On Real Solutions of the Equation Φ\u3csup\u3e\u3cem\u3et\u3c/em\u3e\u3c/sup\u3e (\u3cem\u3eA\u3c/em\u3e) = 1/\u3cem\u3en\u3c/em\u3e J\u3csub\u3e\u3cem\u3en\u3c/em\u3e\u3c/sub\u3e

For a class of n × n-matrices, we get related real solutions to the matrix equation Φt (A) = 1/n Jn by generalizing the approach of and applying the results of Zhang, Yang, and Cao [SIAM J. Matrix Anal. Appl., 21 (1999), pp. 642–645]. These solutions contain not only those obtained by Zhang, Yang, and Cao but also some which are neither diagonally nor permutation equivalent to those obtained by Zhang, Yang, and Cao. Therefore, the open problem proposed by Zhang, Yang, and Cao in the cited paper is solved

A New Lower Bound for the Distinct Distance Constant

The reciprocal sum of Zhang sequence is not equal to the Distinct Distance Constant. This note introduces a $B_2$-sequence with larger reciprocal sum, and provides a more precise estimation of the reciprocal sums of Mian-Chowla sequence and Zhang sequence.Comment: 4 pages, 3 ancillary table

Alternative Derivation of the Hu-Paz-Zhang Master Equation for Quantum Brownian Motion

Hu, Paz and Zhang [ B.L. Hu, J.P. Paz and Y. Zhang, Phys. Rev. D {\bf 45} (1992) 2843] have derived an exact master equation for quantum Brownian motion in a general environment via path integral techniques. Their master equation provides a very useful tool to study the decoherence of a quantum system due to the interaction with its environment. In this paper, we give an alternative and elementary derivation of the Hu-Paz-Zhang master equation, which involves tracing the evolution equation for the Wigner function. We also discuss the master equation in some special cases.Comment: 17 pages, Revte

On the self-convolution of generalized Fibonacci numbers

We focus on a family of equalities pioneered by Zhang and generalized by Zao and Wang and hence by Mansour which involves self convolution of generalized Fibonacci numbers. We show that all these formulas are nicely stated in only one equation involving a bivariate ordinary generating function and we give also a formula for the coefficients appearing in that context. As a consequence, we give the general forms for the equalities of Zhang, Zao-Wang and Mansour

Alcove path model for B(∞)B(\infty)

We construct a model for $B(\infty)$ using the alcove path model of Lenart and Postnikov. We show that the continuous limit of our model recovers a dual version of the Littelmann path model for $B(\infty)$ given by Li and Zhang. Furthermore, we consider the dual version of the alcove path model and obtain analogous results for the dual model, where the continuous limit gives the Li and Zhang model.Comment: 19 pages, 7 figures; improvements from comments, added more figure