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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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We consider a function from the Euclidean three space whose zero set is the image of the standard cuspidal edge. The composition of a parametrized singular surface in the three space with this function provides an approximation of the surface by the standard cuspidal edge. Taking a look at singularities of this composition, we study various approximations of singular surfaces like the cross cap, the generalized cuspidal edge and the swallowtail by standard cuspidal edges.

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Based on Peter’s work from 2003, quadrilaterals can be characterized in the following way: “among all quadrilaterals with given side lengths 𝑎, 𝑏, 𝑐 and 𝑑, those of the largest possible area are exactly the cyclic ones”. In this paper, we will give the corresponding characterization for every polygon, by means of quasicyclic polygons properties.

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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.

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We present examples of multiplicative semigroups of positive reals (Beurling’s generalized integers) with gaps bounded from below.

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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.

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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.

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The paper is devoted to some extremal problems for convex polygons on the Euclidean plane, related to the concept of self Chebyshev radius for the polygon boundary. We consider a general problem of minimization of the perimeter among all 𝑛-gons with a fixed self Chebyshev radius of the boundary. The main result of the paper is the complete solution of the mentioned problem for 𝑛 = 4: We proved that the quadrilateral of minimum perimeter is a so called magic kite, that verified the corresponding conjecture by Rolf Walter.

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Let 𝑛 ≥ 2 be an integer. The graph G n ¯ is obtained by letting all the elements of {0, … , 𝑛 − 1} to be the vertices and defining distinct vertices 𝑥 and 𝑦 to be adjacent if and only if gcd(𝑥 + 𝑦, 𝑛) ≠ 1. In this paper, we give some bounds for the Castelnuovo–Mumford regularity of the edge ideals and their powers for G n ¯ .

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Motivated by the examples of Heppes and Wegner, we present several other examples of the following kind: a bounded convex region 𝐷 and a convex disk 𝐾 in the plane are described, such that every thinnest covering of 𝐷 with congruent copies of 𝐾 contains crossing pairs.

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In this paper we show that the spherical cap discrepancy of the point set given by centers of pixels in the HEALPix tessellation (short for Hierarchical, Equal Area and iso-Latitude Pixelation) of the unit 2-sphere is lower and upper bounded by order square root of the number of points, and compute explicit constants. This adds to the currently known (short) collection of explicitly constructed sets whose discrepancy converges with order 𝑁 −1/2, matching the asymptotic order for i.i.d. random point sets. We describe the HEALPix framework in more detail and give explicit formulas for the boundaries and pixel centers. We then introduce the notion of an 𝑛-convex curve and prove an upper bound on how many fundamental domains are intersected by such curves, and in particular we show that boundaries of spherical caps have this property. Lastly, we mention briefly that a jittered sampling technique works in the HEALPix framework as well.

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