also offer such powers to local authorities. The first jurisdiction to enact unregistered cohabitation was British Columbia in Canada in July 1992. The first jurisdiction to legalize registered partnership was Greenland as part of the Kingdom of Denmark in April 1996. Finally, the first sub-national jurisdiction to legalize same-sex marriage was the Canadian province of Ontario in June 2003.


title: Same-sex union legislation

text: As of , there are 251 sub-national jurisdictions worldwide that have legalized some kind of alternative form of legal union of same-sex couples other than marriage. Those are:


title: Same-sex union legislation

text: For the time being, 58 sub-national jurisdictions worldwide have legalized same-sex marriage in nations where same-sex marriage is not legal throughout the nation's territory. Those are:


title: Same-sex union legislation

text: Various countries had passed o tried to pass legislation to prevent same-sex marriage or repeal the existing laws (in some cases including criminalization or fines), sometimes approving explicit bans or define that marriage is the solely union between a man and a woman, excluding all others.


title: Same-sex union legislation

text: Thirty-two countries have passed constitutional amendments banning a variety of same-sex unions. These amendments have taken several forms. Some are limited to banning only marriage. Others ban marriage and prohibit legislation providing "similar rights".


title: Same-sex union legislation

text: Cuba was the first country to prohibit same-sex marriage in February 1976. Paraguay, Honduras and Bolivia are the only cases that not only marriage is prohibited but also de facto unions. Vietnam, Cuba and Ecuador, repealed their same-sex marriage bans in November 2013, April 2019, and June 2019, respectively.


title: Same-sex union legislation

text: As of , thirty-three countries prohibit same-sex marriage on a national level. Those are Armenia, Belarus, Bolivia, Bulgaria, Burkina Faso, Burundi, Cambodia, the Central African Republic, Croatia, the Democratic Republic of the Congo, Dominican Republic, Georgia, Honduras, Hungary, Jamaica, Kenya, Kyrgyzstan, Latvia, Lithuania, Moldova, Montenegro, Palau, Paraguay, Poland, Russia, Rwanda, Serbia, Slovakia, South Sudan, Uganda, Ukraine, Venezuela and Zimbabwe.


title: Same-sex union legislation

text: The first jurisdiction to explicitly ban same-sex marriage in its Constitution was the U.S. state of Alaska in November 1998, however, same-sex marriage was legalised in the state in October 2014. The first jurisdiction to enact such a ban was Yucatán, in July 2009, but since August 2010 the state recognizes same-sex marriages performed in Mexico and in August 2021 local congress removed the heterosexual definition of marriage from the state's constitution.


title: Layer 2 Tunneling Protocol

text: In computer networking, Layer 2 Tunneling Protocol (L2TP) is a tunneling protocol used to support virtual private networks (VPNs) or as part of the delivery of services by ISPs. It uses encryption ('hiding') only for its own control messages (using an optional pre-shared secret), and does not provide any encryption or confidentiality of content by itself. Rather, it provides a tunnel for Layer 2 (which may be encrypted), and the tunnel itself may be passed over a Layer 3 encryption protocol such as IPsec.


title: Layer 2 Tunneling Protocol

text: Published in 2000 as proposed standard RFC 2661, L2TP has its origins primarily in two older tunneling protocols for point-to-point communication: Cisco's Layer 2 Forwarding Protocol (L2F) and Microsoft's


title: Layer 2 Tunneling Protocol

text: Point-to-Point Tunneling Protocol (PPTP). A new version of this protocol, L2TPv3, appeared as proposed standard RFC 3931 in 2005. L2TPv3 provides additional security features, improved encapsulation, and the ability to carry data links other than simply Point-to-Point Protocol (PPP) over an IP network (for example: Frame Relay, Ethernet, ATM, etc.).


title: Layer 2 Tunneling Protocol

text: The entire L2TP packet, including payload and L2TP header, is sent within a User Datagram Protocol (UDP) datagram. A virtue of transmission over UDP (rather than TCP) is that it avoids the "TCP meltdown problem". It is common to carry PPP sessions within an L2TP tunnel. L2TP does not provide confidentiality or strong authentication by itself. IPsec is often used to secure L2TP packets by providing confidentiality, authentication and integrity. The combination of these two protocols is generally known as L2TP/IPsec (discussed below).


