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Mathematics and statistics journals publish papers on the theory and application of mathematics, statistics, and probability. Most mathematics journals have a broad scope that encompasses most mathematical fields. These commonly include logic and foundations, algebra and number theory, analysis (including differential equations, functional analysis and operator theory), geometry, topology, combinatorics, probability and statistics, numerical analysis and computation theory, mathematical physics, etc.

# Mathematics and Statistics

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# Seiberg–Witten Floer Homotopy Contact Invariant

Studia Scientiarum Mathematicarum Hungarica
Authors: Nobuo Iida and Masaki Taniguchi

We introduce a Floer homotopy version of the contact invariant introduced by Kronheimer–Mrowka–Ozsváth–Szabó. Moreover, we prove a gluing formula relating our invariant with the first author’s Bauer–Furuta type invariant, which refines Kronheimer–Mrowka’s invariant for 4-manifolds with contact boundary. As an application, we give a constraint for a certain class of symplectic fillings using equivariant KO-cohomology.

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# Upsilon Invariants from Cyclic Branched Covers

Studia Scientiarum Mathematicarum Hungarica
Authors: Antonio Alfieri, Daniele Celoria, and András Stipsicz

We extend the construction of Y-type invariants to null-homologous knots in rational homology three-spheres. By considering m-fold cyclic branched covers with m a prime power, this extension provides new knot concordance invariants $YmC(K)$ of knots in S3. We give computations of some of these invariants for alternating knots and reprove independence results in the smooth concordance group.

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# Inequalities for the First and Second Derivatives of Algebraic Polynomials on an Ellipse

Mathematica Pannonica
Author: Tatiana M. Nikiforova

We prove a theorem on the preservation of inequalities between functions of a special form after differentiation on an ellipse. In particular, we obtain generalizations of the Duffin–Schaeffer inequality and the Vidensky inequality for the first and second derivatives of algebraic polynomials to an ellipse.

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# A Riemann–von Mangoldt-Type Formula for the Distribution of Beurling Primes

Mathematica Pannonica
Author: Szilárd Gy. Révész

In this paper we work out a Riemann–von Mangoldt type formula for the summatory function $ψx$:= $∑g∈G,g≤xΛGg$, where $G$ is an arithmetical semigroup (a Beurling generalized system of integers) and $ΛG$ is the corresponding von Mangoldt function attaining with a prime element $p∈G$ and zero otherwise. On the way towards this formula, we prove explicit estimates on the Beurling zeta function $ζG$ , belonging to $G$, to the number of zeroes of $ζG$ in various regions, in particular within the critical strip where the analytic continuation exists, and to the magnitude of the logarithmic derivative of $ζG$, under the sole additional assumption that Knopfmacher’s Axiom A is satisfied. We also construct a technically useful broken line contour to which the technic of integral transformation can be well applied. The whole work serves as a first step towards a further study of the distribution of zeros of the Beurling zeta function, providing appropriate zero density and zero clustering estimates, to be presented in the continuation of this paper.

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# A Theory of Congruences and Birkhoff’s Theorem for Matroids

Mathematica Pannonica
Author: Stefan Veldsman

A congruence is defined for a matroid. This leads to suitable versions of the algebraic isomorphism theorems for matroids. As an application of the congruence theory for matroids, a version of Birkhoff’s Theorem for matroids is given which shows that every nontrivial matroid is a subdirect product of subdirectly irreducible matroids.

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# The Metrics G = agS + bgH + cgV on the Tangent Bundle of a Weyl Manifold

Mathematica Pannonica
Author: Murat Altunbaş

Let (M, [g]) be a Weyl manifold and TM be its tangent bundle equipped with Riemannian g−natural metrics which are linear combinations of Sasaki, horizontal and vertical lifts of the base metric with constant coefficients. The aim of this paper is to construct a Weyl structure on TM and to show that TM cannot be Einstein-Weyl even if (M, g) is fiat.

