Results 71 to 80 of about 1,408,918 (247)

Integers of Biquadratic Fields

, 1970
Let Q denote the field of rational numbers. If m, n are distinct squarefree integers the field formed by adjoining √m and √n to Q is denoted by Q(√m, √n). Since Q(√m, √n) = Q(√m, √n) and √m + √n has for its unique minimal polynomial x4 —2(m + n)x2 + (m -
Kenneth S. Williams
core   +1 more source

Integers without large prime factors [PDF]

, 1973
Let u > 3 and β > √e/(√e−1) be real numbers and let β0=β−√e/(√e−1). Let a and q be relatively prime positive integers. Let Ψa(X, Y) denote the number of positive integers ⩽ X and ≡ a (mod q), whose largest prime factor is ⩽ Y.
Friedlander, John B
core   +1 more source

Extrinsic Limitations of Stealthy Hyperuniform Devices

Advanced Optical Materials, EarlyView.
Stealthy hyperuniform devices exhibit a scattering‐free angular region whose extent follows a simple quenching equation. Experimental measurements confirm this prediction but reveal quenching efficiencies far below theoretical expectations. Multiple scattering and finite‐size effects are quantified, establishing realistic performance limits for ...
Yuhao Xu, Miao Chen, Louis Forestier, Franck Carcenac, Laurent Mazenq, Philippe Lalanne   +5 more
wiley   +1 more source

Shape-preserving properties of a new family of generalized Bernstein operators

Journal of Inequalities and Applications, 2018
In this paper, we introduce a new family of generalized Bernstein operators based on q integers, called (α,q) $(\alpha,q)$-Bernstein operators, denoted by Tn,q,α(f) $T_{n,q,\alpha}(f)$. We investigate a Kovovkin-type approximation theorem, and obtain the
Qing-Bo Cai, Xiao-Wei Xu
doaj   +1 more source

Hybridization of Gap Plasmons and Grating‐Coupled Surface Plasmon Polaritons in Metal Nanoparticle Cluster Arrays on a Mirror

Advanced Optical Materials, EarlyView.
Here we use a template‐assisted self‐assembly approach of metal colloids onto metal films to produce hybrid plasmonic metasurfaces that integrate nanoparticle‐on‐mirror cavities with periodic metal colloid arrays. The resulting coupling between gap plasmons and grating‐coupled surface plasmon polaritons enables programmable hybrid modes with tailored ...
Afroditi Koutsogianni, Xiaoyu Qi, Jose Mendoza‐Carreño, Pedro Moronta, Maria Isabel Alonso, David B. Amabilino, Agustín Mihi   +6 more
wiley   +1 more source

Helix Alignment, Chevrons, and Edge Dislocations in Twist‐Bend Ferroelectric Nematics

Advanced Science, EarlyView.
The recently discovered twist‐bend ferroelectric nematic (NTBF) is the new member of the multiferroic family, representing a fluid with an oblique helicoidal (heliconical) periodic structure of spontaneous electric polarization. The work presents a thorough exploration of the material properties of this phase, how the periodic modulation of ...
Bijaya Basnet, Priyanka Kumari, Sathyanarayana Paladugu, Damian Pociecha, Jakub Karcz, Przemysław Kula, Nataša Vaupotič, Ewa Górecka, Oleg D Lavrentovich   +8 more
wiley   +1 more source

q-Analogue of a binomial coefficient congruence

International Journal of Mathematics and Mathematical Sciences, 1995
We establish a q-analogue of the congruence (papb)≡(ab)   (modp2) where p is a prime and a and b are positive integers.
W. Edwin Clark
doaj   +1 more source

Physics‐Embedded Neural Network: A Novel Approach to Design Polymeric Materials

Advanced Science, EarlyView.
Traditional black‐box models for polymer mechanics rely solely on data and lack physical interpretability. This work presents a physics‐embedded neural network (PENN) that integrates constitutive equations into machine learning. The approach ensures reliable stress predictions, provides interpretable parameters, and enables performance‐driven, inverse ...
Siqi Zhan, Hengheng Zhao, Haotian Wang, Zhanjie Liu, Qian Li, Weifeng Zhang, Qingsong Zhao, Liqun Zhang, Jun Liu   +8 more
wiley   +1 more source

ML Workflows for Screening Degradation‐Relevant Properties of Forever Chemicals

Advanced Science, EarlyView.
The environmental persistence of per‐ and polyfluoroalkyl substances (PFAS) necessitates efficient remediation strategies. This study presents physics‐informed machine learning workflows that accurately predict critical degradation properties, including bond dissociation energies and polarizability.
Pranoy Ray, Andrew R. Castillo, Manoj Kolel‐Veetil, Surya R. Kalidindi   +3 more
wiley   +1 more source

A new class of infinite products, and Euler's totient

International Journal of Mathematics and Mathematical Sciences, 1994
We introduce some new infinite products, the simplest being(1−y)∏k=2∞∏j∈ϕk(1−ykqj)1/k=(1−y1−qy)1/(1−q),where ϕk is the set of positive integers less than and relatively prime to k, valid for |y|∧|qy| both less than unity, with q≠1.
Geoffrey B. Campbell
doaj   +1 more source