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On dual hyperbolic numbers with generalized Jacobsthal numbers components
In this paper, we introduce the generalized dual hyperbolic Jacobsthal numbers. As special cases, we deal with dual hyperbolic Jacobsthal and dual...
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Generalized hyper-Lucas numbers and applications
In this paper, we give some combinatorial properties of a new generalization of hyper-Lucas numbers in order to extend the Cassini determinant. We...
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On dual hyperbolic generalized Fibonacci numbers
In this paper, we introduce the generalized dual hyperbolic Fibonacci numbers. As special cases, we deal with dual hyperbolic Fibonacci and dual...
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A Note on Special Matrices Involving k-Bronze Fibonacci Numbers
In this work, we consider a generalization of the Bronze Fibonacci sequence, called the k-Bronze Fibonacci sequence, in which the recurrence formula...
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From Fibonacci Sequence to More Recent Generalisations
Number sequences have been the subject of several research studies. From the algebraic properties to the generating matrices and generating functions...
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On generalization for Tribonacci Trigintaduonions
The trigintaduonions form a 32-dimensional Cayley–Dickson algebra. In this paper, we intend to make a new approach to introduce the concept of...
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Properties of Multivariate b-Ary Stern Polynomials
Given an integer base b ≥ 2, we investigate a multivariate b-ary polynomial analogue of Stern’s diatomic sequence which arose in the study of hyper...
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Spherical coordinates from persistent cohomology
We describe a method to obtain spherical parameterizations of arbitrary data through the use of persistent cohomology and variational optimization....
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Divisibility properties of hyperharmonic numbers
We extend Wolstenholme’s theorem to hyperharmonic numbers. Then, we obtain infinitely many congruence classes for hyperharmonic numbers using...
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Look Back
All four problems are based on the operation of subtraction, the computation of differences. A practical scenario is the measurement of length....
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On the bounds for the spectral norms of geometric circulant matrices
In this paper, we define a geometric circulant matrix whose entries are the generalized Fibonacci numbers and hyperharmonic Fibonacci numbers. Then...
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Distances on Numbers, Polynomials, and Matrices
Here we consider the most important metrics on the classical number systems: the semiring...
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Rogers-Ramanujan Functions, Modular Functions, and Computer Algebra
Many generating functions for partitions of numbers are strongly related to modular functions. This article introduces such connections using the...
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On the harmonic and hyperharmonic Fibonacci numbers
In this paper, we study the theory of the harmonic and the hyperharmonic Fibonacci numbers. Also, we get some combinatoric identities like as...
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Rational integrability of trigonometric polynomial potentials on the flat torus
We consider a lattice ℒ ⊂ ℝ n and a trigonometric potential V with frequencies k ∈ ℒ. We then prove a strong rational integrability condition on V ,...
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Linear Forms in Logarithms
Hilbert’s problems form a list of twenty-three problems in mathematics published by David Hilbert, a German mathematician, in 1900. The problems were...
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Problems related to graph indices in trees
In this chapter we explore recent development on various problems related to graph indices in trees. We focus on indices based on distances between...