Results 111 to 120 of about 111,899 (306)
Linear Algebra and its Applications, 2002 Suppose that \(P_1\) and \(P_2\) are (orthogonal) projectors in an \(n\)-dimensional (unitary) complex vector space. There are many papers that give necessary and/or sufficient conditions for the sum \(P_1+P_2\), the difference \(P_1-P_2\) or the product \(P_1P_2\) to be a projector or an orthogonal projector; see, among others, \textit{J.
Jerzy K. Baksalary +1 more
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Exploration, EarlyView.Traditional neuromodulation using rigid electrodes has been limited by low precision, large stimulating currents, and the risk of tissue damage. In this work, we developed a biocompatible flexible electrode array that allows for both neural recording of spike firings and high‐precision, low‐threshold stimulation for neuromodulation.
Yifei Ye +16 more
wiley +1 more source
Commutativity and structure of rings with commuting nilpotents [PDF]
International Journal of Mathematics and Mathematical Sciences, 1983 Let R be a ring and let N denote the set of nilpotent elements of R. Let Z denote the center of R. Suppose that (i) N is commutative, (ii) for every x in R there exists x′ϵ < x> such that x − x2x′ϵN, where <x> denotes the subring generated by x, (iii) for every x, y in R, there exists an integer n = n(x, y) ≥ 1 such that both (xy) n − (yx ...
Hazar Abu-Khuzam, Adil Yaqub
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Commuting Pairs in Quasigroups
Journal of Combinatorial Designs, EarlyView.ABSTRACT A quasigroup is a pair (Q,∗) $(Q,\ast )$, where Q $Q$ is a nonempty set and ∗ $\ast $ is a binary operation on Q $Q$ such that for every (a,b)∈Q2 $(a,b)\in {Q}^{2}$, there exists a unique (x,y)∈Q2 $(x,y)\in {Q}^{2}$ such that a∗x=b=y∗a $a\ast x=b=y\ast a$. Let (Q,∗) $(Q,\ast )$ be a quasigroup. A pair (x,y)∈Q2 $(x,y)\in {Q}^{2}$ is a commuting
Jack Allsop, Ian M. Wanless
wiley +1 more source
Extended Conformal Symmetry [PDF]
, 2000 We show that the grading of fields by conformal weight, when built into the initial group symmetry, provides a discrete, non-central conformal extension of any group containing dilatations.
Wheeler, James T.
core +2 more sources
Combs, Fast and Slow: Non‐Adiabatic Mean‐Field Theory of Active Cavities
Laser &Photonics Reviews, EarlyView.A unified mean‐field theory is developed that describes active cavities with dynamics of any speed, whether they be fast, slow, or anything in between. By creating an operator‐based framework that makes no adiabatic approximation, this approach delivers more efficient simulations and new analytical insights for a wide range of integrated combs, such as
David Burghoff
wiley +1 more source
On the commutator map for real semisimple Lie algebras [PDF]
, 2015 We find new sufficient conditions for the commutator map of a real semisimple Lie algebra to be surjective. As an application we prove the surjectivity of the commutator map for all simple algebras except $\mathfrak su_{p,q}$ ($p$ or $q$ >1), $\mathfrak ...
D. Akhiezer
semanticscholar +1 more source
Global and microlocal aspects of Dirac operators: Propagators and Hadamard states
Mathematische Nachrichten, EarlyView.Abstract We propose a geometric approach to construct the Cauchy evolution operator for the Lorentzian Dirac operator on Cauchy‐compact globally hyperbolic 4‐manifolds. We realize the Cauchy evolution operator as the sum of two invariantly defined oscillatory integrals—the positive and negative Dirac propagators—global in space and in time, with ...
Matteo Capoferri, Simone Murro
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Meta‐Metamodelling of Engineering Systems by Help of Abstract Mathematics
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT The growing trend of automation in engineering significantly increases the complexity of engineering systems and necessitates a deeper understanding of the coupling of physical and cyber components interacting within the systems. A typical example of such a highly coupled system is an autonomous construction site, where robotic systems aim to ...
Daniel Luckey, Dmitrii Legatiuk
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Psychology in the Schools, EarlyView.ABSTRACT Despite extensive research suggesting the importance of students developing strong foundational math skills during early grades, more than 60% of 4th graders in the United States lack proficiency in mathematics. Such data are influenced by several factors, including summer learning loss in math, negative impacts from the COVID‐19 pandemic, and
Natasha K. Newson +5 more
wiley +1 more source