Results 1 to 10 of about 15 (15)
Identities Arising from Binomial-Like Formulas Involving Divisors of Numbers
Annales Mathematicae Silesianae, 2023 In this article, we derive a great number of identities involving the ω function counting distinct prime divisors of a given number n. These identities also include Pochhammer symbols, Fibonacci and Lucas numbers and many more.
Gryszka Karol
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CYCLOTOMIC POLYNOMIALS WITH PRESCRIBED HEIGHT AND PRIME NUMBER THEORY
Mathematika, Volume 67, Issue 1, Page 214-234, January 2021., 2021 Abstract Given any positive integer n, let A(n) denote the height of the nth cyclotomic polynomial, that is its maximum coefficient in absolute value. It is well known that A(n) is unbounded. We conjecture that every natural number can arise as value of A(n) and prove this assuming that for every pair of consecutive primes p and p′ with p⩾127, we have ...
Alexandre Kosyak +3 more
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Learning linear non-Gaussian graphical models with multidirected edges
Journal of Causal Inference, 2021 In this article, we propose a new method to learn the underlying acyclic mixed graph of a linear non-Gaussian structural equation model with given observational data.
Liu Yiheng, Robeva Elina, Wang Huanqing
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Inequalities between height and deviation of polynomials
Open Mathematics, 2021 In this paper, for polynomials with real coefficients P,QP,Q satisfying ∣P(x)∣≤∣Q(x)∣| P\left(x)| \le | Q\left(x)| for each xx in a real interval II, we prove the bound L(P)≤cL(Q)L\left(P)\le cL\left(Q) between the lengths of PP and QQ with a constant ...
Dubickas Artūras
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Several explicit formulas for (degenerate) Narumi and Cauchy polynomials and numbers
Open Mathematics, 2021 In this paper, with the aid of the Faà di Bruno formula and by virtue of properties of the Bell polynomials of the second kind, the authors define a kind of notion of degenerate Narumi numbers and polynomials, establish explicit formulas for degenerate ...
Qi Feng +2 more
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Cauchy-Riemann ̄∂-equations with some applications
Complex Manifolds, 2022 This paper shows that given 0 < p < 3 and a complex Borel measure µ on the unit disk 𝔻 the inhomogeneous Cauchy-Riemann ...
Xiao Jie, Yuan Cheng
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Demonstratio Mathematica, 2022 In this article, by virtue of expansions of two finite products of finitely many square sums, with the aid of series expansions of composite functions of (hyperbolic) sine and cosine functions with inverse sine and cosine functions, and in the light of ...
Qi Feng
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Combinatorial and harmonic-analytic methods for integer tilings
Forum of Mathematics, Pi, 2022 A finite set of integers A tiles the integers by translations if $\mathbb {Z}$ can be covered by pairwise disjoint translated copies of A. Restricting attention to one tiling period, we have $A\oplus B=\mathbb {Z}_M$ for some $M\in \mathbb {N}$ and $B ...
Izabella Łaba, Itay Londner
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Sums of Powers and Special Polynomials
Discussiones Mathematicae - General Algebra and Applications, 2020 In this paper, we discuss sums of powers 1p + 2p + + np and compute both the exponential and ordinary generating functions for these sums. We express these generating functions in terms of exponential and geometric polynomials and also show their ...
Boyadzhiev Khristo N.
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On some special Legendre sums of the form
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2017 We prove that sums of the form with f(X), g(X) ∈ ℤ[X] can be explicitly computed whenever f and g are subject to some certain conditions which are defined in the paper.
Andrica Dorin, Crişan Vlad
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