共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
VINCENZO DE FILIPPIS MOHD ARIF RAZA NADEEM UR REHMAN 《Proceedings Mathematical Sciences》2017,127(1):91-98
Let R be a prime ring of characteristic different from 2, C its extended centroid, d a nonzero derivation of R, f(x 1, . . . , x n ) a multilinear polynomial over C, ρ a nonzero right ideal of R and m > 1 a fixed integer such that for all r 1, . . . , r n ∈ρ. Then either [f(x 1,…,x n ),x n+1]x n+2 is an identity for ρ or d(ρ)ρ = 0.
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$$\qquad \left ([d(f(r_{1},\ldots ,r_{n})),f(r_{1},\ldots ,r_{n})]\right )^{m}=[d(f(r_{1},\ldots ,r_{n})),f(r_{1},\ldots ,r_{n})] $$
3.
Pedro L. Q. Pergher 《Israel Journal of Mathematics》2012,188(1):431-439
Let (M m , T) be a smooth involution on a closed smooth m-dimensional manifold and F = ∪ j=0 n F j (n ≤ m) its fixed point set, where F j denotes the union of those components of F having dimension j. The famous Five Halves Theorem of J. Boardman, announced in 1967, establishes that, if F is nonbounding, then m ≤ 5/2n. In this paper we obtain an improvement of the Five Halves Theorem when the top dimensional component of F, F n , is nonbounding. Specifically, let ω = (i 1, i 2, …, i r ) be a non-dyadic partition of n and s ω (x 1, x 2, …, x n ) the smallest symmetric polynomial over Z 2 on degree one variables x 1, x 2, …, x n containing the monomial \(x_1^{i_1 } x_2^{i_2 } \cdots x_r^{i_r }\). Write s ω (F n ) ∈ H n (F n , Z 2) for the usual cohomology class corresponding to s ω (x 1, x 2, …, x n ), and denote by ?(F n ) the minimum length of a nondyadic partition ω with s ω (F n ) ≠ 0 (here, the length of ω = (i 1, i 2, …, i r ) is r). We will prove that, if (M m , T) is an involution for which the top dimensional component of the fixed point set, F n , is nonbounding, then m ≤ 2n + ?(F n ); roughly speaking, the bound for m depends on the degree of decomposability of the top dimensional component of the fixed point set. Further, we will give examples to show that this bound is best possible. 相似文献
4.
A. V. Grishin 《Mathematical Notes》2018,104(1-2):22-28
The paper studies the additive structure of the algebra F(7), i.e., a relatively free associative countably generated algebra with the identity [x1,..., x7] = 0 over an infinite field of characteristic ≠ 2, 3. First, the space of proper multilinear polynomials in this algebra is investigated. As an application, estimates for the codimensions cn = dimFn(7) are obtained, where Fn(7) stands for the subspace of multilinear polynomials of degree n in the algebra F(7). 相似文献
5.
Let R be a prime ring of char R ≠ 2, let d be a nonzero derivation of R, and let ρ be a nonzero right ideal of R such that [[d(x)x n , d(y)] m , [y, x] s ] t = 0 for all x, y ? ρ, where n ≥ 1, m ≥ 0, s ≥ 0, and t ≥ 1 are fixed integers. If [ρ, ρ]ρ ≠ 0 then d(ρ)ρ = 0. 相似文献
6.
Let O ? R d be a bounded domain of class C 1,1. Let 0 < ε - 1. In L 2(O;C n ) we consider a positive definite strongly elliptic second-order operator B D,ε with Dirichlet boundary condition. Its coefficients are periodic and depend on x/ε. The principal part of the operator is given in factorized form, and the operator has lower order terms. We study the behavior of the generalized resolvent (B D,ε ? ζQ 0(·/ε))?1 as ε → 0. Here the matrix-valued function Q 0 is periodic, bounded, and positive definite; ζ is a complex-valued parameter. We find approximations of the generalized resolvent in the L 2(O;C n )-operator norm and in the norm of operators acting from L 2(O;C n ) to the Sobolev space H 1(O;C n ) with two-parameter error estimates (depending on ε and ζ). Approximations of the generalized resolvent are applied to the homogenization of the solution of the first initial-boundary value problem for the parabolic equation Q 0(x/ε)? t v ε (x, t) = ?(B D,ε v ε )(x, t). 相似文献
7.