title: Layer 2 Tunneling Protocol

text: The two endpoints of an L2TP tunnel are called the L2TP access concentrator (LAC) and the L2TP network server (LNS). The LNS waits for new tunnels. Once a tunnel is established, the network traffic between the peers is bidirectional. To be useful for networking, higher-level protocols are then run through the L2TP tunnel. To facilitate this, an L2TP "session" is established within the tunnel for each higher-level protocol such as PPP. Either the LAC or LNS may initiate sessions. The traffic for each session is isolated by L2TP, so it is possible to set up multiple virtual networks across a single tunnel.


title: Layer 2 Tunneling Protocol

text: The packets exchanged within an L2TP tunnel are categorized as either "control packets" or "data packets". L2TP provides reliability features for the control packets, but no reliability for data packets. Reliability, if desired, must be provided by the nested protocols running within each session of the L2TP tunnel.


title: Layer 2 Tunneling Protocol

text: L2TP allows the creation of a virtual private dialup network (VPDN) to connect a remote client to its corporate network by using a shared infrastructure, which could be the Internet or a service provider's network.


title: Layer 2 Tunneling Protocol

text: An L2TP tunnel can extend across an entire PPP session or only across one segment of a two-segment session. This can be represented by four different tunneling models, namely:


title: Layer 2 Tunneling Protocol

text: At the time of setup of L2TP connection, many control packets are exchanged between server and client to establish tunnel and session for each direction. One peer requests the other peer to assign a specific tunnel and session id through these control packets. Then using this tunnel and session id, data packets are exchanged with the compressed PPP frames as payload.


title: Layer 2 Tunneling Protocol

text: The list of L2TP Control messages exchanged between LAC and LNS, for handshaking before establishing a tunnel and session in voluntary tunneling method are


title: Layer 2 Tunneling Protocol

text: Because of the lack of confidentiality inherent in the L2TP protocol, it is often implemented along with IPsec. This is referred to as L2TP/IPsec, and is standardized in IETF RFC 3193. The process of setting up an L2TP/IPsec VPN is as follows:


title: Layer 2 Tunneling Protocol

text: When the process is complete, L2TP packets between the endpoints are encapsulated by IPsec. Since the L2TP packet itself is wrapped and hidden within the IPsec packet, the original source and destination IP address is encrypted within the packet. Also, it is not necessary to open UDP port 1701 on firewalls between the endpoints, since the inner packets are not acted upon until after IPsec data has been decrypted and stripped, which only takes place at the endpoints.


title: Layer 2 Tunneling Protocol

text: A potential point of confusion in L2TP/IPsec is the use of the terms tunnel and secure channel. The term tunnel-mode refers to a channel which allows untouched packets of one network to be transported over another network. In the case of L2TP/PPP, it allows L2TP/PPP packets to be transported over IP. A secure channel refers to a connection within which the confidentiality of all data is guaranteed. In L2TP/IPsec, first IPsec provides a secure channel, then L2TP provides a tunnel. IPsec also specifies a tunnel protocol: this is not used when a L2TP tunnel is used.


title: Layer 2 Tunneling Protocol

text: Windows has had native support (configurable in control panel) for L2TP since Windows 2000. Windows Vista added 2 alternative tools, an MMC snap-in called "Windows Firewall with Advanced Security" (WFwAS) and the "netsh advfirewall" command-line tool. One limitation with both of the WFwAS and netsh commands is that servers must be specified by IP address. Windows 10 added the "Add-VpnConnection" and "Set-VpnConnectionIPsecConfiguration" PowerShell commands. A registry key must be created on the client and server if the server is behind a NAT-T device.


title: Layer 2 Tunneling Protocol

text: L2TP is often used by ISPs when internet service over for example ADSL or cable is being "resold". From the end user, packets travel over a wholesale network service provider's network to a server called a Broadband Remote Access Server (BRAS), a protocol converter and router combined. On legacy networks the path from end user customer premises' equipment to the BRAS may be over an ATM network.


