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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
Following previous observations on 𝑞-Appell and 𝑞-Lauricella functions, the purpose of this article is to find canonical 𝑞-difference equations for the four intermediate 𝑞-Lauricella functions
We prove that, when 𝑛 goes to infinity, Kostant’s problem has negative answer for almost all simple highest weight modules in the principal block of the BGG category O for the Lie algebra sl𝑛(ℂ).
Recent results have provided important functional generalizations, extensions and improvements of the Hardy and Levinson integral inequalities. However, they require some assumptions on the main functions, such as monotonicity or convexity assumptions, which remain somewhat restrictive. In this article, we propose two new ideas of functional generalizations, one based on a series expansion approach and the other on an integral approach. Both achieve the goal of offering adaptable generalizations and extensions of the Hardy and Levinson integral inequalities. They are formulated in two different general theorems, which are proved in detail. Several examples of new integral inequalities are derived.
Let {𝐿𝑛}≥0 be the sequence of Lucas numbers. In this paper, we determine all Lucas numbers that are palindromic concatenations of two distinct repdigits.
The Erdős Matching Conjecture states that the maximum size 𝑓 (𝑛, 𝑘, 𝑠) of a family
In this short note, we are concerned with the case 𝑠 ≥ 3 fixed, 𝑘 tending to infinity and 𝑛 ∈ {𝑠𝑘, 𝑠𝑘 + 1}. For 𝑛 = 𝑠𝑘, we show the stability of the unique extremal construction of size
We study the property of Kelley and the property of Kelley weakly on Hausdorff continua. We extend results known for metric continua to the class of Hausdorff continua. We also present new results about these properties.
The aim of this paper is to study the interrelationship between various forms of (F, G)-shadowing property and represent it through the diagram. We show that asymptotic shadowing is equivalent to (ℕ0, F 𝑐𝑓 )-shadowing property and that (ℕ0, F 𝑐𝑓 )-shadowing implies (F 𝑐𝑓 , F 𝑐𝑓 )-shadowing. Necessary examples are discussed to support the diagram. We also give characterization for maps to have the (F, G)-shadowing property through the shift map on the inverse limit space. Further, we relate the (F, G)-shadowing property to the positively F 𝑠-expansive map. Also, we obtain the necessary and sufficient condition for the identity map to have (ℕ0, F 𝑡)-shadowing property.
In this article, we present new results on specific cases of a general Young integral inequality established by Páles in 1990. Our initial focus is on a bivariate function, defined as the product of two univariate and separable functions. Based on this, some new results are established, including particular Young integral-type inequalities and some upper bounds on the corresponding absolute errors. The precise role of the functions involved in this context is investigated. Several applications are presented, including one in the field of probability theory. We also introduce and study reverse variants of our inequalities. Another important contribution is to link the setting of the general Young integral inequality established by Páles to a probabilistic framework called copula theory. We show that this theory provides a wide range of functions, often dependent on adjustable parameters, that can be effectively applied to this inequality. Some illustrative graphics are provided. Overall, this article broadens the scope of bivariate inequalities and can serve related purposes in analysis, probability and statistics, among others.
In this work we single out a scheduling problem in which tasks are coupled and the time delay between the first and second members of the couple is fixed by technological constraints. We will show that this scheduling problem can be reduced to the question to decide if a tactically constructed 𝑘-partite auxiliary graph contains a 𝑘-clique. We will point out that before submitting the auxiliary graph to a clique solver it is expedient to carry out various inspections in order to delete nodes and edges of the graph and consequently speed up the computations. In the lack of theoretical tools we will carry out numerical experiments to test the practicality of the clique approach.
In this paper, we define the discretized Voros–Li coefficients associated to the zeta function on function fields of genus 𝑔 over a finite fields 𝔽𝑞. Furthermore, we give a finite sum representation, an integral formula and an asymptotic formula for these coefficients.
