29445330
Bifurcations of travelling wave solutions in a model of the hydrogen-bonded systems
By using the theory of bifucations of dynamical systems to a model of the Hydrogen-bonded systems, the existence of solitary wave, kink and anti-kink wave solutions and uncountably infinite many smooth and non-smooth periodic wave solutions is obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. In some simple parametric conditions, exact explicit and implicit solution formulas are listed.
5556814
Travelling wave solutions in the generalized Hirota-Satsuma coupled KdV system
By using the bifurcation theory of dynamical systems to the generalized Hirota-Satsuma coupled KdV system, bifurcation parameter sets are shown. Numbers of solitary waves, kink waves and periodic waves are given. Under various parameter conditions, all explicit formulas of solitary wave solutions and kink wave solutions and periodic wave solutions are listed.
11656353
Bifurcations of traveling wave solutions for a class of the nonlinear equations
Abstract The dynamical behavior of traveling wave solutions in a class of the nonlinear k ( n ,  n ) equations with negative exponents is studied by using the theory of bifurcations of dynamical systems. As a result, the dynamical behavior of different physical structure: solitary patterns, solitons, periodic, kink and anti-kink wave solutions are obtained. When parameters are varied, the conditions under which the above solutions appear are also shown. In addition, some exact explicit solutions are given.
644571
Parametric inference for progressive Type-I hybrid censored data on a simple step-stress accelerated life test model
This paper considers a simple step-stress accelerated life test model under progressive Type-I hybrid censoring scheme. The progressive Type-I hybrid censoring scheme and statistical method in synthetic accelerated stresses are provided so as to decrease the lifetime and reduce the test cost. An exponentially distributed life of test units and a cumulative exposure model are assumed. The maximum likelihood estimates of the model parameters are obtained using a pivotal quantity. Two useful lemmas and a theorem are given to construct the approximate confidence intervals for the model parameters. Finally, simulation results are provided to assess the method of inference developed in this article. The simulation results show that the method does improve for large sample size.
29892228
Bifurcations of traveling wave solutions for a class of the generalized Benjamin-Bona-Mahony equation
Abstract By using the theory of bifurcations of dynamical systems to a class of the generalized Benjamin–Bona–Mahony (GBBM) equation, the existence of solitary wave solutions and uncountably infinite, many smooth and non-smooth periodic wave solutions are obtained. It can be shown that the existence of singular curves in a traveling wave system is the reason why smooth waves converge to cusp waves, finally. When parameters are varied, under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given.
11714898
On the number of limit cycles of a cubic polynomials Hamiltonian system under quintic perturbation
Abstract This paper is concerned with the number and distribution of limit cycles of a cubic Hamiltonian system under quintic perturbation. By using the bifurcation theory and the method of detection function, we obtain that this system exists at least 14 limit cycles with the distribution C 9 1 ⊃ [ C 1 1 + 2 ( C 3 2 ⊃ 2 C 1 2 ) ] . These results in the paper are useful for the study of the weakened Hilbert’s 16th problem.
115232895
Elastostatic inverse formulation
Abstract. In this paper an inverse method for solving elastostatic problems with incomplete boundary conditions is presented. In general, inverse problems are ill-posed boundary value problems whose stability and uniqueness of solution and sensitivity-based formulations require additional constraints. In the development we use the Betti-reciprocal theorem to represent the boundary traction field in terms of the boundary and field displacements in an integral form. Initially, we assume the unknown boundary conditions and deformations required to solve the problem. In this way we equate the work done by the exact solution (unknown) to the work done by an assumed solution. Discretizing the resulting equations and using an iterative procedure each step in the solution process becomes the solution to a well-posed problem. Thus, with sufficient perturbations the correct boundary conditions are reconstructed.

2239051
Detecting large-scale system problems by mining console logs
Surprisingly, console logs rarely help operators detect problems in large-scale datacenter services, for they often consist of the voluminous intermixing of messages from many software components written by independent developers. We propose a general methodology to mine this rich source of information to automatically detect system runtime problems. We first parse console logs by combining source code analysis with information retrieval to create composite features. We then analyze these features using machine learning to detect operational problems. We show that our method enables analyses that are impossible with previous methods because of its superior ability to create sophisticated features. We also show how to distill the results of our analysis to an operator-friendly one-page decision tree showing the critical messages associated with the detected problems. We validate our approach using the Darkstar online game server and the Hadoop File System, where we detect numerous real problems with high accuracy and few false positives. In the Hadoop case, we are able to analyze 24 million lines of console logs in 3 minutes. Our methodology works on textual console logs of any size and requires no changes to the service software, no human input, and no knowledge of the software's internals.
1787368
Subdivision Tree Representation of Arbitrary Triangle Meshes
We investigate a new way to represent arbitrary triangle meshes. We prove that a large class of triangle meshes, called normal triangle meshes, can be represented by a subdivision tree, where each subdivision is one of four elementary subdivision types. We also show how to partition an arbitrary triangle mesh into a small set of normal meshes. The subdivision tree representation can be used to encode mesh connectivity information. Our theoretical analysis shows that such a coding scheme is very promising.
7346557
Predictive Control for Dynamic Resource Allocation in Enterprise Data Centers
It is challenging to reduce resource over-provisioning for enterprise applications while maintaining service level objectives (SLOs) due to their time-varying and stochastic workloads. In this paper, we study the effect of prediction on dynamic resource allocation to virtualized servers running enterprise applications. We present predictive controllers using three different prediction algorithms based on a standard auto-regressive (AR) model, a combined ANOVA-AR model, as well as a multi-pulse (MP) model. We compare the properties of the predictive controllers with an adaptive integral (I) controller designed in our earlier work on controlling relative utilization of resource containers. The controllers are evaluated in a hypothetical virtual server environment where we use the CPU utilization traces collected on 36 servers in an enterprise data center. Since these traces were collected in an open-loop environment, we use a simple queuing algorithm to simulate the closed-loop CPU usage under dynamic control of CPU allocation. We also study the controllers by emulating the utilization traces on a test bed where a Web server was hosted inside a Xen virtual machine. We compare the results of these controllers from all the servers and find that the MP-based predictive controller performed slightly better statistically than the other two predictive controllers. The ANOVA-AR-based approach is highly sensitive to the existence of periodic patterns in the trace, while the other three methods are not. In addition, all the three predictive schemes performed significantly better when the prediction error was accounted for using a feedback mechanism. The MP-based method also demonstrated an interesting self-learning behavior
24579136
The Periodic Solution of a Class of Two Neurons Hopfield Network with Distributed Delay
This paper considers the two neurons Hopfield network with distributed delay, which can be transformed into the three-dimensional differential system. Then we use the result of competitive system to get the periodic solution of the system. We also show that existence and uniqueness of equilibrium point, and if the equilibrium is unstable, then an orbitally asymptotically stable periodic solution exists.