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# Arithmetical Functions Commutable with Sums of Squares II

Mathematica Pannonica
Authors: Imre Kátai and Bui Minh Phong

We give all functions ƒ , E: ℕ → ℂ which satisfy the relation

for every a, b, c ∈ ℕ, where h ≥ 0 is an integers and K is a complex number. If n cannot be written as a2 + b2 + c2 + h for suitable a, b, c ∈ ℕ, then ƒ (n) is not determined. This is more complicated if we assume that ƒ and E are multiplicative functions.

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# Harvest Management Problem with a Fractional Logistic Equation

Mathematica Pannonica
Authors: Melani Barrios, Gabriela Reyero, and Mabel Tidball

In this article, we study a fractional control problem that models the maximization of the profit obtained by exploiting a certain resource whose dynamics are governed by the fractional logistic equation. Due to the singularity of this problem, we develop different resolution techniques, both for the classical case and for the fractional case. We perform several numerical simulations to make a comparison between both cases.

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# On the Negativity of the Walsh–Kaczmarz–Riesz Logarithmic Kernels

Mathematica Pannonica
Authors: György Gát and Gábor Lucskai

The main aim of this paper is to prove that the nonnegativity of the Riesz’s logarithmic kernels with respect to the Walsh– Kaczmarz system fails to hold.

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# Another Look at Threshold Phenomena for Random Cones

Studia Scientiarum Mathematicarum Hungarica
Authors: Daniel Hug and Rolf Schneider

In stochastic geometry there are several instances of threshold phenomena in high dimensions: the behavior of a limit of some expectation changes abruptly when some parameter passes through a critical value. This note continues the investigation of the expected face numbers of polyhedral random cones, when the dimension of the ambient space increases to infinity. In the focus are the critical values of the observed threshold phenomena, as well as threshold phenomena for differences instead of quotients.

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# From Binary Groups to Terminal Rings

Mathematica Pannonica
Author: Stuart D. Scott

Binary groups are a meaningful step up from non-associative rings and nearrings. It makes sense to study them in terms of their nearrings of zero-fixing polynomial maps. As this involves algebras of a more specialized nature these are looked into in sections three and four. One of the main theorems of this paper occurs in section five where it is shown that a binary group V is a P 0(V) ring module if, and only if, it is a rather restricted form of non-associative ring. Properties of these non-associative rings (called terminal rings) are investigated in sections six and seven. The finite case is of special interest since here terminal rings of odd order really are quite restricted. Sections eight to thirteen are taken up with the study of terminal rings of order p n (p an odd prime and n ≥ 1 an integer ≤ 7).

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# On Zero Determinant Matrices that are Full

Mathematica Pannonica
Authors: Grigore Călugăreanu and Horia F. Pop

Column-row products have zero determinant over any commutative ring. In this paper we discuss the converse. For domains, we show that this yields a characterization of pre-Schreier rings, and for rings with zero divisors we show that reduced pre-Schreier rings have this property.

Finally, for the rings of integers modulo n, we determine the 2x2 matrices which are (or not) full and their numbers.

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# Error Bounds Related to Midpoint and Trapezoid Rules for the Monotonic Integral Transform of Positive Operators in Hilbert Spaces

Mathematica Pannonica
Author: Silvestru Sever Dragomir

For a continuous and positive function w(λ), λ > 0 and μ a positive measure on (0, ∞) we consider the followingmonotonic integral transform

where the integral is assumed to exist forT a positive operator on a complex Hilbert spaceH. We show among others that, if β ≥ A, B ≥ α > 0, and 0 < δ ≤ (B − A)2 ≤ Δ for some constants α, β, δ, Δ, then

$0≤124δM″(w,μ)(β)≤M(w,μ)A+B2−∫01M(w,μ)((1−t)A+tB)dt≤−124ΔM″(w,μ)(α)$

and

$0≤−112δM″(w,μ)(β)≤∫01M(w,μ)((1−t)A+tB)dt−M(w,μ)(A)+M(w,μ)(B)2≤112ΔM″(w,μ)(α),$

where$M″(w,μ)$ is the second derivative of$M(w,μ)$ as a real function.

