共查询到20条相似文献,搜索用时 15 毫秒
1.
We study the approximation of the imbedding of functions from anisotropic and general-ized Sobolev classes into Lq([0,1]d) space in the quantum model of computation. Based on the quantum algorithms for approximation of finite imbedding from LpN to LNq , we develop quantum algorithms for approximating the imbedding from anisotropic Sobolev classes B(Wpr ([0,1]d)) to Lq([0,1]d) space for all 1 q,p ∞ and prove their optimality. Our results show that for p < q the quantum model of computation can bring a speedup roughly up to a squaring of the rate in the classical deterministic and randomized settings. 相似文献
2.
Pei Xin Ye 《数学学报(英文版)》2010,26(4):669-678
We study the approximation of the integration of multivariate functions in the quantum model of computation. Using a new reduction approach we obtain a lower bound of the n-th minimal query error on anisotropic Sobolev class R(Wpr([0, 1]d)) (r R+d). Then combining this result with our previous one we determine the optimal bound of n-th minimal query error for anisotropic Hblder- Nikolskii class R(H∞r([0,1]d)) and Sobolev class R(W∞r([0,1]d)). The results show that for these two types of classes the quantum algorithms give significant speed up over classical deterministic and randomized algorithms. 相似文献
3.
L.N Carling 《Journal of Functional Analysis》1977,25(3):236-243
G is a locally compact group that contains the semidirect product J of a closed normal subgroup H and a closed connected subgroup K. Conditions on J are given that imply that the restriction map Bp(G) → Bp(H) (1 < p < ∞; G amenable if p ≠ 2) of the Fourier-Stieltjes algebras is not surjective. It is also shown that if the restriction map B(J) → B(H) is surjective, J need not be a direct product, even if H is nilpotent. 相似文献
4.
Let (T, Σ, μ) be a measure space, E a Banach space, and Lp(E, μ) the Lebesque-Bochner function spaces for 1 < p < ∞. It is shown that Lp(E, μ) is smooth if and only if E is smooth. From this result a Radon-Nikodym theorem for conjugates of smooth Banach spaces is established, and thus a general geometric condition on E sufficient to ensure that for all p, 1 < p < ∞. Alternate proofs of certain known results concerning the duals of Lp(E, μ) spaces are provided. 相似文献
5.
J. Ka?kol 《Journal of Mathematical Analysis and Applications》2003,280(1):155-162
It is well known that the space Cp([0,1]) has countable tightness but it is not Fréchet-Urysohn. Let X be a Cech-complete topological space. We prove that the space Cp(X) of continuous real-valued functions on X endowed with the pointwise topology is Fréchet-Urysohn if and only if Cp(X) has countable bounded tightness, i.e., for every subset A of Cp(X) and every x in the closure of A in Cp(X) there exists a countable and bounding subset of A whose closure contains x. We study also the problem when the weak topology of a locally convex space has countable bounded tightness. Additional results in this direction are provided. 相似文献
6.
The classic Rosenthal–Lacey theorem asserts that the Banach space of continuous real-valued maps on an infinite compact space K has a quotient isomorphic to c or . More recently, Ka?kol and Saxon [20] proved that the space endowed with the pointwise topology has an infinite-dimensional separable quotient algebra iff K has an infinite countable closed subset. Hence lacks infinite-dimensional separable quotient algebras. This motivates the following question: (?) Doesadmit an infinite-dimensional separable quotient (shortly SQ) for any infinite compact space K? Particularly, does admit SQ? Our main theorem implies that has SQ for any compact space K containing a copy of . Consequently, this result reduces problem (?) to the case when K is an Efimov space (i.e. K is an infinite compact space that contains neither a non-trivial convergent sequence nor a copy of ). Although, it is unknown if Efimov spaces exist in ZFC, we show, making use of some result of R. de la Vega (2008) (under ?), that for some Efimov space K the space has SQ. Some applications of the main result are provided. 相似文献
7.
We use the Ringel-Hall algebra approach to study the canonical basis elements for the quantum group of type B2 which are characterized in Xi [12]. However, our approach simplifies several computations there. 相似文献
8.
This paper gives the optimal order l of smoothness in the Mihlin and Hörmander conditions for operator-valued Fourier multiplier theorems. This optimal order l is determined by the geometry of the underlying Banach spaces (e.g. Fourier type). This requires a new approach to such multiplier theorems, which in turn leads to rather weak assumptions formulated in terms of Besov norms. 相似文献
9.
David D Yao 《Operations Research Letters》1985,4(2):79-83
We develop for the queue Mx/M/c an upper bound for the mean queue length and lower bounds for the delay probabilities (that of an arrival group and that of an arbitrary customer in the arrival group). An approximate formula is also developed for the general bulk-arrival queue GIx/G/c. Preliminary numerical studies have indicated excellent performance of the results. 相似文献
10.
