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On the integrality of the second elementary symmetric function of $1,1/3^{s_{1}},...,1/(2n-1)^{s_{n-1}}

四川大学学报. 自然科学版, 2020
Let $d,m$ and $n$ be positive integers. In 1915, Theisinger proved that if $n\ge 2$, then the $n$-th harmonic sum $\sum_{k=1}^n\frac{1}{k}$ is not an integer.
Feng Yu-Lu, Zhao Wei
doaj

Estimating the $p$-adic valuation of the resultant

, 2021
Let $f$ and $g$ be two monic polynomials with integer coefficients and nonzero resultant $r$. Assume that $v_p(f(n))\ge s_1$ and $v_p(g(n))\ge s_2$ hold for all integers $n$ for some $s_1, s_2$ fixed non-negative integers. Let $S$ denote the maximum of $v_p(gcd(f(n),g(n)))$ over all integers $n$.
openaire +2 more sources

Novel Bernstein‐Kantorovich Type Operators

Mathematical Methods in the Applied Sciences, Volume 49, Issue 16, Page 17069-17095, 15 November 2026.
ABSTRACT In this paper, we introduce a novel class of Bernstein‐Kantorovich operators, denoted as K β n , θ $$ {K}_{\beta}^{n,\theta } $$ , parameterized by 0 < β < 1 $$ 0<\beta <1 $$ and θ > 0 $$ \theta >0 $$ . We first derive a recurrence formula that facilitates the computation of moments and central moments and provide explicit expressions for K β ...
Pembe Sabancigil, Nazim I. Mahmudov
wiley +1 more source

The $p$-Adic Valuation Trees for Quadratic Polynomials for Odd Primes [PDF]

, 2023
We examine the behavior of the sequences of $p$-adic valuations of quadratic polynomials with integer coefficients for an odd prime $p$ through tree representations.
Snyder, Rachel +5 more
core

On the p-adic valuations of values of Legendre polynomials

Research in Number Theory
We prove an explicit formula for the $p$-adic valuation of the Legendre polynomials $P_n(x)$ evaluated at a prime $p$, and generalize an old conjecture of the third author. We also solve a problem proposed by Cigler in 2017.
Max A. Alekseyev +3 more
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Amino Acid Functionalization Influences the Binding of Thiophene‐Vinylene‐Benzothiazolium‐Based Fluorescent Ligands to Protein Deposits in Tissue Sections With Alzheimer’s Disease Pathology

ChemMedChem, Volume 21, Issue 21, 12 November 2026.
Bi‐thiophene‐vinyl‐benzothiazolium (bTVBT) ligands with distinct amino acid functionalities displayed differential binding to protein aggregates in human brain tissue sections with Alzheimer's disease pathology. bTVBT‐G‐OMe showed staining of GT‐38‐positive tau aggregates, whereas staining was weaker for bTVBT‐E‐diOMe.
Linnea Björk +5 more
wiley +1 more source

The p-adic valuation of k-central binomial coefficients [PDF]

Acta Arithmetica, 2009
11 ...
Straub, Armin, Amdeberhan, Tewodros, Moll, Victor H. +2 more
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Cumulative Social Disadvantage and Disease Activity in Juvenile Idiopathic Arthritis: A Childhood Arthritis and Rheumatology Research Alliance Registry Study

Arthritis Care &Research, Volume 78, Issue 10, Page 1552-1563, October 2026.
Objective Social determinants of health (SDOH) contribute to juvenile idiopathic arthritis (JIA) disparities, but most studies have assessed SDOH independently rather than cumulatively across individual, family, and neighborhood levels. Using a socioecological framework, we investigated the relationship among cumulative social disadvantage ...
William Daniel Soulsby +448 more
wiley +1 more source

Hearing the Serre Invariant of a Compact p‐Adic Analytic Manifold

Mathematische Nachrichten, Volume 299, Issue 10, Page 3126-3138, October 2026.
ABSTRACT Using a previous novel way of defining kernel functions for Laplacian integral operators on a compact p$p$‐adic analytic manifold X$X$, one such operator Δ0s$\Delta _0^s$ with s∈R$s\in \mathbb {R}$ is applied to hearing the Serre invariant i(X)$i(X)$ by showing that a wavelet eigenvalue (with the wavelet having small support) is always ...
Patrick Erik Bradley, Ángel Morán Ledezma +1 more
wiley +1 more source

A 5-Adic Ultrametric Framework for Alignment-Free Phylogenetic Analysis of Hantavirus RNA Sequences

Mathematics
We develop a non-Archimedean framework for the representation and analysis of genomic sequences based on the arithmetic and geometric structure of the ring of 5-adic integers.
Anselmo Torresblanca-Badillo
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mathematics
diophantine equation