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Let F be a field of characteristic p > 3, and L = ⊕i≥minus;1Li the finite-dimensional transitive Z-graded simple Lie superalgebral over F. In this paper L is determined if the Z-graded Lie superalgebra L−1 ⊕L0 is isomorphic to the L−1⊕pl (L−1) or L−1⊕spl (L−1).

The aim of this paper is to investigate abundant semigroups with a multiplicative adequate transversal. Some properties and characterizations for such semigroups are obtained. In particular, we establish the structure of this class of abundant semigroups in terms of left normal bands, right normal bands and adequate semigroups with some simple compatibility conditions. Finally, we apply this structure to some special cases.

In this paper it is proved that for all completely distributive lattices L, the category of L-fuzzifying topological spaces can be embedded in the category of L-topological spaces (stratified Chang-Goguen spaces) as a simultaneously bireflective and bicoreflective full subcategory.

In this paper we initiate a study of covariance and variance for two operators on a Hilbert space, proving that the c-v (covariance-variance) inequality holds, which is equivalent to the Cauchy-Schwarz inequality. As for applications of the c-v inequality we prove uniformly the Bernstein-type inequalities and equalities, and show the generalized Heinz-Kato-Furuta-type inequalities and equalities, from which a generalization and sharpening of Reid's inequality is obtained. We show that every operator can be expressed as a p-hyponormal-type, and a hyponormal-type operator. Finally, some new characterizations of the Furuta inequality are given.

In this paper we study Toeplitz operators on Dirichlet spaces and describe the boundedness and compactness of Toeplitz operators on Dirichlet spaces. Meanwhile, we give density theorems for Toeplitz operators on Dirichlet spaces

In this paper, we introduce a new class of ergodic sequences, pseudo almost periodic sequences, and study the existence of pseudo almost periodic sequences to difference equations. On the basis of these, we investigate the existence of pseudo almost periodic solutions for neutral delay differential equations with piecewise constant argument, $${d\over dt}(y(t)+py(t-1))=qy(2[{t+1\over 2}])+g(t,y(t),y([t])).$$

In this paper, we characterize the pointwise multiplier space M (Dτ, Dμ) of Dirichlet type spaces in the unit ball of Cn for the values of τ, μ in three cases: (i) τ n, and construct two functions to show that M(Dτ) ⊂Dτ properly if τ≤n and M(Dτ) ⊂M(Dμ) properly if τ > μ and τ > n− 1.

In this paper we consider the boundedness of all the solutions for the equation x″ + ax+−bx− = f(t) is a smooth 2π-periodic function, a and b are positive constants (a≠b).

In this paper, the average σ-Κ width of Sobolev-Wiener classes \( S^{r}_{{pq}} W \) with mixed smoothness in L q (ℝ d ) is studied for 1 < q≤p < ∞, and the weak asymptotical behaviour of these quantities is obtained.

Let ƒ∈C 1 (R 1, R 2), ƒ(0) = 0. The Jacobian Conjecture states that if for any x∈R 2, the eigenvalues of the Jacobian matrix Dƒ(x) have negative real parts, then the zero solution of the differential equation x = ƒ(x) is globally asymptotically stable. In this paper we prove that the conjecture is true.

Rips conjectured that a non-clementary word hyperbolic group is cohopfian if and only if it is freely indecomposable. The results and examples in this paper show that cohopficity phenomenon in the case of word hyperbolic group with torsion is much more complicated than the conjecture. In particular, the cohopficity of such groups is not determined by the numbers of their ends and the cohopficity is not preserved by finite index subgroups. Our results and examples arise from Kleinian groups. Orbifold structures and orbifold maps are the new tools in our discussions.

