具有不同分布NA随机变量列的强大数律及应用

给出了具有不同分布的NA随机变量列满足的若干强大数律;作为应用,不仅将独立随机变量的一类强极限定理完整的推广到NA随机变量情形,而且关于NA随机变量的一些已有结果可以作为推论得出.     

NA随机变量列一类强大数律的充分必要条件

本文给出了具有不同分布NA随机变量列满足一类强大数律的充分必要条件, 从而将Egorov对独立随机变量列建立的结果推广到NA随机变量情形; 作为应用, 我们还建立了一个新的强大数律.     

A simple characterization of almost uniform convergence by stochastic convergence

Motivated by Egorov's theorem and the characterization of the equivalence of P-stochastic convergence and P-almost convergence by the property of the probability distribution P to be purely atomic and concentrated on a countable number of pairwise disjoint P-atoms (cf. [1], p. 68), it is proved that P-stochastic resp. P-almost convergence is equivalent to P-almost uniform convergence (cf. [2], p. 89/90) if and only if P is purely atomic and concentrated on a finite number of pairwise disjoint P-atoms. Furthermore, this property of P is equivalent to the condition that any P-stochastic convergent sequence admits a P-almost uniform convergent subsequence. Finally a proof is given that P is purely atomic and concentrated on a finite number of pairwise disjoint P-atoms if and only if there does not exist a purely finitely additive {0,1}-valued probability charge, which vanishes for all P-zero sets.     

Maximality of linear continuous logic

The linear compactness theorem is a variant of the compactness theorem holding for linear formulas. We show that the linear fragment of continuous logic is maximal with respect to the linear compactness theorem and the linear elementary chain property. We also characterize linear formulas as those preserved by the ultramean construction.     

解析hyponormal算子的α-Weyl定理

本文通过定义新的谱集,给出了算子满足a-Browder定理和a-Weyl定理的充要条件,运用了文章中新定义的谱集,研究了解析hyponormal算子的a-Weyl定理．     

解析hyponormal算子的α-Weyl定理

本文通过定义新的谱集,给出了算子满足a-Browder定理和a-Weyl定理的充要条件,运用了文章中新定义的谱集,研究了解析hyponormal算子的a-Weyl定理．     

Quasi-periodic solutions of forced isochronous oscillators at resonance

We deal with the existence of quasi-periodic solutions of forced isochronous oscillators with a repulsive singularity, the nonlinearity is a bounded perturbation. Using a variant of Moser's twist theorem of invariant curves, due to Ortega [R. Ortega, Boundedness in a piecewise linear oscillator and a variant of the small twist theorem, Proc. London Math. Soc. 79 (1999) 381-413], we show that there are many quasi-periodic solutions and the boundedness of all solutions.     

Motzkin’s theorem of the alternative: a continuous-time generalization

We revisit Zalmai’s theorem, which is a partial generalization of Motzkin’s theorem of the alternative in the continuous-time setting. In particular, we provide two simple examples demonstrating that its existing proof is incorrect, and we demonstrate that a suitably modified variant of Zalmai’s theorem, concerned with the inconsistency of systems of convex inequalities and affine equalities, can be verified. We also derive two generalized variants of Motzkin’s theorem of the alternative in the continuous-time setting.     

Variations on Weyl's theorem

In this note we study the property (w), a variant of Weyl's theorem introduced by Rako?evi?, by means of the localized single-valued extension property (SVEP). We establish for a bounded linear operator defined on a Banach space several sufficient and necessary conditions for which property (w) holds. We also relate this property with Weyl's theorem and with another variant of it, a-Weyl's theorem. We show that Weyl's theorem, a-Weyl's theorem and property (w) for T (respectively T^*) coincide whenever T^* (respectively T) satisfies SVEP. As a consequence of these results, we obtain that several classes of commonly considered operators have property (w).     

