Results 41 to 50 of about 271 (247)
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
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Exact Discrete Stochastic Simulation With Deep‐Learning‐Scale Gradient Optimization
Advanced Science, EarlyView.A 203,796‐parameter gene regulatory network classifies handwritten digits with 98.4% accuracy using exact stochastic dynamics. The framework decouples forward simulation from backward differentiation, making continuous‐time Markov chain models compatible with deep‐learning optimization.
Jose M. G. Vilar, Leonor Saiz
wiley +1 more source
Quaternion group algebra and representations of the quaternions [PDF]
Communications in Algebra, 2019 AbstractIn this paper, we provide a concrete and explicit decomposition of the quaternion group algebra through a suitable basis of the algebra.
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The “fundamental theorem of algebra” for quaternions [PDF]
Bulletin of the American Mathematical Society, 1944 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Eilenberg, Samuel, Niven, Ivan
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Advanced Science, EarlyView.We report the solid‐state ball milling, a traditional, reliable, mass‐productive material processing, to prepare the air‐stable and dual‐phase GeSe2‐x nanoparticles with extended photodetection feasibility toward optical‐wavelength regions. We further display photonic multi‐valued logic (MVL) circuit through the employment of a hybrid PMMA/GeSe2‐x ...
An‐Ting Tsai +8 more
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Symmetry‐Imposed Selection Rules for Excitations of Nontrivial Plasmonic Topologies
Advanced Science, EarlyView.A unified group‐theory selection rule governs the excitation of vectorial nearfield topologies across three plasmonic spin states. Derived from first principles, it predicts spin–orbit vortex splitting and multidimensional nested vortices, confirmed by phase‐resolved in situ measurements.
Jie Yang +14 more
wiley +1 more source
On Identities of a Ternary Quaternion Algebra [PDF]
Communications in Algebra, 2011 This article studies a simple 4-dimensional ternary algebra 𝒜 which appears analogously to the quaternions from the Lie algebra 𝔰𝔩(2). We describe the heights 1 and 2 identities, and the derivations of 𝒜. Based on 𝒜, some ternary enveloping algebras for ternary Filippov algebras are constructed.
Beites, P. D. +3 more
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Updatable Closed‐Form Evaluation of Arbitrarily Complex Multiport Network Connections
Advanced Electronic Materials, EarlyView.The inverse design of electrically large wave devices often uses reduced‐order multiport models with discrete optimization, requiring many evaluations of complex interconnections between subsystems that differ only in a few blocks. This paper introduces a closed‐form framework enabling efficient Woodbury low‐rank updates of related, previous ...
Hugo Prod'homme, Philipp del Hougne
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LEVELS AND SUBLEVELS OF QUATERNION ALGEBRAS [PDF]
Mathematical Proceedings of the Royal Irish Academy, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Synchronization of Analog Neuron Circuits With Digital Memristive Synapses: An Hybrid Approach
Advanced Electronic Materials, EarlyView.An hybrid circuit mimicking neural units coupled using memristive synapses is introduced. The analog neurons provide flexibility and robustness, and the digital memristive coupling guarantees the full reconfigurability of the interconnection. The onset of a synchronized spiking behavior in two circuits mimicking the Izhikevich neuron is discussed from ...
Lamberto Carnazza +3 more
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