Results 81 to 90 of about 189,405 (333)
Matrix Type of Some Algebras over a Field of Characteristic p
, 2002 It was proven in [1] that for every associative PI-algebra A over a field F of characteristic p there exists a number m such that the algebra A satisfies all multilinear polynomial identities of the matrix algebra Mm F .
A. Kemer
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Waring's problem for algebras over fields
Journal of Number Theory, 1987 For a ring A let \(w_ k(A)\) denote the smallest s such that every sum of kth powers in A is a sum of s kth powers; let \(v_ k(A)\) denote the corresponding infimum for the sum-or-difference of kth powers. This paper gives a detailed study of \(v_ k(A)\) and \(w_ k(A)\) when A is an algebra over a field F. The main result can be stated as follows: \(v_
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Advanced Intelligent Systems, EarlyView.Herein, a deep reinforcement learning‐based multi‐UAV formation control approach is proposed. By optimizing the utilization of historical data through correcting of offline samples, the past experience is better leveraged and learning performance is improved.
Zhongkai Chen +4 more
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Interaction of non-Abelian tensor gauge fields
Physics Letters B, 2018 The non-Abelian tensor gauge fields take value in extended Poincaré algebra. In order to define the invariant Lagrangian we introduce a vector variable in two alternative ways: through the transversal representation of the extended Poincaré algebra and ...
George Savvidy
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Advanced Intelligent Systems, EarlyView.This article proposes a method that combines coordinated trajectory generation with decoupled tracking control to improve end‐effector tracking accuracy for quadrupedal mobile manipulators. By leveraging whole‐body motion and modeling subsystems independently with interaction forces, the method achieves significant reductions in tracking error and ...
Kun Xu +4 more
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Non-finitary Generalizations of Nil-triangular Subalgebras of Chevalley Algebras
Известия Иркутского государственного университета: Серия "Математика", 2019 Let $N\Phi(K)$ be a niltriangular subalgebra of Chevalley algebra over a field or ring $K$ associated with root system $\Phi$ of classical type. For type $A_{n-1}$ it is associated to algebra $NT(n,K)$ of (lower) nil-triangular $n \times n$- matrices ...
J. V. Bekker +2 more
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Algebraic dimension over Frobenius fields
Forum Mathematicum, 1994 Let \(K\) be a field, \(M\) be a field extension of \(K\). For a nonempty subset \(S\subset M^ n\) every polynomial \(f\in M[X_ 1,\dots,X_ n]\) defines a function from \(S\) into \(M\). Denote the ring of all such functions by \(M[S]\). \(f_ 1,\dots, f_ m\in M[S]\) are called algebraically independent if for every nonzero polynomial \(g\in M[Y_ 1,\dots,
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The Picard group of algebras over an algebraically nonclosed field
Journal of Pure and Applied Algebra, 2011 AbstractLet k be a field that is not algebraically closed, and let A be a k-algebra, whose each maximal ideal has residue field k. We prove that each element of the Picard group of A is of finite order and give an optimal upper bound for its order.
Wojciech Kucharz, Kamil Rusek
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Annals of Neurology, EarlyView.Objective Socioeconomic status (SES) and lifestyle activities (LA) are strongly related, and both are associated with dementia risk. We investigated the influence of SES and LA on brain atrophy and cognitive decline considering amyloid‐beta (Aβ) positron emission tomography and white matter hyperintensity (WMH) load.
Dario Bachmann +11 more
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Hom-structures on semi-simple Lie algebras
Open Mathematics, 2015 A Hom-structure on a Lie algebra (g,[,]) is a linear map σ W g σ g which satisfies the Hom-Jacobi identity: [σ(x), [y,z]] + [σ(y), [z,x]] + [σ(z),[x,y]] = 0 for all x; y; z ∈ g. A Hom-structure is referred to as multiplicative if it is also a Lie algebra
Xie Wenjuan, Jin Quanqin, Liu Wende
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