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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
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.
