This paper makes qualitative analysis to the bounded traveling wave solutions for a kind of nonlinear dispersive-dissipative equation, and considers its solving problem. The relation is investigated between behavior of its solution and the dissipation coefficient. Further, all approximate damped oscillatory solutions when dissipation coefficient is small are presented by utilizing the method of undetermined coefficients according to the theory of rotated vector field in planar dynamical systems. Finally, error estimate is given by establishing the integral equation which reflects the relation between approximate and exact damped oscillatory solutions applying the idea of homogenization principle.
We consider the Cauchy problem for one-dimensional compressible isentropic Navier-Stokes equations with density-dependent viscosity μ(ρ)=Aρ^{α}, where α > 0 and A > 0. The global existence of strong solutions is obtained, which improves the previous results by enlarging the interval of α. Moreover, our result shows that no vacuum is developed in a finite time provided the initial data does not contain vacuum.
We study the DeGroot model for continuous opinion dynamics under the influence of innovations. In the original model, individuals' opinions, after given their initial values, evolve merely according to the given learning topology. The main contribution of this paper is that external innovation effects are introduced:each individual is given the opportunity to change her opinion to a randomly selected opinion according to a given distribution on the opinion space and then the external opinion is either adapted by the individual, or combined into her learning process. It turns out that all the classical results of the DeGroot model are violated in this new model. We prove that convergence can still be guaranteed in the expectation sense, regardless of the learning topology. We also study the steady distributions of opinions among the society and the time spent to reach a steady state by means of Monte-Carlo simulations.
This paper shows that monotone self-dual Boolean functions in irredundant disjuntive normal form(IDNF) do not have more variables than disjuncts. Monotone self-dual Boolean functions in IDNF with the same number of variables and disjuncts are examined. An algorithm is proposed to test whether a monotone Boolean function in IDNF with n variables and n disjuncts is self-dual. The runtime of the algorithm is O(n^{3}).
This paper investigates the optimal reinsurance and investment in a hidden Markov financial market consisting of non-risky(bond) and risky(stock) asset. We assume that only the price of the risky asset can be observed from the financial market. Suppose that the insurance company can adopt proportional reinsurance and investment in the hidden Markov financial market to reduce risk or increase profit. Our objective is to maximize the expected exponential utility of the terminal wealth of the surplus of the insurance company. By using the filtering theory, we establish the separation principle and reduce the problem to the complete information case. With the help of Girsanov change of measure and the dynamic programming approach, we characterize the value function as the unique solution of a linear parabolic partial differential equation and obtain the Feynman-Kac representation of the value function.
This paper studies heat equation with variable exponent u_{t}=Δu+u_{p}(x)+u^{q} in R^{N}×(0, T), where p(x) is a nonnegative continuous, bounded function, 0 < p-=inf p(x) ≤ p(x) ≤ sup p(x)=p+. It is easy to understand for the problem that all nontrivial nonnegative solutions must be global if and only if max{p+, q} ≤ 1. Based on the interaction between the two sources with fixed and variable exponents in the model, some Fujita type conditions are determined that that all nontrivial nonnegative solutions blow up in finite time if 0 < q ≤ 1 with p+> 1, or 1 < q < 1+(N)/(2). In addition, if q > 1+(N)/(2), then(i) all solutions blow up in finite time with 0 < p-≤ p+≤ 1+(N)/(2);(ii) there are both global and nonglobal solutions for p-> 1+(N)/(2);and(iii) there are functions p(x) such that all solutions blow up in finite time, and also functions p(x) such that the problem possesses global solutions when p-< 1+(N)/(2) < p+.
Let Γ_{t}^{-}(G) be upper minus total domination number of G. In this paper, We establish an upper bound of the upper minus total domination number of a regular graph G and characterize the extremal graphs attaining the bound. Thus, we answer an open problem by Yan, Yang and Shan
This paper deals with the solutions defined for all time of the degenerate Fisher equation. Some solutions are obtained by considering two traveling fronts with critical speed that come from both sides of the X-axis and mix. Unfortunately, the entire solutions which behave as two opposite wave fronts with non-critical speed approaching each other from both sides of the X-axis can not be obtained, because the essential difficulty originates from the algebraic decay rate of the fronts with non-critical speed.