Applications for power function and logarithm are also provided.

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# Hankel Determinant of Second Order for Some Classes of Analytic Functions

Mathematica Pannonica
Authors: Milutin Obradović and Nikola Tuneski

Let ƒ be analytic in the unit disk B and normalized so that ƒ (z) = z + a2z2 + a3z3 +܁܁܁. In this paper, we give upper bounds of the Hankel determinant of second order for the classes of starlike functions of order α, Ozaki close-to-convex functions and two other classes of analytic functions. Some of the estimates are sharp.

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# Circles of Curvature at Points of Parabola in Isotropic Plane

Mathematica Pannonica
Authors: Vladimir Volenec, Marija Šimić Horvath, and Ema Jurkin

The authors have studied the curvature of the focal conic in the isotropic plane and the form of the circle of curvature at its points has been obtained. Hereby, we discuss several properties of such circles of curvature at the points of a parabola in the isotropic plane.

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# A Combinatorial Approach to the Stirling Numbers of the First Kind with Higher Level

Studia Scientiarum Mathematicarum Hungarica
Authors: Takao Komatsu, José L. Ramírez, and Diego Villamizar

In this paper, we investigate a generalization of the classical Stirling numbers of the first kind by considering permutations over tuples with an extra condition on the minimal elements of the cycles. The main focus of this work is the analysis of combinatorial properties of these new objects. We give general combinatorial identities and some recurrence relations. We also show some connections with other sequences such as poly-Cauchy numbers with higher level and central factorial numbers. To obtain our results, we use pure combinatorial arguments and classical manipulations of formal power series.

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# Corrigendum: Ideals of Residuated Lattices

Studia Scientiarum Mathematicarum Hungarica
Authors: Liviu-Constantin Holdon and Arsham Borumand Saeid
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# A Corson Compact Space is Countable if the Complement of its Diagonal is Functionally Countable

Studia Scientiarum Mathematicarum Hungarica

A space X is called functionally countable if ƒ (X) is countable for any continuous function ƒ : X → Ø. Given an infinite cardinal k, we prove that a compact scattered space K with d(K) > k must have a convergent k+-sequence. This result implies that a Corson compact space K is countable if the space (K × K) \ ΔK is functionally countable; here ΔK = {(x, x): x ϵ K} is the diagonal of K. We also establish that, under Jensen’s Axiom ♦, there exists a compact hereditarily separable non-metrizable compact space X such that (X × X) \ ΔX is functionally countable and show in ZFC that there exists a non-separable σ-compact space X such that (X × X) \ ΔX is functionally countable.

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# Criterion for the Coincidence of Strong and Weak Orlicz Spaces

Studia Scientiarum Mathematicarum Hungarica
Authors: Maria Rosaria Formica and Eugeny Ostrovsky

We provide necessary and sufficient conditions for the coincidence, up to equivalence of the norms, between strong and weak Orlicz spaces. Roughly speaking, this coincidence holds true only for the so-called exponential spaces.

We also find the exact value of the embedding constant which appears in the corresponding norm inequality.

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# Heegaard Floer Homology, Degree-One Maps and Splicing Knot Complements

Studia Scientiarum Mathematicarum Hungarica
Authors: Narges Bagherifard and Eaman Eftekhary

Suppose that K and K' are knots inside the homology spheres Y and Y', respectively. Let X = Y (K, K') be the 3-manifold obtained by splicing the complements of K and K' and Z be the three-manifold obtained by 0 surgery on K. When Y' is an L-space, we use the splicing formula of [1] to show that the rank of $HY^$(X ) is bounded below by the rank of $HY^$(Y ) if τ(K 2) = 0 and is bounded below by rank($HY^$(Z)) − 2 rank($HY^$(Y)) + 1 if τ(K') ≠ 0.