In this article, we use the idea of “negation” to construct new unit distributions, i.e., continuous distributions with support equal to the unit interval [0, 1]. A notable feature of these distributions is that they have opposite shape properties to the unit distributions from which they are derived; “opposite” in the sense that, from a graphical point of view, a certain horizontal symmetry is operated. We then examine the main properties of these negation-type distributions, including distributional functions, moments, and entropy measures. Finally, concrete examples are described, namely the negation-type power distribution, the negation-type [0, 1]-truncated exponential distribution, the negation-type truncated [0, 1]-sine distribution, the negation-type [0, 1]-truncated Lomax distribution, the negation-type Kumaraswamy distribution, and the negation-type beta distribution. Some of their properties are studied, also with the help of graphics that highlight their original modeling behavior. After the analysis, it appears that the negation-type Kumaraswamy distribution stands out from the others by combining simplicity with a high degree of flexibility, in a sense completing the famous Kumaraswamy distribution. Overall, our results enrich the panel of unit distributions available in the literature with an innovative approach.
This paper is mainly about direct summand right ideals of nearrings with 𝐷𝐶𝐶𝑁 which cannot be expressed as a non-trivial direct sum. A fairly natural condition (Φ-irreducibility) makes it possible to study these right ideals in reasonable depth. It turns out they are either very ring like or right ideals (called shares) controlling considerable nearring structure. The two cases are studied in some detail. A surprising feature of the last section is that, with weak hypercentrality present, the nearring is a unique finite direct sum of these right ideals if, and only if, all such right ideals are ideals.
In the present paper we aim to calculate with the exclusive use of real methods, an atypical harmonic series with a weight 4 structure, featuring the harmonic number of the kind 𝐻2𝑘. Very simple relations and neat results are considered for the evaluation of the main series.
This article describes a general analytical derivation of the Fuss’ relation for bicentric polygons with an odd number of vertices. In particular, we derive the Fuss’ relations for the bicentric tridecagon and the bicentric pentadecagon.
Let 𝑀𝑘 be the 𝑘-th Mulatu number. Let 𝑟, 𝑠 be non-zero integers with 𝑟 ≥ 1 and 𝑠 ∈ {−1, 1}, let {𝑈𝑛}𝑛≥0 be the generalized Lucas sequence and {𝑉𝑛}𝑛≥0 its companion given respectively by 𝑈𝑛+2 = 𝑟𝑈𝑛+1 + 𝑠𝑈𝑛 and 𝑉𝑛+2 = 𝑟𝑉𝑛+1 + 𝑠𝑉𝑛, with 𝑈0 = 0, 𝑈1 = 1, 𝑉0 = 2, 𝑉1 = 𝑟. In this paper, we give effective bounds for the solutions of the following Diophantine equations 𝑀𝑘 = 𝑈𝓁𝑈𝑚𝑈𝑛 and 𝑀𝑘 = 𝑉𝓁𝑉𝑚𝑉𝑛, where 𝓁, 𝑚, 𝑛 and 𝑘 are nonnegative integers and 𝓁 ≤ 𝑚 ≤ 𝑛. Then, we explicitly solve the above Diophantine equations for the Fibonacci, Pell, Balancing sequences and their companions respectively.
Let 𝑛 ≥ 2. A continuous 𝑛-linear form 𝑇 on a Banach space 𝐸 is called norm-peak if there is a unique (𝑥1, … , 𝑥𝑛) ∈ 𝐸𝑛 such that ║𝑥1║ = … = ║𝑥𝑛║ = 1 and for the multilinear operator norm it holds ‖𝑇 ‖ = |𝑇 (𝑥1, … , 𝑥𝑛)|.
Let 0 ≤ 𝜃 ≤
In this note, we characterize all norm-peak multilinear forms on
In this paper we introduce a construction for a weighted CW complex (and the associated lattice cohomology) corresponding to partially ordered sets with some additional structure. This is a generalization of the construction seen in [4] where we started from a system of subspaces of a given vector space. We then proceed to prove some basic properties of this construction that are in many ways analogous to those seen in the case of subspaces, but some aspects of the construction result in complexities not present in that scenario.
We prove zero density theorems for Dedekind zeta functions in the vicinity of the line Re s = 1, improving an earlier result of W. Staś.