In this paper, we establish some new oscillation criteria for a non autonomous second order delay dynamic equation
(r(t)g(x^{Δ}(t)))Δ+p(t)f(x(τ(t)))=0,
on a time scale T. Oscillation behavior of this equation is not studied before. Our results not only apply on differential equations when T=R, difference equations when T=N but can be applied on different types of time scales such as when T=q^{N} for q > 1 and also improve most previous results. Finally, we give some examples to illustrate our main results.
We derive the Γ-limit of scaled elastic energies h^{-4}E^{h}(u^{h}) associated with deformations uh of a family of thin shells S^{h}={z=x+t(x);x∈S, -g_{h}^{1}(x)< t < gh^{2}(x)}. The obtained von Kármán theory is valid for a general sequence of boundaries gh^{1}, gh^{2} converging to 0 in an appropriate manner as h vanishes. Our analysis relies on the techniques and extends the results in[10]and[11].
Nonparametric estimation of a survival function is one of the most commonly asked questions in the analysis of failure time data and for this, a number of procedures have been developed under various types of censoring structures(Kalbfleisch and Prentice, 2002). In particular, several algorithms are available for interval-censored failure time data with independent censoring mechanism(Sun, 2006; Turnbull, 1976). In this paper, we consider the interval-censored data where the censoring mechanism may be related to the failure time of interest, for which there does not seem to exist a nonparametric estimation procedure. It is well-known that with informative censoring, the estimation is possible only under some assumptions. To attack the problem, we take a copula model approach to model the relationship between the failure time of interest and censoring variables and present a simple nonparametric estimation procedure. The method allows one to conduct a sensitivity analysis among others.
A graph is said to be symmetric if its automorphism group acts transitively on its arcs. In this paper, a complete classification of connected pentavalent symmetric graphs of order 16p is given for each prime p. It follows from this result that a connected pentavalent symmetric graph of order 16p exists if and only if p=2 or 31, and that up to isomorphism, there are three such graphs.
In this paper, we consider an inference method for recurrent event data in which the primary exposure covariate is assessed only in a validation set, while as an auxiliary covariate for the main exposure is available for the full cohort. Additive rate model is considered. The existing estimating equations in the absence of primary exposure are corrected by taking use of the validation data and auxiliary information, which yield consistent and asymptotically normal estimators of the regression parameters. The estimated baseline mean process is shown to converge weakly to a zero-mean Gaussian process. Extensive simulations are conducted to evaluate finite sample performance.
In this paper, we consider the eigenvalue problem for integro-differential operators with separated boundary conditions on the finite interval and find a trace formula for the integro-differential operator.
Panel count data occur in many clinical and observational studies and in some situations the observation process is informative. In this article, we propose a new joint model for the analysis of panel count data with time-dependent covariates and possibly in the presence of informative observation process via two latent variables. For the inference on the proposed model, a class of estimating equations is developed and the resulting estimators are shown to be consistent and asymptotically normal. In addition, a lack-of-fit test is provided for assessing the adequacy of the model. The finite-sample behavior of the proposed methods is examined through Monte Carlo simulation studies which suggest that the proposed approach works well for practical situations. Also an illustrative example is provided.
For compressible multiphase flow models the proper definition of averages of nonlinear terms is an essential problem which is called the closure problem. The purpose of the present work is to verify the spatial homogeneity closure, based on analysis of the simulation data. Various proposed closures are compared in a verification study to spatial averages of numerical simulations.
Let G be a k(k ≤ 2)-edge connected simple graph with minimal degree ≥ 3 and girth g, r=「(g-1)/(2)」. For any edge uv ∈ E(G), if
d_{G}(u)+d_{G}(v)>(2ν(G)-2(k+1)(g-2r))/((k+1)(2^{r}-1)(g-2r))+2(g-2r-1),
then G is up-embeddable. Furthermore, similar results for 3-edge connected simple graphs are also obtained.