V. N. Margaryan H. G. Ghazaryan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2018,53(1):6-15
A linear differential operator P(x, D) = P(x1,... x n , D1,..., D n ) = ∑αγα(x)Dα with coefficients γα(x) defined in E n is called formally almost hypoelliptic in E n if all the derivatives DνξP(x, ξ) can be estimated by P(x, ξ), and the operator P(x, D) has uniformly constant power in En. In the present paper, we prove that if P(x, D) is a formally almost hypoelliptic operator, then all solutions of equation P(x, D)u = 0, which together with some of their derivatives are square integrable with a specified exponential weight, are infinitely differentiable functions. 相似文献
8.
A. M. Sedletskii 《Moscow University Mathematics Bulletin》2007,62(1):22-28
Let z n denote the sequence of zeros of the Mittag-Leffler function E ρ (z; μ), ρ > 0, μ ∈ ?, which is an entire function of order ρ. With the exception of the case ρ = 1/2, Re μ = 3 an asymptotic behavior of the sequence z n ρ was known earlier up to infinitesimals o(1) having a sharply defined rate of decrease. In this paper the behavior of the sequence z n 1/2 is studied just in this exceptional case. Furthermore, for ρ = 1/2, μ > 3 we give the form of a curvilinear half-plane which is free of the points z n . 相似文献
9.
Shan Chang 《Czechoslovak Mathematical Journal》2016,66(4):1165-1175
Let H be a finite abelian group of odd order, D be its generalized dihedral group, i.e., the semidirect product of C2 acting on H by inverting elements, where C2 is the cyclic group of order two. Let Ω (D) be the Burnside ring of D, Δ(D) be the augmentation ideal of Ω (D). Denote by Δn(D) and Qn(D) the nth power of Δ(D) and the nth consecutive quotient group Δn(D)/Δn+1(D), respectively. This paper provides an explicit Z-basis for Δn(D) and determines the isomorphism class of Qn(D) for each positive integer n. 相似文献
10.
Luisa Carini Vincenzo De Filippis Giovanni Scudo 《Mediterranean Journal of Mathematics》2016,13(1):53-64
Let R be a non-commutative prime ring of characteristic different from 2 with extended centroid C, F ≠ 0 a generalized skew derivation of R, and n ≥ 1 such that [F(x), x] n = 0, for all x ∈ R. Then there exists an element λ ∈ C such that F(x) = λx, for all x ∈ R. 相似文献
11.
12.
The main purpose of the present work is to establish the functional asymptotic normality of a class of kernel conditional mode estimates when functional stationary ergodic data are considered. More precisely, consider a random variable (X,Z) taking values in some semi-metric abstract space E × F. For a real function φ defined on F and for each x ∈ E, we consider the conditional mode, say ?φ(x), of the real random variable φ(Z) given the event “X = x”. While estimating the conditional mode function by Θ?φ,n(x), using the kernel-type estimator, we establish the limiting law of the family of processes {Θ?φ(x) - Θφ(x)} (suitably normalized) over Vapnik–Chervonenkis class C of functions φ. Beyond ergodicity, no other assumption is imposed on the data. This paper extends the scope of some previous results established under mixing condition for a fixed function φ. From this result, the asymptotic normality of a class of predictors is derived and confidence bands are constructed. Finally, a general notion of bootstrapped conditional mode constructed by exchangeably weighting samples is presented. The usefulness of this result will be illustrated in the construction of confidence bands. 相似文献
13.
Let R be a prime ring of characteristic different from 2, let Q be the right Martindale quotient ring of R, and let C be the extended centroid of R. Suppose that G is a nonzero generalized skew derivation of R and f(x 1,..., x n ) is a noncentral multilinear polynomial over C with n noncommuting variables. Let f(R) = {f(r 1,..., r n ): r i ∈ R} be the set of all evaluations of f(x 1,..., x n ) in R, while A = {[G (f(r 1,..., r n )), f(r 1,..., r n )]: r i ∈ R}, and let C R (A) be the centralizer of A in R; i.e., C R (A) = {a ∈ R: [a, x] = 0, ? x ∈ A }. We prove that if A ≠ (0), then C R (A) = Z(R). 相似文献
14.