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# The “k = 1” Case of a Problem of Greene and Kleitman from 1976: Join-Irreducible Elements in the Lattice of Sperner 1-Families

Mathematica Pannonica
Author: Jonathan David Farley

Let k ≥ 1. A Sperner k-family is a maximum-sized subset of a finite poset that contains no chain with k + 1 elements. In 1976 Greene and Kleitman defined a lattice-ordering on the set Sk(P) of Sperner k-families of a fifinite poset P and posed the problem: “Characterize and interpret the join- and meet-irreducible elements of Sk(P),” adding, “This has apparently not been done even for the case k = 1.”

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# Localization Operators and Uncertainty Principles for the Hankel Wavelet Transform

Studia Scientiarum Mathematicarum Hungarica
Authors: Saifallah Ghobber, Siwar Hkimi, and Slim Omri

The aim of this paper is to prove some uncertainty inequalities for the continuous Hankel wavelet transform, and study the localization operator associated to this transformation.

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# A Note on Generating a Power Basis over a Dedekind Ring

Studia Scientiarum Mathematicarum Hungarica
Authors: Abdulaziz Deajim and Lhoussain El Fadil

In this note, we show that the result [1, Proposition 5.2] is inaccurate. We further give and prove the correct modification of such a result. Some applications are also given.

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# On Power Integral Bases for Certain Pure Number Fields Defined by x36 − m

Studia Scientiarum Mathematicarum Hungarica

Let K = ℚ(α) be a number field generated by a complex root a of a monic irreducible polynomial ƒ (x) = x36 − m, with m ≠ ±1 a square free rational integer. In this paper, we prove that if m ≡ 2 or 3 (mod 4) and m ≠ ±1 (mod 9) then the number field K is monogenic. If m ≡ 1 (mod 4) or m ≡±1 (mod 9), then the number field K is not monogenic.

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# Real Hypersurfaces in ℂP2 and ℂH2 with Cyclic Parallel ∗-Ricci Tensor

Studia Scientiarum Mathematicarum Hungarica
Authors: Yaning Wang and Wenjie Wang

In this paper, we prove that the ∗-Ricci tensor of a real hypersurface in complex projective plane ℂP 2 or complex hyperbolic plane ℂH 2 is cyclic parallel if and only if the hypersurface is of type (A). We find some three-dimensional real hypersurfaces having non-vanishing and non-parallel ∗-Ricci tensors which are cyclic parallel.

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# Some Functional Upper Bounds for Fejér’s Sine Polynomial

Studia Scientiarum Mathematicarum Hungarica
Authors: Jing Quan Chong, Xing Chen Huang, Tuo Yeong Lee, Jing Tao Li, Hui Xiang Sim, Jing Ren Soh, Gabriel Jiaxu Tan, and Jay Kin Heng Tai

We prove that

for all integers n ≥ 1 and ɵ ≤ 8 ≤ π. This result refines inequalities due to Jackson (1911) and Turán (1938).

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# Unmixed and Cohen–Macaulay Weighted Oriented Kőnig Graphs

Studia Scientiarum Mathematicarum Hungarica
Authors: Yuriko Pitones, Enrique Reyes, and Rafael H. Villarreal

Let D be a weighted oriented graph, whose underlying graph is G, and let I (D) be its edge ideal. If G has no 3-, 5-, or 7-cycles, or G is Kőnig, we characterize when I (D) is unmixed. If G has no 3- or 5-cycles, or G is Kőnig, we characterize when I (D) is Cohen–Macaulay. We prove that I (D) is unmixed if and only if I (D) is Cohen–Macaulay when G has girth greater than 7 or G is Kőnig and has no 4-cycles.

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# Weighted Measures of Pseudorandom Binary Lattices

Studia Scientiarum Mathematicarum Hungarica
Authors: Huaning Liu and Yinyin Yang

In cryptography one needs pseudorandom sequences whose short subsequences are also pseudorandom. To handle this problem, Dartyge, Gyarmati and Sárközy introduced weighted measures of pseudorandomness of binary sequences. In this paper we continue the research in this direction. We introduce weighted pseudorandom measure for multidimensional binary lattices and estimate weighted pseudorandom measure for truly random binary lattices. We also give lower bounds for weighted measures of even order and present an example by using the quadratic character of finite fields.