title: Layer 2 Tunneling Protocol

text: From there on, over an IP network, an L2TP tunnel runs from the BRAS (acting as LAC) to an LNS which is an edge router at the boundary of the ultimate destination ISP's IP network. See example of reseller ISPs using L2TP.


title: Sanzu River

text: The is a mythological river in Japanese Buddhist tradition similar to the Hindu concept of the Vaitarna and Greek concept of the Styx.


title: Sanzu River

text: Before reaching the afterlife, the souls of the deceased must cross the river by one of three crossing points: a bridge, a ford, or a stretch of deep, snake-infested waters. The weight of one's offenses while alive determines which path an individual must take. It is believed that a toll of six mon must be paid before a soul can cross the river, a belief reflected in Japanese funerals when the necessary fee is placed in the casket with the dead.


title: Sanzu River

text: The "Sanzu River" is popularly believed to be in Mount Osore, a suitably desolate and remote part of Aomori Prefecture in northern Japan.


title: Sanzu River

text: Similarly to the "Sanzu-no-Kawa", there is also the , a boundary by which the souls of children who died too early cross over to the realm of the Dead, with the help of "Jizō", a "Kami"/"Bodhisattva" who helps the souls of children who died too early to avoid the attentions of the "Oni" and of "Shozuka-no-Baba" and "Datsueba".


title: History of the State of Palestine

text: The history of the State of Palestine describes the creation and evolution of the State of Palestine in the West Bank and Gaza Strip.


title: History of the State of Palestine

text: During the Mandatory period, numerous plans of partition of Palestine were proposed but without the agreement of all parties. In 1947, the United Nations Partition Plan for Palestine was voted. This triggered the 1947–1949 Palestine war and led, in 1948, to the establishment of the state of Israel on a part of Mandate Palestine as the Mandate came to an end. The Gaza Strip came under Egyptian occupation, and the West Bank was ruled by Jordan, before both territories were occupied by Israel in the 1967 Six-Day War. Since then there have been proposals to establish a Palestinian state. In 1969, for example, the PLO proposed the establishment of a binational state over the whole of the former British Mandate territory. This proposal was rejected by Israel, as it would have amounted to the disbanding of the state of Israel. The basis of the current proposals is for a two-state solution on either a portion of or the entirety of the Palestinian territories—the Gaza Strip and the West Bank, including East Jerusalem, which have been occupied by Israel since 1967.


title: History of the State of Palestine

text: At the dissolution of the Ottoman Empire following World War I, the victorious European states divided many of its component regions into newly created states under League of Nations mandates according to deals that had been struck with other interested parties. In the Middle East, Syria (including the Ottoman autonomous Christian Lebanon and the surrounding areas that became the Republic of Lebanon) came under French control, while Mesopotamia and Palestine were allotted to the British.


title: History of the State of Palestine

text: Most of these states achieved independence during the following three decades without great difficulty, though in some regimes, the colonial legacy continued through the granting of exclusive rights to market/manufacture oil and maintain troops to defend it. However, the case of Palestine remained problematic.


title: History of the State of Palestine

text: Arab nationalism was on the rise after World War II, possibly following the example of European nationalism. Pan-Arabist beliefs called for the creation of a single, secular state for all Arabs.


title: History of the State of Palestine

text: In 1917 the British Government issued the Balfour Declaration which declared British support for the creation in Palestine of a "national home for the Jewish people". The declaration was enthusiastically received by many Jews worldwide, but was opposed by Palestinian and Arab leaders, who later claimed that the objective was a breach of promises made to the Sharif of Mecca in 1915, in exchange for Arab help fighting the Ottoman Empire during World War I.


title: History of the State of Palestine

text: Many different proposals have been made and continue to be made to resolve the dilemma of the competing objectives, including an Arab state, with or without a significant Jewish population, a Jewish state, with or without a significant Arab population, a single bi-national state, with or without some degree of cantonization, two states, one bi-national and one Arab, with or without some form of federation, and two states, one Jewish and one Arab, with or without some form of federation.