Leon Bernstein 《Journal of Number Theory》1974,6(4):264-270
The main result of this paper is the following: the only zeros of the title function are at n = 3 and n = 12. This is achieved by means of the recursion function for f(n), viz. F(x) = x3 ? x ? 1 which has only one real root w. This turns out to be the fundamental unit of Q(w). From the norm equation of the units, N(w) = x3 + y3 + z3 ? 3xyz + 2x2z + xz2 ? xy2 ? yz2 = 1, and the negative powers of w which are of binary form, the result follows. The paper concludes with two remarkable combinatorial identities. 相似文献
11.
Compactness criterion for a sequence of infinitely divisible laws in terms of their Lévy-Khinchine representations is obtained. As a consequence, analog of classical central limit theorems without the assumption of bounded variance on the triangular arrays are proved. 相似文献
12.
It is proved that if a locally compact group G acts simplicially on a tree in such a way that the stabilizers of the vertices are amenable, then G is K-amenable. In particular, the canonical map from the full C1-algebra onto the reduced C1-algebra of G induces isomorphisms in K-theory. The main corollary of our result is that SL2(Qp) and some other groups over local fields are K-amenable. 相似文献
13.
Figen Öke 《Applied mathematics and computation》2011,218(3):956-958
Let v be a valuation of a field K, Gv its value group and kv its residue field. Let w be an extension of v to K(x1, … , xn). w is called a residual transcendental extension of v if kw/kv is a transcendental extension. In this study a residual transcendental extension w of v to K(x1, … , xn) such that transdegkw/kv = n is defined and some considerations related with this valuation are given. 相似文献
14.
Stephen James Wolfe 《Stochastic Processes and their Applications》1982,12(3):301-312
Let B1, B2, ... be a sequence of independent, identically distributed random variables, letX0 be a random variable that is independent ofBn forn?1, let ρ be a constant such that 0<ρ<1 and letX1,X2, ... be another sequence of random variables that are defined recursively by the relationshipsXn=ρXn-1+Bn. It can be shown that the sequence of random variablesX1,X2, ... converges in law to a random variableX if and only ifE[log+¦B1¦]<∞. In this paper we let {B(t):0≦t<∞} be a stochastic process with independent, homogeneous increments and define another stochastic process {X(t):0?t<∞} that stands in the same relationship to the stochastic process {B(t):0?t<∞} as the sequence of random variablesX1,X2,...stands toB1,B2,.... It is shown thatX(t) converges in law to a random variableX ast →+∞ if and only ifE[log+¦B(1)¦]<∞ in which caseX has a distribution function of class L. Several other related results are obtained. The main analytical tool used to obtain these results is a theorem of Lukacs concerning characteristic functions of certain stochastic integrals. 相似文献
15.
A matrix A∈Rn×n is called a bisymmetric matrix if its elements ai,j satisfy the properties ai,j=aj,i and ai,j=an-j+1,n-i+1 for 1?i,j?n. This paper considers least squares solutions to the matrix equation AX=B for A under a central principal submatrix constraint and the optimal approximation. A central principal submatrix is a submatrix obtained by deleting the same number of rows and columns in edges of a given matrix. We first discuss the specified structure of bisymmetric matrices and their central principal submatrices. Then we give some necessary and sufficient conditions for the solvability of the least squares problem, and derive the general representation of the solutions. Moreover, we also obtain the expression of the solution to the corresponding optimal approximation problem. 相似文献
16.
17.
Various initial-boundary value problems and Cauchy problems can be written in the form , where ?:R→ is nondecreasing and A is the linear generator of strongly continuous nonexpansive semigroup e?tA in an L1 space. For example, if A = ?Δ (subject, perhaps, to suitable boundary conditions) we obtain equations arising in flow in a porous medium or plasma physics (depending on the choice of ?) while if acting in L1() we have a scalar conservation law. In this paper we show that if M, m > 0 and m?′2 ? ν??′' ? M?′2, where ν ? {1,?1}, then (roughly speaking), the norm of may be estimated in terms of the initial data u0 in L1. Such estimates give information about the regularity of solutions, asymptotic behaviour, etc., in applications. Side issues, such as the introduction of sufficiently regular approximate problems on which estimates can be made and the assignment of a precise meaning to the operator A?, are also dealt with. These considerations are of independent interest. 相似文献
18.
19.
20.
Derivations and Automorphisms of the Positive Part of the Two-parameter Quantum Group Ur,s(B3) 下载免费PDF全文
We compute the derivations of the positive part of the two-parameter quantum group U_(r,s)(B_3) and show that the Hochschild cohomology group of degree 1 of this algebra is a threedimensional vector space over the base field C. We also compute the groups of(Hopf) algebra automorphisms of the augmented two-parameter quantized enveloping algebra ?_(r,s)~(≥0)(B_3). 相似文献