In this paper, we investigate the existence of multiple positive solutions for the following fourthorder p-Laplacian Sturm-Liouville boundary value problems on time scales
where ø_{p}(s) is the p-Laplacian operator. Under growth conditions on the nonlinearity f some existence results of at least two and three positive solutions for the above problem are obtained by virtue of fixed point theorems on cone. In particular, the nonlinearity f may be both sublinear and superlinear.
In a recent papers, some authors applied Nevanlinna theory to prove some results on complex difference equations reminiscent of the classical Malmquist theorem in complex differential equations. We will mainly investigate Malmquist theorem of a type of systems of complex partial difference equations on C^{n}, improvements and extensions of such results are presented in this paper.
It is proved that if a nonlinear system possesses some group-symmetry, then under certain transver-sality it admits solutions with the corresponding symmetry. The method is due to Mawhin's guiding function one.
The perfect matching polytope of a graph G is the convex hull of the incidence vectors of all perfect matchings in G. A graph is called perfect matching compact (shortly, PM-compact), if its perfect matching polytope has diameter one. This paper gives a complete characterization of simple PM-compact Hamiltonian bipartite graphs. We first define two families of graphs, called the H2C-bipartite graphs and the H23-bipartite graphs, respectively. Then we show that, for a simple Hamiltonian bipartite graph G with |V (G)|≥ 6, G is PM-compact if and only if G is K_{3, 3}, or G is a spanning Hamiltonian subgraph of either an H2C-bipartite graph or an H23-bipartite graph.
In this paper, a new global algorithm is presented to globally solve the linear multiplicative pro-gramming (LMP). The problem (LMP) is firstly converted into an equivalent programming problem (LMP (H)) by introducing p auxiliary variables. Then by exploiting structure of (LMP(H)), a linear relaxation program-ming (LP (H)) of (LMP (H)) is obtained with a problem (LMP) reduced to a sequence of linear programming problems. The algorithm is used to compute the lower bounds called the branch and bound search by solving linear relaxation programming problems (LP(H)). The proposed algorithm is proven that it is convergent to the global minimum through the solutions of a series of linear programming problems. Some examples are given to illustrate the feasibility of the proposed algorithm.
Josephson system with parametric excitation is investigated. Using second-order averaging method and Melnikov function, we analyze the existence and bifurcations for harmonic, (2, 3, n-order) subharmonics and (2, 3-order) superharmonics and the heterocilinic and homoclinic bifurcations for chaos under periodic perturbation. Using numerical simulation, we check our theoretical analysis and further study the effect of the parameters on dynamics. We find the complex dynamics, including the jumping behaviors, symmetry-breaking, chaos converting to periodic orbits, interior crisis, non-attracting chaotic set, interlocking (reverse) period-doubling bifurcations from periodic orbits, the processes from interlocking period-doubling bifurcations of periodic orbits to chaos after strange non-chaotic motions when the parameter β increases, etc.
Given two closed, in general unbounded, operators A and C, we investigate the left invertible completion of the partial operator matrix (_{0}^{A}_{C}^{?}). Based on the space decomposition technique, the alternative sufficient and necessary conditions are given according to whether the dimension of R(A)┴ is finite or infinite. As a direct consequence, the perturbation of left spectra is further presented.
Self-similar sets (SSS) are the most important class of Fractals and play an important role in the studies in Fractal. In this note, we introduce self-similar-like sets (SSLS) which generalize self-similar sets, we will show some properties of SSLS which distinguish essentially that of SSS, and we will give also some applications of SSLS.
In this paper, we consider the problem of construction of exponentially many distinct genus embed-dings of complete graphs. There are three approaches to solve the problem. The first approach is to construct exponentially many current graphs by the theory of graceful labellings of paths; the second approach is to find a current assignment of the current graph by the theory of current graph; the third approach is to find exponen-tially many embedding (or rotation) scheme of complete graph by finding exponentially many distinct maximum genus embeddings of the current graph. According to these three approaches, we can construct exponentially many distinct genus embeddings of complete graph K_{12s+3}, which show that there are at least 1/2 × (200/9)^{s} distinct genus embeddings for K_{12s+3}.
The maximum entropy method has been widely used in many fields, such as statistical mechanics, economics, etc. Its crucial idea is that when we make inference based on partial information, we must use the distribution with maximum entropy subject to whatever is known. In this paper, we investigate the empirical entropy method for right censored data and use simulation to compare the empirical entropy method with the empirical likelihood method. Simulations indicate that the empirical entropy method gives better coverage probability than that of the empirical likelihood method for contaminated and censored lifetime data.
In this paper, we consider the problem of optimal dividend payout and equity issuance for a company whose liquid asset is modeled by the dual of classical risk model with diffusion. We assume that there exist both proportional and fixed transaction costs when issuing new equity. Our objective is to maximize the expected cumulative present value of the dividend payout minus the equity issuance until the time of bankruptcy, which is defined as the first time when the company's capital reserve falls below zero. The solution to the mixed impulse-singular control problem relies on two auxiliary subproblems: one is the classical dividend problem without equity issuance, and the other one assumes that the company never goes bankrupt by equity issuance. We first provide closed-form expressions of the value functions and the optimal strategies for both auxiliary subproblems. We then identify the solution to the original problem with either of the auxiliary problems. Our results show that the optimal strategy should either allow for bankruptcy or keep the company's reserve above zero by issuing new equity, depending on the model's parameters. We also present some economic interpretations and sensitivity analysis for our results by theoretical analysis and numerical examples.