title: History of the State of Palestine

text: At the same times, many Arab leaders maintained that Palestine should join a larger Arab state covering the imprecise region of the Levant. These hopes were expressed in the Faisal–Weizmann Agreement, which was signed by soon-to-be Iraqi ruler Faisal I and the Zionist leader Chaim Weizmann. Despite this, the promise of a Pan-Arab state including Palestine were dashed as Syria, Lebanon, and Jordan declared independence from their European rulers, while western Palestine festered in the developing Arab-Jewish conflict.


title: History of the State of Palestine

text: In light of these developments, Arabs began calling for both their own state in the British Mandate of Palestine and an end to the British support of the Jewish homeland's creation and to Jewish immigration. The movement gained steam through the 1920s and 1930s as Jewish immigration picked up. Under pressure from the arising nationalist movement, the British enforced the White Papers, a series of laws greatly restricting Jewish immigration and the sale of lands to Jews. The laws, passed in 1922, 1930, and 1939, varied in severity, but all attempted to find a balance between British sympathies with the Jews and the Arabs.


title: History of the State of Palestine

text: In the early years of World War I, negotiations took place between the British High Commissioner in Egypt Henry McMahon and Sharif of Mecca Husayn bin Ali for an alliance of sorts between the Allies and the Arabs in the Near East against the Ottomans. On 24 October 1915, McMahon sent to Hussein a note which the Arabs came to regard as their "Declaration of Independence". In McMahon's letter, part of the McMahon–Hussein Correspondence, McMahon declared Britain's willingness to recognise the independence of the Arabs, both in the Levant and the Hejaz, subject to certain exemptions. It stated on behalf of the Government of Great Britain that:


title: History of the State of Palestine

text: The two districts of Mersina and Alexandretta and portions of Syria lying to the west of the districts of Damascus, Homs, Hama and Aleppo cannot be said to be purely Arab, and should be excluded from the limits demanded.


title: History of the State of Palestine

text: With the above modification, and without prejudice of our existing treaties with Arab chiefs, we accept those limits.


title: History of the State of Palestine

text: As for those regions lying within those frontiers wherein Great Britain is free to act without detriment to the interest of her ally, France, I am empowered in the name of the Government of Great Britain to give the following assurances and make the following reply to your letter:


title: History of the State of Palestine

text: The exemptions from Arab control of certain areas set out in the McMahon note were to seriously complicate the problems of peace in the Near East. At the time, the Arab portions of the Ottoman Empire were divided into administrative units called "vilayets" and "sanjaks". Palestine was divided into the "sanjuks" of Acre and Nablus, both of which were a part of the vilayet of Beirut, and an independent "sanjak" of Jerusalem. The areas exempted from Arab control by the McMahon note included "Syria lying to the west of the districts of Damascus, Homs, Hama, and Aleppo." Between 1916 and 1920, the British government interpreted these commitments as including Palestine in the Arab area. However, in the Churchill White Paper they argued instead that "Damascus" meant the "vilayet" and not the city of Damascus, and accordingly virtually all of Palestine was excluded from Arab control. The British entered into the secret Sykes–Picot Agreement on 16 May 1916 and the commitment of the Balfour Declaration, for example, on that understanding.


title: History of the State of Palestine

text: The Arabs, however, insisted at the 1919 Paris Peace Conference at the end of the war that "Damascus" meant the city of Damascus – which left Palestine in their hands. However, in 1915, these problems of interpretation did not occur to Hussein, who agreed to the British wording.


title: History of the State of Palestine

text: Despite Arab objections based in part on the Arab interpretation of the McMahon correspondence noted above, Britain was given the League of Nations Mandate for Palestine. The Mandate was administered as two territories: Palestine and Transjordan, with the Jordan River being the boundary between them. The boundaries under the Mandate also did not follow those sought by the Jewish community, which sought the inclusion of the east bank of the Jordan into the Palestinian territory, to which the objective of the Mandate for a homeland for the Jewish people would apply. It was made clear from before the commencement of the Mandate, and a clause to that effect was inserted in the Mandate, that the objective set out in the Mandate would not apply to Transjordan following the passing of the Transjordan memorandum. Transjordan was destined for early independence. The objective of the Mandate was to apply only to territory west of the Jordan, which was commonly referred to as Palestine by the British administration, and as Eretz Israel by the Hebrew-speaking Jewish population.


