On some cycles in linearized Wenger graphs

Let ${\mathbb{F}}_q$ be the finite field of $q$ elements for prime power $q$ and let $p$ be the character of ${\mathbb{F}}_q$. For any positive integer $m$, the linearized Wenger graph $L_m\left(q\right)$ is defined as follows: it is a bipartite graph with the vertex partitions being two copies of the $(m+1)$-dimensional vector space ${\mathbb{F}}_q^{m+1}$, and two vertices $p=\left(p\left(1\right),\dots ,p(m+1)\right)$ and $l=\left[l\left(1\right),\dots ,l(m+1)\right]$ being adjacent if $p\left(i\right)+l\left(i\right)=p\left(1\right){\left(l\left(1\right)\right)}^{p^{i?2}}$, for all $i=2,3,\dots ,m+1$. In this paper, we show that for any positive integers $m$ and $k$ with $3\le k\le p^2$, $L_m\left(q\right)$ contains even cycles of length $2k$ which is an open problem put forward by Cao et al. (2015).     

Reconfigurable chaotic logic gates based on novel chaotic circuit

The logical operations are one of the key issues in today’s computer architecture. Nowadays, there is a great interest in developing alternative ways to get the logic operations by chaos computing. In this paper, a novel implementation method of reconfigurable logic gates based on one-parameter families of chaotic maps is introduced. The special behavior of these chaotic maps can be utilized to provide same threshold voltage for all logic gates. However, there is a wide interval for choosing a control parameter for all reconfigurable logic gates. Furthermore, an experimental implementation of this nonlinear system is presented to demonstrate the robustness of computing capability of chaotic circuits.     

Diophantine Inequality by Unlike Powers of Primes*

Suppose that λ₁, · · ·, λ₅ are nonzero real numbers, not all of the same sign,satisfying that λ₁/λ₂is irrational. Then for any given real number η and ε > 0, the inequality |λ₁p₁+ λ₂p₂~2+ λ₃p₃~3+ λ₄p₄~4+ λ₅p₅~5+ η| <(■)^-19/756+ε has infinitely many solutions in prime variables p₁, · · ·, p₅. This result co...     

Edge - Odd Graceful Graphs

Graph labeling of a graph was introduced by Rosa [A. Rosa, “Theory of graphs” (International Symposium, Rome, July 1966), Gordon and Breach, N. Y. and Dunod Paris (1967) 349-355] and the concept of an edge graceful labeling was introduced by Lo [S. Lo, “On edge graceful labeling of graphs”, Congress Numer., 50(1985) 231-241]. We introduced a new type of labeling called an edge - odd graceful labeling (EOGL)[A. Solairaju and K. Chithra, “Edge-Odd graceful labeling of some graphs”, proceedings of the ICMCS, Vol.1, 101-107(2008)]. In this paper, we proved that the Edge - Odd Graceful Labeling of some graphs.     

Lie bialgebra structures on generalized loop Schr?dinger-Virasoro algebras

We give a classification of Lie bialgebra structures on generalized loop Schr?dinger-Virasoro algebras st). Then we find out that not all Lie bialgebra structures on generalized loop Schr?dinger-Virasoro algebras st) are triangular coboundary.     

A new inexact SQP algorithm for nonlinear systems of mixed equalities and inequalities

Traditional inexact SQP algorithm can only solve equality constrained optimization (Byrd et al. Math. Program. 122, 273–299 2010). In this paper, we propose a new inexact SQP algorithm with affine scaling technique for nonlinear systems of mixed equalities and inequalities, which arise in complementarity and variational inequalities. The nonlinear systems are transformed into a special nonlinear optimization with equality and bound constraints, and then we give a new inexact SQP algorithm for solving it. The new algorithm equipped with affine scaling technique does not require a quadratic programming subproblem with inequality constraints. The search direction is computed by solving one linear system approximately using iterative linear algebra techniques. Under mild assumptions, we discuss the global convergence. The preliminary numerical results show the effectiveness of the proposed algorithm.