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# Hyperspace of finite unions of convergent sequences

Studia Scientiarum Mathematicarum Hungarica
Authors: JingLing Lin, Fucai Lin, and Chuan Liu

The symbol S(X) denotes the hyperspace of finite unions of convergent sequences in a Hausdor˛ space X. This hyper-space is endowed with the Vietoris topology. First of all, we give a characterization of convergent sequence in S(X). Then we consider some cardinal invariants on S(X), and compare the character, the pseudocharacter, the sn-character, the so-character, the network weight and cs-network weight of S(X) with the corresponding cardinal function of X. Moreover, we consider rank k-diagonal on S(X), and give a space X with a rank 2-diagonal such that S(X) does not Gδ-diagonal. Further, we study the relations of some generalized metric properties of X and its hyperspace S(X). Finally, we pose some questions about the hyperspace S(X).

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# The Erdős–Rényi Law and Strong Limit Theorems of Probability

Studia Scientiarum Mathematicarum Hungarica
Author: Andrei N. Frolov

Fifty years ago P. Erdős and A. Rényi published their famous paper on the new law of large numbers. In this survey, we describe numerous results and achievements which are related with this paper or motivated by it during these years.

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# Finite Groups with Some Subgroups of Sylow Subgroups s∗-Semipermutable

Studia Scientiarum Mathematicarum Hungarica
Authors: Qingjun Kong and Xiuyun Guo

We introduce a new subgroup embedding property in a finite group called s -semipermutability. Suppose that G is a finite group and H is a subgroup of G. H is said to be s -semipermutable in G if there exists a subnormal subgroup K of G such that G = HK and H ∩ K is s-semipermutable in G. We fix in every non-cyclic Sylow subgroup P of G some subgroup D satisfying 1 < |D| < |P | and study the structure of G under the assumption that every subgroup H of P with |H | = |D| is s -semipermutable in G. Some recent results are generalized and unified.

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# Ideals of Residuated Lattices

Studia Scientiarum Mathematicarum Hungarica
Authors: Liviu-Constantin Holdon and Arsham Borumand Saeid

In this article, we study ideals in residuated lattice and present a characterization theorem for them. We investigate some related results between the obstinate ideals and other types of ideals of a residuated lattice, likeness Boolean, primary, prime, implicative, maximal and ʘ-prime ideals. Characterization theorems and extension property for obstinate ideal are stated and proved. For the class of ʘ-residuated lattices, by using the ʘ-prime ideals we propose a characterization, and prove that an ideal is an ʘ-prime ideal iff its quotient algebra is an ʘ-residuated lattice. Finally, by using ideals, the class of Noetherian (Artinian) residuated lattices is introduced and Cohen’s theorem is proved.

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# Interpolation by Differences In H∞

Studia Scientiarum Mathematicarum Hungarica
Authors: Francesc Tugores and Laia Tugores

We pose an interpolation problem for the space of bounded analytic functions in the disk. The interpolation is performed by a function and its di˛erence of values in points whose subscripts are related by an increasing application. We impose that the data values satisfy certain conditions related to the pseudohyperbolic distance, and characterize interpolating sequences in terms of uniformly separated subsequences.

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# Nearly s-Semipermutable Subgroups

Studia Scientiarum Mathematicarum Hungarica
Author: Changwen Li

In this paper, we investigate the infiuence of nearly s-semipermutable subgroups on the structure of finite groups. Several recent results from the literature are improved and generalized.

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# On Some Continued Fractions and Series

Studia Scientiarum Mathematicarum Hungarica
Authors: Khalil Ayadi, Chiheb Ben Bechir, and Iheb Elouaer

We exhibit some explicit continued fraction expansions and their representation series in different fields. Some of these continued fractions have a type of symmetry, known as folding symmetry. We will extracted those whose are specialized.

