Results 61 to 70 of about 48,912 (312)
Hecke grids and congruences for weakly holomorphic modular forms
, 2013 Let $U(p)$ denote the Atkin operator of prime index $p$. Honda and Kaneko proved infinite families of congruences of the form $f|U(p) \equiv 0 \pmod{p}$ for weakly holomorphic modular forms of low weight and level and primes $p$ in certain residue ...
Ahlgren, Scott, Andersen, Nickolas
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Arthritis Care &Research, Accepted Article.Objective The objective of this study was to describe the longitudinal disease course and pulmonary outcomes of North American patients with melanoma differentiation‐associated gene 5 antibody (MDA5 ab) associated dermatomyositis (DM). Methods Thirty patients with MDA5 ab DM were identified in a single center longitudinal cohort of 352 patients with ...
Jenice X Cheah +8 more
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Arithmetic properties for Andrews’ (48,6)- and (48,18)-singular overpartitions
Open Mathematics, 2019 Singular overpartition functions were defined by Andrews. Let Ck,i(n) denote the number of (k, i)-singular overpartitions of n, which counts the number of overpartitions of n in which no part is divisible by k and only parts ±i (mod k) may be overlined ...
Liu Eric H., Du Wenjing
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Some Congruences for Sums Involving Harmonic Numbers
Cumhuriyet Science Journal, 2018 In this paper, we establish some congruences involving sums withharmonic numbers and the terms of second-order linear sequences.
Neşe Ömür, Sibel Koparal
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Advanced Functional Materials, EarlyView.A novel phthalocyanine (PC)‐based metal–organic framework (MOFs) is synthesized using ditopic PC linkers obtained through regioselective statistical condensation. The resulting MOF exhibits significant improvements in electronic absorption, thereby enhancing the material's performance in light harvesting and energy conversion.
Lukas S. Langer +12 more
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Proofs of Some Conjectures of Chan on Appell-Lerch Sums
, 2018 On page 3 of his lost notebook, Ramanujan defines the Appell-Lerch sum $$\phi(q):=\sum_{n=0}^\infty \dfrac{(-q;q)_{2n}q^{n+1}}{(q;q^2)_{n+1}^2},$$ which is connected to some of his sixth order mock theta functions. Let $\sum_{n=1}^\infty a(n)q^n:=\phi(q)$
Baruah, Nayandeep Deka +1 more
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Advanced Functional Materials, EarlyView.This study presents novel anti‐counterfeiting tags with multilevel security features that utilize additional disguise features. They combine luminescent nanosized Ln‐MOFs with conductive polymers to multifunctional mixed‐matrix membranes and powder composites. The materials exhibit visible/NIR emission and matrix‐based conductivity even as black bodies.
Moritz Maxeiner +9 more
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Advanced Functional Materials, EarlyView.The study presents biodegradable and recyclable mixed‐matrix membranes (MMMs), hydrogels, and cryogels using luminescent nanoscale metal‐organic frameworks (nMOFs) and biopolymers. These bio‐nMOF‐MMMs combine europium‐based nMOFs as probes for the status of the materials with the biopolymers agar and gelatine and present alternatives to conventional ...
Moritz Maxeiner +4 more
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Parity results for broken 11-diamond partitions
Open Mathematics, 2019 Recently, Dai proved new infinite families of congruences modulo 2 for broken 11-diamond partition functions by using Hecke operators. In this note, we establish new parity results for broken 11-diamond partition functions.
Wu Yunjian
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Some fundamental Fibonacci number congruences [PDF]
Notes on Number Theory and Discrete MathematicsThis paper investigates a number of congruence properties related to the coefficients of a generalized Fibonacci polynomial. This polynomial was defined to produce properties comparable with those of the standard polynomials of some special functions ...
Anthony G. Shannon +3 more
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