Results 131 to 140 of about 55,236 (313)
Gauss Sums and Binomial Coefficients
Journal of Number Theory, 2002 Let \(p= tn+r\) be a prime which splits in \(\mathbb{Q}(\sqrt{-t})\) where \(t\) has one of the following forms \[ \begin{aligned} t= k>3 &\;\text{ for a prime } k\equiv 3\pmod 4,\\ t= 4k &\;\text{ for a prime } k\equiv 1\pmod 4,\\ t= 8k &\;\text{ for an odd prime } k.
Lee, DH, Hahn, SG Hahn, Sang-Geun
openaire +2 more sources
Advanced Physics Research, EarlyView.ABSTRACT We introduce a family of bosonic quantum error‐correcting codes built as a rotation‐symmetric superposition of squeezed vacuum states, which promise protection against both loss and dephasing noise channels. The robustness of these “squeezed‐vacuum codes” arises from being arranged at evenly spaced angles in phase‐space, and simultaneously in ...
Nir Gutman +4 more
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AppliedMathTwo classes of series involving differences of harmonic numbers and the binomial coefficients C(3n,n) are evaluated in closed form. The classes under consideration are ∑k=0∞H3k+1−Hk(3k+1)3kkkmzkand∑k=0∞H2k−Hk(3k+1)3kkkmzk, where z is a complex number and
Kunle Adegoke, Robert Frontczak
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Modeling and parameter estimation for fractional large‐scale interconnected Hammerstein systems
Asian Journal of Control, EarlyView.Abstract This paper addresses the challenge of modeling and identifying large‐scale interconnected systems exhibiting memory effects, hereditary properties, and non‐local interactions. We propose a fractional‐order extension of the Hammerstein architecture that incorporates Grünwald–Letnikov operators to capture complex dynamics through multiple ...
Mourad Elloumi +2 more
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Binomial sums about Bernoulli, Euler and Hermite polynomials [PDF]
Discrete Mathematics Letters, 2020 Xiaoyuan Wang, Wenchang Chu
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British Educational Research Journal, EarlyView.Abstract This article examines the factors associated with persistent absenteeism (an absence rate of 10% or higher) and authorised and unauthorised absence among secondary school pupils in Scotland. Using linked administrative data, the analysis focuses on secondary school stages S1–S6 in three academic years.
Silvia Behrens +6 more
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Mid‐Domain Effect and Wooded Habitat Shape Mediterranean Reptile Communities
Biological Diversity, EarlyView.Analyzing a large number of reptiles observed across protected areas in Central Italy, we tested whether the mid‐domain effect explains hump‐shaped richness–elevation patterns. Species richness was best predicted by the combined influence of geometric constraints and woodland cover, revealing two contrasting species clusters and offering a robust ...
Daniele Dendi +3 more
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Orchard netting impacts on biodiversity leading to cascading effects at the ecosystem level
Biological Reviews, EarlyView.ABSTRACT Agriculture must ensure food production without further compromising the ecosystem functions upon which it depends. Agricultural practices should therefore avoid harming farmland biodiversity, especially of taxa that supply the key ecosystem services (e.g.
Corrado Alessandrini +13 more
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Estimation for random coefficient integer-valued autoregressive model under random environment
Advances in Difference Equations, 2019 A first-order random coefficient integer-valued autoregressive model based on the negative binomial thinning operator under r states random environment is introduced.
Yan Cui, Yun Y. Wang
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