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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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# On Derivations and Lie Ideals of Semirings

Mathematica Pannonica

In this paper, centralizing (semi-centralizing) and commuting (semi-commuting) derivations of semirings are characterized. The action of these derivations on Lie ideals is also discussed and as a consequence, some significant results are proved. In addition, Posner’s commutativity theorem is generalized for Lie ideals of semirings and this result is also extended to the case of centralizing (semi-centralizing) derivations of prime semirings. Further, we observe that if there exists a skew-commuting (skew-centralizing) derivation D of S, then D = 0. It is also proved that for any two derivations d 1 and d 2 of a prime semiring S with char S ≠ 2 and x d1 x d2 = 0, for all xS implies either d 1 = 0 or d 2 = 0.

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# In Memoriam István Győri

Mathematica Pannonica
Authors: Ferenc Hartung and Mihály Pituk
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# Convexity of Distinct Sum Sets

Studia Scientiarum Mathematicarum Hungarica
Author: Alexander Lemmens

We study a combinatorial notion where given a set S of lattice points one takes the set of all sums of p distinct points in S, and we ask the question: ‘if S is the set of lattice points of a convex lattice polytope, is the resulting set also the set of lattice points of a convex lattice polytope?’ We obtain a positive result in dimension 2 and a negative result in higher dimensions. We apply this to the corner cut polyhedron.

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# Degree Conditions for Claw-Free Graphs to Have Spanning Trees with at Most Five Branch Vertices and Leaves in Total

Studia Scientiarum Mathematicarum Hungarica
Author: Dang Dinh Hanh

A leaf of a tree is a vertex of degree one and a branch vertex of a tree is a vertex of degree at least three. In this paper, we show a degree condition for a claw-free graph to have spanning trees with at most five branch vertices and leaves in total. Moreover, the degree sum condition is best possible.

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# An Improved Constant Factor for the Unit Distance Problem

Studia Scientiarum Mathematicarum Hungarica
Authors: Péter Ágoston and Dömötör Pálvölgyi

We prove that the number of unit distances among n planar points is at most 1.94 • n 4/3, improving on the previous best bound of 8 n 4/3. We also give better upper and lower bounds for several small values of n. We also prove some variants of the crossing lemma and improve some constant factors.

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# Intersecting Hexagons in 3-Space

Studia Scientiarum Mathematicarum Hungarica
Authors: József Solymosi and Ching Wong

Two hexagons in the space are said to intersect heavily if their intersection consists of at least one common vertex as well as an interior point. We show that the number of hexagons on n points in 3-space without heavy intersections is o(n 2), under the assumption that the hexagons are ‘fat’.

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# Lazarsfeld-Mukai Bundles on K3 Surfaces Associated with a Pencil Computing the Clifford Index

Studia Scientiarum Mathematicarum Hungarica
Author: Sarbeswar Pal

Let X be a smooth projective K3 surface over the complex numbers and let C be an ample curve on X. In this paper we will study the semistability of the Lazarsfeld-Mukai bundle EC,A associated to a line bundle A on C such that |A| is a pencil on C and computes the Clifford index of C. We give a necessary and sufficient condition for EC,A to be semistable.

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# Realization of a Graph as the Reeb Graph of a Morse–Bott or a Round Function

Studia Scientiarum Mathematicarum Hungarica
Author: Irina Gelbukh

We prove criteria for a graph to be the Reeb graph of a function of a given class on a closed manifold: Morse–Bott, round, and in general smooth functions whose critical set consists of a finite number of submanifolds. The criteria are given in terms of whether the graph admits an orientation, which we call S-good orientation, with certain conditions on the degree of sources and sinks, similar to the known notion of good orientation in the context of Morse functions. We also study when such a function is the height function associated with an immersion of the manifold. The condition for a graph to admit an S-good orientation can be expressed in terms of the leaf blocks of the graph.

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# The Sl(2, )-Character Variety of a Montesinos Knot

Studia Scientiarum Mathematicarum Hungarica
Author: Haimiao Chen

For each Montesinos knot K, we propose an efficient method to explicitly determine the irreducible SL(2, )-character variety, and show that it can be decomposed as χ0(K)⊔χ1(K)⊔χ2(K)⊔χ'(K), where χ0(K) consists of trace-free characters χ1(K) consists of characters of “unions” of representations of rational knots (or rational link, which appears at most once), χ2(K) is an algebraic curve, and χ'(K) consists of finitely many points when K satisfies a generic condition.

