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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
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 2^{ n } ⊕ 1 can be characterized by the property of not having a * homomorphism onto 2^{ i } ⊕ 1 for 1 < i < n.
In this article, this question is answered.
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 Stolarskytype inequality is obtained. We study the properties of the linear functional related to the new Stolarskytype 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 highorder 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 𝑑dimensional Euclidean space. The 𝑟ball 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–Santalótype inequalities for 𝑟ball bodies: for all 0 < 𝑘 < 𝑑 and for any set of given 𝑑dimensional volume in 𝔼 ^{𝑑} the 𝑘th intrinsic volume of the 𝑟ball 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 L_{k} ’s, which determine the graphical shapes of χ^{2} statistics. This means that the denominator q_{m} of mth convergent and the large partial quotient a_{m} _{+1} determine the outline of shapes of graphs, when we observe values of χ ^{2} statistics with step q_{m} .
In this note, we introduce the concept of semi*IFP, the involutive version of semiIFP, 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}, … , x_{n}
) ∈ E^{n}
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 settheoretic 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.
We give all solutions of completely multiplicative functions ƒ , g, for which the equation Ag(n + 1) = Bƒ (n) + C holds for every n ∈ ℕ. We also study the equation G(p + 1) = F(p − 1) + D and we prove some results concerning it.
We consider a graph whose vertices are legally colored using k colors and ask if the graph contains a kclique. As it turns out this very special type of kclique problem is in an intimate connection with constructing schedules. The practicality this clique search based construction of schedules is checked by carrying out numerical experiments.
Assume that A_{j} , j ∈ {1, … , m} are positive definite matrices of order n. In this paper we prove among others that, if 0 < l I_{n} ≤ A_{j} , j ∈ {1, … , m} in the operator order, for some positive constant l, and I_{n} is the unity matrix of order n, then
where Pk ≥ 0 for k ϵ {1, …, m} and
The evolute of a conic in the pseudoEuclidean plane is the locus of centers of all its osculating circles. It’s a curve of order six and class four in general case. In this paper we discuss and compute the order and class of evolutes of different types of conics. We will highlight those cases that have no analogy in the Euclidean plane.
Fast [12] is credited with pioneering the field of statistical convergence. This topic has been researched in many spaces such as topological spaces, cone metric spaces, and so on (see, for example [19, 21]). A cone metric space was proposed by Huang and Zhang [17]. The primary distinction between a cone metric and a metric is that a cone metric is valued in an ordered Banach space. Li et al. [21] investigated the definitions of statistical convergence and statistical boundedness of a sequence in a cone metric space. Recently, Sakaoğlu and Yurdakadim [29] have introduced the concepts of quasistatistical convergence. The notion of quasi Istatistical convergence for triple and multiple index sequences in cone metric spaces on topological vector spaces is introduced in this study, and we also examine certain theorems connected to quasi Istatistically convergent multiple sequences. Finally, we will provide some findings based on these theorems.
For a graph G, we define the lower bipartite number LB(G) as the minimum order of a maximal induced bipartite subgraph of G. We study the parameter, and the related parameter bipartite domination, providing bounds both in general graphs and in some graph families. For example, we show that there are arbitrarily large 4connected planar graphs G with LB(G) = 4 but a 5connected planar graph has linear LB(G). We also show that if G is a maximal outerplanar graph of order n, then LB(G) lies between (n + 2)/3 and 2 n/3, and these bounds are sharp.
We study the path behavior of the symmetric walk on some special combtype subsets of ℤ^{2} which are obtained from ℤ^{2} by generalizing the comb having finitely many horizontal lines instead of one.
In a typical maximum clique search algorithm when optimality testing is inconclusive a forking takes place. The instance is divided into smaller ones. This is the branching step of the procedure. In order to ensure a balanced work load for the processors for parallel algorithms it is essential that the resulting smaller problems are do not overly vary in difficulty. The socalled splitting partitions of the nodes of the given graph were introduced earlier to meliorate this problem. The paper proposes a splitting partition of the edges for the same purpose. In the lack of available theoretical tools we assess the practical feasibility of constructing suboptimal splitting edge partitions by carrying out numerical experiments. While working with splitting partitions we have realized that they can be utilized as preconditioning tools preliminary to a large scale clique search. The paper will discuss this new found role of the splitting edge partitions as well.
In this paper, we introduce the notion of a Gel’fand Γsemiring and discuss the various characterization of simple, kideal, strong ideal, tsmall elements and additively cancellative elements of a Gel’fand Γsemiring R, and prove that the set of additively cancellative elements, set of all tsmall elements of R and set of all maximal ideal of R are strong ideals. Further, let R be a simple Gel’fand Γsemiring and 1 ≠ t ∈ R. Let M be the set of all maximal left (right) ideals of R. Then an element x of R is tsmall if and only if it belongs to every maximal one sided left (right)ideal of R containing t.
