PRODUCTS OF RESOLVENTS AND MULTIVALUED HYBRID MAPPINGS IN C AT(0) SPACES

In this article, we introduce and investigate the concept of multivalued hybrid mappings in C AT（0） spaces by using the concept of quasilinearization. Also, we present a new iterative algorithm involving products of Moreau-Yosida resolvents for finding a common element of the set of minimizers of a finite family of convex functions and a common fixed point of two multivalued hybrid mappings in C AT（0） spaces.

On the Cozero-Divisor Graphs of Commutative Rings

Let R be a commutative ring with non-zero identity. The cozero-divisor graph of R, denoted by , is a graph with vertices in , which is the set of all non-zero and non-unit elements of R, and two distinct vertices a and b in are adjacent if and only if and . In this paper, we investigate some combinatorial properties of the cozero-divisor graphs and such as connectivity, diameter, girth, clique numbers and planarity. We also study the cozero-divisor graphs of the direct products of two arbitrary commutative rings.

Use of FFT in Protein Sequence Comparison under Their Binary Representations

The paper considers Voss type representation of amino acids and uses FFT on the represented binary sequences to get the spectrum in the frequency domain. Based on the analysis of this spectrum by using the method of inter coefficient difference (ICD), it compares protein sequences of ND5 and ND6 category. Results obtained agree with the standard ones. The purpose of the paper is to extend the ICD method of comparison of DNA sequences to comparison of protein sequences. The topic of discussion is to develop a novel method of comparing protein sequences. The main achievements of the work are that the method applied is completely new of its kind, so far as protein sequence comparison is concerned and moreover the results of comparison agree with the previous results obtained by other methods for the same category of protein sequences.

MEAN APPROXIMATION BY DILATATIONS IN BERGMAN SPACES ON THE UPPER HALF-PLANE

We study sufficient conditions on radial and non-radial weight functions on the upper half-plane that guarantee norm approximation of functions in weighted Bergman,weighted Dirichlet,and weighted Besov spaces on the upper half-plane by dilatations and eventually by analytic polynomials.

CONTINUOUS FRAME WAVELETS

Let π be a unitary representation of a locally compact topological group G on a separable Hilbert space H. A vector ψ∈ H is called a continuous frame wavelet if there exist A, B 〉 0 such that A｜｜Ф｜｜2≤fG｜〈π（G）ψ,Ф｜2dg≤B｜｜Ф｜｜2（Ф∈H）,in which dg is the left Haar measure of G. Similar to the study of wavelets, an essential problem in the study of continuous frame wavelets is how to characterize them under the given unitary representation. Moreover, we investigate a relation between admissible vectors of π and its components.

EXISTENCE TO FRACTIONAL CRITICAL EQUATION WITH HARDY-LITTLEWOOD-SOBOLEV NONLINEARITIES

In this paper,we consider the following new Kirchhoff-type equations involving the fractional p-Laplacian and Hardy-Littlewood-Sobolev critical nonlinearity:(A+B∫∫_(R^(2N))|u(x)-u(y)|^(p)/|x-y|^(N+ps)dxdy)^(p-1)(-△)_(p)^(s)u+λV(x)|u|^(p-2)u=(∫_(R^(N))|U|^(P_(μ,S)^(*))/|x-y|^(μ)dy)|u|^(P_(μ,S)^(*))^(-2)u,x∈R^(N),where(-△)_(p)^(s)is the fractional p-Laplacian with 0<s<1<p,0<μ<N,N>ps,a,b>0,λ>0 is a parameter,V:R^(N)→R^(+)is a potential function,θ∈[1,2_(μ,s)^(*))and P_(μ,S)^(*)=pN-pμ/2/N-ps is the critical exponent in the sense of Hardy-Littlewood-Sobolev inequality.We get the existence of infinitely many solutions for the above problem by using the concentration compactness principle and Krasnoselskii’s genus theory.To the best of our knowledge,our result is new even in Choquard-Kirchhoff-type equations involving the p-Laplacian case.

A STRONG CONVERGENCE THEOREM FOR QUASI-EQUILIBRIUM PROBLEMS IN BANACH SPACES

In this paper,we study an extragradient algorithm for approximating solutions of quasi-equilibrium problems in Banach spaces.We prove strong convergence of the sequence generated by the extragradient method to a solution of the quasi-equilibrium problem.

Nonmonotonic logics and algebras

Several nonmonotonic logic systems together with their algebraic semantics are discussed.NM-algebra is defined.An elegant construction of an NM-algebra starting from a Boolean algebra is described which gives rise to a few interesting algebraic issues.

Condensed Matrix Descriptor for Protein Sequence Comparison

The present paper develops a novel way of reducing a protein sequence of any length to a real symmetric condensed 20 × 20 matrix. This condensed matrix can be nicely applied as a protein sequence descriptor. In fact, with such a condensed representation, comparison of two protein sequences is reduced to a comparison of two such 20 × 20 matrices. As each square matrix has a unique Alley Index/normalized Alley Index, such index is conveniently used in getting distance matrix to construct Phylogenetic trees of different protein sequences. Finally protein sequence comparison is made based on these Phylogenetic trees. In this paper three types viz., NADH dehydrogenase subunit 3 (ND3), subunit 4 (ND4) and subunit 5 (ND5) of protein sequences of nine species, Human, Gorilla, Common Chimpanzee, Pygmy Chimpanzee, Fin Whale, Blue Whale, Rat, Mouse and Opossum are used for comparison.

