In this paper, we obtain some stability results for perturbed vector equilibrium problems. Under new assumptions, which are weaker than the assumption of C-strict monotonicity, we provide sufficient conditions for the Painlevé-Kuratowski Convergence of the weak efficient solution sets and efficient solution sets for the perturbed vector equilibrium problems with a sequence of mappings converging in real linear metric spaces. These results extend and improve some known results in the literature.
We consider the compound binomial model, and assume that dividends are paid to the shareholders according to an admissible strategy with dividend rates bounded by a constant.The company controls the amount of dividends in order to maximize the cumulative expected discounted dividends prior to ruin. We show that the optimal value function is the unique solution of a discrete HJB equation. Moreover, we obtain some properties of the optimal payment strategy, and offer a simple algorithm for obtaining the optimal strategy. The key of our method is to transform the value function. Numerical examples are presented to illustrate the transformation method.
The discrete mathematical model for the respiratory process in bacterial culture obtained by Euler method is investigated. The conditions of existence for flip bifurcation and Hopf bifurcation are derived by using center manifold theorem and bifurcation theory, condition of existence of chaos in the sense of Marotto's definition of chaos is proved. The bifurcation diagrams, Lyapunov exponents and phase portraits are given for different parameters of the model, and the fractal dimension of chaotic attractor was also calculated. The numerical simulation results confirm the theoretical analysis and also display the new and complex dynamical behaviors compared with the continuous model. In particular, we found that the new chaotic attractor, and new types of two or four coexisting chaotic attractors, and two coexisting invariant torus.
The smooth integration of counting and absolute deviation (SICA) penalized variable selection procedure for high-dimensional linear regression models is proposed by Lv and Fan (2009). In this article, we extend their idea to Cox's proportional hazards (PH) model by using a penalized log partial likelihood with the SICA penalty. The number of the regression coefficients is allowed to grow with the sample size. Based on an approximation to the inverse of the Hessian matrix, the proposed method can be easily carried out with the smoothing quasi-Newton (SQN) algorithm. Under appropriate sparsity conditions, we show that the resulting estimator of the regression coefficients possesses the oracle property. We perform an extensive simulation study to compare our approach with other methods and illustrate it on a well known PBC data for predicting survival from risk factors.
In this paper, we establish the boundedness of commutators generated by the multilinear Calderón-Zygmud type singular integrals and Lipschitz functions on the Triebel-Lizorkin space and Lipschitz spaces.
The dynamics of a single strain HIV model is studied. The basic reproduction number R_{0} used as a bifurcation parameter shows that the system undergoes transcritical and saddle-node bifurcations. The usual threshold unit value of R_{0} does not completely determine the eradication of the disease in an HIV infected person. In particular, a sub-threshold value R_{c} is established which determines the system's number of endemic states: multiple if R_{c} < R_{0} < 1, only one if R_{c}=R_{0}=1, and none if R_{0} < R_{c} < 1.
In this paper, we prove a strong convergence theorem for finding a common element of the set of solutions for a generalized mixed equilibrium problems, the set of fixed points of infinite family of quasi-∅-asymptotically non-expansive mappings in a Banach space by using the CQ method. Our results improve the main results of Takahashi and Takahashi and Takahashi and Zembayashi. Moreover, the method of proof adopted in the paper is different from that of them.
The paper deals with oscillation of Runge-Kutta methods for equation x'(t)=ax(t)+a_{0}x([t]). The conditions of oscillation for the numerical methods are presented by considering the characteristic equation of the corresponding discrete scheme. It is proved that any nodes have the same oscillatory property as the integer nodes. Furthermore, the conditions under which the oscillation of the analytic solution is inherited by the numerical solution are obtained. The relationships between stability and oscillation are considered. Finally, some numerical experiments are given.
A nonlinear discrete time Cournot duopoly game is investigated in this paper. The conditions of existence for saddle-node bifurcation, transcritical bifurcation and flip bifurcation are derived using the center manifold theorem and the bifurcation theory. We prove that there exists chaotic behavior in the sense of Marotto's definition of chaos. The numerical simulations not only show the consistence with our theoretical analysis, but also exhibit the complex but interesting dynamical behaviors of the model. The computation of maximum Lyapunov exponents confirms the theoretical analysis of the dynamical behaviors of the system.
In this work the existence of solutions of one-dimensional backward doubly stochastic differential equations (BDSDEs) with coefficients left-Lipschitz in y (may be discontinuous) and Lipschitz in z is studied. Also, the associated comparison theorem is obtained.
In this paper, we discuss the existence of pseudo-almost automorphic solutions to linear differential equation which has an exponential trichotomy, and the results also hold for some nonlinear equations with the form x'(t)=f(t, x(t))+g(t, x(t)), where f, g are pseudo-almost automorphic functions. We prove our main result by the application of Leray-Schauder fixed point theorem.
This is a continuation of the paper (J. Math. Phys., 52(2011), 093102). We consider the Cauchy problem to the three-dimensional viscous liquid-gas two-fluid flow model. The global existence of classical solution is proved, where the initial vacuum is allowed.
Some new direct criteria of boundedness in terms of two measures for impulsive integro-differential systems with fixed moments of impulse effects are established by Lyapunov functions coupled with Razumikhin techniques.
Based on the generalized dressing method, we propose integrable variable coefficient coupled cylindrical nonlinear Schrödinger equations and their Lax pairs. As applications, their explicit solutions and their reductions are constructed.