title: History of the State of Palestine

text: During the 1936–39 Arab revolt in Palestine the British government formed the Peel Commission, which recommended the formation of a Jewish and an Arab state. It called for a small Jewish state in the Galilee and maritime strip, a British enclave stretching from Jerusalem to Jaffa, and an Arab state covering the rest. The Commission recommended the creation of a small Jewish state in a region less than 1/5 of the total area of Palestine. The Arab area was to be joined to Transjordan. The Arab population in the Jewish areas was to be removed, by force if necessary, and vice versa, although this would mean the movement of far more Arabs than Jews. The Zionist Congress rejected the proposal, while allowing the leadership to continue negotiating with the British. The Arab leadership rejected the proposal outright. It all came to nothing, as the British government shelved the proposal altogether by the middle of 1938.


title: History of the State of Palestine

text: In February 1939, the St. James Conference convened in London, but the Arab delegation refused to formally meet with its Jewish counterpart or to recognize them. The Conference ended on March 17, 1939, without making any progress. On May 17, 1939, the British government issued the White Paper of 1939, in which the idea of partitioning the Mandate was abandoned in favor of Jews and Arabs sharing one government and put strict quotas on further Jewish immigration. Because of impending World War II and the opposition from all sides, the plan was dropped.


title: History of the State of Palestine

text: World War II (1939–1945) gave a boost to the Jewish nationalism, as the Holocaust reaffirmed their call for a Jewish homeland. At the same time, many Arab leaders had even supported Nazi Germany, a fact which could not play well with the British. As a result, Britain pooled its energy into winning over Arab opinions by abandoning the Balfour Declaration and the terms of the League of Nations mandate which had been entrusted to it in order to create a "Jewish National Home". Britain did this by issuing the 1939 white paper which officially allowed a further 75,000 Jews to move over five years (10,000 a year plus an additional 25,000) which was to be followed by Arab majority independence. The British would later claim that that quota had already been fulfilled by those who had entered without its approval.


title: History of the State of Palestine

text: The framers of the Arab League sought to include the Palestinian Arabs within the framework of the League from its inception. An annex to the League Pact declared:


title: History of the State of Palestine

text: Even though Palestine was not able to control her own destiny, it was on the basis of the recognition of her independence that the Covenant of the League of Nations determined a system of government for her. Her existence and her independence among the nations can, therefore, no more be questioned "de jure" than the independence of any of the other Arab States... Therefore, the States signatory to the Pact of the Arab League consider that in view of Palestine's special circumstances, the Council of the League should designate an Arab delegate from Palestine to participate in its work until this country enjoys actual independence.


title: History of the State of Palestine

text: In November 1945, the Arab League reconstituted the Arab Higher Committee comprising twelve members as the supreme executive body of Palestinian Arabs in the territory of the British Mandate of Palestine. The committee was dominated by the Palestine Arab Party and was immediately recognised by Arab League countries. The Mandate government recognised the new Committee two months later. The Constitution of the League of Arab States says the existence and independence of Palestine cannot be questioned "de jure" even though the outward signs of this independence have remained veiled as a result of "force majeure".


title: History of the State of Palestine

text: In 1946, Jewish leaders – including Nahum Goldmann, Rabbi Abba Silver, Moshe Shertok, and David Ben-Gurion – proposed a union between Arab Palestine and Transjordan. Also in 1946, leaders of the Zionist movement in the U.S. sought the postponement of a determination of the application by Transjordan for United Nations membership until the status of Mandate Palestine as a whole was determined. However, at its final session the League of Nations recognized the independence of Transjordan, with the agreement of Britain.


title: History of the State of Palestine

text: In April 1947, during the activity of the United Nations Special Committee on Palestine, the Arab Higher Committee articulated its demands in the solution for the Question of Palestine: