Related papers: Sur le minimum de la fonction de Brjuno
A special theorem related to the Fagnano's problem is proved and an example of the theorem is shown in a golden rectangle.
We defined several functionals on the set of all triangulations of the finite system of points in d-space achieving global minimum on the Delaunay triangulation (DT). We consider a so called "parabolic" functional and prove it attains its…
In this paper we investigate k-submodular functions. This natural family of discrete functions includes submodular and bisubmodular functions as the special cases k = 1 and k = 2 respectively. In particular we generalize the known…
We establish a quantitative lower bound on the reach of flat norm minimizers for boundaries in $\mathbb{R}^2$.
The paper explores the differential inclusion of a special form. It is supposed that the support function of the set in the right-hand side of an inclusion may contain the sum of the maximum and the minimum of the finite number of…
In this paper, we study the submodularity of the covolume function in global function fields. The submodular property is often needed in the study of homogeneous dynamics, especially to define a Margulis function. We proved that the…
We prove a general functional limit theorem for multiparameter fractional Brownian motion. The functional law of the iterated logarithm, functional L\'{e}vy's modulus of continuity and many other results are its particular cases.…
The aim of this paper is to present an original approach that takes advantage from the geometric features of strictly convex functions to tackle the problem of finding the minimum from another perspective. The general idea is that near the…
In the paper, some lower bounds for polygamma functions are refined.
We extend deconvolution in a periodic setting to deal with functional data. The resulting functional deconvolution model can be viewed as a generalization of a multitude of inverse problems in mathematical physics where one needs to recover…
In this note we prove optimal inequalities for bounded functions in terms of their deviation from their mean. These results extend and generalize some known inequalities due to Thong (2011) and Perfetti (2011)
The paper addresses the study and applications of a broad class of extended-real-valued functions, known as optimal value or marginal functions, which are frequently appeared in variational analysis, parametric optimization, and a variety…
We give a nontrivial lower bound for global dimension of a spherical fusion category.
This paper discusses the frequency function of multiple-valued Dirichlet minimizing functions in the special case when the domain and range are both two dimensional. It shows that the frequency function must be of value k/2 for some…
We consider functionals given by the sum of the perimeter and the double integral of some kernel $g:\mathbb R^N\times\mathbb R^N\to \mathbb R^+$, multiplied by a "mass parameter" $\varepsilon$. We show that, whenever $g$ is admissible,…
In this paper, we analyze some theoretical properties of the problem of minimizing a quadratic function with a cubic regularization term, arising in many methods for unconstrained and constrained optimization that have been proposed in the…
We discuss some surprising phenomena from basic calculus related to oscillating functions and to the theorem on the differentiability of inverse functions. Among other things, we see that a continuously differentiable function with a strict…
We give an elementary proof for new strict upper and lower bounds for the correction term in Ramanujan's approximation for the factorial function
By using definition of Golden derivative, corresponding Golden exponential function and Fibonomial coefficients, we introduce generating functions for Bernoulli-Fibonacci polynomials and related numbers. Properties of these polynomials and…
A class of distortions termed functional Bregman divergences is defined, which includes squared error and relative entropy. A functional Bregman divergence acts on functions or distributions, and generalizes the standard Bregman divergence…