共查询到20条相似文献,搜索用时 31 毫秒
1.
Let(E)z xy+A(x, y)zx+B(x, y)zy+C(x, y)z=U(x, y) a.e. in Δ=]0,a[×]0,b[, be a distributed parameter control process. We study the uniqueness of some optimal control problems (minimum distance and minimum effort problems) relative to (E). We take the Orlicz spaceL M(Δ) as the «permanent control space, whereas both the «initial control» space and the «target» space are subspaces of the Orlicz-Sobolev spaceW 1,M (]0,a[)×W 1,M (]0,b[). 相似文献
2.
Gábor P. Nagy 《代数通讯》2013,41(2):549-555
ABSTRACT Let (A, ?) be a structurable algebra. Then the opposite algebra (A op , ?) is structurable, and we show that the triple system B op A(x, y, z):=Vopx,y(z)=x(y¯z)+z(y¯x)?y(x¯z), x, y, z ∈ A, is a Kantor triple system (or generalized Jordan triple system of the second order) satisfying the condition (A). Furthermore, if A=𝔸1?𝔸2 denotes tensor products of composition algebras, (?) is the standard conjugation, and (∧) denotes a certain pseudoconjugation on A, we show that the triple systems B op 𝔸1?𝔸2 ( x , y¯∧, z) are models of compact Kantor triple systems. Moreover these triple systems are simple if (dim𝔸1, dim𝔸2) ≠ (2, 2). In addition, we obtain an explicit formula for the canonical trace form for compact Kantor triple systems defined on tensor products of composition algebras. 相似文献
3.
Summary Motivated by results on the classical cocycle equation, we solved the more general equationF
1
(x + y, z) + F
2
(y + z, x) + F
3
(z + x, y) + F
4
(x, y) + F
5
(y, z) + F
6
(z, x) = 0 for six unknown functions mapping ordered pairs from an abelian group into a vector space over the rationals.Dedicated to the memory of Alexander M. Ostrowski on the occasion of the 100th anniversary of his birth. 相似文献
4.
Zhu Xuexian 《逼近论及其应用》2001,17(4):65-76
Let Mg be the maximal operator defined by
Mg f( x ) = sup\fracòab f( y )g( y )\textdy òab g( y )\textdy M_g f\left( x \right) = \sup \frac{{\int_a^b {f\left( y \right)g\left( y \right){\text{d}}y} }}{{\int_a^b {g\left( y \right){\text{d}}y} }} 相似文献
5.
Summary The paper investigates the equation(1.1) in the two cases:i) p≡0,ii) p(≠0) is either bounded or satisfies |(p(t,x,y,z,u)|⩽(A0+|y|+|u|+|z| Ψ(t) where A0 is a constant. For the casei) the asymptotic stability (in the large) of the trivial solution x=0 is investigated and for the caseii) a general estimate and two boundedness results are obtained for solutions of(1.1). The results extend those obtained by Harrow[1] for the same equation(1.1).
Entrata in Redazione il 18 novembre 1971. 相似文献
6.
R.J. McCann 《Geometric And Functional Analysis》2001,11(3):589-608
Let (M,g) be a connected compact manifold, C3 smooth and without boundary, equipped with a Riemannian distance d(x,y). If s : M ? M s : M \to M is merely Borel and never maps positive volume into zero volume, we show s = t °u s = t \circ u factors uniquely a.e. into the composition of a map t(x) = expx[-?y(x)] t(x) = {\rm exp}_x[-\nabla\psi(x)] and a volume-preserving map u : M ? M u : M \to M , where y: M ? \bold R \psi : M \to {\bold R} satisfies the additional property that (yc)c = y (\psi^c)^c = \psi with yc(y) :=inf{c(x,y) - y(x) | x ? M} \psi^c(y) :={\rm inf}\{c(x,y) - \psi(x)\,\vert\,x \in M\} and c(x,y) = d2(x,y)/2. Like the factorization it generalizes from Euclidean space, this non-linear decomposition can be linearized around the identity to yield the Hodge decomposition of vector fields.¶The results are obtained by solving a Riemannian version of the Monge--Kantorovich problem, which means minimizing the expected value of the cost c(x,y) for transporting one distribution f 3 0 f \ge 0 of mass in L1(M) onto another. Parallel results for other strictly convex cost functions c(x,y) 3 0 c(x,y) \ge 0 of the Riemannian distance on non-compact manifolds are briefly discussed. 相似文献
7.