The purpose of this paper is to investigate the asymptotic behavior of solutions of the forced nonlinear delay differential equations with impulses $$ \left\{ {\begin{array}{*{20}l} {{{x}\ifmmode{'}\else$'$\fi{\left( t \right)} + {\sum\limits_{i = 1}^n {p_{i} {\left( t \right)}f{\left( {x{\left( {t - \tau _{i} } \right)}} \right)} = h{\left( t \right)},{\kern 1pt} t \ne t_{k} ,} }} \hfill} \\ {{x{\left( {t^{ + }_{k} } \right)} - x{\left( {t_{k} } \right)} = b_{k} x{\left( {t_{k} } \right)}.} \hfill} \\ \end{array} } \right. $$ Our results, which hold for linear and nonlinear equations, forced and unforced equations, impulsive and nonimpulsive equations, improve and generalize the known results recently obtained in [8].

The main purpose of this paper is to prove a good λ inequality for a multilinear singular integral in ℝ n .

In this paper, we study multilinear oscillatory singular integrals with rough kernel, and give a criterion of certain boundedness for this kind of operator

In this paper we use the Calderon-Zygmund operator theory to provide a discrete Calderon-type reproducing formula. Since translation, dilation and, in particular, the Fourier transform are never used in the proofs, all results still hold on spaces of homogenous type introduced by Coifman and Weiss. As a consequence, we obtain a class of frames with the minimum regularity properties.

In this paper, we study the boundedness and compactness of composition operator C φ on the Bloch space β(Ω), Ω being a bounded homogeneous domain. For Ω = B n, we give the necessary and sufficient conditions for a composition operator C φ to be compact on β(B n) or β 0(B n).

In this paper, a sufficient condition is given under which the smash product A#H is a transfinite left free normalizing extension of an algebra A. Moreover, the result is applied to a skew semigroup ring, a skew group ring and the quantum group U q (sl(2)) such that some properties are shown.

Let G be a finite group and k a field of characteristic p > 0. In this paper we consider the support variety for the cohomology module Ext kG * (M, N) where M and N are kG-modules. It is the subvariety of the maximal ideal spectrum of H*(G, k) of the annihilator of the cohomology module. For modules in the principal block we show that that the variety is contained in the intersections of the varieties of M and N and the difference between the that intersection and the support variety of the cohomology module is contained in the group theoretic nucleus. For other blocks a new nucleus is defined and a similar theorem is proven. However in the case of modules in a nonprincipal block several new difficulties are highlighted by some examples.

In this paper, we will prove that Floer homology equipped with either the intrinsic or exterior product is isomorphic to quantum homology as a ring. We will also prove that GW-invariants in Floer homology and quantum homology are equivalent.

LetF be an algebraically closed field, $$\bar \Delta $$ be a quiver of typeA n . In this paper we prove that the endomorphism algebras of exceptional sequences over $$F\bar \Delta $$ are sums of finitely many tilted algebras of typeA m wherem≤n by using perpendicular categories, and thus the endomorphism algebras of exceptional sequences of typeA n are representation-finite.

In this paper the characterizations of conjugate hulls ψ (S). ϕ(S),T(S) and θ(S) on a Brandt semigroupS are given. By using these results we can pro thatT(S) is self-conjugate in ψ(S) for a Brandt semigroupS.

LetG be a second countable groupoid with Haar system {λ u },A be an abelian group which left invariant acts onG. Then we have aC *-dynamic system (C * (G, A, β). In this paper we have studied the existence of quasi-invariant measure with certain properties; using these measures some important results about crossed products and groupoidC *-algebras have been obtained.

In this paper we study the kernels of a linear operator and its algebraic adjoint by studying their restriction on a subspace, a Banach space, such that the restriction is the difference of the identity and a compact operator under some conditions, and therefore some results on compact operator theory can be applied. As an example we study theM-scale subdivision operators.

In this paper, we study the class of ortho-u-monoids which are generalized orthogroups within the class of E(S)-semiabundant semigroups. After introducing the concept of (∼)-Green’s relations, and obtaining some important properties of (∼)-Green’s relations and super E(S)-semiabundant semigroups, we have given the semilattice decomposition of ortho-u-monoids and a structure theorem for regular ortho-u-monoids. The main techniques that we used in the study are the (∼)-Green’s relations, and the semi-spined product of semigroups.