Let Z and R be the sets of all integers and real numbers, respectively. For a,b ∈ Z, define Z(a)= {a,a+1, . . .} and Z(a,b)= {a,a+1, . . . ,b} when a≤ b. Let A be an n×m matrix. Aτ denotes the transpose ofA.When n=m, σ(A) and det(A) denote the set of eigenvalues and the determinant of A, respectively. In this paper, we study the existence of multiple p-periodic solutions to the following discre...

A few years ago, Grimmett, Kesten and Zhang proved that for supercritical bond percolation on Z 3 , simple random walk on the innnite cluster is a.s. transient. We generalize this result to a class of wedges in Z 3 including, for any " 2 (0; 1), the wedge W " = f(x; y; z) 2 Z 3 : x 0; jzj x " g which can be thought of as representing a (2 + ")-dimensional lattice. Our proof builds on recent wor...

We investigate the separability of arbitrary n-dimensional multipartite identical bosonic systems. An explicit relation between the dimension and the separability is presented. In particular, for n = 3, it is shown that the property of PPT (positive partial transpose) and the separability are equivalent for tripartite systems.

Benjamini, Häggström, Peres and Steif introduced the model of dynamical random walk on Z [2]. This is a continuum of random walks indexed by a parameter t. They proved that for d = 3, 4 there almost surely exist t such that the random walk at time t visits the origin infinitely often, but for d ≥ 5 there almost surely do not exist such t. Hoffman showed that for d = 2 there almost surely exists...

To say that positive political theory (PPT) scholarship on the hierarchy of justice is theory rich and data poor is to make a rather uncontroversial claim. For over a decade now, scholars have offered intriguing theoretical accounts aimed at understanding why lower courts defy (comply with) higher courts. But only rarely do they subject the accounts to rigorous empirical interrogation. The chie...

We prove that there is a set F in the plane so that the distance between any two points of F is at least 1, and for any positive < 1, and every line segment in the plane of length at least −1−o(1) there is a point of F within distance of the segment. This is tight up to the o(1) term in the exponent, improving earlier estimates of Peres, of Solomon and Weiss, and of Adiceam. Mathematics subject...

Satoshi Ishizaka 2 and Martin B. Plenio 4 Fundamental and Environmental Research Laboratories, NEC Corporation, 34 Miyukigaoka, Tsukuba, 305-8501, Japan PRESTO, Japan Science and Technology Agency, 4-1-8 Honcho Kawaguchi, 332-0012, Japan QOLS, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW, UK Institute for Mathematical Sciences, Imperial College London, 53 Ex...

We show that the recent technique of computationally complete symbolic attackers proposed by Bana and Comon-Lundh [6] for computationally sound verification of security protocols is powerful enough to verify actual protocols. In their work, Bana and Comon-Lundh presented only the general framework, but they did not introduce sufficiently many axioms to actually prove protocols. We present a set...

This research aims to develop a multiple-choice Web-based quiz-game-like formative assessment system, named GAM-WATA. The unique design of ‘Ask-Hint Strategy’ turns the Web-based formative assessment into an online quiz game. ‘Ask-Hint Strategy’ is composed of ‘Prune Strategy’ and ‘Call-in Strategy’. ‘Prune Strategy’ removes one incorrect option and turns the original 4-option item into a 3-opt...

Benjamini, Häggström, Peres and Steif [2] introduced the concept of a dynamical random walk. This is a continuous family of random walks, {Sn(t)}n∈N,t∈R. Benjamini et. al. proved that if d = 3 or d = 4 then there is an exceptional set of t such that {Sn(t)}n∈N returns to the origin infinitely often. In this paper we consider a dynamical random walk on Z2. We show that with probability one there...