The approximation characteristic of diagonal matrix in probabilistic setting

In this paper, the approximation characteristic of a diagonal matrix in probabilistic and average case settings is investigated. And the asymptotic degree of the probabilistic linear (n,δ)$(n,\delta )$-width and p$p$-average linear n$n$-width of diagonal matrix M$M$ are determined.     

A variant smoothing Newton method for P0-NCP based on a new smoothing function

In this paper, we present a new one-step smoothing Newton method proposed for solving the non-linear complementarity problem with _P0$P_0$-function based on a new smoothing NCP$NCP$-function. We adopt a variant merit function. Our algorithm needs only to solve one linear system of equations and perform one line search per iteration. It shows that any accumulation point of the iteration sequence generated by our algorithm is a solution of _P0-NCP$P_0\text{-}NCP$. Furthermore, under the assumption that the solution set is non-empty and bounded, we can guarantee at least one accumulation point of the generated sequence. Numerical experiments show the feasibility and efficiency of the algorithm.     

Gradient estimates in Orlicz spaces for quasilinear elliptic equation

In this paper we generalize classical L^q$L^q$, q≥p$q\ge p$, estimates of the gradient to the Orlicz space for weak solutions of quasilinear elliptic equations of p-Laplacian type.     

Periodic solutions for a Rayleigh system of p-Laplacian type

By using the generalized Borsuk theorem in coincidence degree theory, some criteria for guaranteeing the existence of ω$\omega$-periodic solutions for a Rayleigh system of p$p$-Laplacian type are derived.     

Minimax inequalities and fixed points of expansive set-valued mappings with noncompact and nonconvex domains and ranges in topological spaces

Some minimax inequalities involving two bifunctions with noncompact and nonconvex domains are first proved in finite continuous topological spaces (in short, FC$FC$-spaces) without convexity structure. As applications some new Fan–Browder type fixed point theorems for expansive set-valued maps with noncompact and nonconvex domains and ranges are obtained in general topological spaces. These results generalize some known results in the recent literature.     

Second-order multiobjective symmetric duality with cone constraints

In this paper, we formulate Wolfe and Mond–Weir type second-order multiobjective symmetric dual problems over arbitrary cones. Weak, strong and converse duality theorems are established under η$\eta$-bonvexity/η$\eta$-pseudobonvexity assumptions. This work also removes several omissions in definitions, models and proofs for Wolfe type problems studied in Mishra [9]. Moreover, self-duality theorems for these pairs are obtained assuming the function involved to be skew symmetric.     

Stable categories of higher preprojective algebras

We introduce (n+1)$(n+1)$-preprojective algebras of algebras of global dimension n$n$. We show that if an algebra is n$n$-representation-finite then its (n+1)$(n+1)$-preprojective algebra is self-injective. In this situation, we show that the stable module category of the (n+1)$(n+1)$-preprojective algebra is (n+1)$(n+1)$-Calabi–Yau, and, more precisely, it is the (n+1)$(n+1)$-Amiot cluster category of the stable n$n$-Auslander algebra of the original algebra. In particular this stable category contains an (n+1)$(n+1)$-cluster tilting object. We show that even if the (n+1)$(n+1)$-preprojective algebra is not self-injective, under certain assumptions (which are always satisfied for n∈{1,2}$n\in \{1,2\}$) the results above still hold for the stable category of Cohen–Macaulay modules.     

