共查询到20条相似文献,搜索用时 31 毫秒
1.
The authors consider irreducible representations of a nilpotent Lie group and define a Fourier transform for Schwartz class (and other) functions φ on N by forming the kernels Kφ(x, y) of the trace class operations πφ = ∝Nφ(n)πndn, regarding the π as modeled in L2(Rk) for all π in general position. For a special class of groups they show that the models, and parameters λ labeling the representations in general position, can be chosen so the joint behavior of the kernels Kφ(x, y, λ) can be interpreted in a useful way. The variables (x, y, λ) run through a Zariski open set in Rn, n = dim N. The authors show there is a polynomial map u = A(x, y, λ) that is a birational isomorphism A: Rn → Rn with the following properties. The Fourier transforms F1φ = Kφ(x, y, λ) all factor through A to give “rationalized” Fourier transforms Fφ(u) such that Fφ ° A = F1φ. On the rationalized parameter space a function f(u) is of the form Fφ = f ? f is Schwartz class on Rn. If polynomial operators T?P(N) are transferred to operators on Rn such that is transformed isomorphically to P(Rn). 相似文献
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Cheng-Kai Liu 《Algebras and Representation Theory》2013,16(6):1561-1576
We investigate the commutativity in a (semi-)prime ring R which admits skew derivations δ 1, δ 2 satisfying [δ 1(x), δ 2(y)]?=?[x, y] for all x, y in a nonzero right ideal of R. This result is a natural generalization of Bell and Daif’s theorem on strong commutativity preserving derivations and a recent result by Ali and Huang. 相似文献
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A ring R is called almost-quasi-commutative if for each x, y ∈ R there exist nonzero relatively prime integers j = j(x, y) and k = k(x, y) and a non-negative integer n = n(x, y) such that jxy = k(yx) n . We establish some general properties of such rings, study commutativity of almost-quasi-commutative R, and consider several examples. 相似文献
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Strong commutativity preserving maps on Lie ideals 总被引:2,自引:0,他引:2
Jer-Shyong Lin 《Linear algebra and its applications》2008,428(7):1601-1609
Let A be a prime ring and let R be a noncentral Lie ideal of A. An additive map f:R→A is called strong commutativity preserving (SCP) on R if [f(x),f(y)]=[x,y] for all x,y∈R. In this paper we show that if f is SCP on R, then there exist λ∈C, λ2=1 and an additive map μ:R→Z(A) such that f(x)=λx+μ(x) for all x∈R where C is the extended centroid of A, unless charA=2 and A satisfies the standard identity of degree 4. 相似文献
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This paper presents a demonstrably convergent method of feasible directions for solving the problem min{φ(ξ)| gi(ξ)?0i=1,2,…,m}, which approximates, adaptively, both φ(x) and ▽φ(x). These approximations are necessitated by the fact that in certain problems, such as when , a precise evaluation of φ(x) and ▽φ(x) is extremely costly. The adaptive procedure progressively refines the precision of the approximations as an optimum is approached and as a result should be much more efficient than fixed precision algorithms.It is outlined how this new algorithm can be used for solving problems of the form under the assumption that Ωmξ={x|gi(x)?0, j=1,…,s} ∩n, Ωy={y|ζi(y)?0, i-1,…,t} ∩ m, with f, gj, ζi continuously differentiable, f(x, ·) concave, ζi convex for compact. 相似文献
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Adil Yaqub 《Results in Mathematics》2006,49(3-4):377-386
A well-known theorm of Jacobson asserts that a ring R with the property that for every x in R there exists an integer n(x) > 1 such that xn(x) = x is necessarily commutative. With this as motivation, we define an N0-ring to be a ring which satisfies a weaker hypothesis than the “xn(x) = x” condition in Jacobson’s Theorem. We consider commutativity of N0-rings, usually with the additional hypothesis that the ground ring is also weakly periodic-like. 相似文献
9.
Mikhail A. Chebotar Wen-Fong Ke Pjek-Hwee Lee Ruibin Zhang 《Monatshefte für Mathematik》2006,162(1):91-101
Let R be a ring, A = M
n
(R) and θ: A → A a surjective additive map preserving zero Jordan products, i.e. if x,y ∈ A are such that xy + yx = 0, then θ(x)θ(y) + θ(y)θ(x) = 0. In this paper, we show that if R contains
\frac12\frac{1}{2}
and n ≥ 4, then θ = λϕ, where λ = θ(1) is a central element of A and ϕ: A → A is a Jordan homomorphism. 相似文献
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A. Firat 《Siberian Mathematical Journal》2006,47(1):169-172
Given a prime ring R, a skew g-derivation for g : R → R is an additive map f : R → R such that f(xy) = f(x)g(y) + xf(y) = f(x)y + g(x)f(y) and f(g(x)) = g(f(x)) for all x, y ∈ R. We generalize some properties of prime rings with derivations to the class of prime rings with skew derivations. 相似文献
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Let R be a prime ring of char R≠2, d a non-zero derivation of R and ρ a non-zero right ideal of R such that [[d(x),d(y)]n [y,x]m] = 0 for all x,y ∈ ρ or [[d(x),d(y)]n d[y,x]m] = 0 for all x,y ∈ ρ, n, m ≥ 0 are fixed integers. If [ρ,ρ]ρ ≠ 0, then d(ρ)ρ = 0. 相似文献
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Mikhail A. Chebotar Wen-Fong Ke Pjek-Hwee Lee Ruibin Zhang 《Monatshefte für Mathematik》2006,149(2):91-101
Let R be a ring, A = M
n
(R) and θ: A → A a surjective additive map preserving zero Jordan products, i.e. if x,y ∈ A are such that xy + yx = 0, then θ(x)θ(y) + θ(y)θ(x) = 0. In this paper, we show that if R contains
and n ≥ 4, then θ = λϕ, where λ = θ(1) is a central element of A and ϕ: A → A is a Jordan homomorphism.