For a continuous and positive function w(λ), λ > 0 and μ a positive measure on (0, ∞) we consider the following integral transform
where the integral is assumed to exist for t > 0.
We show among others that D(w, μ) is operator convex on (0, ∞). From this we derive that, if f : [0, ∞) → R is an operator monotone function on [0, ∞), then the function [f(0) f(t)] t
^{1} is operator convex on (0, ∞). Also, if f : [0, ∞) → R is an operator convex function on [0, ∞), then the function
under some natural assumptions for the positive operators A and B are given. Examples for power, exponential and logarithmic functions are also provided.
Problem 2 of Welsh’s 1976 text Matroid Theory, asking for criteria telling when two families of sets have a common transversal, is solved.
Another unsolved problem in the text Matroid Theory, on whether the “join” of two nondecreasing submodular functions is submodular, is answered in the negative. This resolves an issue first raised by Pym and Perfect in 1970.
This manuscript deals with the global existence and asymptotic behavior of solutions for a Kirchhoff beam equation with internal damping. The existence of solutions is obtained by using the FaedoGalerkin method. Exponential stability is proved by applying Nakao’s theorem.
We consider hypersphere x = x(u, v, w) in the four dimensional Euclidean space. We calculate the Gauss map, and the curvatures of it. Moreover, we compute the second LaplaceBeltrami operator the hypersphere satisfying Δ^{II}x = Ax, where A ϵ Mat (4,4).
In this paper, we show a Marcinkiewicz type interpolation theorem for Orlicz spaces. As an application, we obtain an existence result for a parabolic equation in divergence form.
Let E, G be Fréchet spaces and F be a complete locally convex space. It is observed that the existence of a continuous linear not almost bounded operator T on E into F factoring through G causes the existence of a common nuclear Köthe subspace of the triple (E, G, F). If, in addition, F has the property (y), then (E, G, F) has a common nuclear Köthe quotient.
In this paper we study the sum
In this paper we derive new inequalities involving the generalized Hardy operator. The obtained results generalized known inequalities involving the Hardy operator. We also get new inequalities involving the classical Hardy–Hilbert inequality.
The bipartite domination number of a graph is the minimum size of a dominating set that induces a bipartite subgraph. In this paper we initiate the study of this parameter, especially bounds involving the order, the ordinary domination number, and the chromatic number. For example, we show for an isolatefree graph that the bipartite domination number equals the domination number if the graph has maximum degree at most 3; and is at most half the order if the graph is regular, 4colorable, or has maximum degree at most 5.
This short note deals with polynomial interpolation of complex numbers verifying a Lipschitz condition, performed on consecutive points of a given sequence in the plane. We are interested in those sequences which provide a bound of the error at the first uninterpolated point, depending only on its distance to the last interpolated one.
For a lattice L of finite length n, let RCSub(L) be the collection consisting of the empty set and those sublattices of L that are closed under taking relative complements. That is, a subset X of L belongs to RCSub(L) if and only if X is joinclosed, meetclosed, and whenever {a, x, b} ⊆ S, y ∈ L, x ∧ y = a, and x ∨ y = b, then y ∈ S. We prove that (1) the poset RCSub(L) with respect to set inclusion is lattice of length n + 1, (2) if RCSub(L) is a ranked lattice and L is modular, then L is 2distributive in András P. Huhn’s sense, and (3) if L is distributive, then RCSub(L) is a ranked lattice.
In this paper, centralizing (semicentralizing) and commuting (semicommuting) 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 (semicentralizing) derivations of prime semirings. Further, we observe that if there exists a skewcommuting (skewcentralizing) 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 ^{ d 1 } x ^{ d 2 } = 0, for all x ∈ S implies either d _{1} = 0 or d _{2} = 0.
We offer new properties of the special Gini mean S(a, b) = a^{a} ^{/(} ^{a} ^{+} ^{b} ^{)} ⋅ b^{b} ^{/(} ^{a} ^{+} ^{b} ^{)}, in connections with other special means of two arguments.
We treat a variation of graph domination which involves a partition (V _{1}, V _{2},..., V_{k} ) 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.
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 dcomplete posets, is proven.
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.
We prove certain Menontype identities associated with the subsets of the set {1, 2,..., n} and related to the functions f, f_{k} , Ф and Ф _{k} , defined and investigated by Nathanson.
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.
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.
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.
We prove the weak consistency of the trimmed least square estimator of the covariance parameter of an AR(1) process with stable errors.
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.
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.
In this paper we work out a Riemann–von Mangoldt type formula for the summatory function
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.
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 EinsteinWeyl even if (M, g) is fiat.
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 a^{2} + b^{2} + c^{2} + 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.
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.
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.