ON ORTHOGONAL (0,f)-FACTORIZATIONS

Let G be a graph and f an integer-valued function defined on V(G). It is proved that every (0,mf - m+1)-graph G has a (0,f)-factorization orthogonal to any given subgraph with m edges.

A Generalization of Orthogonal Factorizations in Graphs

Let G be a graph with vertex set V（G） and edge set E（G）, and let g and f be two integer- valued functions defined on V（G） such that g（x）≤f（x） for all x ∈ V（G）. Then a （g, f）-factor of G is a spanning subgraph H of G such that g（x）≤dH（x）≤f（x） for all x ∈ V（G）. A （g, f）-factorization of G is a partition of E（G） into edge-disjoint （g,f）-factors. Let F={F1, F2...., Fm} be a factorization of G, and H be a subgraph of G with mr edges. If Fi. 1≤i≤m, has exactly r edges in common with H. then F is said to be r-orthogonal to H. In this paper it is proved that every （mg+kr, mf-kr）-graph. where m, k and r are positive integers with k【m and g≥r, contains a subgraph R such that R has a （g, f）-factorization which is r-orthogonal to a given subgraph H with kr edges.

Discussions on Orthogonal Factorizations in Digraphs

Let m,t,r and k_(i)(1≤i≤m)be positive integers with k_(i)≥(t+3)r/2,and G be a digraph with vertex set V(G)and arc set E(G).Let H_(1),H_(2),…,H_(t) be t vertex-disjoint subdigraphs of G with mr arcs.In this article,it is verified that every[0,k_(1)+k_(2)+…+k_(m)-(m-1)r]-digraph G has a[0,k_(i)]_(1)^(m)-factorization r-orthogonal to every H_(i) for 1≤i≤t.

[0, ki ]1m -FACTORIZATIONS ORTHOGONAL TO A SUBGRAPH

Let G be a graph, k(1), ... , k(m) be positive integers. If the edges of graph G can be decomposed into some edge disjoint [0, k(1)]-factor F-1, ..., [0, k(m)]-factor F-m, then we can say (F) over bar = {F-1, ..., F-m}, is a [0, k(i)](1)(m) -factorization of G. If H is a subgraph with m edges in graph G and / E (H) boolean AND E(F-i) / = 1 for all 1 less than or equal to i less than or equal to m, then we can call that (F) over bar is orthogonal to H. It is proved that if G is a [0, k(1) + ... + k(m) - m + 1]-graph, H is a subgraph with m edges in G, then graph G has a [0, k(i)](1)(m)-factorization orthogonal to H.

ORTHOGONAL (g,f)-FACTORIZAFIONS OF BIPARTITE GRAPHS

Let G be a bipartite graph with vertex set V(G) and edge set E(G), and let g and f be two positive integer-valued functions defined on V(G) such that g(x) ≤ f(x) for every vertex x of V(G). Then a (g, f)-factor of G is a spanning subgraph H of G such that g(x) ≤ dH(x) 5 f(x) for each x ∈ V(H). A (g, f)-factorization of G is a partition of E(G) into edge-disjoint (g, f)-factors. Let F = {F1, F2,…… ， Fm } and H be a factorization and a subgraph of G, respectively. If F, 1 ≤ i ≤ m， has exactly one edge in common with H, then it is said that ■ is orthogonal to H. It is proved that every bipartite (mg + m - 1, mf - m + 1 )-graph G has a (g, f)-factorization orthogonal to k vertex disjoint m-subgraphs of G if 2-k ≤ g(x) for all x ∈ V(G). Furthermore, it is showed that the results in this paper are best possible.

Randomized Algorithms for Orthogonal Nonnegative Matrix Factorization

Orthogonal nonnegative matrix factorization(ONMF)is widely used in blind image separation problem,document classification,and human face recognition.The model of ONMF can be efficiently solved by the alternating direction method of multipliers and hierarchical alternating least squares method.When the given matrix is huge,the cost of computation and communication is too high.Therefore,ONMF becomes challenging in the large-scale setting.The random projection is an efficient method of dimensionality reduction.In this paper,we apply the random projection to ONMF and propose two randomized algorithms.Numerical experiments show that our proposed algorithms perform well on both simulated and real data.

New code match strategy for wideband code division multiple access code tree management

Orthogonal variable spreading factor channelization codes are widely used to provide variable data rates for supporting different bandwidth requirements in wideband code division multiple access (WCDMA) systems. A new code match scheme for WCDMA code tree management was proposed. The code match scheme is similar to the existing crowed-first scheme. When choosing a code for a user, the code match scheme only compares the one up layer of the allocated codes, unlike the crowed-first scheme which perhaps compares all up layers. So the operation of code match scheme is simple, and the average time delay is decreased by 5.1%. The simulation results also show that the code match strategy can decrease the average code blocking probability by 8.4%.

AN EFFECTIVE INITIALIZATION FOR ORTHOGONAL NONNEGATIVE MATRIX FACTORIZATION

The orthogonal nonnegative matrix factorization （ONMF） has many applications in a variety of areas such as data mining, information processing and pattern recognition. In this paper, we propose a novel initialization method for the ONMF based on the Lanczos bidiagonalization and the nonnegative approximation of rank one matrix. Numerical experiments are given to show that our initialization strategy is effective and efficient.

Does the system of independent directors help improve the quality of accounting information： From the perspective of earnings conservatism

Based on the sample data of the listed firms on the A stock market, we analyze how the system of independent directors influence the earning conservatism from 4 dimensions designed to measure the monitoring power of these independent directors： Percentage within BDs, professional capacities, stimulation and work conditions. From the empirical results, we conclude that the more powerful of the independent directors, the better the accounting conservatism, and that their positive impact increases along with the improvement on corporate governance, meanwhile the work conditions plays the most important role, and then are the percentage within BDs and their professional capacities, the stimulation and personal reputation appear the least importance.

THE RESTRICTIVELY PRECONDITIONED CONJUGATE GRADIENT METHODS ON NORMAL RESIDUAL FOR BLOCK TWO-BY-TWO LINEAR SYSTEMS

The restrictively preconditioned conjugate gradient （RPCG） method is further developed to solve large sparse system of linear equations of a block two-by-two structure. The basic idea of this new approach is that we apply the RPCG method to the normal-residual equation of the block two-by-two linear system and construct each required approximate matrix by making use of the incomplete orthogonal factorization of the involved matrix blocks. Numerical experiments show that the new method, called the restrictively preconditioned conjugate gradient on normal residual （RPCGNR）, is more robust and effective than either the known RPCG method or the standard conjugate gradient on normal residual （CGNR） method when being used for solving the large sparse saddle point problems.