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Zhao and Ho asked in a recent paper that for each T0 space X, whether KB(X) (the set of all irreducible closed sets of X whose suprema exist) is the canonical k-bounded sobrification of X in the sense of Keimel and Lawson. In this paper, we construct a counterexample to give a negative answer. We also consider the subcategory Topκ of the category Top0 of T0 spaces, and prove that the category KBSob of k-bounded sober spaces is a full reflective subcategory of the category KBSob of k-bounded sober spaces is a full reflective subcategory of the category Topκ. [ABSTRACT FROM AUTHOR]

In this paper, we prove the Hyers-Ulam-Rassias stability of isometric homomorphisms in proper CQ*-algebras for the following Cauchy-Jensen additive mapping: The concept of Hyers-Ulam-Rassias stability originated from the Th.M. Rassias’ stability theorem that appeared in the paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297–300. This is applied to investigate isometric isomorphisms between proper CQ*-algebras. [ABSTRACT FROM AUTHOR]

In this paper, the existence and multiplicity of a class of double resonant semilinear elliptic equations with the Dirichlet boundary value are studied. [ABSTRACT FROM AUTHOR]

This paper is concerned with the L- L estimates of the solutions for a class of pseudodifferential equations under some suitable degenerate assumptions. As applications, these estimates can be used to show that a generalized Schrödinger operator with some integrable potential generates a fractionally integrated group in L(ℝ). [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the following implicit iteration scheme recently introduced by Xu and Ori [ Numer. Funct. Anal. Optim., 22, (2001) 767–773]: and to prove several strongly and weakly convergent theorems of the iteration for a finite family of pseudocontractive mappings under condition α n ∈ (0, b] ⊂ (0, 1). [ABSTRACT FROM AUTHOR]

A labeling f of a graph G is a bijection from its edge set E( G) to the set {1, 2, ..., | E( G)|}, which is antimagic if for any distinct vertices x and y, the sum of the labels on edges incident to x is different from the sum of the labels on edges incident to y. A graph G is antimagic if G has an f which is antimagic. Hartsfield and Ringel conjectured in 1990 that every connected graph other than K2 is antimagic. In this paper, we show that if G is an n-vertex graph with minimum degree at least r, and G2 is an m-vertex graph with maximum degree at most 2 r − 1 ( m ≥ n), then G ∀ G is antimagic. [ABSTRACT FROM AUTHOR]

In this paper, we investigate what are Carleson measures on open subsets in the complex plane. A circular domain is a connected open subset whose boundary consists of finitely many disjoint circles. We call a domain G multi-nicely connected if there exists a circular domain W and a conformal map ψ from W onto G such that ψ is almost univalent with respect the arclength on ϖW. We characterize all Carleson measures for those open subsets so that each of their components is multinicely connected and harmonic measures of the components are mutually singular. Our results suggest the extension of Carleson measures probably is up to this class of open subsets [ABSTRACT FROM AUTHOR]

Let $${\fancyscript G}$$ be a generalized Kac–Moody algebra with an integral Borcherds–Cartan matrix. In this paper, we define a d-type weak quantum generalized Kac–Moody algebra $$ wU^{d}_{q} {\left( {\fancyscript G} \right)} $$ , which is a weak Hopf algebra. We also study the highest weight module over the weak quantum algebra $$ wU^{d}_{q} {\left( {\fancyscript G} \right)} $$ and weak A-forms of $$ wU^{d}_{q} {\left( {\fancyscript G} \right)} $$ . [ABSTRACT FROM AUTHOR]

We describe the relationship between the fuzzy sets and the algebraic hyperstructures. In fact, this paper is a continuation of the ideas presented by Davvaz in ( Fuzzy Sets Syst., 117: 477– 484, 2001) and Bhakat and Das in ( Fuzzy Sets Syst., 80: 359–368, 1996). The concept of the quasicoincidence of a fuzzy interval value with an interval-valued fuzzy set is introduced and this is a natural generalization of the quasi-coincidence of a fuzzy point in fuzzy sets. By using this new idea, the concept of interval-valued ( α, β)-fuzzy sub-hypermodules of a hypermodule is defined. This newly defined interval-valued ( α, β)-fuzzy sub-hypermodule is a generalization of the usual fuzzy sub-hypermodule. We shall study such fuzzy sub-hypermodules and consider the implication-based interval-valued fuzzy sub-hypermodules of a hypermodule. [ABSTRACT FROM AUTHOR]

In this paper, we prove several results concerning meromorphic functions f and g of hyperorder less than one such that f ( j) and g ( j) have the same zeros and poles for j = 0, 1, 2. We provide some examples to show that our results are sharp. [ABSTRACT FROM AUTHOR]

In this paper the following theorem is proved: Every group L3( q) for q = 3(2 m–1)( m ≥ 2) is characterized by its set of element orders. [ABSTRACT FROM AUTHOR]