In this paper, we are concerned with the global existence of smooth solutions for the one dimensional relativistic Euler-Poisson equations. Combining certain physical background, the relativistic Euler-Poisson model is derived mathematically. By using an invariant of Lax's method, we will give a sufficient condition for the existence of a global smooth solution to the one-dimensional Euler-Poisson equations with repulsive force.
The pyrotechnic control subsystem plays an important role in opening the solar array of a satellite. Assessing the reliability of the subsystem requires determining the level of a control factor that is needed to cause the desired response and energy output with high probability. A two-phase adaptive design to estimate the level of interest is proposed and studied. The convergence of the design is obtained. A simulation study shows that the estimate is very close to its population value and is robust to the initial guess of the design. As an application, the design is used to assess the reliability of a real pyrotechnic control subsystem.
A new generalized linear exponential distribution (NGLED) is considered in this paper which can be deemed as a new and more flexible extension of linear exponential distribution. Some statistical properties for the NGLED such as the hazard rate function, moments, quantiles are given. The maximum likelihood estimations (MLE) of unknown parameters are also discussed. A simulation study and two real data analyzes are carried out to illustrate that the new distribution is more flexible and effective than other popular distributions in modeling lifetime data.
Several authors have studied the uniform estimate for the tail probabilities of randomly weighted sums and their maxima. In this paper, we generalize their work to the situation that {X_{i}, i≥1} is a sequence of upper tail asymptotically independent random variables with common distribution from the class D∩L, and {θ_{i}, i≥1} is a sequence of nonnegative random variables, independent of {X_{i},i≥1} and satisfying some regular conditions. Moreover, no additional assumption is required on the dependence structure of {θ_{i}, i≥1}.
In a linear multi-secret sharing scheme with non-threshold structures, several secret values are shared among n participants, and every secret value has a specified access structure. The efficiency of a multi-secret sharing scheme is measured by means of the complexity σ and the randomness τ. Informally, the complexity σ is the ratio between the maximum of information received by each participant and the minimum of information corresponding to every key. The randomness τ is the ratio between the amount of information distributed to the set of users U={1, …, n} and the minimum of information corresponding to every key.
In this paper, we discuss σ and τ of any linear multi-secret sharing schemes realized by linear codes with non-threshold structures, and provide two algorithms to make σ and τ to be the minimum, respectively. That is, they are optimal.
We first propose a way for generating Lie algebras from which we get a few kinds of reduced Lie algebras, denoted by R^{6}, R^{8} and R_{1}^{6},R_{2}^{6}, respectively. As for applications of some of them, a Lax pair is introduced by using the Lie algebra R^{6} whose compatibility gives rise to an integrable hierarchy with 4-potential functions and two arbitrary parameters whose corresponding Hamiltonian structure is obtained by the variational identity. Then we make use of the Lie algebra R_{1}^{6} to deduce a nonlinear integrable coupling hierarchy of the mKdV equation whose Hamiltonian structure is also obtained. Again,via using the Lie algebra R_{2}^{6}, we introduce a Lax pair and work out a linear integrable coupling hierarchy of the mKdV equation whose Hamiltonian structure is obtained. Finally, we get some reduced linear and nonlinear equations with variable coefficients and work out the elliptic coordinate solutions, exact traveling wave solutions, respectively.
Let T be a tree with n vertices and let A(T) be the adjacency matrix of T. Spectral radius of T is the largest eigenvalue of A(T). Wu et al. [Wu, B.F., Yuan, X.Y., and Xiao, E.L. On the spectral radii of trees, Journal of East China Normal University (Natural Science), 3: 22-28 (2004)] determined the first seven trees of order n with the smallest spectral radius. In this paper, we extend this ordering by determining the trees with the eighth to the tenth smallest spectral radius among all trees with n vertices.
This paper is concerned with the asymptotic stability of the periodic solution to a one-dimensional model system for the compressible viscous van der Waals fluid in Eulerian coordinates. If the initial density and initial momentum are suitably close to the average density and average momentum, then the solution is proved to tend toward a stationary solution as t→∞.
The aim of this paper is to study the nonexistence and existence of nonnegative, nontrivial weak solution for a class of general capillarity systems. The proofs rely essentially on the minimum principle combined with the mountain pass theorem.
In this paper we investigate the existence of solutions of the nonhomogeneous three-point boundary value problem
The coefficient functions a and b are continuous real-valued functions on [0, 1], η and ζ are some positive constants. Denote by E a Banach space and assume, that u belongs to an Orlicz space i.e., u(·)∈L_{M}([0, 1],R), where M is an N-function and c∈E.
We search for solutions of the above problem in the Banach space of continuous functions C([0, 1],E) with the Pettis integrability assumptions imposed on f. Some classes of Pettis-integrable functions are described in the paper and exploited in the proofs of main results. We stress on a class of pseudo-solutions of considered problem. Our results extend previous results of the same type for both Bochner and Pettis integrability settings. Similar results are also proved for differential inclusions i.e. when f is a multivalued function.
Case-cohort sampling is a commonly used and efficient method for studying large cohorts. In many situations, some covariates are easily measured on all cohort subjects, and surrogate measurements of the expensive covariates also may be observed. In this paper, to make full use of the covariate data collected outside the case-cohort sample, we propose a class of weighted estimators with general time-varying weights for the additive hazards model, and the estimators are shown to be consistent and asymptotically normal. We also identify the estimator within this class that maximizes efficiency, and simulation studies show that the efficiency gains of the proposed estimator over the existing ones can be substantial in practical situations. A real example is provided.