Results 91 to 100 of about 165,977,654 (290)
A Perspective on Interactive Theorem Provers in Physics
Advanced Science, EarlyView.Into an interactive theorem provers (ITPs), one can write mathematical definitions, theorems and proofs, and the correctness of those results is automatically checked. This perspective goes over the best usage of ITPs within physics and motivates the open‐source community run project PhysLean, the aim of which is to be a library for digitalized physics
Joseph Tooby‐Smith
wiley +1 more source
Perspective: Hollow Core Optical Fibres for Ultraviolet and Visible Wavelengths
Advanced Science, EarlyView.Hollow core optical fibres bypass material constraints that limit optical fibres at ultraviolet and visible wavelengths. However, their challenging fabrication has limited their development, and significant gains in performance remain possible. In this perspective we outline approaches to enable the next generation of fibres for shorter wavelengths ...
Robbie Mears +5 more
wiley +1 more source
Signature Scheme Using the Root Extraction Problem on Quaternions
Journal of Applied Mathematics, 2014 The root extraction problem over quaternion rings modulo an RSA integer is defined, and the intractability of the problem is examined. A signature scheme is constructed based on the root extraction problem.
Baocang Wang, Yupu Hu
doaj +1 more source
The ring of integers in the canonical structures of the plane
Boletim da Sociedade Paranaense de MatemáticaThe canonical structures of the plane are those that result, up to isomorphism, from the rings that have the form $\mathds{R}[x]/(ax^2+bx+c)$ with $a\neq 0$. That ring is isomorphic to $\mathds{R}[\theta]$, where $\theta$ is the equivalence class of x, which satisfies $\theta^2 = \left( -\dfrac{c}{a} \right) + \theta \left(-\dfrac{b}{a}\right)$. On the
Cifuente, José C. +3 more
openaire +2 more sources
Zassenhaus conjecture for central extensions of S5 [PDF]
, 2008 We confirm a conjecture of Zassenhaus about rational conjugacy of torsion units in integral group rings for a covering group of the symmetric group S5 and for the general linear group GLð2; 5Þ. The first result, together with others from the literature,
Bódi, Viktor +4 more
core +1 more source
Advanced Science, EarlyView.Laser‐induced graphene (LIG) provides a scalable, laser‐direct‐written route to porous graphene architecture with tunable chemistry and defect density. Through heterojunction engineering, catalytic functionalization, and intrinsic self‐heating, LIG achieves highly sensitive and selective detection of NOX, NH3, H2, and humidity, supporting next ...
Md Abu Sayeed Biswas +6 more
wiley +1 more source
Codes over integer residue rings
Information and Control, 1975 Using module theoretic techniques, a linear code is defined as a submodule of \(Z_mC_n\), the group ring of the cyclic group \(C_n\) of order \(n\) over the ring of integers modulo \(m\), \(Z_m\). A cyclic code is defined as an ideal in \(Z_mC_n\). Natural analogs to Hamming, Reed-Solomon and BCH codes are defined over \(Z_m\) and some of the ring ...
openaire +2 more sources
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 +8 more
wiley +1 more source
Commutativity theorems for rings with constraints on commutators
International Journal of Mathematics and Mathematical Sciences, 1991 In this paper, we generalize some well-known commutativity theorems for associative rings as follows: Let n>1, m, s, and t be fixed non-negative integers such that s≠m−1, or t≠n−1, and let R be a ring with unity 1 satisfying the polynomial identity ys[xn,
Hamza A. S. Abujabal
doaj +1 more source
, 2005 In this paper, we study the concept of Smarandache groupoids, subgroupoids, ideal of groupoids, semi-normal subgroupoids, Smarandache-Bol groupoids and Strong Bol groupoids and obtain many interesting results about ...
Vasantha Kandasamy, W.B.
core +1 more source