On the Kirchhoff index of some toroidal lattices

The resistance distance is a novel distance function on a graph proposed by Klein and Randi? [D.J. Klein and M. Randi?, Resistance distance, J. Math. Chem. 12 (1993), pp. 81–85]. The Kirchhoff index of a graph G is defined as the sum of resistance distances between all pairs of vertices of G. In this article, based on the result by Gutman and Mohar [I. Gutman and B. Mohar, The quasi-Wiener and the Kirchhoff indices coincide, J. Chem. Inf. Comput. Sci. 36 (1996), pp. 982–985], we compute the Kirchhoff index of the square, 8.8.4, hexagonal and triangular lattices, respectively.     

A topological approach to divisibility of arithmetical functions and GCD matrices

Considering lower closed sets as closed sets on a preposet (P, ≤), we obtain an Alexandroff topology on P. Then order preserving functions are continuous functions. In this article we investigate order preserving properties (and thus continuity properties) of integer-valued arithmetical functions under the usual divisibility relation of integers and power GCD matrices under the divisibility relation of integer matrices.     

Some results on resistance distances and resistance matrices

In this paper, we obtain formulas for resistance distances and Kirchhoff index of subdivision graphs. An application of resistance distances to the bipartiteness of graphs is given. We also give an interlacing inequality for eigenvalues of the resistance matrix and the Laplacian matrix.     

A Combined Logarithmic Bound on the Chromatic Index of Multigraphs

For a multigraph G, the integer round‐up of the fractional chromatic index provides a good general lower bound for the chromatic index . For an upper bound, Kahn 1996 showed that for any real there exists a positive integer N so that whenever . We show that for any multigraph G with order n and at least one edge, ). This gives the following natural generalization of Kahn's result: for any positive reals , there exists a positive integer N so that + c whenever . We also compare the upper bound found here to other leading upper bounds.     

Portfolio selection with a minimax measure in safety constraint

In this paper, we attempt to design a portfolio optimization model for investors who desire to minimize the variation around the mean return and at the same time wish to achieve better return than the worst possible return realization at every time point in a single period portfolio investment. The portfolio is to be selected from the risky assets in the equity market. Since the minimax portfolio optimization model provides us with the portfolio that maximizes (minimizes) the worst return (worst loss) realization in the investment horizon period, in order to safeguard the interest of investors, the optimal value of the minimax optimization model is used to design a constraint in the mean-absolute semideviation model. This constraint can be viewed as a safety strategy adopted by an investor. Thus, our proposed bi-objective linear programming model involves mean return as a reward and mean-absolute semideviation as a risk in the objective function and minimax as a safety constraint, which enables a trade off between return and risk with a fixed safety value. The efficient frontier of the model is generated using the augmented -constraint method on the GAMS software. We simultaneously solve the ratio optimization problem which maximizes the ratio of mean return over mean-absolute semideviation with same minimax value in the safety constraint. Subsequently, we choose two portfolios on the above generated efficient frontier such that the risk from one of them is less and the mean return from other portfolio is more than the respective quantities of the optimal portfolio from the ratio optimization model. Extensive computational results and in-sample and out-of-sample analysis are provided to compare the financial performance of the optimal portfolios selected by our proposed model with that of the optimal portfolios from the existing minimax and mean-absolute semideviation portfolio optimization models on real data from S&P CNX Nifty index.     

具有中间亏指数的线性哈密顿算子的点谱

本文讨论具有任意亏指数d的自伴线性哈密顿算子点谱与对应的线性哈密顿系统的平方可积解之间的关系.若对于某个实开区间中的任意点λ,系统总有d个线性无关解,则它的任何自伴算子的点谱在这个开区间上是不稠密的.     

A Family of Finite Simple Groups Which Are 2-Recognizable by Their Elements Order

Abstract

Let G be a finite group and ω(G) the set of all orders of elements in G. Denote by h(ω(G)) the number of isomorphism classes of finite groups H satisfying ω(H) = ω(G), and put h(G) = h(ω(G)). A group G is called k-recognizable if h(G) = k < ∞ , otherwise G is called non-recognizable. In the present article we will show that the simple groups PSL(3, q), where q ≡ ±2(mod 5) and (6, (q ? 1)/2) = 2, are 2-recognizable. Therefore if q is a prime power and q ≡ 17, 33, 53 or 57 (mod 60), then the groups PSL(3, q) are 2-recognizable. Hence proving the existing of an infinite families of 2-recognizable simple groups.     

On Boundary Conditions for Wedge Operators on Radial Sets

We present a theorem about calculation of fixed point index for k-ψ-contractive operators with 0 ≤ k < 1 defined on a radial set of a wedge of an infinite-dimensional Banach space. Then, results on the existence of eigenvectors and nonzero fixed points are obtained.     

Free Groups and Subgroups of Finite Index in the Unit Group of an Integral Group Ring

In this article we construct free groups and subgroups of finite index in the unit group of the integral group ring of a finite non-Abelian group G for which every nonlinear irreducible complex representation is of degree 2 and with commutator subgroup G′ a central elementary Abelian 2-group.