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# On a Special Gini Mean

Mathematica Pannonica
Author: József Sándor

We offer new properties of the special Gini mean S(a, b) = aa /( a + b )bb /( a + b ), in connections with other special means of two arguments.

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# Distance Domination in Vertex Partitioned Graphs

Mathematica Pannonica
Authors: Allan Frendrup, Zsolt Tuza, and Preben Dahl Vestergaard

We treat a variation of graph domination which involves a partition (V 1, V 2,..., Vk) of the vertex set of a graph G and domination of each partition class V i over distance d where all vertices and edges of G may be used in the domination process. Strict upper bounds and extremal graphs are presented; the results are collected in three handy tables. Further, we compare a high number of partition classes and the number of dominators needed.

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# Proof of a Conjecture of Proctor and Scoppetta Related to d-Complete Posets

Mathematica Pannonica
Author: Jonathan David Farley

Proctor and Scoppetta conjectured that

• (1) there exists an infinite locally finite poset that satisfies their conditions VT and NTC but not SIS;

• (2) there exists an infinite locally finite poset satisfying their conditions D3-C and D3MF but not both VT and FT; and

• (3) there exists an infinite locally finite poset satisfying their conditions D3-C and D3MD but not NCC.

In this note, the conjecture of Proctor and Scoppetta, which is related to d-complete posets, is proven.

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# Hamilton Triangle of a Triangle in the Isotropic Plane

Mathematica Pannonica
Authors: Zdenka Kolar-Begović and Vladimir Volenec

In this paper we introduce the concept of the Hamilton triangle of a given triangle in an isotropic plane and investigate a number of important properties of this concept. We prove that the Hamilton triangle is homological with the observed triangle and with its contact and complementary triangles. We also consider some interesting statements about the relationships between the Hamilton triangle and some other significant elements of the triangle, like e.g. the Euler and the Feuerbach line, the Steiner ellipse and the tangential triangle.

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# Menon-Type Identities Concerning Subsets of the Set {1, 2,..., n}

Mathematica Pannonica
Author: László Tóth

We prove certain Menon-type identities associated with the subsets of the set {1, 2,..., n} and related to the functions f, fk, Ф and Фk, defined and investigated by Nathanson.

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# On the Almost Sure Central Limit Theorem Along Subsequences

Mathematica Pannonica
Authors: István Berkes and Endre Csáki

Generalizing results of Schatte [11] and Atlagh and Weber [2], in this paper we give conditions for a sequence of random variables to satisfy the almost sure central limit theorem along a given sequence of integers.

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# On the Mean Value of Arithmetic Error Terms

Mathematica Pannonica
Author: János Pintz

In the 1980’s the author proved lower bounds for the mean value of the modulus of the error term of the prime number theorem and other important number theoretic functions whose oscillation is in connection with the zeros of the Riemann zeta function. In the present work a general theorem is shown in a simple way which gives a lower bound for the mentioned mean value as a function of a hypothetical pole of the Mellin transform of the function. The conditions are amply satisfied for the Riemann zeta function. In such a way the results recover the earlier ones (even in a slightly sharper form). The obtained estimates are often optimal apart from a constant factor, at least under reasonable conditions as the Riemann Hypothesis. This is the case, in particular, for the error term of the prime number theorem.

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# Some Inequalities of Ostrowski Type for Double Integral Mean of Absolutely Continuous Functions

Mathematica Pannonica
Author: Silvestru Sever Dragomir

In this paper we establish some Ostrowski type inequalities for double integral mean of absolutely continuous functions. An application for special means is given as well.

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# Trimmed Least Square Estimators for Stable Ar(1) Processes

Mathematica Pannonica
Authors: Alina Bazarova, István Berkes, and Lajos Horváth

We prove the weak consistency of the trimmed least square estimator of the covariance parameter of an AR(1) process with stable errors.

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# Interval Chains and Completeness in Ultrapowers of Ordered Sets

Mathematica Pannonica
Authors: Zoltán Boros and Péter Tóth

The ultrapower T* of an arbitrary ordered set T is introduced as an infinitesimal extension of T. It is obtained as the set of equivalence classes of the sequences in T, where the corresponding relation is generated by a free ultrafilter on the set of natural numbers. It is established that T* always satisfies Cantor’s property, while one can give the necessary and sufficient conditions for T so that T* would be complete or it would fulfill the open completeness property, respectively. Namely, the density of the original set determines the open completeness of the extension, while independently, the completeness of T* is determined by the cardinality of T.

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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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