Results 41 to 50 of about 59,541 (246)
Riemann–Roch for the ring $\mathbb{Z}$
Comptes Rendus. MathématiqueWe show that by working over the absolute base $\mathbb{S}$ (the categorical version of the sphere spectrum) instead of ${\mathbb{S}[\pm 1]}$ improves our previous Riemann–Roch formula for ${\overline{\operatorname{Spec}\mathbb{Z}}}$. The formula equates
Connes, Alain, Consani, Caterina
doaj +1 more source
Advanced Intelligent Discovery, EarlyView.This article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Yiming Ren, Guo‐Wei Wei
wiley +1 more source
Advanced Intelligent Systems, EarlyView.This study provides an introduction to Bayesian optimisation targeted for experimentalists. It explains core concepts, surrogate modelling, and acquisition strategies, and addresses common real‐world challenges such as noise, constraints, mixed variables, scalability, and automation.
Chuan He +2 more
wiley +1 more source
Asia-Pacific Journal of Chemical Engineering, EarlyView.ABSTRACT In order to reflect the actual production situation more comprehensively and optimize the production cost, this paper solves the short‐term scheduling optimization problem for a single pipeline containing high melting point crude oil. Based on the refining plan given by the upper layer, a multi‐objective optimization model with high melting ...
Jing Yao +5 more
wiley +1 more source
Integer-valued polynomials, Prüfer domains, and localization [PDF]
Proceedings of the American Mathematical Society, 1993 Let A A be an integral domain with quotient field K K and let Int ( A ) \operatorname {Int} (A) be the ring of integer-valued polynomials on A : { P ∈ K [ X ] | P (
openaire +2 more sources
Irreducibility of integer-valued polynomials I [PDF]
Communications in Algebra, 2020 Accepted for publication in Communications in ...
openaire +2 more sources
Split Primes and Integer-Valued Polynomials
Journal of Number Theory, 1993 Let \(R\) be a Dedekind domain with finite residue fields, \(K\) its field of fractions, and denote by \(I\) the ring of integer-valued polynomials over \(R\), \(I=\{g(x)\in K[x];\;g(R)\subseteq R\}\). Let \(L\) be a finite separable extension of \(K\) and \(S\) be the integral closure of \(R\) in \(L\). For a nonzero prime ideal \(P\) of \(S\) write \(
openaire +2 more sources
Metasurfaces and Metadevices for Topological Electromagnetic Waves
Advanced Physics Research, EarlyView.Optical topologies refer to diverse topological localized structures made by diverse parameters of light fields, such as vortices, skyrmions, and hopfions. This article navigates a direction of metasurface‐based integrated devices for generation, manipulation and detection of novel topologies of light, which would be a rapidly growing interdisciplinary
Rensheng Xie +3 more
wiley +1 more source
Integer-Valued Polynomials on a Subset
Journal of Number Theory, 1997 If \(R\) is a domain with quotient field \(K\) and \(E\) is a subset of \(R\), then let \(\text{Int} (E)\) be the set of all polynomials \(f\in K[X]\) satisfying \(f(E)\subset R\). Moreover denote by \(cl_R(E)\), the closure of \(E\), the largest subset \(F\) of \(R\) for which \(\text{Int}(F)= \text{Int}(E)\).
openaire +2 more sources
Clinical Anatomy, EarlyView.ABSTRACT Understanding how pancreas size and shape change with normal aging is critical for establishing a baseline to detect deviations in type 2 diabetes and other pancreatic disease. We measure pancreas size and shape using morphological measurements from early development through aging (ages 0–90).
Lucas W. Remedios +13 more
wiley +1 more source