Results 91 to 100 of about 666,240 (259)

Quaternion Algebras and the Algebraic Legacy of Hamilton's Quaternions

Irish Mathematical Society Bulletin, 2006
We describe the basic definitions and fundamen- tal properties of quaternion algebras over fields and proceed to give an account of how Hamilton's 1843 discovery of the quaternions was a major turning point in the subject of al- gebra. Noncommutative algebra started here! We will em- phasize especially the theory of division algebras and other kinds of
openaire   +1 more source

Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real‐World Data

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

Deep Learning Approaches for Classifying Crack States With Overload and Predicting Fatigue Parameters in a Titanium Alloy

Advanced Intelligent Systems, EarlyView.
This study proposes a deep learning approach to evaluate the fatigue crack behavior in metals under overload conditions. Using digital image correlation to capture the strain near crack tips, convolutional neural networks classify crack states as normal, overload, or recovery, and accurately predict fatigue parameters.
Seon Du Choi, Suman Timilsina, Youn Woo Shin, Yong Nam Kwon, Kee‐Sun Sohn, Ji Sik Kim   +5 more
wiley   +1 more source

Robotic Arm‐Assisted Conformal 3D Printing of Displays for Structural Electronics

Advanced Intelligent Systems, EarlyView.
This study presents a robotics‐enabled platform combining 3D scanning and a 6‐DOF robotic arm for conformal printing on complex non‐planar structures. By maintaining nozzle perpendicularity, the system enables high‐fidelity direct ink writing on steep sidewalls, spherical surfaces, successfully demonstrating a fully printed 7‐segment dynamic display ...
Chanbin Yoo, Jongcheon Bae, Seonghyeon Kim, Jun Chang Yang, Seung Kwon Seol, Jaeyeon Pyo   +5 more
wiley   +1 more source

The Herfindahl neutral point: A firm‐level threshold for managing market concentration with evidence from US hog packing

American Journal of Agricultural Economics, EarlyView.
Abstract This paper derives a firm‐level threshold, the Herfindahl Neutral Point, from the standard concentration index used in merger review. At this threshold, a marginal expansion leaves the index unchanged. Firms below the threshold reduce concentration when they expand; firms above it increase concentration.
Andrew J. Keller, Krishna P. Paudel
wiley   +1 more source

Corestrictions of algebras and splitting fields

, 2007
Given a field $F$, an \'etale extension $L/F$ and an Azumaya algebra $A/L$, one knows that there are extensions $E/F$ such that $A \otimes_F E$ is a split algebra over $L \otimes_F E$.
Krashen, Daniel
core   +1 more source

Advanced Investigation of the Elimination of Methylene Blue From Wastewater Using Activated Carbon–Copper Oxide Nanowires: New Perspectives With Statistical Physical Modeling

Asia-Pacific Journal of Chemical Engineering, EarlyView.
ABSTRACT In this study, the actual route of methylene blue (MB) dye adsorption by using fabricated polyfunctional activated carbon–copper oxide nanowires (AC@CuO‐NWs) from bulky wastewater bodies has been investigated. To better understand the exact pathway of the adsorption process, a prominent statistical physics formalism or grand canonical ...
Abdellatif Sakly, Nizar Lefi, Mohamed Bouzid, Salah Knani, Md. Mahmudur Rahman, Besma Graba, Sivarama Krishna Lakkaboyana, Abdelmottaleb Ben Lamine   +7 more
wiley   +1 more source

Multi-body kinematics and dynamics in terms of quaternions: Langrange formulation in covariant form: Rodriguez approach [PDF]

FME Transactions, 2010
This paper suggests a quaternion approach for the modeling kinematics and dynamics of rigid multi-body systems. Instead of the regular 'Newton-Euler' and Lagrange method used in the traditional way, Lagrange's equations of second kind in the covariant ...
Zorić Nemanja D., Lazarević Mihailo P., Simonović Aleksandar M.   +2 more
doaj  

On free ring extensions of degree n

International Journal of Mathematics and Mathematical Sciences, 1981
Nagahara and Kishimoto [1] studied free ring extensions B(x) of degree n for some integer n over a ring B with 1, where xn=b, cx=xρ(c) for all c and some b in B(ρ=automophism of  B), and {1,x…,xn−1} is a basis.
George Szeto
doaj   +1 more source

Research on splitting quaternions with generalized Tribonacci hybrid number components [PDF]

Notes on Number Theory and Discrete Mathematics
This paper introduces the Generalized Tribonacci Hybrid Split Quaternion (GTHSQ), a novel split quaternion with coefficients derived from generalized Tribonacci hybrid numbers.
Yanni Yang, Yong Deng
doaj   +1 more source