A positive integer
Let (𝑃𝑛)𝑛≥0 and (𝑄𝑛)𝑛≥0 be the Pell and Pell–Lucas sequences. Let 𝑏 be a positive integer such that 𝑏 ≥ 2. In this paper, we prove that the following two Diophantine equations 𝑃𝑛 = 𝑏𝑑𝑃𝑚 + 𝑄𝑘 and 𝑃𝑛 = 𝑏𝑑𝑄𝑚 + 𝑃𝑘 with 𝑑, the number of digits of 𝑃𝑘 or 𝑄𝑘 in base 𝑏, have only finitely many solutions in nonnegative integers (𝑚, 𝑛, 𝑘, 𝑏, 𝑑). Also, we explicitly determine these solutions in cases 2 ≤ 𝑏 ≤ 10.
Grätzer and Lakser asked in the 1971 Transactions of the American Mathematical Society if the pseudocomplemented distributive lattices in the amalgamation class of the subvariety generated by 𝟐𝑛 ⊕ 𝟏 can be characterized by the property of not having a *-homomorphism onto 𝟐𝑖 ⊕ 𝟏 for 1 < 𝑖 < 𝑛.
In this article, their question from 1971 is answered.
This paper introduces and examines the concept of a *-Rickart *-ring, and proves that every Rickart *-ring is also a *-Rickart *-ring. A necessary and sufficient condition for a *-Rickart *-ring to be a Rickart *-ring is also provided. The relationship between *-Rickart *-rings and *-Baer *-rings is investigated, and several properties of *-Rickart *-rings are presented. The paper demonstrates that the property of *-Rickart extends to both the center and *-corners of a *-ring, and investigates the extension of a *-Rickart *-ring to its polynomial *-ring. Additionally, *-Rickart *-rings with descending chain condition on *-biideals are studied, and all *-Rickart (*-Baer) *-rings with finitely many elements are classified.
Very recently, the authors in [5] proposed the exponential-type operator connected with
A classical result of Dowker (Bull. Amer. Math. Soc. 50: 120-122, 1944) states that for any plane convex body 𝐾, the areas of the maximum (resp. minimum) area convex 𝑛-gons inscribed (resp. circumscribed) in 𝐾 is a concave (resp. convex) sequence. It is known that this theorem remains true if we replace area by perimeter, or convex 𝑛-gons by disk-𝑛-gons, obtained as the intersection of 𝑛 closed Euclidean unit disks. It has been proved recently that if 𝐶 is the unit disk of a normed plane, then the same properties hold for the area of 𝐶-𝑛-gons circumscribed about a 𝐶-convex disk 𝐾 and for the perimeters of 𝐶-𝑛-gons inscribed or circumscribed about a 𝐶-convex disk 𝐾, but for a typical origin-symmetric convex disk 𝐶 with respect to Hausdorff distance, there is a 𝐶-convex disk 𝐾 such that the sequence of the areas of the maximum area 𝐶-𝑛-gons inscribed in 𝐾 is not concave. The aim of this paper is to investigate this question if we replace the topology induced by Hausdorff distance with a topology induced by the surface area measure of the boundary of 𝐶.
In this paper, some basic characterizations of a weighted Bloch space with the differentiable strictly positive weight 𝜔 on the unit disc are given, including the growth, the higher order or free derivative descriptions, and integral characterizations of functions in the space.
We present examples of multiplicative semigroups of positive reals (Beurling’s generalized integers) with gaps bounded from below.
In this paper, we propose some new positive linear approximation operators, which are obtained from a composition of certain integral type operators with certain discrete operators. It turns out that the new operators can be expressed in discrete form. We provide representations for their coefficients. Furthermore, we study their approximation properties and determine their moment generating functions, which may be useful in finding several other convergence results in different settings.
Let 𝑓 be a normalized primitive cusp form of even integral weight for the full modular group Γ = 𝑆𝐿(2, ℤ). In this paper, we investigate upper bounds for the error terms related to the average behavior of Fourier coefficients 𝜆𝑓 ⊗𝑓 ⊗⋯⊗𝑙𝑓 (𝑛) of 𝑙-fold product 𝐿-functions, where 𝑓 ⊗ 𝑓 ⊗ ⋯ ⊗𝑙 𝑓 denotes the 𝑙-fold product of 𝑓. These results improves and generalizes the recent developments of Venkatasubbareddy and Sankaranarayanan [41]. We also provide some other similar results related to the error terms of general product 𝐿-functions.