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# Polynomial Entropy of the Logistic Map

Studia Scientiarum Mathematicarum Hungarica
Author: Milan Perić

We study the polynomial entropy of the logistic map depending on a parameter, and we calculate it for almost all values of the parameter. We show that polynomial entropy distinguishes systems with a low complexity (i.e. for which the topological entropy vanishes).

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# Some Landau–Kolmogorov Type Inequalities for Differential Operators Generated by Polynomials

Studia Scientiarum Mathematicarum Hungarica
Authors: Vu Nhat Huy, Nguyen Ngoc Huy, and Chu Van Tiep
In this paper, we establish some Landau–Kolmogorov type inequalities for differential operators generated by polynomials in the following form
$P(D)fp≤K1(ε,P)fq+K2(ε,m)Dm(P(D)f)p$

for all $ε>0$ , where 0 < gp ≤ ∞, and the differential operator P (D) is obtained from the polynomial P (x) by substituting$x→−i∂/∂x$ . Moreover, the explicit form of $K1(ε,p)$ and $K2(ε,m)$

are given.

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# A Unified Version of Weighted Weak Type Inequality for Martingale Maximal Operators

Studia Scientiarum Mathematicarum Hungarica
Authors: Yanbo Ren and Congbian Ma
Let ɣ and Φ1 be nondecreasing and nonnegative functions defined on [0, ∞), and Φ2 is an N -function, u, v and w are weights. A unified version of weighted weak type inequality of the form
$Φ1(λ)ℙu(f*>λ)≤C𝔼Φ2Cf∞υγ(λ)w$

for martingale maximal operators f is considered, some necessary and su@cient conditions for it to hold are shown. In addition, we give a complete characterization of three-weight weak type maximal inequality of martingales. Our results generalize some known results on weighted theory of martingale maximal operators.

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# Weak Solutions for Obstacle Problems with Weak Monotonicity

Studia Scientiarum Mathematicarum Hungarica
Authors: Farah Balaadich and Elhoussine Azroul

This paper is concerned with the existence of weak solutions for obstacle problems. By means of the Young measure theory and a theorem of Kinderlehrer and Stampacchia, we obtain the needed result.

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# Limiting distributions associated with moments of exponential Brownian functionals

Studia Scientiarum Mathematicarum Hungarica
Authors: Y. Hariya and M. Yor

During the last decade, a number of explicit results about the distributions of exponential functionals of Brownian motion with drift: have been obtained, often originating with the works of D. Dufresne.

In the present paper, we rely extensively on these results to show the existence of limiting measures as$T→∞$, when the law of ${Bt+μt,0≤_t≤_T}$ is perturbed by the Radon-Nikodym density consisting of either of the normalized functionals exp $(−αAT(μ))$ or $1/(AT(μ))m$. The results exhibit different regimes according to whether in the first case, and to a partition of the $(μ,m)$-plane in the second case.

Although a large number of similar studies have been made for, say, one-dimensional diffusions, the present study, which focuses upon Brownian exponential functionals, appears to be new.

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# Automorphisms of Finite Order of Soluble Groups of Finite Rank

Studia Scientiarum Mathematicarum Hungarica
Author: Bertram A. F. Wehrfritz

We study the effect on sections of a soluble-by-finite group G of finite rank of an almost fixed-point-free automorphism φ of G of finite order. We also elucidate the structure of G if φ has order 4 and if G is also (torsion-free)-by-finite. The latter extends recent work of Xu, Zhou and Liu.

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# Borel Directions and the Uniqueness of Algebroid Functions Dealing with Multiple Values

Studia Scientiarum Mathematicarum Hungarica
Authors: Yang Tan and Qingcai Zhang

In this paper, we investigate the uniqueness of algebroid functions in angular domain by the method of conformal mapping. We discuss the relations between the Borel directions and uniquenss with the multiple values of algebroid functions and obtain some results which extend some uniqueness results of meromorphic functions to that of algebroid functions.

