Definition 1.1. If S is a multiplicative subset of a ring A (commutative with 1), the quotient hyperring A/mS = (A/mS,+, ·,−, 0, 1) is defined as follows: A/mS is the set of equivalence classes with respect to the equivalence relation ∼ on A defined by a ∼ b iff as = bt for some s, t ∈ S. The operations on A/mS are the obvious ones induced by the corresponding operations on A: Denote by a the e...

Let F be a finite group with a Sylow 2-subgroup S that is normal and abelian. Using hyperelementary induction and cartesian squares, we prove that Cappell’s unitary nilpotent groups UNil∗(Z[F ];Z[F ],Z[F ]) have an induced isomorphism to the quotient of UNil∗(Z[S];Z[S],Z[S]) by the action of the group F/S. In particular, any finite group F of odd order has the same UNil-groups as the trivial gr...

BACKGROUND Empathizing is a specific component of social cognition. Empathizing is also specifically impaired in autism spectrum condition (ASC). These are two dimensions, measurable using the Empathy Quotient (EQ) and the Autism Spectrum Quotient (AQ). ASC also involves strong systemizing, a dimension measured using the Systemizing Quotient (SQ). The present study examined the relationship bet...

A. If a (cusped) surface S admits an ideal triangulation T with no shears, we show an efficient algorithm to give S as a quotient of hypebolic plane H by a subgroup of PSL(2,Z). The algorithm runs in time O(n logn), where n is the number of triangles in the triangulation T . The algorithm generalizes to producing fundamental groups of general surfaces and geometric manifolds of higher di...

This paper concerns with the study of EGG (electroglottalgram by laryngograph) model of ditoneme in Mandarin. The parameters for establishing models are fundamental frequency (F0), which is regarded as reference, speed quotient and open quotient, which are all extracted from the EGG signal by using the software EGG.exe, an option of CSL, Model 4300B, KAY. The result shows that speed quotient an...

A magnetic monopole is placed at the centre of a ball whose surface S 2 is tiled by the symmetry group, Γ, of a regular solid. The quantum mechanics on the two-dimensional quotient S 2 /Γ is developed and the monopole charge is found to be quantised in an expected manner. The heat-kernel and ζ–functions are evaluated and the Casimir energy is computed. Numerical approaches to the calculation of...

A Banach algebra A with radical R is said to have property (S) if the natural mapping from the algebraic tensor product 2 A ® A onto A is open, when A ® A is given the protective norm. The purpose of this note is to provide a counterexample to Zinde's claim that when A is commutative and R is one dimensional the fulfillment of property (S) in A implies its fulfillment in the quotient algebra A/R .

We consider closed topological 4-manifolds M with universal cover S × S and Euler characteristic χ(M) = 1. All such manifolds with π = π1(M) ∼= Z/4 are homotopy equivalent. In this case, we show that there are four homeomorphism types, and propose a candidate for a smooth example which is not homeomorphic to the geometric quotient. If π ∼= Z/2×Z/2, we show that there are three homotopy types (a...

We construct a birational equivalence between certain quotients of s-tuples of equidimensional linear subspaces of Cn and some quotients of products of square matrices modulo diagonal conjugations. In particular, we prove the rationality of the quotient space of s-tuples of linear 2-planes in Cn modulo the diagonal GLn(C)-action . Furthermore, we compute generators of the field of the rational ...