The group Sn, n ≥ 1, is usually defined as the group of all permutations of the set Xn = {1, 2, . . . , n}. So, an element s ∈ Sn is a bijection (i.e., one-to-one map) from Xn to Xn : k 7→ s(k). The composition of two such map is denoted by s1 ◦ s2 : k 7→ s1 ( s2(k) ) . It is convenient to depict the permutation s as follows. Take two copy of Xn represented as column vectors and draw a system o...

We introduce a large class of infinite dimensional associative algebras which generalize down-up algebras. Let K be a field and fix f ∈ K[x] and r, s, γ ∈ K. Define L = L(f, r, s, γ) to be the algebra generated by d, u and h with defining relations: [d, h]r + γd = 0, [h, u]r + γu = 0, [d, u]s + f(h) = 0. Included in this family are Smith’s class of algebras similar to U(sl2), Le Bruyn’s conform...

The paper examines the basic properties of linear relative widths as well as the different ways of finding their estimates. AMS Subject Classification: 41A35, 41A29

In this paper S, X denote non empty sets and R denotes a binary relation on X . We introduce orthorelational structures which are extensions of relational structure and ComplStr and are systems 〈 a carrier, an internal relation, a complement operation 〉, where the carrier is a set, the internal relation is a binary relation on the carrier, and the complement operation is a unary operation on th...

We study three-leg antiferromagnetic Heisenberg model with the periodic boundary conditions in the rung direction. Since the rungs form regular triangles, spin frustration is induced. We use the density-matrix renormalization group method to investigate the ground state. We find that the spin excitations are always gapped to remove the spin frustration as long as the rung coupling is nonzero. W...

It is known that the ratio of Gaussian hypergeometric functions can be represented by means of g -fractions. In this work, the ratio of q -hypergeometric functions are represented by means of g -fractions that lead to certain results on q -starlikeness of the q -hypergeometric functions defined on the open unit disk. Corresponding results for the q -convex case are also obtained.

1 Definitions and Examples 1.1 Metric and Normed Spaces Definition 1.1. A metric space is a pair (X, d), where X is a set and d is a function from X ×X to R such that the following conditions hold for every x, y, z ∈ X. 1. Non-negativity: d(x, y) ≥ 0. 2. Symmetry: d(x, y) = d(y, x). 3. Triangle inequality: d(x, y) + d(y, z) ≥ d(x, y) . 4. d(x, y) = 0 if and only if x = y. Elements of X are call...

This paper presents two classes of propositional logics (understood as a consequence relation). First we generalize the well-known class of implicative logics of Rasiowa and introduce the class of weakly implicative logics. This class is broad enough to contain many “usual” logics, yet easily manageable with nice logical properties. Then we introduce its subclass— the class of weakly implicativ...

In this paper I is an element of Z8, S is a non empty 1-sorted structure, t is an element of the carrier of S, and x is a set. Let R be a good ring. The functor SCM(R) yields a strict AMI over {the carrier of R} and is defined by the conditions (Def. 1). (Def. 1)(i) The objects of SCM(R) = N, (ii) the instruction counter of SCM(R) = 0, (iii) the instruction locations of SCM(R) = Instr-LocSCM, (...