In this paper we study boundary eigenvalue problems for first order systems of ordinary differential equations of the form \[zy'\left( z \right) = \left( {\lambda A_1 \left( z \right) + A_0 \left( z \right)} \right)y\left( z \right),\,\,y\left( {ze^{2\pi i} } \right) = e^{2\pi iv} y\left( z \right)\] for z ? Slog, where S is a ring region around zero, Slog denotes the Riemann surface of the logarithm over S, the coefficient matrix functions A1(z) and A0(z) are holomorphic on S, and v is a complex number. The eigenfunctions of this eigenvalue problem are the Floquet solutions of the differential system with v as characteristic exponent. For an open subset S0 of S, the notion of A1-convexity of the pair (S0, S) is introduced. For A1-convex pairs (S0, S) it is shown that the expansion into eigenfunctions and associated functions of holomorphic functions on Slog, satisfying the monodromy condition y(ze2πi) = e2πivy(z), converges regularly on Slog0 and is unique. If S is a pointed neighbourhood of 0 and A1(z) is holomorphic in SU{0}, it is shown that there is a pointed neighbourhood S0 of 0 such that (S0, S) is A1-convex. It follows from the results of this paper that many expansions of analytic functions in terms of special functions can be considered as eigenfunction expansions of this kind. 相似文献
8.
A p-local module M is called (fully) transitive if for all x,y ? Mx,y\in M with UM(x) = UM(y) ( UM(x)\leqq UM(y)U_M(x)\leqq U_M(y)) there exists an automorphism (endomorphism) of M which maps x onto y. In this paper we examine the relationship of these two notions in the case of p-local modules. We show that a module M is fully transitive if and only if M?MM\oplus M is transitive in the case where the divisible part of M/tMM/tM has rank at most one. Moreover, we show that for the same class of modules transitivity implies full transitivity if p > 2. This extends theorems of Files, Goldsmith and of Kaplansky for torsion p-local modules. 相似文献
9.
We are concerned here with certain Banach algebras of operators contained within a fixed II factor N. These algebras may be thought of as noncommutative classifying spaces for the functor Ext
*
N
The basic objects of study are the algebras A
kN (for n=1, 2,...). Here, we are given an essentially unique representation of the complex Clifford algebra C
k N and the elements of A
k are those operators in N which exactly commute with the first k–1 generators of C
k and also commute with the kth generator modulo a symmetric ideal
N. Up to isomorphism, these algebras are periodic with period 2.We determine completely the homotopy types of A
1
–1
and A
2
–1
Here, A
1
–1
is homotopy equivalent to the space of (Breuer) Fredholm operators in N, while A
2
–1
is homotopy equivalent to the group K
N
–1
={x N–1¦ x=1+k, k KN}. We use these results to compute the K-theory of A
1 and A
2.For a fixed C
*-algebra A, we define abelian groups G
k,N(A) of equivalence classes of homomorphisms AA
k. Letting N = M
(H) for a II1 factor M we define similar abelian groups G
k(A, M) where we replace N by L(E) for countably generated right Hilbert M-modules E with (left) actions C
k L(E). Using ideas of Skandalis, we show that G
k,NGk(A, M) so that the G
k,N are stable half-exact homotopy functors because the G
k(·, M) are such.In general, we show that G
k(A, M)KK k(A, M) and so our theory fits neatly into Kasparov KK-theory. We investigate many interesting examples from our point of view. 相似文献
10.
LiJunjie BianBaojun 《高校应用数学学报(英文版)》2000,15(3):273-280
The following regularity of weak solutions of a class of elliptic equations of the form are investigated. 相似文献
11.
