Abstract: The idea of summing pairs of so-called semi-wavelets has been found to be very useful for constructing piecewise linear wavelets over refinements of arbitrary triangulations. In this paper we demonstrate the versatility of the semi-wavelet approach by using it to construct bases for the piecewise linear wavelet spaces induced by uniform refinements of four-directional box-spline grids.

We initiate a systematic study of linear sketching over F2. For a given Boolean function f : {0, 1} → {0, 1} a randomized F2-sketch is a distributionM over d×n matrices with elements over F2 such thatMx suffices for computing f(x) with high probability. We study a connection between F2-sketching and a two-player one-way communication game for the corresponding XOR-function. Our results show tha...

let $g={rm sl}_2(p^f)$ be a special linear group and $p$ be a sylow‎ ‎$2$-subgroup of $g$‎, ‎where $p$ is a prime and $f$ is a positive‎ ‎integer such that $p^f>3$‎. ‎by $n_g(p)$ we denote the normalizer of‎ ‎$p$ in $g$‎. ‎in this paper‎, ‎we show that $n_g(p)$ is nilpotent (or‎ ‎$2$-nilpotent‎, ‎or supersolvable) if and only if $p^{2f}equiv‎ ‎1,({rm mod},16)$‎.

SPICE-compatible equivalent circuits were developed to facilitate the analysis and envelope simulation of electric circuits driven by modulated signals. The circuits are based on a novel complex phasor-domain transformation. The proposed method facilitates simulation of any general linear circuit driven by a modulated signal such as amplitude modulation, frequency modulation, or phase modulatio...

We provide in this paper sufficient conditions for the complete convergence for the partial sums and the random selected partial sums of B-valued Lp-mixingales.

We present some results on instanton corrections to the hypermultiplet moduli space in Calabi-Yau compactifications of Type II string theories. Previously, using twistor methods, only a class of D-instantons (D2-instantons wrapping A-cycles) was incorporated exactly and the rest was treated only linearly. We go beyond the linear approximation and give a set of holomorphic functions which, throu...