When is a spherical body of constant diameter of constant width?

Aequationes mathematicae - We prove that a smooth convex body of diameter $$\delta < \frac{\pi }{2}$$ on the d-dimensional unit sphere $$S^d$$ is of constant diameter $$\delta $$ if and only...     

The Euler—Kronecker constant

We consider lower bounds for the Euler—Kronecker constant in the case of number fields and upper and lower bounds in the case of algebraic manifolds over a finite field.     

A generalization of Euler’s constant

The purpose of this paper is to evaluate the limit γ(a) of the sequence , where a ∈ (0, + ∞ ).      

Submanifolds in S~N with constant mean curvature

1.IntroductionLet M be a submanifold in the unit sphere S~N.Denote by S the squarelength of the second foundamental form.Let H/n denote the mean curvatureof M and suppose that H=constant.In this paper,we have proved following:     

Ruzsa’s constant on additive functions

A function f : N → R is called additive if f(mn)= f(m)+f(n)for all m, n with(m, n)= 1. Let μ(x)= max n≤x(f(n)f(n + 1))and ν(x)= max n≤x(f(n + 1)f(n)). In 1979, Ruzsa proved that there exists a constant c such that for any additive function f , μ(x)≤ cν(x 2 )+ c f , where c f is a constant depending only on f . Denote by R af the least such constant c. We call R af Ruzsa's constant on additive functions. In this paper, we prove that R af ≤ 20.     

A variant of Davenport’s constant

Let p be a prime number. Let G be a finite abelian p-group of exponent n (written additively) and A be a non-empty subset of ]n[≔ {1, 2,…, n} such that elements of A are incongruent modulo p and non-zero modulo p. Let k ≥ D(G/|A| be any integer where D(G) denotes the well-known Davenport’s constant. In this article, we prove that for any sequence g ₁, g ₂,…, g _k (not necessarily distinct) in G, one can always extract a subsequence with 1 ≤ ℓ ≤ k such that

Computing Feigenbaum's δ constant using the Ricker map

The Feigenbaum constant δ is frequently met by students in a first course on chaos, and discussed with reference to the period doubling within the logistic map. The details of the actual calculation of δ are, however, nontrivial, and form the basis for an undergraduate project which may be used to develop skills in discrete maps and numerical methods. This paper considers how the Ricker map can be used to evaluate δ, and also suggests a number of problems which can be solved by students along the way.     

Packing constant for Cesàro-Orlicz sequence spaces

The packing constant is an important and interesting geometric parameter of Banach spaces. Inspired by the packing constant for Orlicz sequence spaces, the main purpose of this paper is calculating the Kottman constant and the packing constant of the Cesàro-Orlicz sequence spaces \(({\text{ce}}{{\text{s}}_\varphi })\) defined by an Orlicz function φ equipped with the Luxemburg norm. In order to compute the constants, the paper gives two formulas. On the base of these formulas one can easily obtain the packing constant for the Cesàro sequence space ces_p and some other sequence spaces. Finally, a new constant \(\widetilde D\)(X), which seems to be relevant to the packing constant, is given.     

Best constant in a three-parameter Poincaré inequality

We study the problem of finding the best constant in the generalized Poincaré inequality

Willmore surfaces of constant Möbius curvature

We study Willmore surfaces of constant Möbius curvature \({\mathcal{K}}\) in \({\mathbb{S}}^4\) . It is proved that such a surface in \({\mathbb{S}}^3\) must be part of a minimal surface in \({\mathbb{R}}^3\) or the Clifford torus. Another result in this paper is that an isotropic surface (hence also Willmore) in \({\mathbb{S}}^4\) of constant \({\mathcal{K}}\) could only be part of a complex curve in \({\mathbb{C}}^2 \cong {\mathbb{R}}^4\) or the Veronese 2-sphere in \({\mathbb{S}}^4\) . It is conjectured that they are the only possible examples. The main ingredients of the proofs are over-determined systems and isoparametric functions.     

Stanley–Reisner resolution of constant weight linear codes

Given a constant weight linear code, we investigate its weight hierarchy and the Stanley–Reisner resolution of its associated matroid regarded as a simplicial complex. We also exhibit conditions on the higher weights sufficient to conclude that the code is of constant weight.     

On pseudoanalyticity of continuous functions with constant σ-extension

The theorem on pseudoanalyticity of continuous functions with constant -extension is proved; this is an analog of the well known results due to Bohr, Rademacher, Men'shov, and Trokhimchuk concerning the analyticity of functions with constant extension.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 4, pp. 459–465, April, 1993.     

Stochastic Komatu–Loewner evolutions and BMD domain constant

For Komatu–Loewner equation on a standard slit domain, we randomize the Jordan arc in a manner similar to that of Schramm (2000) to find the SDEs satisfied by the induced motion $\xi \left(t\right)$ on $?\mathbb{H}$ and the slit motion $\mathbf{s}\left(t\right)$. The diffusion coefficient $\alpha$ and drift coefficient $b$ of such SDEs are homogeneous functions.Next with solutions of such SDEs, we study the corresponding stochastic Komatu–Loewner evolution, denoted as ${\mathrm{SKLE}}_{\alpha ,b}$. We introduce a function $b_{\mathrm{BMD}}$ measuring the discrepancy of a standard slit domain from $\mathbb{H}$ relative to BMD. We show that ${\mathrm{SKLE}}_{\sqrt{6},?b_{\mathrm{BMD}}}$ enjoys a locality property.     

Numerical estimates for a Grötzsch ring constant

Numerical lower and upper estimates are obtained for the constant λ_n defined by λn =lim _a→0(modR _G,n (a)+loga) associated with the Grötzsch extremal ringR _G,n (a) in euclideann-space, for 3≤n≤22. Improved lower estimates in terms ofn are provided for λ_n, the modulus ofR _G,n (a) is compared with its counterpart in the plane, and bounds for modR _G,n (a) are obtained that are of the correct order asa tends either to 0 or to 1. The ratio of the latter bounds is bounded by constants depending only onn.     

A low bound for the de Bruijn-newman constant Λ

Summary A lower bound is constructively found for the de Bruijn-Newman constant , which is related to the Riemann Hypothesis. This lower bound is determined by explicitly exhibiting an associated jensen polynomial with nonreal zeros.Dedicated to the memory of our good friend Peter Henrici (Sept. 13, 1923-March 13, 1987)Research supported by the Airforce Office of Scientific Research and the National Science Foundation