Double Derangement Permutations

Let n be a positive integer. A permutation a of the symmetric group of permutations of is called a derangement if for each . Suppose that x and y are two arbitrary permutations of . We say that a permutation a is a double derangement with respect to x and y if and for each . In this paper, we give an explicit formula for , the number of double derangements with respect to x and y. Let and let and be two subsets of with and . Suppose that denotes the number of derangements x such that . As the main result, we show that if and z is a permutation such that for and for , then where .

The Eigenvalues of a Class of Elliptic Differential Operators

Consider(M,g)as an n-dimensional compact Riemannian manifold.In this paper we are going to study a class of elliptic differential operators which appears naturally in the study of hypersurfaces with constant mean curvature and also the study of variation theory for 1-area functional.

The Order Properties of r-compact Operators on Banach Lattices

We present here that F（E,F）, the space of all r-compact operators from E into F, is a generalised sublattice of L^r（E, F） for arbitary Banach lattices E and F, and that the characterization of the regular norm on F（E, F） is order continuous. Some conditions for F（E, F） to be a KB-space or a band in .L（E, F） are also provided.

A class of singular integrals on the n-complex unit sphere

The operators on the n-complex unit sphere under study have three forms: the singular integrals with holomorphic kernels, the bounded and holomorphic Fourier multipliers, and the Cauchy-Dunford bounded and holomorphic functional calculus of the radial Dirac operator. The equivalence between the three forms and the strong-type (p, p), 1【p【∞, and weak-type (1,1)-boundedness of the operators is proved. The results generalise the work of L. K. Hua, A. Korányli and S. Vagi, W. Rudin and S. Gong on the Cauchy-Szeg(?) kernel and the Cauchy singular integral operator.

Applications of differential algebra for computing Lie algebras of infinitesimal CR-automorphisms

We perform detailed computations of Lie algebras of infinitesimal CR-automorphisms associated to three specific model real analytic CR-generic submanifolds in C9by employing differential algebra computer tools—mostly within the Maple package DifferentialAlgebra—in order to automate the handling of the arising highly complex linear systems of PDE’s.Before treating these new examples which prolong previous works of Beloshapka,of Shananina and of Mamai,we provide general formulas for the explicitation of the concerned PDE systems that are valid in arbitrary codimension k 1 and in any CR dimension n 1.Also,we show how Ritt’s reduction algorithm can be adapted to the case under interest,where the concerned PDE systems admit so-called complex conjugations.

On Radicals of Skew Inverse Laurent Series Rings

Let R be a ring and a an automorphism of R. Amitsur proved that the Jacobson radical J（R[x]） of the polynomial ring R[x] is the polynomial ring over the nil ideal J（R[x]）∩R. Following Amitsur, it is shown that when R is an Armendaxiz ring of skew inverse Laurent series type and S is any one of the ring extensions R[x; α], R[x,x^-1;α], R[[x^-1;α]] and R（（x^-1; α））, then （S） = （R）S = Nil（S）, （S） ∩ R = Nil（R）, where is a radical in a class of radicals which includes the Wedderburn, lower nil, Levitzky and upper nil radicals.

Reconstruction of Singular Second-order Differential Equations From Spectral Characteristics

In this work,we study boundary value problems for second-order differential equations with singularities of second kind inside an interval.First,we investigate properties of the spectrum,then prove a theorem on completeness of eigenfunctions,and study the inverse problem of reconstructing the differential equation from spectral characteristics.

On Annihilator Ideals of Pseudo-differential Operator Rings

Let R be a ring with a derivation 5 and R（（x-1;5）） denote the pseudo- differential operator ring over R. We study the relations between the set of annihilators in R and the set of annihilators in R（（x-1; 5））. Among applications, it is shown that for an Armendariz ring R of pseudo-differential operator type, the ring R（（x-1; 5）） is Baer （resp., quasi-Baer, PP, right zip） if and only if R is a Baer （resp., quasi-Baer, PP, right zip） ring. For a 5-weakly rigid ring R, R（（x-1;5）） is a left p.q.-Baer ring if and only if R is left p.q.-Baer and every countable subset of left semicentral idempotents of R has a generalized countable join in R.

The Zariski Topology on the Second Spectrum of a Module

Let R be a commutative ring and M be an R-module. The second spectrum Spec^S（M） of M is the collection of all second submodules of M. We topologize Spec^S（M） with Zariski topology, which is analogous to that for Spec（R）, and investigate this topolog- ical space. For various types of modules M, we obtain conditions under which Spec^S（M） is a spectral space. We also investigate Specs （M） with quasi-Zariski topology.

Geometric Estimates of the First Eigenvalue of(p,q)-elliptic Quasilinear System Under Integral Curvature Condition

Consider(M,g)as a complete,simply connected Riemannian manifold.The aim of this paper is to provide various geometric estimates in different cases for the first eigenvalue of(p,q)-elliptic quasilinear system in both Dirichlet and Neumann conditions on Riemannian manifold.In some cases we add integral curvature condition and maybe we prove some theorems under other conditions.

Cohen-Macaulay and Gorenstein Path Ideals of Trees

Let R = k[x1,...,xn], where k is a field. The path ideal （of length t ≥ 2） of a directed graph G is the monomial ideal], denoted by It （G）, whose generators correspond to the directed paths of length t in G. Let F be a directed rooted tree. We characterize all such trees whose path ideals are unmixed and Cohen-Macaulay. Moreover, we show that R/It（F） is Corenstein if and only if the Stanley-Reisner simplicial complex of It（Г） is a matroid.