Cyclic intersections and control of fusion

In this paper we study factorizable groups. An extension of a famous theorem of H. Wielandt on groups factorizable by two nilpotent subgroups of relatively prime orders is obtained. We also present a variant of a theorem of A. Gonçalves and C. Y. Ho.     

Global variants of Hartogs’ theorem

Hartogs’ theorem asserts that a separately holomorphic function, defined on an open subset of $$\mathbb {C}^n$$ , is holomorphic in all the variables. We prove a global variant of this theorem for functions defined on an open subset of the product of complex algebraic manifolds. We also obtain global Hartogs-type theorems for complex Nash functions and complex regular functions.     

Existence and multiplicity of solutions for second order periodic systems with the p-Laplacian and a nonsmooth potential

In this paper we study nonlinear periodic systems driven by the ordinary p-Laplacian with a nonsmooth potential. We prove an existence theorem using a nonsmooth variant of the reduction method. We also prove two multiplicity results. The first is for scalar problems and uses the nonsmooth second deformation lemma. The second is for systems and it is based on the nonsmooth local linking theorem.     

On the symbol homomorphism of a certain Frechet algebra of singular integral operators

We prove the surjectivity of the symbol map of the Frechet algebra obtained by completing an algebra of convolution and multiplication operators in the topology generated by all L²-Sobolev norms. The proof is based on an ⁿ of Egorov's theorem valid for non-homogeneous principal symbols, discussed in [5], [6]. We use the hyperbolic equation u/t=i|D|u, 0<<1, which has its characteristic flow constant at infinity, so that no differentiability of the symbol is required there.     

Fourier multipliers on the real Hardy spaces

We provide a variant of Hytönen’s embedding theorem, which allows us to extend and unify several sufficient conditions for a function to be a Fourier multiplier on the real Hardy spaces.     

Existence and multiplicity of solutions for second order periodic systems with the <Emphasis Type="Italic">p</Emphasis>-Laplacian and a nonsmooth potential

In this paper we study nonlinear periodic systems driven by the ordinary p-Laplacian with a nonsmooth potential. We prove an existence theorem using a nonsmooth variant of the reduction method. We also prove two multiplicity results. The first is for scalar problems and uses the nonsmooth second deformation lemma. The second is for systems and it is based on the nonsmooth local linking theorem.     

(ω)性质及Weyl型定理

(ω)性质是Rakocevic给出的Weyl定理的一种变化.本文通过定义新的谱集,给出了有界线性算子同时满足(ω)性质和a-Weyl定理的充要条件.同时,利用所得的主要结论,研究了H(p)算子的(ω)性质.     

New restriction estimates for the 3-d paraboloid over finite fields

We improve the range of exponents for the restriction problem for the 3-d paraboloid over finite fields. The key new ingredient is a variant of the Bourgain–Katz–Tao finite field incidence theorem derived from sum-product estimates. In prime order fields, we give an explicit relationship between the exponent in this incidence theorem and restriction estimates for the paraboloid.     

A Łoś type theorem for linear metric formulas

We define an ultraproduct of metric structures based on a maximal probability charge and prove a variant of ?o? theorem for linear metric formulas. We also consider iterated ultraproducts (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Note on Property(ω)

In this note we study the property(ω),a variant of Weyl's theorem introduced by Rakoevic,by means of the new spectrum.We establish for a bounded linear operator defined on a Banach space a necessary and sufficient condition for which both property(ω) and approximate Weyl's theorem hold.As a consequence of the main result,we study the property(ω) and approximate Weyl's theorem for a class of operators which we call the λ-weak-H(p) operators.     

On reality and asymptotics of zeros of -Hankel transforms

We give sufficient conditions which guarantee that the finite q-Hankel transforms have only real zeros which satisfy some asymptotic relations. The study is carried out using two different techniques. The first is by a use of Rouché's theorem and the other is by applying a theorem of Hurwitz and Biehler. In every study further restrictions are imposed on q(0,1). We compare the results via some interesting applications involving second and third q-Bessel functions as well as q-trigonometric functions.