In this paper, we study the compactness of the product of a composition operator with another one’s adjoint on the Bergman space. Some necessary and sufficient conditions for such operators to be compact are given. [ABSTRACT FROM AUTHOR]

Let G be a graph (i.e., a finite one–dimensional polyhedron) and f : G → G be a continuous map. In this paper, we show that every isolated recurrent point of f is an isolated non–wandering point; every accumulation point of the set of non–wandering points of f with infinite orbit is a two–order accumulation point of the set of recurrent points of f; the derived set of an ω–limit set of f is equal to the derived set of an the set of recurrent points of f; and the two–order derived set of non–wandering set of f is equal to the two–order derived set of the set of recurrent points of f. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the canonical foliations of an almost cosymplectic or almost Kenmotsu manifold M in a unified way. We prove that the canonical foliation ℱ defined by the contact distribution is Riemannian and tangentially almost Kähler of codimension 1 and that ℱ is tangentially Kähler if the manifold M is normal. Furthermore, we show that a semi–invariant submanifold N of such a manifold M admits a canonical foliation ℱ N which is defined by the antiinvariant distribution and a canonical cohomology class c(N) generated by a transversal volume form for ℱ N. In addition, we investigate the conditions when the even–dimensional cohomology classes of N are non–trivial. Finally, we compute the Godbillon–Vey class for ℱ N. [ABSTRACT FROM AUTHOR]

In this paper, for an arbitrary regular biordered setE, by using biorder-isomorphisms between the ?-ideals ofE, we construct a fundamental regular semigroupWE called NH-semigroup ofE, whose idempotent biordered set is isomorphic toE. We prove further thatWE can be used to give a new representation of general regular semigroups in the sense that, for any regular semigroupSwith the idempotent biordered set isomorphic toE, there exists a homomorphism fromStoWE whose kernel is the greatest idempotent-separating congruence onSand the image is a full symmetric subsemigroup ofWE. Moreover, whenEis a biordered set of a semilatticeE0,WE is isomorphic to the Munn-semigroup; and whenEis the biordered set of a bandB,WE is isomorphic to the Hall-semigroupWB. [ABSTRACT FROM AUTHOR]

Let $\mathbb{F}_p $ be the finite field of p elements with p prime. If A is a subset of $\mathbb{F}_p $ and g is an element of $\mathbb{F}_p^* $ with order ν, then . [ABSTRACT FROM AUTHOR]

The aim of this work is to present the description of Leibniz superalgebras up to isomorphism with characteristic sequence ( n| m − 1, 1) and nilindex n + m. [ABSTRACT FROM AUTHOR]

Let τ be a premeasure on a complete separable metric space and let τ* be the Method I measure constructed from τ. We give conditions on τ such that τ* has a regularity as follows: Every τ*-measurable set has measure equivalent to the supremum of premeasures of its compact subsets. Then we prove that the packing measure has this regularity if and only if the corresponding packing premeasure is locally finite. [ABSTRACT FROM AUTHOR]

Let ( X, $${\mathfrak{S}}$$ ( X), $${\mathfrak{m}})$$ be a probability space with σ-algebra , $${\mathfrak{S}}$$ ( X) and probability measure $${\mathfrak{m}}.$$ The set V in $${\mathfrak{S}}$$ is called P-admissible, provided that for any positive integer n and positive-measure set V n ∈ $${\mathfrak{S}}$$ contained in V , there exists a Z n ∈ $${\mathfrak{S}}$$ such that Z n ⊂ V n and 0 < $${\mathfrak{m}}$$ ( Z n ) < 1/ n. Let T be an ergodic automorphism of ( X, $${\mathfrak{S}})$$ preserving $${\mathfrak{m}},$$ and A belong to the space of linear measurable symplectic cocycles $${\fancyscript G}$$ IC ( X, SL(2,ℝ)) := { A : X → SL(2,ℝ)| log ∥ A ±1( x)∥ ∈ $${\Bbb L}$$ 1( X, $${\mathfrak{m}}).$$ We prove that for any P–admissible set V and ε > 0, there exists a B ∈ $${\fancyscript G}$$ IC ( X, SL(2,ℝ)) such that max{∥ A( x) − B( x)∥, ∥ A −1( x) − B −1( x)∥} < ε for all x ∈ V, A( x) = B( x) for all x ∈ X \ V, and B has the simple Lyapunov spectrum over the system ( X, $${\mathfrak{m}},$$ T). [ABSTRACT FROM AUTHOR]

It is proved that with at mostO(N11/12+e) exceptions, all positive integersn=Nsatisfying some necessary congruence conditions are the sum of three squares of primes. This improves substantially the previous results in this direction. [ABSTRACT FROM AUTHOR]

Abstract In this note, we use the so-called microlocal energy method to give a characterization of the Gevrey Sobolev wave front set WF[sub H[sup s[sub tau, sigma]](u), which will be useful iii the study of non-linear microlocal analysis in Gevrey classes. Keywords Gevrey-Sobolev space, Wave front set, Microlocal energy method [ABSTRACT FROM AUTHOR]