The main aim of this paper is to investigate the effects of the impulse and time delay on a type of parabolic equations. In view of the characteristics of the equation, a particular iteration scheme is adopted. The results show that Under certain conditions on the coefficients of the equation and the impulse, the solution oscillates in a particular manner---called ``asymptotic weighted-periodicity".
This paper considers a kind of strongly coupled cross diffusion parabolic system, which can be used as the multi-dimensional {\it Lyumkis} energy transport model in semiconductor science. The global existence and large time behavior are obtained for smooth solution to the initial boundary value problem. When the initial data are a small perturbation of an isothermal stationary solution, the smooth solution of the problem under the insulating boundary condition, converges to that stationary solution exponentially fast as time goes to infinity.
In this paper, the $\mathcal{UV}$-theory and P-differential calculus are employed to study second-order expansion of a class of D.C. functions and minimization problems. Under certain conditions, some properties of the ${\cal U}$-Lagrangian, the second-order expansion of this class of functions along some trajectories are formulated. Some first and second order optimality conditions for the class of D.C. optimization problems are given.
By using the continuation theorem of coincidence degree theory, the sufficient conditions to guarantee the existence of positive periodic solutions are established for nonautonomous predator-prey systems with discrete and continuously distributed delays.
The Navier-Stokes-$\alpha$ equations subject to the periodic boundary conditions are considered. Analyticity in time for a class of solutions taking values in a Gevrey class of functions is proven. Exponential decay of the spatial Fourier spectrum for the analytic solutions and the lower bounds on the rate defined by the exponential decay are also obtained.
In this paper, two auxiliary functions for global optimization are proposed. These two auxiliary functions possess all characters of tunnelling functions and filled functions under certain general assumptions. Thus, they can be considered as the unification of filled function and tunnelling function. Moreover, the process of tunneling or filling for global optimization can be unified as the minimization of such auxiliary functions. Result of numerical experiments shows that such two auxiliary functions are effective.
In an anonymous secret sharing scheme the secret can be reconstructed without knowledge of which participants hold which shares. In this paper some constructions of anonymous secret sharing schemes with 2 thresholds by using combinatorial designs are given. Let $v(t,w,q)$ denote the minimum size of the set of shares of a perfect anonymous $(t,w)$ threshold secret sharing scheme with $q$ secrets. In this paper we prove that $v(t,w,q)=\Theta(q)$ if $t$ and $w$ are fixed and that the lower bound of the size of the set of shares in [4] is not optimal under certain condition.
We consider several synchronous and asynchronous multisplitting iteration schemes for solving a class of nonlinear complementarity problems with the system matrix being an $H-$matrix. We establish the convergence theorems for the schemes. The numerical experiments show that the schemes are efficient for solving the class of nonlinear complementarity problems.
In this note, we prove that the efficient solution set for a vector optimization problem with a continuous, star cone-quasiconvex objective mapping is connected under the assumption that the ordering cone is a $D$-cone. A $D$-cone includes any closed convex pointed cones in a normed space which admits strictly positive continuous linear functionals.
This paper is concerned with time decay rates for weak solutions to a class system of isotropic incompressible non-Newtonian fluid motion in $\R^n$. With the use of the spectral decomposition methods of Stokes operator, the optimal decay estimates of weak solutions in L${^2}$ norm are derived under the different conditions on the initial velocity. Moreover, the error estimates of the difference between non-Newtonian flow and Navier-Stokes flow are also investigated.
It is useful to know the maximum number of clear two-factor interactions in a $2^{m-(m-k)}_{\rm III}$ design. This paper provides a method to construct a $2^{m-(m-k)}_{\rm III}$ design with the maximum number of clear two-factor interactions. And it is proved that the resulting designs have more clear two-factor interactions than those constructed by Tang et al.$^{[6]}$. Moreover, the designs constructed are shown to have concise grid representations.
Let $[b,T]$ be the commutator generated by a Lipschitz function $b\in \text{Lip}(\beta)(0<\beta<1)$ and multiplier $T$. The authors studied the boundedness of $[b,T]$ on the Lebesgue spaces and Hardy spaces.
There are six types of triangles: undirected triangle, cyclic triangle, transitive triangle, mixed-1 triangle, mixed-2 triangle and mixed-3 triangle. The triangle-decompositions for the six types of triangles have already been solved. For the first three types of triangles, their large sets have already been solved, and their overlarge sets have been investigated. In this paper, we establish the spectrum of $LT_i(v,\lambda)$, $OLT_i(v) (i=1,2)$, and give the existence of $LT_3(v,\lambda)$ and $OLT_3(v,\lambda)$ with $\lambda$ even.
In this paper, we extend the autonomous n-Dimensional Volterra Mutualistic System to a non-autonomous system. The condition of persistence and extinction is obtained for each population, and the threshold is established for asymptotically autonomous system.
In this paper, we derive a general vector Ekeland variational principle for set-valued mappings, which has a closed relation to $\varepsilon k^0$ -efficient points of set-valued optimization problems. The main result presented in this paper is a generalization of the corresponding result in [3].
This paper characterizes the optimal solution of subjective expected utility with S-shaped utility function, by using the prospect theory (PT). We also prove the existence of Arrow-Debreu equilibrium.
Let $\phi (G)$, $\kappa (G)$, $\alpha (G)$, $\chi (G)$, $cl(G)$, diam$(G)$ denote the number of perfect matchings, connectivity, independence number, chromatic number, clique number and diameter of a graph $G$, respectively. In this note, by constructing some extremal graphs, the following extremal problems are solved:\\ 1. max $\{\phi (G)$: $|V(G)|=2n$, $\kappa (G)\leq k\}=k[(2n-3)!!]$,\\ 2. max$\{\phi (G)$: $|V(G)|=2n$, $\alpha (G)\geq k\}=\Big[\prod\limits_{i=0}^{k-1}(2n-k-i)\Big][(2n-2k-1)!!]$,\\ 3. max$\{\phi (G)$: $|V(G)|=2n$, $\chi (G)\leq k\}=\phi (T_{k,2n})$ \ $T_{k,2n}$ is the Tur$\acute{a}$n graph, that is a complete $k$-partite graph on $2n$ vertices in which all parts are as equal in size as possible,\\ 4. max$\{\phi (G)$: $|V(G)|=2n$, $cl(G)=2\}=n!$,\\ 5. max$\{\phi (G)$: $|V(G)|=2n$, diam$(G)\geq 2\}=(2n-2)(2n-3)[(2n-5)!!]$,\\ max$\{\phi (G)$: $|V(G)|=2n$, diam$(G)\geq 3\}=(n-1)^2[(2n-5)!!]$.
In this paper, we study structure-preserving algorithms for dynamical systems defined by ordinary differential equations in $R^n$. The equations are assumed to be of the form $\dot{y}=A(y)+D(y)+R(y)$, where $A(y)$ is the conservative part subject to $\langle A(y), y\rangle=0$; $D(y)$ is the damping part or the part describing the coexistence of damping and expanding; $R(y)$ reflects strange phenomenon of the system. It is shown that the numerical solutions generated by the symplectic Runge-Kutta(SRK) methods with $b_{i}>0\;(\;i=1,\cdots,s)$ have long-time approximations to the exact ones, and these methods can describe the structural properties of the quadratic energy for these systems. Some numerical experiments and backward error analysis also show that these methods are better than other methods including the general algebraically stable Runge-Kutta(RK)methods.