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On trigonometric sums with random frequencies

Studia Scientiarum Mathematicarum Hungarica
Authors: Alina Bazarova, István Berkes, and Marko Raseta

We prove that if I k are disjoint blocks of positive integers and n k are independent random variables on some probability space (Ω,F,P) such that n k is uniformly distributed on I k, then $N−1/2∑k=1N(sin2πnkx−E(sin2πnkx))$ has, with P-probability 1, a mixed Gaussian limit distribution relative to the probability space ((0, 1),B, λ), where B is the Borel σ-algebra and λ is the Lebesgue measure. We also investigate the case when n k have continuous uniform distribution on disjoint intervals I k on the positive axis.

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Approximation in weighted generalized grand smirnov classes

Studia Scientiarum Mathematicarum Hungarica
Authors: Daniyal M. Israfilov and Ahmet Testici

Let G be a finite simple connected domain in the complex plane C, bounded by a Carleson curve Γ := ∂G. In this work the direct and inverse theorems of approximation theory by the algebraic polynomials in the weighted generalized grand Smirnov classes εp),θ(G,ω) and $εp),θ(G−,ω)$, 1 < p < ∞, in the term of the rth, r = 1, 2,..., mean modulus of smoothness are proved. As a corollary the constructive characterizations of the weighted generalized grand Lipschitz classes are obtained.

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A characterization of signed discrete infinitely divisible distributions

Studia Scientiarum Mathematicarum Hungarica
Authors: Huiming Zhang, Bo Li, and G. Jay Kerns

In this article, we give some reviews concerning negative probabilities model and quasi-infinitely divisible at the beginning. We next extend Feller’s characterization of discrete infinitely divisible distributions to signed discrete infinitely divisible distributions, which are discrete pseudo compound Poisson (DPCP) distributions with connections to the Lévy-Wiener theorem. This is a special case of an open problem which is proposed by Sato (2014), Chaumont and Yor (2012). An analogous result involving characteristic functions is shown for signed integer-valued infinitely divisible distributions. We show that many distributions are DPCP by the non-zero p.g.f. property, such as the mixed Poisson distribution and fractional Poisson process. DPCP has some bizarre properties, and one is that the parameter λ in the DPCP class cannot be arbitrarily small.

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The drazin invertibility of an anti-triangular matrix over a ring

Studia Scientiarum Mathematicarum Hungarica
Authors: Honglin Zou, Jianlong Chen, and Dijana Mosić

Let R be a ring. The purpose of this paper is to study the existence and the representation for the anti-triangular matrix $[abc0]$ under some conditions, where a, b, cR. The results extend recent works given in the literature.

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Generalized q-starlike functions

Studia Scientiarum Mathematicarum Hungarica
Authors: Khalida Inayat Noor and Sadia Riaz

In this paper, we introduce a new concept of q-bounded radius rotation and define the class R*m(q), m ≥ 2, q ∈ (0, 1). The class R*2(q) coincides with S*q which consists of q-starlike functions defined in the open unit disc. Distortion theorems, coefficient result and radius problem are studied. Relevant connections to various known results are pointed out.

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Infinitely many solutions for semilinear Δλ-Laplace equations with sign-changing potential and nonlinearity

Studia Scientiarum Mathematicarum Hungarica
Authors: Jianhua Chen, Xianhua Tang, and Zu Gao

In this paper, we prove the existence of infinitely many solutions for the following class of boundary value elliptic problems ${−Δλu+V(x)u=f(x,u),x∈Ω,u=0,x∈∂Ω,$ where Ω is a bounded domain in RN (N ≥ 2), Δλ is a strongly degenerate elliptic operator, V (x) is allowing to be sign-changing and f is a function with a more general super-quadratic growth, which is weaker than the Ambrosetti-Rabinowitz type condition.

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On some differential subordinations

Studia Scientiarum Mathematicarum Hungarica
Authors: Mamoru Nunokawa and Janusz Sokół

The purpose of this work is to present a new geometric approach to some problems in differential subordination theory. We also discuss the new results closely related to the generalized Briot-Bouquet differential subordination.

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On star-C-Hurewicz spaces

Studia Scientiarum Mathematicarum Hungarica
Author: Yankui Song

A space X is star-C-Hurewicz if for each sequence (U n : nN) of open covers of X there exists a sequence (K n : nN) of countably compact subsets of X such that for each xX, xSt(K n, Unn) for all but finitely many n. In this paper, we investigate the relationship between star-C-Hurewicz spaces and related spaces, and study topological properties of star-C-Hurewicz spaces.

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On the distributions of quadratic residues and primitive roots over finite fields

Studia Scientiarum Mathematicarum Hungarica
Author: The-Anh Ta

We give estimates for the number of quadratic residue and primitive root values of polynomials in two variables over finite fields.

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Weakly linearly lindelöf monotonically normal spaces are lindelöf

Studia Scientiarum Mathematicarum Hungarica
Authors: István Juhász, Vladimir V. Tkachuk, and Richard G. Wilson

A space X is weakly linearly Lindelöf if for any family U of non-empty open subsets of X of regular uncountable cardinality κ, there exists a point xX such that every neighborhood of x meets κ-many elements of U. We also introduce the concept of almost discretely Lindelöf spaces as the ones in which every discrete subspace can be covered by a Lindelöf subspace. We prove that, in addition to linearly Lindelöf spaces, both weakly Lindelöf spaces and almost discretely Lindelöf spaces are weakly linearly Lindelöf.

The main result of the paper is formulated in the title. It implies that every weakly Lindelöf monotonically normal space is Lindelöf, a result obtained earlier in [3].

We show that, under the hypothesis 2ω < ω ω, if the co-diagonal Δc X = (X × X) \ΔX is discretely Lindelöf, then X is Lindelöf and has a weaker second countable topology; here ΔX = {(x, x): xX} is the diagonal of the space X. Moreover, discrete Lindelöfness of Δc X together with the Lindelöf Σ-property of X imply that X has a countable network.

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