The k-th power D of a directed graph D is defined to be the directed graph on the vertices of D with an arc from a to b in D iff one can get from a to b in D with exactly k steps. This notion is equivalent to the k-fold composition of binary relations or k-th powers of Boolean matrices. A k-th root of a directed graph D is another directed graph R with R = D. We show that for each k ≥ 2, comput...

—Researchers have used various qualitative and quantitative methods to deal with subjectivity in studying people’s recreation experiences. Q methodology has been the most eff ective approach for analyzing both qualitative and quantitative aspects of experience, including attitudes or perceptions. Th e method is composed of two main components—Q sorting and Q factor analysis—and allows for the s...

The Gaussian matrix model is known to deform the $q,t$-matrix model. We consider further deformation elliptic $q,t$ by properly deforming density as well Vandermonde factor. Properties of an associated basis symmetric functions that provide property $\sim {\rm char}$ in deformed case are discussed.

Difference sets wi th pa rame te r s (v, k, 2) m a y exist even if there are no abelian (v, k, ,~) difference sets; we give the first k n o w n example of this s i tuat ion. This example gives rise to an infinite family of non -abe l i an difference sets w i th pa rameters (4t 2, 2t a t, t 2 t), where t = 2 q. 3 r5 . 1 0 ' , q, r, s >/0, and r > 0 ~ q > 0. N o abel ian difference sets w i th th...

In this report, we propose an extension of the well-known Simultaneous Orthogonal Matching Pursuit (SOMP) algorithm to solve a multi-task multivariate classification problem using sparse representations. This corresponds to the case where an event is described by multiple representations, and separate training dictionaries are designed for each such representation. I. NOTATION Let yi ∈ R, i = 1...

statement of problem: various surgical procedures have been used to achieve root coverage and subepithelial connective tissue graft (sctg) is identified as one of the most successful techniques. recently, acellular dermal matrix allograft (adma) has been developed as a substitute for sctg to avoid removing the palatal connective tissue. purpose: the present study compared the clinical efficienc...

We study the moduli space $\textsf{T}$ of Calabi-Yau $n$-folds arising from Dwork family and enhanced with bases $n$-th de Rham cohomology constant cup product compatible Hodge filtration. also describe a unique vector field $\textsf{R}$ in which contracted Gauss-Manin connection gives an upper triangular matrix some non-constant entries are natural generalizations Yukawa couplings. For $n=1,2$...

Some Realization of gl q (n)-covariant Oscillator Algebra and gl q (n)-covariant q-Virasoro Algebra with q a root of unity. Abstract In this paper some realization of gl q (n)-covariant oscillators is obtained when q is a root of unity. And the gl q (n)-covariant q-Virasoro algebra is presented by using the gl q (n)-covariant oscillators.