The streamline-diffusion method of the lowest order nonconforming rectangular finite element is proposed for convection-diffusion problem. By making full use of the element's special property, the same convergence order as the previous literature is obtained. In which, the jump terms on the boundary are added to bilinear form with simple user-chosen parameter δ_{K} which has nothing to do with perturbation parameter ε appeared in the problem under considered, the subdivision mesh size h_{K} and the inverse estimate coefficient μ in finite element space.
In this paper, we prove a central limit theorem for m-dependent random variables under sublinear expectations. This theorem can be regarded as a generalization of Peng's central limit theorem.
We consider a ruin model with random income and dependence between claim sizes and claim intervals. In this paper, we extend the determinate premium income into a compound Poisson process and assume that the distribution of the time between two claim occurrences depends on the previous claim size. Given the premium size is exponentially distributed, the (Gerber-Shiu) discounted penalty functions is derived. Finally, we consider a similar model.
In this paper, the minimal dissipation local discontinuous Galerkin method is studied to solve the parabolic interface problems in two-dimensional convex polygonal domains. The interface may be arbitrary smooth curves. The proposed method is proved to be L^{2} stable and the order of error estimates in the given norm is O(h|logh|^{1/2}). Numerical experiments show the efficiency and accuracy of the method.
The objective of this paper is to study the oscillatory and asymptotic properties of the general mixed type third order neutral difference equation of the form
△(a_{n} △^{2}(x_{n} + b_{n}x_{n-τ1} + c_{n}x_{n-τ2})) + qnx_{n+1-σ1}^{α}+ pnx_{n+1-σ2}^{β}= 0,
where {a_{n}}, {b_{n}}, {c_{n}}, {q_{n}} and {p_{n}} are positive real sequences, both α and β are ratios of odd positive integers, τ_{1}, τ_{2}, σ_{1} and σ_{2} are positive integers. We establish some sufficient conditions which ensure all solutions are either oscillatory or converge to zero.
This paper introduces the Tukey trimmed and Winsorized means for the transformed data based on a scaled deviation. The trimmed and Winsorized means and scale based on a scaled deviation are as special cases. Meanwhile, the trimmed and Winsorized skewness and kurtosis based on a scaled deviation are given. Furthermore, some of their robust properties (influence function, breakdown points) and asymptotic properties (asymptotic representation and limiting distribution) are also obtained.
A new class of digit sets, which we called very weak product-form digit sets, is introduced and it is shown that they are tile digit set for self-similar tiles. This extends previous results about product-form and weak product-form digit sets.
This paper discusses the sensitivity analysis of semisimple eigenvalues and associated eigen-matrix triples of regular quadratic eigenvalue problems analytically dependent on several parameters. The directional derivatives of semisimple eigenvalues are obtained. The average of semisimple eigenvalues and corresponding eigen-matrix triple are proved to be analytic, and their partial derivatives are given. On these grounds, the sensitivities of the semisimple eigenvalues and corresponding eigenvector matrices are defined.
The problem of reconstruction of a binary image in the field of discrete tomography is a classic instance of seeking solution applying mathematical techniques. Here two such binary image reconstruction problems are considered given some numerical information on the image. Algorithms are developed for solving these problems and correctness of the algorithms are discussed.
In this paper, we first formulate a second-order multiobjective symmetric primal-dual pair over arbitrary cones by introducing two different functions f: R^{n} × R^{m} → R^{k} and g : R^{n} × R^{m} → R^{l} in each k-objectives as well as l-constraints. Further, appropriate duality relations are established under second-order (F, α, ρ, d)-convexity assumptions. A nontrivial example which is second-order (F, α, ρ, d)-convex but not second-order convex/F-convex is also illustrated. Moreover, a second-order minimax mixed integer dual programs is formulated and a duality theorem is established using second-order (F, α, ρ, d)-convexity assumptions. A self duality theorem is also obtained by assuming the functions involved to be skew-symmetric.
Non-self-adjoint quasi-differential expression M and its formal adjoint M^{+} may generate non-symmetric ordinary differential operators. Although minimal operators T_{0}, T_{0}^{+} generated by M, M^{+} are not symmetric, they form an adjoint pair. In this paper, author studies regularly solvable operators with respect to the adjoint pair T_{0}, T_{0}^{+} in two kinds of conditions and give their geometry description in the corresponding ways.
This paper investigates a dynamic asset allocation problem for loss-averse investors in a jump-diffusion model where there are a riskless asset and N risky assets. Specifically, the prices of risky assets are governed by jump-diffusion processes driven by an m-dimensional Brownian motion and a (N -m)-dimensional Poisson process. After converting the dynamic optimal portfolio problem to a static optimization problem in the terminal wealth, the optimal terminal wealth is first solved. Then the optimal wealth process and investment strategy are derived by using the martingale representation approach. The closed-form solutions for them are finally given in a special example.
The present paper is devoted to the existence of the random attractor for partly dissipative stochas-tic lattice dynamical systems with multiplicative white noises.