The third author is Corresponding author. 相似文献
14.
Barry E Willner Thomas J Mahar 《Journal of Mathematical Analysis and Applications》1979,72(2):730-739
We consider the question of finding an extreme value for some function of the eigenvalues of the differential equation y″ + λφ(x) y = 0,y(0) = y(1) = 0, as φ(x) varies over a region in a function space. A characterization of the φ(x) at which the function of the eigenvalues achieves its extremum is derived. 相似文献
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I. N. Herstein [10] proved that a prime ring of characteristic not two with a nonzero derivation d satisfying d(x)d(y) = d(y)d(x) for all x, y must be commutative, and H. E. Bell and M. N. Daif [8] showed that a prime ring of arbitrary characteristic with nonzero derivation d satisfying d(xy) = d(yx) for all x, y in some nonzero ideal must also be commutative. For semiprime rings, we show that an inner derivation satisfying the condition of Bell and Daif on a nonzero ideal must be zero on that ideal, and for rings with identity, we generalize all three results to conditions on derivations of powers and powers of derivations. For example, let R be a prime ring with identity and nonzero derivation d, and let m and n be positive integers such that, when charR is finite, m ∨ n < charR. If d(x m y n ) = d(y n x m ) for all x, y ∈ R, then R is commutative. If, in addition, charR≠ 2 and the identity is in the image of an ideal I under d, then d(x) m d(y) n = d(y) n d(x) m for all x, y ∈ I also implies that R is commutative. 相似文献
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This paper deals with the nonlinear two point boundary value problem y″ = f(x, y, y′, R1,…, Rn), x0 < x < xfS1y(x0) + S2y′(x0) = S3, S4y(xf) + S5y′(xf) = S6 where R1,…, Rn, S1,…, S6 are bounded continuous random variables. An approximate probability distribution function for y(x) is constructed by numerical integration of a set of related deterministic problems. Two distinct methods are described, and in each case convergence of the approximate distribution function to the actual distribution function is established. Primary attention is placed on problems with two random variables, but various generalizations are noted. As an example, a nonlinear one-dimensional heat conduction problem containing one or two random variables is studied in some detail. 相似文献
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Let R be a commutative ring with identity, M n (R) the R-algebra consisting of all n by n matrices over R. In this article, for n ≥ 5 we classify linear maps φ from M n (R) into itself satisfying φ(x)x + xφ(x) = 0 whenever x 2 = 0. We call such maps as square-zero derivations. 相似文献
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Let G be a graph and f:G→G be a continuous map. Denote by P(f), R(f) and Ω(f) the sets of periodic points, recurrent points and non-wandering points of f, respectively. In this paper we show that: (1) If L=(x,y) is an open arc contained in an edge of G such that {fm(x),fk(y)}⊂(x,y) for some m,k∈N, then R(f)∩(x,y)≠∅; (2) Any isolated point of P(f) is also an isolated point of Ω(f); (3) If x∈Ω(f)−Ω(fn) for some n∈N, then x is an eventually periodic point. These generalize the corresponding results in W. Huang and X. Ye (2001) [9] and J. Xiong (1983, 1986) [17] and [19] on interval maps or tree maps. 相似文献
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An efficient procedure for optimizing a nonlinear objective functional ?(x) under linear and/or nonlinear equality constraints is given. The linearly constrained, quadratic ?(x) case is shown to have a solution given by the explicit formula x = xp - N(N′AN)-1N′(Axp + b/2), where ?(x) = a+b′x+x′Ax(x?Rn) is convex, and both xp?Rn and N [an n×(n-r) matrix]; can be obtained simultaneously from the constraint set, Kx=c (K of rank r<n), by a single Gaussian elimination. The nonlinearly constrained, arbitrary ?(x) case is treated by an interative scheme in which the above formula is used to “project” onto approximate solutions satisfying linear approximations of the constraints. This method does not require the initial guess or the iterated values to be in the feasible region. The resulting algorithm does appear to be efficient. 相似文献
20.
Vincenzo De Filippis 《Czechoslovak Mathematical Journal》2016,66(2):481-492
Let R be a prime ring of characteristic different from 2 and 3, Qr its right Martindale quotient ring, C its extended centroid, L a non-central Lie ideal of R and n ≥ 1 a fixed positive integer. Let α be an automorphism of the ring R. An additive map D: R → R is called an α-derivation (or a skew derivation) on R if D(xy) = D(x)y + α(x)D(y) for all x, y ∈ R. An additive mapping F: R → R is called a generalized α-derivation (or a generalized skew derivation) on R if there exists a skew derivation D on R such that F(xy) = F(x)y + α(x)D(y) for all x, y ∈ R. 相似文献