We present a sufficient condition that a pseudointegrable system has weak mixing property. The result is derived from Veech’s weak mixing theorem for interval exhange [Veech, W.A. Amer.J.Math. 106, 1331 (1984)]. We also present an example whose weak mixing property can be proved by the result.

The problem considered in this paper is whether the capacity of a discrete time Gaussian channel is increased by feedback or not. It is well known that the capacity of a white Gaussian channel under the average power constraint is not changed by feedback. In the previous paper [7] we gave some sufficient conditions under which the capacity of a non-white Gaussian channel is increased by feedbac...

Given an integer k ≥ 1 and any graph G, the path graph Pk(G) has for vertices the paths of length k in G, and two vertices are joined by an edge if and only if the intersection of the corresponding paths forms a path of length k − 1 in G, and their union forms either a cycle or a path of length k + 1. Path graphs were investigated by Broersma and Hoede [Path graphs, J. Graph Theory 13 (1989), 4...

A graph G = (V,E) is said to be 6-mixed-connected if G−U−D is connected for all sets U ⊆ V and D ⊆ E which satisfy 2|U | + |D| ≤ 5. In this note we prove that 6-mixed-connected graphs are (redundantly globally) rigid in the plane. This improves on a previous result of Lovász and Yemini.

A necessary and sufficient condition is given for the exact reduction of systems modeled by linear fractional transformations (LFT’s) on structured operator sets. This condition is based on the existence of a rank-deficient solution to either of a pair of linear matrix inequalities which generalize Lyapunov equations; the notion of Gramians is thus also generalized to uncertain systems, as well...

Three-level logic is shown to have a potential for reduction of the area over two-level implementations, as well as for a gain in speed over multi-level implementations. Algorithms for finding AND-OR-XOR and AND-OR-AND expressions were developed, however an open problem remained which of the algorithms should be used to find an optimal solution for a given function. In this paper we formulate a...

Under what conditions can potential contestants avoid conflicts through a peace settlement? This question is relevant to real world situations such as international conflicts and pre-litigation negotiations. In the spirit of Myerson and Satterthwaite [4] on bilateral trade, where information asymmetry is the impediment to mutually beneficial negotiation outcomes, a natural approach to address t...

A shift space is said to be sofic if it is the factor of a shift of finite type. In one dimension, there are complete characterizations of soficness. There are no characterizations in higher dimensions, and there are few examples of non-sofic Z shifts for d > 1. In this work we give a condition that implies non-soficness in higher-dimensional shift spaces, and we apply it to a variety of exampl...

We give a new equivalent condition for the Riemann hypothesis consisting in an order condition for certain finite rational combinations of the values of ζ(s) at even positive integers.