Related papers: On the third-order Horadam and geometric mean sequ…
In this work, we made a generalization that includes all bicomplex Fibonacci-like numbers such as; Fibonacci, Lucas, Pell, etc.. We named this generalization as bicomplex Horadam numbers. For bicomplex Fibonacci and Lucas numbers we gave…
This paper analyses the convergence and degeneration of sequences of metrics on a 3-manifold, and relations of such with Thurston's geometrization conjecture. The sequences are minimizing sequences for a certain (optimal) scalar-curvature…
The geometric mean of two matrices is considered and analyzed from a computational viewpoint. Some useful theoretical properties are derived and an analysis of the conditioning is performed. Several numerical algorithms based on different…
We present a certain generalization of a recent result of M. I. Cirnu on linear recurrence relations with coefficient in progressions [2]. We provide some interesting examples related to some well-known integer sequences, such as Fibonacci…
In this paper, we define Tribonacci and Tribonacci-Lucas matrix sequences and investigate their properties.
The geometric median, a notion of center for multivariate distributions, has gained recent attention in robust statistics and machine learning. Although conceptually distinct from the mean (i.e., expectation), we demonstrate that both are…
We obtain universal affine type estimates for the location of the geometric medians of triangle perimeters and for the location of the geometric medians of triangular domains. At the end, some alternative implementations of the triangle…
We study the general rational trigonometry of a tetrahedron, based on quadrances, spreads and solid spreads, using vector products associated to an arbitrary symmetric bilinear form over a general field, not of characteristic two. This…
We present an approach to generalized Riordan arrays which is based on operations in one large group of lower triangular matrices. This allows for direct proofs of many properties of weighted Sheffer sequences, and shows that all the groups…
We prove elegant trilinear formulas connecting products of volumes of Euclidean tetrahedra with vertices taken from a given set of 6 points. We propose a way for generalizing those formulas.
We give an upper bound for the weighted geometric mean using the weighted arithmetic mean and the weighted harmonic mean. We also give a lower bound for the weighted geometric mean. These inequalities are proven for two invertible positive…
In this paper, we consider three families of numerical series with general terms containing the harmonic numbers, and we use simple methods from classical and complex analysis to find explicit formulas for their respective sums.
Our main result is the construction of symmetric Hadamard matrices of order q(1 + q) where q is a prime power congruent to 3 mod 8.
We show that essentially the Fibonacci sequence is the unique binary recurrence which contains infinitely many three-term arithmetic progressions. A criterion for general linear recurrences having infinitely many three-term arithmetic…
The objective of the present paper is to establish three Hardy-type inequalities in which the arithmetic mean over a sequence of non-negative real numbers is replaced by some weighted arithmetic mean over some nested subsets of the given…
The Tribonacci sequence $\mathbb{T}$ is the fixed point of the substitution $\sigma(a,b,c)=(ab,ac,a)$. In this note, we get the explicit expressions of all squares, and then establish the tree structure of the positions of repeated squares…
We study growth rates of generalised Fibonacci sequences of a particular structure. These sequences are constructed from choosing two real numbers for the first two terms and always having the next term be either the sum or the difference…
The geometrical theory of partial differential equations in the absolute sense, without any additional structures, is developed. In particular the symmetries need not preserve the hierarchy of independent and dependent variables. The order…
As is well-known, the ratio of adjacent Fibonacci numbers tends to phi = (1 + sqrt(5))/2, and the ratio of adjacent Tribonacci numbers (where each term is the sum of the three preceding numbers) tends to the real root eta of X^3 - X^2 - X -…
In this paper we define $n$th order Hessian structures on manifolds and study them. In particular, when $n = 3$, we make a detailed study and establish a one-to-one correspondence between {\it third-order Hessian structures} and a {\it…