‎we describe a new type of presentation that‎, ‎when consistent‎, ‎describes a polycyclic group‎. ‎this presentation is obtained by‎ ‎refining a series of normal subgroups with‎ ‎abelian sections‎. ‎these presentations can be described effectively in‎ ‎computer-algebra-systems like {scshape gap} or ‎{scshape magma}‎. ‎we study these ‎presentations and‎, ‎in particular‎, ‎we obtain consistency c...

in the present article the frequency and percentage distribution of different verb tenses have been analyzed in books of 1, 2 and 3 of masnavi. the hypothesis is that it is possible to identify the degree of realism, narrative stylistic and some aspects of grammatical voice by using the feature of tense. the theoretical framework is based on systematic functional grammar and traditional grammar...

Walicki and Meldal have deened a calculus DEQ (\Disjunctive EQuational calculus") for reasoning about nondeterministic operators when specifying non-deterministic systems in an equation-oriented style. A variant of DEQ, the calculus DEQ for axiomatic equality theories with cut-like rules introducing as cut formulas only the negative equalities of a spe-ciic axiom, is constructed. For pure posit...

Let R be a Noetherian local ring and Ω an arbitrary R-module of finite depth and finite projective dimension. The flat dimension of Ω is at least depth(R)−depth(Ω) with equality in the following cases: (i) Ω is finitely generated over some Noetherian local R-algebra S; (ii) dim(R) = 1; (iii) dim(R) = 2 and Ω is separated; (iv) R is CohenMacaulay, dim(R) = 3 and Ω is complete.

The X = M conjecture of Hatayama et al. asserts the equality between the one-dimensional configuration sum X expressed as the generating function of crystal paths with energy statistics and the fermionic formula M for all affine Kac–Moody algebra. In this paper we prove the X = M conjecture for tensor products of Kirillov–Reshetikhin crystals B1,s associated to symmetric powers for all nonexcep...

The aim of this paper is to relate initial algebra semantics and final coalgebra semantics. It is shown how these two approaches to the semantics of programming languages are each others dual, and some conditions are given under which they coincide. More precisely, it is shown how to derive initial semantics from final semantics, using the initiality and finality to ensure their equality. Moreo...

We present a short elementary proof of the Lagrange multiplier theorem for equality-constrained optimization. Most proofs in the literature rely on advanced analysis concepts such as the implicit function theorem, whereas elementary proofs tend to be long and involved. By contrast, our proof uses only basic facts from linear algebra, the definition of differentiability, the critical-point condi...

We use the notation A ∈ F to indicate that the set A is in F . Remark that since A∩B = (A ∪B) and more generally ⋂ Ai = ( ⋃ Ai) c (Exercise: Prove this equality) axiom ii) holds with union replaced by intersection. Also we have A−B = A ∩B so if A,B ∈ F then A−B ∈ F . Basically you should think of a σ-algebra as a system of subsets in which you can perform any of the usual set-theoretic operatio...

We construct a realization of the algebra of the Z3-graded topological symmetry of type (1, 1, 1) in terms of a pair of operators D1 : H1 → H2, D2 : H2 → H3 satisfying [D1D † 1,D † 2D2] = 0. We show that the sequence of the restriction of these operators to the zero-energy subspace forms a complex and establish the equality of the corresponding topological invariants with the analytic indices o...