Results 171 to 180 of about 653,122 (340)
, 2007 這篇文章旨在介紹四元素代數裡的秩序。在第二節，我用非常初等的手法，推導出一些我們需要的四元素代數的基本性質；學過一年大學抽象代數並知道一點關於張量積的性質的人應該都能讀的懂。在第三節裡，我證明了秩序的一些性質並引出這篇文章的主角「艾克秩序」。第四節介紹佈於有理數上的秩序的特殊性質。第五節和第六節的目標在描述佈於代數數體上的艾克秩序。在第五節，佈於區域體上的艾克秩序被以清楚明白的式子寫出來。在第六節，我們收集區域的資訊用以瞭解全域體上的艾克秩序。最後，一些有理數上的艾克秩序被清楚地給出。The goal ...
孫嘉梁, Sun, Chia-Liang
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Four‐Dimensional pp‐Wave Lie Groups and Harmonic Curvature
Mathematische Nachrichten, EarlyView.ABSTRACT We determine all four‐dimensional Lie groups which have harmonic curvature. In parallel, a description of four‐dimensional pp‐wave Lie groups is obtained.
E. García‐Río +2 more
wiley +1 more source
Kuga–Satake Construction on Families of K3 Surfaces of Picard Rank 14
Mathematische Nachrichten, EarlyView.ABSTRACT The isometry between the type IV6 and the type II4 hermitian symmetric domains suggests a possible relation between suitable moduli spaces of K3 surfaces of Picard rank 14 and of polarized abelian 8‐folds with totally definite quaternion multiplication. We show how this isometry induces a geometrically meaningful map between such moduli spaces
Flora Poon
wiley +1 more source
Gait Adaptability Training Improves Gait in Spinocerebellar Ataxia Patients
Movement Disorders Clinical Practice, EarlyView.Abstract Background Spinocerebellar ataxia (SCA) is a rare, genetic neurodegenerative movement disorder primarily affecting the cerebellum. So far, there is no available cure for SCA. However, evidence suggests that neurorehabilitation can alleviate symptoms.
Colette J.M. Reniers +5 more
wiley +1 more source
Robot Kinematic Modeling and Control Based on Dual Quaternion Algebra --- Part I: Fundamentals.
, 2017 This is the first part of a three-part tutorial on dual quaternion algebra applied to robotics, whose goal is to help readers grasp the main ideas behind dual quaternions and their application to robot kinematic modeling and control.
Vilhena Adorno, Bruno
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Mathematical Methods in the Applied Sciences, EarlyView.We develop a full randomization of the classical hyper‐logistic growth model by obtaining closed‐form expressions for relevant quantities of interest, such as the first probability density function of its solution, the time until a given fixed population is reached, and the population at the inflection point.
Juan Carlos Cortés +2 more
wiley +1 more source
Dual-arm admittance control using conformal geometric algebra. [PDF]
Front Robot AILöw T +5 more
europepmc +1 more source
Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6425-6446, April 2025.ABSTRACT The well‐posedness results for mild solutions to the fractional neutral stochastic differential system with Rosenblatt process with Hurst index Ĥ∈12,1$$ \hat{H}\in \left(\frac{1}{2},1\right) $$ is discussed in this article. To demonstrate the results, the concept of bounded integral contractors is combined with the stochastic result and ...
Dimplekumar N. Chalishajar +3 more
wiley +1 more source
Hypercomplex neural networks: Exploring quaternion, octonion, and beyond in deep learning. [PDF]
MethodsXDevadas RM +5 more
europepmc +1 more source
Small Zeros of Hermitian Forms over a Quaternion Algebra
, 2010 Let D be a positive definite quaternion algebra over a totally real number field K, F(X,Y) a hermitian form in 2N variables over D, and Z a right D-vector space which is isotropic with respect to F.
Chan, Wai Kiu, Fukshansky, Lenny
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