共查询到20条相似文献,搜索用时 15 毫秒
1.
The notion of a quantum family of maps has been introduced in the framework of C*-algebras. As in the classical case, one may consider a quantum family of maps preserving additional structures (e.g. quantum family of maps preserving a state). In this paper, we define a quantum family of homomorphisms of locally compact quantum groups. Roughly speaking, we show that such a family is classical. The purely algebraic counterpart of the discussed notion, i.e. a quantum family of homomorphisms of Hopf algebras, is introduced and the algebraic counterpart of the aforementioned result is proved. Moreover, we show that a quantum family of homomorphisms of Hopf algebras is consistent with the counits and coinverses of the given Hopf algebras. We compare our concept with weak coactions introduced by Andruskiewitsch and we apply it to the analysis of adjoint coaction. 相似文献
2.
We propose a method for determining parameters in the Schwarz–Christoffel integral.
The desired mapping embeds into a one-parametric family of conformal mappings
of the upper half-plane onto the family of polygons which was obtained by shifting one
or several vertices of some initial polygon with angle preservation.
We consider the case when the family of polygons and the initial
polygon have the same number of vertices; the case when the family of polygons
has two mobile vertices coinciding at the initial moment and not coinciding
with other vertices; and the other case that the family of polygons is a polygon
with mobile cut. The problem of finding the parameters of a family of mappings
is reduced to integrating some system of ordinary differential equations. 相似文献
3.
A Directed Path Family is a family of subsets of some finite ground set whose members can be realized as arc sets of simple directed paths in some directed graph. In this paper we show that recognizing whether a given family is a Directed Path family is an NP-Complete problem, even when all members in the family have at most two elements. If instead of a family of subsets, we are given a collection of words from some finite alphabet, then deciding whether there exists a directed graph G such that each word in the language is the set of arcs of some path in G, is a polynomial-time solvable problem. 相似文献
4.
A geometric permutation induced by a transversal line of a finite family ℱ
of disjoint convex sets in ℝ d is the order in which the transversal
meets the members of the family.
We prove that for each natural k, each family of k permutations is realizable
(as a family of geometric permutations of some ℱ)
in ℝ d for d ≥ 2k – 1, but there is a family of k permutations
which is non-realizable in ℝ d for d ≤ 2k – 2. 相似文献
5.
This paper describes a family of divergences, named herein as the C-divergence family, which is a generalized version of the power divergence family and also includes the density power divergence family as a particular member of this class. We explore the connection of this family with other divergence families and establish several characteristics of the corresponding minimum distance estimator including its asymptotic distribution under both discrete and continuous models; we also explore the use of the C-divergence family in parametric tests of hypothesis. We study the influence function of these minimum distance estimators, in both the first and second order, and indicate the possible limitations of the first-order influence function in this case. We also briefly study the breakdown results of the corresponding estimators. Some simulation results and real data examples demonstrate the small sample efficiency and robustness properties of the estimators. 相似文献
6.
A family of distributions for which an unbiased estimator of a function g(θ) of a real parameter θ can attain the second order Bhattacharyya lower bound is derived. Indeed, we obtain a necessary
and sufficient condition for the attainment of the second order Bhattacharyya bound for a family of mixtures of distributions
which belong to the exponential family. Furthermore, we give an example which does not satisfy this condition, but where the
Bhattacharyya bound is attainable for a non-exponential family of distributions. 相似文献
7.
Summary Any one parameter exponential family of distributions has monotone likelihood ratios. As the product probabilities of n identical distributions of an exponential family form again an exponential family, it has monotone likelihood ratios for arbitrary n. Furthermore, the members of an exponential family are mutually absolutely continuous. In Part 1, we show that these properties uniquely characterize the exponential family. The application of this result to the theory of testing hypotheses (Part 2) shows that if a family of mutually absolutely continuous distributions has uniformly most powerful tests for arbitrary levels of significance, and arbitrary sample sizes, then it is necessarily an exponential family.The research was done while this author was a Visiting Professor in the Department of Statistics at the University of Chicago. It was supported by Research Grants Nos. NSF-G10368 and NSF-G21058 from the Division of Mathematical, Physical and Engineering Sciences of the National Science Foundation. 相似文献
8.
We establish a number of results on numberings, in particular, on Friedberg numberings, of families of d.c.e. sets. First, it is proved that there exists a Friedberg numbering of the family of all d.c.e. sets. We also show that this result, patterned on Friedberg's famous theorem for the family of all c.e. sets, holds for the family of all n-c.e. sets for any n>2. Second, it is stated that there exists an infinite family of d.c.e. sets without a Friedberg numbering. Third, it is shown that there exists an infinite family of c.e. sets (treated as a family of d.c.e. sets) with a numbering which is unique up to equivalence. Fourth, it is proved that there exists a family of d.c.e. sets with a least numbering (under reducibility) which is Friedberg but is not the only numbering (modulo reducibility). 相似文献
9.