The preconditioned Gauss–Seidel method faster than the SOR method

In recent years, a number of preconditioners have been applied to linear systems [A.D. Gunawardena, S.K. Jain, L. Snyder, Modified iterative methods for consistent linear systems, Linear Algebra Appl. 154–156 (1991) 123–143; T. Kohno, H. Kotakemori, H. Niki, M. Usui, Improving modified Gauss–Seidel method for Z-matrices, Linear Algebra Appl. 267 (1997) 113–123; H. Kotakemori, K. Harada, M. Morimoto, H. Niki, A comparison theorem for the iterative method with the preconditioner (I+_Smax)$(I+S_{\mathit{max}})$, J. Comput. Appl. Math. 145 (2002) 373–378; H. Kotakemori, H. Niki, N. Okamoto, Accelerated iteration method for Z$Z$-matrices, J. Comput. Appl. Math. 75 (1996) 87–97; M. Usui, H. Niki, T.Kohno, Adaptive Gauss-Seidel method for linear systems, Internat. J. Comput. Math. 51(1994)119–125 [10]]. Since these preconditioners are constructed from the elements of the upper triangular part of the coefficient matrix, the preconditioning effect is not observed on the n$n$th row of matrix A. In the present paper, in order to deal with this drawback, we propose a new preconditioner. In addition, the convergence and comparison theorems of the proposed method are established. Simple numerical examples are also given, and we show that the convergence rate of the proposed method is better than that of the optimum SOR.     

Vector analysis for Dirichlet forms and quasilinear PDE and SPDE on metric measure spaces

Starting with a regular symmetric Dirichlet form on a locally compact separable metric space X$X$, our paper studies elements of vector analysis, _Lp$L_p$-spaces of vector fields and related Sobolev spaces. These tools are then employed to obtain existence and uniqueness results for some quasilinear elliptic PDE and SPDE in variational form on X$X$ by standard methods. For many of our results locality is not assumed, but most interesting applications involve local regular Dirichlet forms on fractal spaces such as nested fractals and Sierpinski carpets.     

Cycle-maximal triangle-free graphs

We conjecture that the balanced complete bipartite graph _{K⌊n/2⌋,⌈n/2⌉}$K_{\lfloor n/2\rfloor ,\lceil n/2\rceil }$ contains more cycles than any other n$n$-vertex triangle-free graph, and we make some progress toward proving this. We give equivalent conditions for cycle-maximal triangle-free graphs; show bounds on the numbers of cycles in graphs depending on numbers of vertices and edges, girth, and homomorphisms to small fixed graphs; and use the bounds to show that among regular graphs, the conjecture holds. We also consider graphs that are close to being regular, with the minimum and maximum degrees differing by at most a positive integer k$k$. For k=1$k=1$, we show that any such counterexamples have n≤91$n\le 91$ and are not homomorphic to _C5$C_5$; and for any fixed k$k$ there exists a finite upper bound on the number of vertices in a counterexample. Finally, we describe an algorithm for efficiently computing the matrix permanent (a #P$\#P$-complete problem in general) in a special case used by our bounds.     

A perishable inventory system with service facility and finite source

In this article, we consider a continuous review (s,S)$(s\text{,}S)$ perishable inventory system with a service facility, wherein the demand of a customer is satisfied only after performing some service on the item which is assumed to be of random duration. We also assume that the demands are generated by a finite homogeneous population. The service time, the lead time are assumed to have Phase type distribution. The life time of the item is assumed to have exponential distributions. The joint distribution of the number of customers in the system and the inventory level is obtained in the steady state case. The Laplace–Stieltjes transform of the waiting time of the tagged customer is derived. Various system performance measures are derived and the total expected cost rate is computed under a suitable cost structure. The results are illustrated numerically.     

Solutions to degenerate complex Hessian equations

Let (X,ω)$(X,\omega )$ be an n-dimensional compact Kähler manifold and fix an integer m   such that 1?m?n$1?m?n$. We study degenerate complex Hessian equations of the form (ω+dd^cφ)^m∧ω^n−m=F(x,φ)ωⁿ${(\omega +d{d}^c\phi )}^m\wedge {\omega }^{n-m}=F(x,\phi ){\omega }^n$. Under some natural conditions on F, this equation has a unique continuous solution. When X is homogeneous and ω is invariant under the Lie group action, we further show that the solution is Hölder continuous.     

Some decomposition results for a class of vacation queues

We analyze the MAP/PH/1 vacation system at arbitrary times using the matrix-analytic method, and obtain decomposition results for the R$R$ and G$G$ matrices. The decomposition results reduce the amount of computational effort needed to obtain these matrices. The results for the G$G$ matrix are extended to the BMAP/PH/1 system. We also show that in the case of the Geo/PH/1 and M/PH/1 systems with PH vacations both the G$G$ and R$R$ matrices can be obtained explicitly.