Based on Vector Aitken(VA) method, we propose an acceleration Expectation-Maximization(EM) algorithm, VA-accelerated EM algorithm, whose convergence speed is faster than that of EM algorithm. The VA-accelerated EM algorithm does not use the information matrix but only uses the sequence of estimates obtained from iterations of the EM algorithm, thus it keeps the flexibility and simplicity of the EM algorithm. Considering Steffensen iterative process, we have also given the Steffensen form of the VA-accelerated EM algorithm. It can be proved that the reform process is quadratic convergence. Numerical analysis illustrate the proposed methods are efficient and faster than EM algorithm.
Case-cohort design is an efficient and economical design to study risk factors for diseases with expensive measurements, especially when the disease rate is low. When several diseases are of interest, multiple case-cohort design studies may be conducted using the same subcohort. To study the association between risk factors and each disease occurrence or death, we consider a general additive-multiplicative hazards model for case-cohort designs with multiple disease outcomes. We present an estimation procedure for the regression parameters of the additive-multiplicative hazards model, and show that the proposed estimator is consistent and asymptotically normal. Large sample approximation works well in finite sample studies in simulation. Finally, we apply the proposed method to a real data example for illustration.
In this paper, minimax theorems and saddle points for a class of vector-valued mappings f(x, y)=u(x)+β(x) v(y) are first investigated in the sense of lexicographic order, where u, v are two general vector-valued mappings and β is a non-negative real-valued function. Then, by applying the existence theorem of lexicographic saddle point, we investigate a lexicographic equilibrium problem and establish an equivalent relationship between the lexicographic saddle point theorem and existence theorem of a lexicographic equilibrium problem for vector-valued mappings.
The mathematical property of one-dimensional steady solution for reverse smolder waves in the context of a model that permits both fuel-rich and fuel-lean has been studied using the method of analysis. Based on the equations and the boundary conditions some asymptotic properties of the solution at infinity are proved. It is shown that the value of oxygen or the mass of fuel(corresponding to the fuel-rich case and the fuel-lean case, respectively) tends to zero, and the temperature approaches to a fixed value. This is confirmed by other authors using large activation energy asymptotic methods.
In this paper, we consider the Cauchy problem for the 3D Leray-α model, introduced by Cheskidov et al. ^{[11]}. We obtain the global solution for the 3D Leray-α model in the fractional index Sobolev space, and prove that the 3D Leray-α model reduces to the homogeneous incompressible Navier-Stokes equations as α↘0^{+}, and the solution of the 3D Leray-α model will converge to the weak solution of the corresponding Navier-Stokes equations.
This work focuses on numerical methods for finding optimal dividend payment and capital injection policies to maximize the present value of the difference between the cumulative dividend payment and the possible capital injections. Using dynamic programming principle, the value function obeys a quasi-variational inequality(QVI). The state constraint of the impulsive control gives rise to a capital injection region with free boundary. Since the closed-form solutions are virtually impossible to obtain, we use Markov chain approximation techniques to construct a discrete-time controlled Markov chain to approximate the value function and optimal controls. Convergence of the approximation algorithms is proved.
This paper studies serial correlation testing for a general three-dimensional panel data model. As a step for hypothesis testing, the robust within estimation of parameter coefficients is investigated, and shown to asymptotically consistent and normal under some mild conditions. A residual-based statistic is then constructed to test for serial correlation in the idiosyncratic errors, which is based on the parameter estimates for an artificial autoregression modeled by centering and differencing residuals. The test can be shown to asymptotically chisquare distributed under the null hypothesis. Power study shows that the test can detect local alternatives distinct at the parametric rate from the null hypothesis. The test needs no distribution assumptions of the error components, and is robust to the misspecification of various specific effects. Monte Carlo simulations are carried out for illustration.
We study the Cauchy problem of damped generalized Boussinesq equation u_{tt}-u_{xx}+(u_{xx}+f(u))_{xx}-αu_{xxt}=0. First we give the local existence of weak solution and smooth solution. Then by using potential well method and convexity method we prove the global existence and finite time blow up of solution, then we obtain some sharp conditions for the well-posedness problem.