We design a non-commutative version of the Peterson-Gorenstein-Zierler decoding algorithm for a class of codes that we call skew RS codes. These codes are left ideals of a quotient of a skew polynomial ring, which endow them of a sort of non-commutative cyclic structure. Since we work over an arbitrary field, our techniques may be applied both to linear block codes and convolutional codes. In p...

We study the computational power of pure insertion grammars. We show that pure insertion grammars of weight 3 can characterize all recursively enumerable languages. This is achieved by either applying an inverse morphism and a weak coding, or a left (right) quotient with a regular language. A consequences for the closure properties of insertion grammars are shown. We also study an application i...

The left hand side (or A–side) of this identity was a generating series for the numbers n(d) of rational curves of various degrees d lying on a smooth quintic hypersurface in P. The right hand side (B–side) was a certain hypergeometric function. The Mirror Identity states that the two functions become identical after an explicit change of variables which is defined as a quotient of two hypergeo...

Abstract. We provide a direct proof that a finite graded lattice with a maximal chain of left modular elements is supersolvable. This result was first established via a detour through EL-labellings in [MT] by combining results of McNamara [Mc] and Liu [Li]. As part of our proof, we show that the maximum graded quotient of the free product of a chain and a single-element lattice is finite and di...

The non-commutative analytic Toeplitz algebra is the wot–closed algebra generated by the left regular representation of the free semigroup on n generators. We obtain a distance formula to an arbitrary wotclosed right ideal and thereby show that the quotient is completely isometrically isomorphic to the compression of the algebra to the orthogonal complement of the range of the ideal. This is us...

conclusions chronic and moderate malnutrition did not influence the cognitive function, the intelligence quotient, and the impulsivity index. background undernutrition is the most common cause of growth retardation in developing countries. we aimed to assess the effect of undernutrition on cognition, intelligence quotient, and impulsivity index of 7-11 year-old children in shiraz, southern iran...

We show that certain embeddable homogeneous spaces of a quantum group that do not correspond to a quantum subgroup still have the structure of quantum quotient spaces. We propose a construction of quantum fibre bundles on such spaces. The quantum plane and the general quantum two-spheres are discussed in detail. 0. Introduction A homogeneous space X of a Lie group G may be always identified wit...

Assume that A is a bounded self-adjoint operator in a Hilbert space H. Then, the variational principle max v |(Au, v)|2 (Av, v) = (Au, u) (*) holds if and only if A ≥ 0, that is, if (Av, v) ≥ 0 for all v ∈ H. We define the quotient on the left-hand side in (*) to be zero if (Av, v) = 0. As an application of this principle a variational principle for the electrical capacitance of a conductor of ...

The paper addresses two problems belonging to the basic combinatorics of words. They are connected with the operations of sequential insertion and deletion, which are nondeterministic versions of catenation and right/ left quotient. Necessary and sufficient conditions, under which the result of sequential insertion or deletion of two words is a singleton set, are given. Also the situation when ...