In this paper, we introduce the synthesis problem for Halpern and Shoham’s interval temporal logic [5] extended with an equivalence relation ∼ over time points (HS ∼ for short). In analogy to the case of monadic second-order logic of one successor [2], given an HS ∼ formula φ and a finite set ΣT of proposition letters and temporal requests, the problem consists of establishing whether or not, f...

Given a definite nonnegative matrix A ∈ Mn(C), we study the minimal index of A : I(A) = max{λ ≥ 0 : A ◦ B ≥ λB for all 0 ≤ B}, where A ◦ B denotes the Hadamard product (A ◦ B)ij = AijBij . For any unitary invariant norm N in Mn(C), we consider the Nindex of A: I(N,A) = min{N(A ◦ B) : B ≥ 0 and N(B) = 1} If A has nonnegative entries, then I(A) = I(‖ · ‖sp, A) if and only if there exists a vector...

We construct explicit Boolean square matrices whose rectifier complexity (OR-complexity) differs significantly from the complexity of the complement matrices. This note can be viewed as an addition to the material of [2, §5.6]. Recall that rectifier (m,n)-circuit is an oriented graph with n vertices labeled as inputs and m vertices labeled as outputs. Rectifier circuit (ORcircuit) implements a ...

The secular evolution of the orbital angular momentum (OAM), the systemic mass (M = M1+M2) and the orbital period of 114 chromospherically active binaries (CABs) were investigated after determining the kinematical ages of the sub-samples which were set according to OAM bins. OAMs, systemic masses and orbital periods were shown to be decreasing by the kinematical ages. The first order decreasing...

We perform a smoothed analysis of the GCC-condition number C (A) of the linear programming feasibility problem ∃x ∈ R Ax < 0. Suppose that Ā is any matrix with rows ai of euclidean norm 1 and, independently for all i, let ai be a random perturbation of ai following the uniform distribution in the spherical disk in S of angular radius arcsinσ and centered at ai. We prove that E(ln C (A)) = O(mn/...

Trials on Mobile Games are presenting a huge potential in cognitive, physical and mental rehabilitation. This paper is to discuss user viewpoints of trials with mobile games combining cognitive stimulation and physical exercise in rehabilitation: Game#1 controlled by tilting the mobile phone embedded in a balance board; Game#2 controlled by tilting the tablet pc; and Game#3 a modified game vers...

Recently Nolan constructed a spherically-symmetric spacetime admitting a spacelike curvature singularity with a regular C metric. We show here that this singularity is in fact weak. In a recent paper Nolan [1] constructed a simple spherically-symmetric spacetime which includes a spacelike curvature singularity with a continuous (C) metric. The goal was to use this example to demonstrate that a ...

This preliminary research was aimed at finding the roots in various Eurasian proto-languages directly related to pulses and giving the words denoting the same in modern European languages. Six Proto-Indo-European roots were indentified, namely arnk(')- ('a leguminous plant'), *bhabh- ('field bean'), *[Formula: see text] ('a kernel of leguminous plant', 'pea'), ghArs- ('a leguminous plant'), *ke...

1 Pān. ini’s grammar Pān. ini’s grammar (ca. 500 B.C.) seeks to provide a complete, maximally concise, and theoretically consistent analysis of Sanskrit grammatical structure. It is the foundation of all traditional and modern analyses of Sanskrit, as well as having great historical and theoretical interest in its own right. Western grammatical theory has been influenced by it at every stage of...

Recently, adaptive beamforming has been widely used in wireless communications, microphone array speech processing and so on. One of the adaptive beamforming methods is directionally constrained minimization of power. However, this method is known to degrade if some of underlying assumptions on the environment, sources, or sensor array become violated [5]. To resolve this disadvantage, some met...