Related papers: On the third-order Horadam and geometric mean sequ…
The mixed-norm versions of the H\"older and Minkowski integral inequalities are used to produce new, general estimates involving symmetric geometric means of mixed norms. Various existing mixed-norm estimates are shown to be simple special…
We show how the recent improvement of the Hermite-Hadamard inequality can be applied to some (not necessarily convex) planar figures and three-dimensional bodies satisfying some kind of regularity.
The summation formula within pascalian triangle resulting in the fibonacci sequence is extended to the $q$-binomial coefficients $q$-gaussian triangles.
In terms of the derivative operator and three hypergeometric series identities, several interesting summation formulas involving generalized harmonic numbers are established.
These notes are based on a course for a general audience given at the Centro de Modeliamento Matem\'atico of the University of Chile, in December 2004. We study the mean convergence of multiple ergodic averages, that is, averages of a…
The Tribonacci sequence $\mathbb{T}$ is the fixed point of the substitution $\sigma(a,b,c)=(ab,ac,a)$. In this note, we give the explicit expressions of the numbers of distinct squares and cubes in $\mathbb{T}[1,n]$ (the prefix of…
The aim of this paper is the introduction of a new method for the numerical computation of the rank of a three-way array. We show that the rank of a three-way array over R is intimately related to the real solution set of a system of…
In this note we revisit the classical geometric-arithmetic mean inequality and find a formula for the difference of the arithmetic and the geometric means of given $n\in\mathbb N$ nonnegative numbers $x_1,x_2,\dots,x_n$. The formula yields…
In the last 30 years, the mathematical theory of aperiodic order has developed enormously. Many new tilings and properties have been discovered, few of which are covered or anticipated by the early papers and books. Here, we start from the…
The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.
After a Hessian computation, we quickly prove the 3D simplex mean width conjecture using classical methods. Then, we generalize some components to $d$ dimensions.
A dual approach to defining the triangle sequence (a type of multidimensional continued fraction algorithm, initially developed in NT/9906016) for a pair of real numbers is presented, providing a new, clean geometric interpretation of the…
Convolutions for Tribonacci numbers involving binomial coefficients are treated with ordinary generating functions and the diagonalization method of Hautus and Klarner. In this way, the relevant generating function can be established, which…
We study random homogenization of second-order, degenerate and quasilinear Hamilton-Jacobi equations which are positively homogeneous in the gradient. Included are the equations of forced mean curvature motion and others describing…
The purpose of this paper is to introduce the space of geometric sequences that are strongly summable with respect to an Orlicz function and the Fibonacci difference sequences.Also some topological properties and inclusion relations between…
This paper is dedicated to the analysis and detailed study of a procedure to generate both the weighted arithmetic and harmonic means of $n$ positive real numbers. Together with this interpretation, we prove some relevant properties that…
This paper presents new identities expressing the terms of Fibonacci, Lucas, and generalized Fibonacci sequences with multiple indices through powers of Lucas numbers and binomial coefficients. The obtained formulas rely on the application…
A Circumconic passes through a triangle's vertices. We define the Circumbilliard, a circumellipse to a generic triangle for which the latter is a 3-periodic. We study its properties and associated loci.
In this paper the approach to obtaining nonrecurrent formulas for some recursively defined sequences is illustrated. The most interesting result in the paper is the formula for the solution of quadratic map-like recurrence. Also, some…
We introduce the triangulant of two matrices, and relate it to the existence of orthogonal eigenvectors. We also use it for a new characterization of mutually unbiased bases. Generalizing the notion, we introduce higher order triangulants…