Let n and t be positive integers with t < n, and let q be a prime power. A partial (t− 1)-spread of PG(n− 1, q) is a set of (t− 1)-dimensional subspaces of PG(n− 1, q) that are pairwise disjoint. Let r = n mod t. We prove that if t > (q − 1)/(q − 1), then the maximum size, i.e., cardinality, of a partial (t− 1)-spread of PG(n−1, q) is (q− q)/(q−1)+1. This essentially settles a main open problem...

begin{abstract} the relations between the spectrum of the matrix $q+r$ and the spectra of the matrices $(gamma + delta)q+(alpha + beta)r-qr-rq$, $qr-rq$, $alpha beta r-qrq$, $alpha rqr-(qr)^{2}$, and $beta r-qr$ have been given on condition that the matrix $q+r$ is diagonalizable, where $q$, $r$ are ${alpha, beta}$-quadratic matrix and ${gamma, delta}$-quadratic matrix, respectively, of order $...

T h i s paper d i s c u s s e s e x p l a n a t o r y schema a c q u i s i t i o n , a l e a r n i n g t e c h n i q u e w i t h s e v e r a l i n t e r e s t i n g p r o p e r t i e s . I t does n o t r e q u i r e a t e a c h e r o r concep t m a t c h i n g p r e d i c a t e t o b e p r o v i d e d . I t does n o t r e l y o n s e a r c h i n g a concep t space t o p roduce g e n e r a l i z...

This paper discusses some spectral properties of class wF(p,r,q) operators for p > 0, r > 0, p + r ≤ 1, and q ≥ 1. It is shown that if T is a class wF(p,r,q) operator, then the Riesz idempotent Eλ of T with respect to each nonzero isolated point spectrum λ is selfadjoint and Eλ = ker(T − λ)= ker(T − λ)∗ . Afterwards, we prove that every class wF(p,r,q) operator has SVEP and property (β), andWey...

By comparing curve length in a manifold and a standard sphere, we prove a local uniform bound for the exponent in the Large Deviation formula that describes the concentration of Brownian bridges to geodesics. Let M be an m-dimensional complete riemannian manifold with distance function d, Ω(M) := C(R0 ,M) the associated space of continuous paths and p ∈M . Let expp denote the exponential map as...

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We study homogeneous nucleation in the two-dimensional $q-$state Potts model for $q=3,5,10,20$ and ferromagnetic couplings $J_{ij} \propto \Theta (R - |i-j|)$, by means of Monte Carlo simulations employing heat bath dynamics. Metastability is induced low temperature phase through an instantaneous quench magnetic field coupled to one $q$ spin states. The depth adjusted, depending on value $T$, i...