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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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# Existence results for a class of p(x)-Kirchhoff problems

Studia Scientiarum Mathematicarum Hungarica
Author: Mostafa Allaoui

This paper is concerned with the existence of solutions to a class of p(x)-Kirchhofftype equations with Robin boundary data as follows: $−M(∫Ω1p(x)|∇u|p(x)dx+∫∂Ωβ(x)p(x)|∇u|p(x)dσ)div(|∇u|p(x)−2∇u)=f(x,u)$ in Ω, $|∇u|p(x)−2∂u∂v+β(x)|u|p(x)−2u=0$ on ∂Ω, where βL (∂Ω) and f : Ω × $ℝ$$ℝ$ satisfies the Carathéodory condition. By means of variational methods and the theory of the variable exponent Sobolev spaces, we establish conditions for the existence of weak solutions.

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# Extreme 2-homogeneous polynomials on the plane with a hexagonal norm and applications to the polarization and unconditional constants

Studia Scientiarum Mathematicarum Hungarica
Author: Sung Guen Kim

We classify the extreme 2-homogeneous polynomials on $ℝ$ 2 with the hexagonal norm of weight ½. As applications, using its extreme points with the Krein-Milman Theorem, we explicitly compute the polarization and unconditional constants of $P(2ℝh(12)2)$.

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# General normal forms for any additive logic

Studia Scientiarum Mathematicarum Hungarica
Author: Mohamed Khaled

In this article, we define general normal forms for any logic that has propositional part and whose non-propositional connectives distribute over finite disjunctions. We do not require the non-propositional connectives to be closed on the set of formulas, so our normal forms cover logics with partial connectives too. We also show that most of the known normal forms in the literature are in fact particular cases of our general forms. These general normal forms are natural improvement of the distributive normal forms of J. Hintikka [6] and their modal analogues, e.g. [1] and [4].

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# On osp(n|2)-relative cohomology on ℝ1|n

Studia Scientiarum Mathematicarum Hungarica
Authors: Nizar Ben Fraj, Hafedh Khalfoun, and Imed Basdouri

We compute the second differential osp(n|2)-relative cohomology of the Lie superalgebra К(n) of contact vector fields with coefficients in the superspace of weighted densities on the (1, n)-dimensional real superspace, n > 1, where osp(n|2) is the orthosymplectic Lie superalgebra. We explicitly give 2-cocycles spanning theses cohomology spaces. This work is the simplest generalization of a result by Basdouri [ On osp(1|2)-Relative Cohomology on S 1|1. Communications in Algebra 42:4, 1698–1710 (2014)].

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