We apply a recent general zero density theorem of us (valid for a large class of complex functions) to improve earlier density theorems of Heath-Brown and Paul–Sankaranarayanan for Dedekind zeta functions attached to a number field 𝐾 of degree 𝑛 with 𝑛 > 2.
Asymptotic uniform upper density, shortened as a.u.u.d., or simply upper density, is a classical notion which was first introduced by Kahane for sequences in the real line.
Syndetic sets were defined by Gottschalk and Hendlund. For a locally compact group 𝐺, a set 𝑆 ⊂ 𝐺 is syndetic, if there exists a compact subset 𝐶 ⋐ 𝐺 such that 𝑆𝐶 = 𝐺. Syndetic sets play an important role in various fields of applications of topological groups and semigroups, ergodic theory and number theory. A lemma in the book of Fürstenberg says that once a subset 𝐴 ⊂ ℤ has positive a.u.u.d., then its difference set 𝐴 − 𝐴 is syndetic.
The construction of a reasonable notion of a.u.u.d. in general locally compact Abelian groups (LCA groups for short) was not known for long, but in the late 2000’s several constructions were worked out to generalize it from the base cases of ℤ𝑑 and ℝ𝑑. With the notion available, several classical results of the Euclidean setting became accessible even in general LCA groups.
Here we work out various versions in a general locally compact Abelian group 𝐺 of the classical statement that if a set 𝑆 ⊂ 𝐺 has positive asymptotic uniform upper density, then the difference set 𝑆 − 𝑆 is syndetic.
Recently [3] we proved a general zero density theorem for a large class of functions which included among others the Riemann zeta function, Dedekind zeta functions, Dirichlet 𝐿-functions. The goal of the present work is a (slight) improvement of this general theorem which might lead to stronger results in some applications.
This paper serves as a kick-off to address the question of how to define and investigate the stability of bi-continuous semigroups. We will see that the mixed topology is the key concept in this framework.
An endo-commutative algebra is a nonassociative algebra in which the square mapping preserves multiplication. In this paper, we give a complete classification of 2-dimensional endo-commutative straight algebras of rank one over an arbitrary non-trivial field, where a straight algebra of dimension 2 satisfies the condition that there exists an element x such that x and x 2 are linearly independent. We list all multiplication tables of the algebras up to isomorphism.
In this paper, we consider the simultaneous sign changes of coefficients of Rankin–Selberg L-functions associated to two distinct Hecke eigenforms supported at positive integers represented by some certain primitive reduced integral binary quadratic form with negative discriminant D. We provide a quantitative result for the number of sign changes of such sequence in the interval (x, 2x] for sufficiently large x.
In this paper, we derive several asymptotic formulas for the sum of d(gcd(m,n)), where d(n) is the divisor function and m,n are in Piatetski-Shapiro and Beatty sequences.
Let 𝑛 ∈ ℕ. An element (x
1, … , x
𝑛) ∈ En
is called a norming point of T ∈
Norm(T) = {(x 1, … , x n) ∈ En ∶ (x 1, … , x n) is a norming point of T}.
Norm(T) is called the norming set of T. We classify Norm(T) for every T ∈
In this paper, we introduce and study the class of k-strictly quasi-Fredholm linear relations on Banach spaces for nonnegative integer k. Then we investigate its robustness through perturbation by finite rank operators.
We construct an algebra of dimension 2ℵ0 consisting only of functions which in no point possess a finite one-sided derivative. We further show that some well known nowhere differentiable functions generate algebras, which contain functions which are differentiable at some points, but where for all functions in the algebra the set of points of differentiability is quite small.