Abstract Let x(ti), y(ti) be two time series such that y(ti) = μ(ti, x) + εi, where μ is a smooth function and εi is a zero mean stationary process. Which model may be assumed for μ depends on the subject specific context. This article was motivated by questions raised in the context of musical performance theory. The general problem is to understand the relationship between the symbolic structure of a music score and its performance. Musical structure typically consists of a hierarchy of global and local structures. This motivates the definition of hierarchical smoothing models (or HISMOOTH models) that are characterized by a hierarchy of bandwidths b 1 > b 2 > … > bM and a vector of coefficients β ∈ RM. The expected value μ(ti x) = E[y(ti)‖x] is equal to a weighted sum of smoothed versions of x. The “errors” εi are modeled by a Gaussian process that may exhibit long memory. More generally, we may observe a collection of time series yr (r = 1, …, N) that are related to a common time series x by yr(ti) = μ r(ti, x) + εr, i where ε r are independent error processes. For repeated time series, HISMOOTH models lead to a visual and formal classification into clusters that can be interpreted in terms of the relationship to x. An analysis of tempo curves from 28 performances of Schumann's “Träumerei” op. 15/7 illustrates the method. In particular, similarities and differences of “melodic styles” can be identified. 相似文献
12.
The Bass–Heller–Swan–Farrell–Hsiang–Siebenmann decomposition of the Whitehead group K
1(A[z,z-1]) of a twisted Laurent polynomial extension A[z,z-1] of a ring A is generalized to a decomposition of the Whitehead group K
1(A((z))) of a twisted Novikov ring of power series A((z))=A[[z]][z-1]. The decomposition involves a summand W1(A, ) which is an Abelian quotient of the multiplicative group W(A,) of Witt vectors 1+a1z+a2z2+ ··· A[[z]]. An example is constructed to show that in general the natural surjection W(A, )ab W1(A, ) is not an isomorphism. 相似文献
13.
Arrangements and cohomology 总被引:11,自引:0,他引:11
Michael Falk 《Annals of Combinatorics》1997,1(1):135-157
14.
Vincent Thilliez 《Monatshefte für Mathematik》2010,13(2):443-453
In the first part of this work, we consider a polynomial j(x,y)=yd+a1(x)yd-1+?+ad(x){\varphi(x,y)=y^d+a_1(x)y^{d-1}+\cdots+a_d(x) } whose coefficients a
j
belong to a Denjoy-Carleman quasianalytic local ring E1(M){\mathcal{E}_1(M) }. Assuming that E1(M){\mathcal{E}_1(M) } is stable under derivation, we show that if h is a germ of C
∞ function such that j(x,h(x))=0{ \varphi(x,h(x))=0 }, then h belongs to E1(M){\mathcal{E}_1(M) }. This extends a well-known fact about real-analytic functions. We also show that the result fails in general for non-quasianalytic
ultradifferentiable local rings. In the second part of the paper, we study a similar problem in the framework of ultraholomorphic
functions on sectors of the Riemann surface of the logarithm. We obtain a result that includes suitable non-quasianalytic
situations. 相似文献
15.
Elements a,b of a group G are said to be fused if a = bσ and to be inverse-fused if a =(b-1)σ for some σ ? Aut(G). The fusion class of a ? G is the set {aσ | σ ? Aut(G)}, and it is called a fusion class of order i if a has order iThis paper gives a complete classification of the finite nonabelian simple groups G for which either (i) or (ii) holds, where: (i) G has at most two fusion classes of order i for every i (23 examples); and (ii) any two elements of G of the same order are fused or inversenfused. The examples in case (ii) are: A5, A6,L2(7),L2(8), L3(4), Sz(8), M11 and M23An application is given concerning isomorphisms of Cay ley graphs. 相似文献
16.
Yu. Kh. Eshkabilov 《Siberian Advances in Mathematics》2009,19(3):151-161
Let Ω = [a, b]
ν
and let T be a partially integral operator defined in L
2(Ω2) as follows:
|