The aim of this paper is to study semigroups possessing $E$-regular elements, where an element $a$ of a semigroup $S$ is {em $E$-regular} if $a$ has an inverse $a^circ$ such that $aa^circ,a^circ a$ lie in $ Esubseteq E(S)$. Where $S$ possesses `enough' (in a precisely defined way) $E$-regular elements, analogues of Green's lemmas and even of Green's theorem hold, where Green's relations ${mathc...

Hence, any party can convert a signature from Sign to one from Sign′ and vice versa. (a) According to the note above, Verify′(pk,M, σ′) = Verify(pk,M, σ) where σ = ([s]P − [e]Q, s). Specifically, Verify′(pk,M, σ) works as follows: 1. Compute R = [s]P − [e]Q 2. Compute e′ = H(M ||R) 3. Accept if R + [e′]Q = [s]P . Note that this condition is equivalent to e = e′ (b) Suppose we have an adversary ...

In this short note, we give a description of semisimple orbits in the restricted Cartan type Lie algebras W, S, H.

In this note, we consider special algebraic cycles on the Shimura variety S associated to a quadratic space V over totally real field F, |F:\Q|=d, of signature ((m,2)^{d_+},(m+2,0)^{d-d_+}), 1\le d_+<d. For each n, n\le m, there are Z(T) in S, codimension nd_+, indexed by positive semi-definite matrices with coefficients ring integers O_F. The generating series for classes these cohomology grou...

where dist denotes the Euclidean distance. Note that for Lipα(D) and A∞ the zero sequences Z are characterized by (1) and (2), with S replaced by Z. 3. The Blaschke sets S for the class D of analytic functions with finite Dirichlet integral are characterized by (2) (see [B]). Note that D-zero sequences cannot be described this way because there are f ∈ D whose zeros come arbitrarily close to ev...

in this article, according to the 5 transcriptions of iranian vocal masters, we try to observe some of various functions of tahrir in iranian classical music with comparative - analytic method and schenkerian analysis. the goal of usage schenkerian analysis is to interpret the underlying structure of tahrirs by showing hierarchical relationships among tones, and also drawing the graphs  of redu...