Results 71 to 80 of about 1,179 (268)
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
Photon‐Sphere Modes in Curved Optical Microcavities: A Black‐Hole Analogue Laser
Advanced Science, EarlyView.An optical analogue of a Schwarzschild black hole is realized using curved microcavities that preserve light‐like geodesics. A new family of laser modes confined around the photon sphere is identified alongside conventional whispering‐gallery modes. Analytical theory, numerical simulations, and experiments reveal curvature‐induced confinement, enabling
Chenni Xu +9 more
wiley +1 more source
RING STRUCTURE OF INTEGER-VALUED RATIONAL FUNCTIONS
Journal of Commutative Algebra$\DeclareMathOperator{\IntR}{Int{}^\text{R}}$Integer-valued rational functions are a natural generalization of integer-valued polynomials. Given a domain $D$, the collection of all integer-valued rational functions over $D$ forms a ring extension $\IntR(D)$ of $D$. For a valuation domain $V$, we characterize when $\IntR(V)$ is a Prüfer domain and when $
openaire +2 more sources
Let F:K be a Galois extension of number fields and Q a prime ideal of O_F lying over the prime P of O_K. By analyzing the Q-adic closure of O_K in O_F we characterize those rings of integers O_K for which every residue class ring of Int(O_K) modulo a non-zero prime ideal is GE2 (meaning that every unimodular pair can be trasformed to (1,0) by a series ...
Frisch, Sophie, Halter-Koch, Franz
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Rings of integer-valued rational functions
Journal of Pure and Applied Algebra, 1998 For \(D\) an integral domain with quotient field \(K\) and \(E \subseteq D\), let \(\text{Int} (E, D)= \{f \in K[x]\mid f(E) \subseteq D\}\) and \(\text{Int}^R (E, D) = \{f \in K (x) \mid f(E) \subseteq D\}\). For a large class of rings, called \(D\)-rings (which includes \({\mathbb Z}\)), \(\text{Int}^R (D, D) = \text{Int} (D, D)\).
Loper, Alan, Cahen, Paul-Jean
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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
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Matrices over rings of algebraic integers
Linear Algebra and its Applications, 1991 For matrices over a domain R of algebraic integers the authors investigate: (i) completions, (ii) the Hermite form, (iii) the Schur form, (iv) the Smith form, and (v) links relating eigenvalues and Smith invariants. These items have been investigated previously but not in the present context.
Newman, Morris, Thompson, Robert C.
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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
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