A proper edge coloring of a graph 𝐺 is strong if the union of any two color classes does not contain a path with three edges (i.e. the color classes are induced matchings). The strong chromatic index 𝑞(𝐺) is the smallest number of colors needed for a strong coloring of 𝐺. One form of the famous (6, 3)-theorem of Ruzsa and Szemerédi (solving the (6, 3)-conjecture of Brown–Erdős–Sós) states that 𝑞(𝐺) cannot be linear in 𝑛 for a graph 𝐺 with 𝑛 vertices and 𝑐𝑛2 edges. Here we study two refinements of 𝑞(𝐺) arising from the analogous (7, 4)-conjecture. The first is 𝑞𝐴(𝐺), the smallest number of colors needed for a proper edge coloring of 𝐺 such that the union of any two color classes does not contain a path or cycle with four edges, we call it an A-coloring. The second is 𝑞𝐵(𝐺), the smallest number of colors needed for a proper edge coloring of 𝐺 such that all four-cycles are colored with four different colors, we call it a B-coloring. These notions lead to two stronger and one equivalent form of the (7, 4)-conjecture in terms of 𝑞𝐴(𝐺), 𝑞𝐵(𝐺) where 𝐺 is a balanced bipartite graph. Since these are questions about graphs, perhaps they will be easier to handle than the original special(7, 4)-conjecture. In order to understand the behavior of 𝑞𝐴(𝐺) and 𝑞𝐵(𝐺), we study these parameters for some graphs.
We note that 𝑞𝐴(𝐺) has already been extensively studied from various motivations. However, as far as we know the behavior of 𝑞𝐵(𝐺) is studied here for the first time.
Over integral domains of characteristics different from 2, we determine all the matrices
We present generalizations of the Pinelis extension of Stolarsky’s inequality and its reverse. In particular, a new Stolarsky-type inequality is obtained. We study the properties of the linear functional related to the new Stolarsky-type inequality, and finally apply these new results in the theory of fractional integrals.
In this paper, we consider the Feuerbach point and the Feuerbach line of a triangle in the isotropic plane, and investigate some properties of these concepts and their relationships with other elements of a triangle in the isotropic plane. We also compare these relationships in Euclidean and isotropic cases.
We define the order of the double hypergeometric series, investigate the properties of the new confluent Kampé de Fériet series, and build systems of partial differential equations that satisfy the new Kampé de Fériet series. We solve the Cauchy problem for a degenerate hyperbolic equation of the second kind with a spectral parameter using the high-order Kampé de Fériet series. Thanks to the properties of the introduced Kampé de Fériet series, it is possible to obtain a solution to the problem in explicit forms.
Let 𝔼 𝑑 denote the 𝑑-dimensional Euclidean space. The 𝑟-ball body generated by a given set in 𝔼 𝑑 is the intersection of balls of radius 𝑟 centered at the points of the given set. The author [Discrete Optimization 44/1 (2022), Paper No. 100539] proved the following Blaschke–Santaló-type inequalities for 𝑟-ball bodies: for all 0 < 𝑘 < 𝑑 and for any set of given 𝑑-dimensional volume in 𝔼 𝑑 the 𝑘-th intrinsic volume of the 𝑟-ball body generated by the set becomes maximal if the set is a ball. In this note we give a new proof showing also the uniqueness of the maximizer. Some applications and related questions are mentioned as well.
We discuss the outline of the shapes of graphs of χ 2 statistics for distributions of leading digits of irrational rotations under some conditions on mth convergent. We give some estimates of important coefficients Lk ’s, which determine the graphical shapes of χ2 statistics. This means that the denominator qm of mth convergent and the large partial quotient am +1 determine the outline of shapes of graphs, when we observe values of χ 2 statistics with step qm .
In this note, we introduce the concept of semi-*-IFP, the involutive version of semi-IFP, which is a generalization of quasi-*-IFP and *-reducedness of *-rings. We study the basic structure and properties of *-rings having semi-*-IFP and give results for IFPs in rings with involution. Several results and counterexamples are stated to connect the involutive versions of IFP. We discuss the conditions for the involutive IFPs to be extended into *-subrings of the ring of upper triangular matrices. In *-rings with quasi-*-IFP, it is shown that Köthe’s conjecture has a strong affirmative solution. We investigate its related properties and the relationship between *-rings with quasi-*-IFP and *-Armendariz properties.
In the present paper, we establish the convergence rates of the single logarithm and the iterated logarithm for martingale differences which give some further results for the open question in Stoica [6].
Let n ∈ ℕ. An element (x
1, … , xn
) ∈ En
is called a norming point of
Norm(T) is called the norming set of T.
Let
In this paper, we classify Norm(T) for every
This article indicates another set-theoretic formula, solely in terms of union and intersection, for the set of the limits of any given sequence (net, in general) in an arbitrary T 1 space; this representation in particular gives a new characterization of a T 1 space.