从Yang-Baxter簇方程和Volterra积分方程得到的Rota-Baxter簇代数的概念出发,我们引入Rota-Baxter簇系统的概念,推广了Brzezinski提出的Rota-Baxter系统.我们证明这个概念也与结合Yang-Baxter簇对和pre-Lie簇代数有关.此外,作为Rota-Baxter簇系统的一个类比,我们引入平均簇系统的概念,并证明平均簇系统会得到dialgebra簇结构.我们还研究dendriform代数上的Rota-Baxter簇系统,并展示它们如何诱导quadri簇代数结构.最后,我们用Gr\"obner-Shirshov基的方法给出Rota-Baxter簇系统的一个线性基. 相似文献
10.
We obtain conditions for the existence of a linear feedback providing the existence of a family ( N
t
) of subspaces such that this family is invariant under the closed system and the output variable is zero on all motions lying
in this family. 相似文献
11.
We will consider a certain kind of intersection family: a family of vectors over a field of finite characteristic q, such that the generalized inner products of every q or fewer vectors take on prescribed values. For certain values of the parameters, these values distinguish the generalized inner product of any q distinct vectors, from that of any q vectors in which some vector is repeated.We will represent such an intersection family by its incidence matrix, and show that the matrix product of two such matrices is itself an intersection family of the type under consideration. If the factor families distinguish between generalized inner products of q vectors with or without repetition, then so does the product family. 相似文献
12.
An m-transversal to a family of convex sets in the plane is an m-point set which intersects every members of the family. One of Grübaum’s conjectures says that a planar family of translates of a convex compact set has a 3-transversal provided that any two of its members intersect. Recently the conjecture has been proved affirmatively (see [4]). In the present paper we provide a different and straightforward proof for the conjecture for the family of translates of a closed trapezoid in the plane and give several concrete 3-transversals. 相似文献
13.
In the first part of the present paper, we established estimates for the rate of approach of the integrals of a family of
“physical” white noises to a family of Wiener processes. We use this result to establish the estimate for the rate of approach
of a family of solutions of ordinary differential equations perturbed by some “physical” white noises to a family of solutions
of the corresponding It? equations. We consider both the case where the coefficient of random perturbation is separated from
zero and the case where it is not separated from zero. 相似文献
14.
Shafarevich’s hyperbolicity conjecture asserts that a family of curves over a quasi-projective 1-dimensional base is isotrivial
unless the logarithmic Kodaira dimension of the base is positive. More generally it has been conjectured by Viehweg that the
base of a smooth family of canonically polarized varieties is of log general type if the family is of maximal variation. In
this paper, we relate the variation of a family to the logarithmic Kodaira dimension of the base and give an affirmative answer
to Viehweg’s conjecture for families parametrized by surfaces. 相似文献
15.
We investigate the algebra of repeated integrals of semimartingales. We prove that a minimal family of semimartingales generates a quasi-shuffle algebra. In essence, to fulfil the minimality criterion, first, the family must be a minimal generator of the algebra of repeated integrals generated by its elements and by quadratic covariation processes recursively constructed from the elements of the family. Second, recursively constructed quadratic covariation processes may lie in the linear span of previously constructed quadratic covariation processes and of the family, but may not lie in the linear span of repeated integrals of these. We prove that a finite family of independent Lévy processes that have finite moments generates a minimal family. Key to the proof are the Teugels martingales and a strong orthogonalization of them. We conclude that a finite family of independent Lévy processes forms a quasi-shuffle algebra. We discuss important potential applications to constructing efficient numerical methods for the strong approximation of stochastic differential equations driven by Lévy processes. 相似文献
16.
A group of orthogonal operators is considered which transforms a given family of Gaussian random variables into a family independent
of another given Gaussian family. A way to study distributions of suprema for such families is proposed. Bibliography: 5 titles.
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 228, 1996, pp. 300–311 相似文献
17.
Two combinatorial methods for constructing a family of symmetric trivalent graphs are presented in this paper. Each family of graphs contains a member for every odd prime number p. It is proved that in one of the families the girth is unbounded as a function of p; the other family contains the smallest known trivalent graphs of girth 18 and 19. 相似文献
18.
In the present paper we introduce notions of A-splitting and A-jointly continuous topology on the set C(Y,Z) of all continuous
maps of a topological space Y into a topological space Z, where A is any family of spaces. These notions satisfy the basic
properties of splitting and jointly continuous topologies on C(Y,Z). In particular, for every A, the greatest A-splitting
topology on C(Y,Z) (denoted by τ(A) always exists. We indicate some families A of spaces for which the topology τ(A) coincides
with the greatest splitting topology on C(X,Y). We give a notion of equivalent families of spaces and try to find a “simple”
family which is equivalent to a given family. In particular, we prove that every family is equivalent to a family consisting
of one space, and the family of all spaces is equivalent to a family of all T 1-spaces containing at most one nonisolated point. We compare the topologies τ({X}) for distinct compact metrizable spaces
X and give some examples. Bibliography: 13 titles.
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 208, 1993, pp. 82–97.
Translated by A. A. Ivanov. 相似文献
20.
Abstract The concept of Wick product is strongly related to the underlying Brownian motion we have fixed on the probability space. Via the Girsanov's theorem we construct a family of new Brownian motions, obtained as translations of the original one, and to each of them we associate a Wick product. This produces a family of Wick products, named γ-Wick products, parameterized by the performed translations. We aim to describe this family of products. We also define a new family of stochastic integrals, which are related in a natural way to the γ-Wick products. 相似文献
|