On the limiting behavior of randomly weighted partial sums

We study the almost sure limiting behavior and convergence in probability of weighted partial sums of the form where {W_nj, 1jn, n1} and {X_nj, 1jn, n1} are triangular arrays of random variables. The results obtain irrespective of the joint distributions of the random variables within each array. Applications concerning the Efron bootstrap and queueing theory are discussed.     

Laminar flow and heat transfer over a two-dimensional triangular step

The velocity correction algorithm is used in the finite element method to solve forced convection problems between parallel plates with a triangular step, for Reynolds numbers up to 1000. Equal-order interpolation functions for velocity, pressure and temperature are used. The solutions show a smooth variation of pressure. The streamfunction, isotherms, isobars and velocity profiles are presented for a typical Reynolds number of 500. The skin friction and heat transfer results are presented for Reynolds numbers up to 1000.     

A Fixed Point Theorem in Intuitionistic Fuzzy Metric Spaces by Using New Commutativity Condition

We prove a common fixed point theorem for discontinuous,noncompatible mappings on noncomplete intuitionistic fuzzy metric spaces by using a new commutativity condition.We validate our main result by an example.     

完备分配格L上的S-幂零矩阵

利用完备分配格L上的s-模定义格L上的矩阵运算,给出这些运算的一些基本性质,并且定义格L上的s-幂零矩阵,给出一些全新的结果.     

An optimal locating-dominating set in the infinite triangular grid

Assume that G=(V,E) is an undirected graph, and C⊆V. For every v∈V, we denote by I(v) the set of all elements of C that are within distance one from v. If all the sets I(v) for v∈V?C are non-empty, and pairwise different, then C is called a locating-dominating set. The smallest possible density of a locating-dominating set in the infinite triangular grid is shown to be .     

On the packing chromatic number of some lattices

For a positive integer k, a k-packing in a graph G is a subset A of vertices such that the distance between any two distinct vertices from A is more than k. The packing chromatic number of G is the smallest integer m such that the vertex set of G can be partitioned as V₁,V₂,…,V_m where V_i is an i-packing for each i. It is proved that the planar triangular lattice T and the three-dimensional integer lattice Z³ do not have finite packing chromatic numbers.     

A note on “A new method for solving fully fuzzy linear programming problems”

This note shows that solving fully fuzzy linear programming (FFLP) model presented by Kumar et al. [A. Kumar, J. Kaur, P. Singh, A new method for solving fully fuzzy linear programming problems, Appl. Math. Model. 35 (2011) 817–823] needs some corrections to make the model well in general. A new version is provided in this note. A simple example is also presented to demonstrate the new form.     

Rank-one nonincreasing mappings on triangular matrices and some related preserver problems

Let T_n (F) be the algebra of all n×n upper triangular matrices over an arbitrary field F. We first characterize those rank-one nonincreasing mappings ψ: T_n (F)→T_m (F)n?m such that ψ(I_n ) is of rank n. We next deduce from this result certain types of singular rank-one r-potent preservers and nonzero r-potent preservers on T_n (F). Characterizations of certain classes of homomorphisms and semi-homomorphisms on T_n (F) are also given.     

Progressive meshes transmission over a wired-to-wireless network

The evolution of mobile network and the popularization of mobile devices; the demand for multimedia services and 3D graphics applications on limited resource devices is more contemporary. Most of the works on multimedia transmission are focused on bit errors and packet losses due to the fading channel environment of a wireless network. Error resilient multimedia is significant research topic which can be adapted to the different conditions in a wireless environment. The current solutions in transmission of multimedia across different networks include some type of transcoder where the source is partially or fully decoded, and re-encoded to suit the network conditions. This paper introduces a flexible progressive coding framework for 3D meshes, which can be adapted to the different conditions imposed by wired and wireless channels at the bitstream level. By avoiding the computationally complex steps of transcoding between networks, could deteriorate decoded model quality. The framework also allows refined degradation of model quality when the network conditions are poor due to congestion or deep fades. Xiaonan Luo, male, born in Feb. 1963 in Jiangxi Province, China, Ph. D., completed his post-doctorate training in Mar. 1995. He is a professor and Ph. D. advisor of the School of Information Science and Technology, and the Chairman of Computer Application Institute of Sun Yat-sen University. His current interests are in mobile graphics transmission and 3D geometric simulation methods. He enjoys the government special allowance granted by the State Council of China. He won the National Science & Technology Progress Prize awarded by the Ministry of Science and Technology of China and the National Natural Science Funds granted by the National Nature Science Foundation of China. Guifeng Zheng, male, born in Jan. 1977 in Guangdong Province, China, Ph. D., received his Ph.D. degree from Sun Yat-sen University in 2005. He is currently an research assistant in the Computer Application Institute of Sun Yat-sen University. His research interests span the areas of wireless networks and mobile graphics computing.