In this paper we prove the following result. Let m ≥ 1, n ≥ 1 be fixed integers and let R be a prime ring with m + n + 1 ≤ char(R) or char(R) = 0. Suppose there exists an additive nonzero mapping D : R → R satisfying the relation 2D(x n+m+1) = (m + n + 1)(x m D(x)x n + x n D(x)x m ) for all \({x\in R}\). In this case R is commutative and D is a derivation. 相似文献
15.
16.
K. S. Platonova 《Differential Equations》2017,53(6):796-808
We obtain relations that define the equivalence algebra of the family of one-dimensional Boltzmann equations f t + cf x + F(t, x, c)f c = 0 and show that all equations of that form are locally equivalent. We carry out the group classification of the equation with respect to the function F in the special case where the function F and the transformations of the variables t and x are assumed to be independent of c. We show that, under such constraints for the transformation and the family of equations, the maximum possible symmetry algebra is eight-dimensional, which corresponds to an equation with a linear function F. 相似文献
17.
Let the independent random variables X1, X2, … have the same continuous distribution function. The upper record values X(1) = X1 < X(2) < … generated by this sequence of variables, as well as the lower record values x(1) = X1 > x(2) > …, are considered. It is known that in this situation, the mean value c(n) of the total number of the both types of records among the first n variables X is given by the equality c(n)=2(1+1/2+…+1/n), n = 1, 2, …. The problem considered here is following: how, sequentially obtaining the observed values x1, x2, … of variables X and selecting one of them as the initial point, to obtain the maximal mean value e(n) of the considered numbers of records among the rest random variables. It is not possible to come back to rejected elements of the sequence. Some procedures of the optimal choice of the initial element X r are discussed. The corresponding tables for the values e(n) and differences δ(n)= e(n)–c(n) are presented for different values of n. The value of δ= limn→∞δ(n)is also given. In some sense, the considered problem and optimization procedure presented in this paper are quite similar to the classical “secretary problem,” in which the probability of selecting the last record value in the set of independent identically distributed X is maximized. 相似文献
18.
D. V. Zakablukov 《Moscow University Mathematics Bulletin》2016,71(3):89-97
The paper discusses the asymptotic depth of a reversible circuits consisting of NOT, CNOT and 2-CNOT gates. The reversible circuit depth function D(n, q) is introduced for a circuit implementing a mapping f: Z2n → Z2n as a function of n and the number q of additional inputs. It is proved that for the case of implementation of a permutation from A(Z2n) with a reversible circuit having no additional inputs the depth is bounded as D(n, 0) ? 2n/(3log2n). It is also proved that for the case of transformation f: Z2n → Z2n with a reversible circuit having q0 ~ 2n additional inputs the depth is bounded as D(n,q0) ? 3n. 相似文献
19.
Let R be a prime ring of characteristic not 2, A be an additive subgroup of R, and F, T, D, K: A-R be additive maps such that F([x, y]) = F(x)y-yK(x)-T(y)x + xD(y) for all x, yEA. Our aim is to deal with this functional identity when A is R itself or a noncentral Lie ideal of R. Eventually, we are able to describe the forms of the mappings F, T, D, and K in case A = R with deg(R) > 3 and also in the case A is a noncentral Lie ideal and deg(R) > 9. These enable us in return to characterize the forms of both generalized Lie derivations, D-Lie derivations and Lie centralizers of R under some mild assumptions. Finally, we give a generalization of Lie homomorphisms on Lie ideals. 相似文献
20.
Let G be a connected graph with vertex set V(G) = {v1, v2,..., v n }. The distance matrix D(G) = (d ij )n×n is the matrix indexed by the vertices of G, where d ij denotes the distance between the vertices v i and v j . Suppose that λ1(D) ≥ λ2(D) ≥... ≥ λ n (D) are the distance spectrum of G. The graph G is said to be determined by its D-spectrum if with respect to the distance matrix D(G), any graph having the same spectrum as G is isomorphic to G. We give the distance characteristic polynomial of some graphs with small diameter, and also prove that these graphs are determined by their D-spectra. 相似文献