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# Estimates of Functions with Transformed Double Fourier Series

Studia Scientiarum Mathematicarum Hungarica
Author: Boris V. Simonov

The paper provides a detailed study of inequalities of complete moduli of smoothness of functions with transformed Fourier series by moduli of smoothness of initial functions. Upper and lower estimates of the norms and best approximations of the functions with transformed Fourier series by the best approximations of initial functions are also obtained.

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# Exceptional Set in Waring–Goldbach Problem Involving Squares, Cubes and Sixth Powers

Studia Scientiarum Mathematicarum Hungarica
Authors: Jinjiang Li, Min Zhang, and Haonan Zhao

Let N be a sufficiently large integer. In this paper, it is proved that, with at most O(N 119/270+ s) exceptions, all even positive integers up to N can be represented in the form $p12+p22+p33+p43+p56+p66,$

where p 1 , p 2 , p 3 , p 4 , p 5 , p 6 are prime numbers.

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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)-Kirchhoff-type equations with Robin boundary data as follows:

$−M∫Ω1p(x)∇up(x)dx+∫∂Ωβ(x)p(x)∇up(x)dσdiv(∇up(x)-2∇u)=f(x,u)inΩ,$

Where $β∈L∞(∂Ω)$ and $f:Ω×ℝ→ℝ$ satisfies 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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# A Note on Weakly 𐒎 -Subgroups

Studia Scientiarum Mathematicarum Hungarica
Author: Changwen Li

The major aim of the note is to give new brief proofs of the results in the paper “The influence of weakly H -subgroups on the structure of finite groups” [Studia Scientiarum Mathematicarum Hungarica, 51 (1), 27–40 (2014)].

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# On the Maximal Operators of T Means with Respect to Walsh–Kaczmarz System

Studia Scientiarum Mathematicarum Hungarica
Authors: Nata Gogolashvili and George Tephnadze

In this paper we prove and discuss some new (Hp, Lp,∞) type inequalities of the maximal operators of T means with monotone coefficients with respect to Walsh–Kaczmarz system. It is also proved that these results are the best possible in a special sense. As applications, both some well-known and new results are pointed out. In particular, we apply these results to prove a.e. convergence of such T means.

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# Sticky Polymatroids on At Most Five Elements

Studia Scientiarum Mathematicarum Hungarica
Author: László Csirmaz

The sticky polymatroid conjecture states that any two extensions of the polymatroid have an amalgam if and only if the polymatroid has no non-modular pairs of flats. We show that the conjecture holds for polymatroids on five or less elements.

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Mathematica Pannonica
Author: Péter Berkics

A linear operator on a Hilbert space $ℍ$, in the classical approach of von Neumann, must be symmetric to guarantee self-adjointness. However, it can be shown that the symmetry could be omitted by using a criterion for the graph of the operator and the adjoint of the graph. Namely, S is shown to be densely defined and closed if and only if $k+l:k,l∈GS∩GS*=ℍ$.

In a more general setup, we can consider relations instead of operators and we prove that in this situation a similar result holds. We give a necessary and sufficient condition for a linear relation to be densely defined and self-adjoint.

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# Conceptions of Topological Transitivity on Symmetric Products

Mathematica Pannonica
Authors: Franco Barragán, Sergio Macías, and Anahí Rojas

Let X be a topological space. For any positive integer n, we consider the n-fold symmetric product of X, ℱn(X), consisting of all nonempty subsets of X with at most n points; and for a given function ƒ : XX, we consider the induced functions ℱn(ƒ): ℱn(X) → ℱn(X). Let M be one of the following classes of functions: exact, transitive, ℤ-transitive, ℤ+-transitive, mixing, weakly mixing, chaotic, turbulent, strongly transitive, totally transitive, orbit-transitive, strictly orbit-transitive, ω-transitive, minimal, I N, T T++, semi-open and irreducible. In this paper we study the relationship between the following statements: ƒM and ℱn(ƒ) ∈ M.

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