Browse Our Mathematics and Statistics Journals
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
We prove that the filtered GRID invariants of Legendrian links in link Floer homology, and consequently their associated invariants in the spectral sequence, obstruct decomposable Lagrangian cobordisms in the symplectization of the standard contact structure on ℝ3, strengthening a result by Baldwin, Lidman, and the fifth author.
In [3] it is shown, answering a question of Jordán and Nguyen [9], that universal rigidity of a generic bar-joint framework in ℝ1 depends on more than the ordering of the vertices. The graph 𝐺 that was used in that paper is a ladder with three rungs. Here we provide a general answer when that ladder with three rungs in the line is universally rigid and when it is not.
In this paper the author studies the problem of finding the farthest points in an intersection of balls to a given point 𝐶0. A polynomial algorithm is presented which solves the problem under the conditions that the given point is outside of the convex hull of the balls centers. It is shown that in this particular case the problem of finding the smallest ball centered in 𝐶0 which includes the intersection of balls is actually convex.
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.
Let 𝑛, 𝑠, 𝑣 be positive integers and F ⊂ 2[𝑛]. Suppose that the union of any 𝑠 sets of F has size at most 𝑠𝑣 and 𝑛 ≥ 2𝑠+3𝑣. The main result implies the best possible bound
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 the case of symmetries with respect to 𝑛 independent linear hyperplanes, a stability versions of the Logarithmic Brunn–Minkowski Inequality and the Logarithmic Minkowski Inequality for convex bodies are established.
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.
High proved the following theorem. If the intersections of any two congruent copies of a plane convex body are centrally symmetric, then this body is a circle. In our paper we extend the theorem of High to the sphere and the hyperbolic plane. Let us have in 𝑆2, ℝ2 or 𝐻2 a pair of convex bodies (for 𝑆2 different from 𝑆2), such that the intersections of any congruent copies of them are centrally symmetric. Then our bodies are congruent circles. If the intersections of any congruent copies of them are axially symmetric, then our bodies are (incongruent) circles. Let us have in 𝑆2, ℝ2 or 𝐻2 proper closed convex subsets 𝐾, 𝐿 with interior points, such that the numbers of the connected components of the boundaries of 𝐾 and 𝐿 are finite. If the intersections of any congruent copies of 𝐾 and 𝐿 are centrally symmetric, then 𝐾 and 𝐿 are congruent circles, or, for ℝ2, parallel strips. For ℝ2 we exactly describe all pairs of such subsets 𝐾, 𝐿, whose any congruent copies have an intersection with axial symmetry (there are five cases).
