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1.
This paper deals with the ideals of identities of certain associative algebras over a field F of characteristic zero. An algebra W of matrices of the form ,,,M, where and , are F-algebras with unity and M is a (,)-bimodule, is considered. Under certain natural restrictions on M one obtains the equality of ideals of identities T(W)=T()T(), if [[x1,x2], x3[x4,x5]]T().Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 114, pp. 7–27, 1982.  相似文献   

2.
For 0 < let Tf denote one of the operators
We characterize the pairs of weights (u, v) for which T is a bounded operator from Lp(v) to Lq(u), 0 <p q < . This extends to > 0 the norm inequalities for =0 in [4, 16]. As an application we give lower bounds for convolutions f, where is a radially decreasing function.  相似文献   

3.
A bifurcation problem for variational inequalities
,
is studied, where K is a closed convex cone in , 3, B is a × matrix, G is a small perturbation, a real parameter. The main goal of the paper is to simplify the assumptions of the abstract results concerning the existence of a bifurcation of periodic solutions developed in the previous paper and to give examples in more than three dimensional case.  相似文献   

4.
5.
We consider a four-dimensional compact projective plane whose collineation group is six-dimensional and solvable with a nilradical N isomorphic to Nil×R, where Nil denotes the three-dimensional, simply connected, non-Abelian, nilpotent Lie group. We assume that fixes a flag p W, acts transitively on and fixes no point in the set W\p. Under these conditions, we will prove that either contains a three-dimensional group of elations or acts doubly transitively on .  相似文献   

6.
Lie theory renders a concept of curvature for the geometries (,) introduced by W. Benz [1]. Among regular curves in the chains of (, ) are characterized by =0.  相似文献   

7.
We solve an asymptotic problem in the geometry of numbers, where we count the number of singular n×n matrices where row vectors are primitive and of length at most T. Without the constraint of primitivity, the problem was solved by Y. Katznelson. We show that as T, the number is asymptotic to for n3. The 3-dimensional case is the most problematic and we need to invoke an equidistribution theorem due to W. M. Schmidt.  相似文献   

8.
9.
Let (, ) be a measurable space and C a nonempty bounded closed convex separable subset of p-uniformly convex Banach space E for some p > 1. We prove random fixed point theorems for a class of mappings T: × C C satisfying: for each x, y C, and integer n 1,
where a, b, c: [0, ) are functions satisfying certain conditions and T n(, x) is the value at x of the n-th iterate of the mapping T(, ·). Further we establish for these mappings some random fixed point theorems in a Hilbert space, in L p spaces, in Hardy spaces H p and in Sobolev spaces H k,p for 1 < p < and k 0. As a consequence of our main result, we also extend the results of Xu [43] and randomize the corresponding deterministic ones of Casini and Maluta [5], Goebel and Kirk [13], Tan and Xu [37], and Xu [39, 41].  相似文献   

10.
11.
Boboc  Nicu  Bucur  Gheorghe 《Potential Analysis》1998,8(4):345-357
It is proved that if S, T are two elliptic Dirichlet operators on an ordered Hilbert space such that the excessive (resp. coexcessive) elements with respect to S and T are the same then there exists > 0 with T = S. Particularly if , are two elliptic Dirichlet forms on L2 ( ) having the same domain of definition and the same -excessive (resp. -coexcessive) elements for any > 0 then = .  相似文献   

12.
We study the large-time behavior and rate of convergence to the invariant measures of the processes dX (t)=b(X) (t)) dt + (X (t)) dB(t). A crucial constant appears naturally in our study. Heuristically, when the time is of the order exp( – )/2 , the transition density has a good lower bound and when the process has run for about exp( – )/2, it is very close to the invariant measure. LetL =(2/2) – U · be a second-order differential operator on d. Under suitable conditions,L z has the discrete spectrum
- \lambda _2^\varepsilon ...and lim \varepsilon ^2 log \lambda _2^\varepsilon = - \Lambda \hfill \\ \varepsilon \to 0 \hfill \\ \end{gathered} $$ " align="middle" vspace="20%" border="0">  相似文献   

13.
Variational inequalities are studied, where K is a closed convex cone in , 3, B is a × matrix, G is a small perturbation, a real parameter. The assumptions guaranteeing a Hopf bifurcation at some 0 for the corresponding equation are considered and it is proved that then, in some situations, also a bifurcation of periodic solutions to our inequality occurs at some I 0. Bifurcating solutions are obtained by the limiting process along branches of solutions to penalty problems starting at 0 constructed on the basis of the Alexander-Yorke theorem as global bifurcation branches of a certain enlarged system.  相似文献   

14.
Given distinct varieties and of the same type, we say that is relatively -universal if there exists an embedding :K from a universal categoryK such that for every pairA, B ofK-objects, a homomorphismf:A B has the formf=g for someK-morphismg:A B if and only if Im(f) . Finitely generated relatively -universal varieties of Heyting algebras are described for the variety of Boolean algebras, the variety generated by a three element chain, and for the variety generated by the four element Boolean algebra with an added greatest element.Dedicated to the memory of Alan DayPresented by J. Sichler.The support of the NSERC is gratefully acknowledged.  相似文献   

15.
Summary We give some applications of infimal generators of complete lattices, in the sense of Kutateladze and Rubinov [12], to the study of dualities between two complete lattices E and F (i.e., mappings : E F satisfying for all and all index sets I, including the empty set I=Ø). We give some additional results for E=(2X, ), F=(2W, ) and E=(¯RX, ), F=(¯RW, ) (where X and W are arbitrary sets), with suitable families of infimal generators. We obtain some lattice- theoretic properties of the relations of [22] between dualities : (2X, ) (2W, ), binary relations X×W, polarities (): (2X, ) (2W, ), coupling functionals : X×W ¯R and Fenchel-Moreau conjugations c():(¯RX, ) (¯RW,).  相似文献   

16.
On recurrence     
Summary LetT be a non-singular ergodic automorphism of a Lebesgue space (X,L,) and letf: X be a measurable function. We define the notion of recurrence of such a functionf and introduce the recurrence setR(f)={:f– is recurrent}. If , then R()={0}, but in general recurrence sets can be very complicated. We prove various conditions for a number to lie in R(f) and, more generally, forR(f) to be non-empty. The results in this paper have applications to the theory of random walks with stationary increments.  相似文献   

17.
Let T() be the ordinal notation system from Buchholz-Schütte (1988). [The order type of the countable segmentT()0 is — by Rathjen (1988) — the proof-theoretic ordinal the proof-theoretic ordinal ofACA 0 + ( 1 lTR).] In particular let a denote the enumeration function of the infinite cardinals and leta 0 a denote the partial collapsing operation on T() which maps ordinals of T() into the countable segment T 0 of T(). Assume that the (fast growing) extended Grzegorczyk hierarchy and the slow growing hierarchy are defined with respect to the natural system of distinguished fundamental sequences of Buchholz and Schütte (1988) in the following way:
  相似文献   

18.
Let be the set of all primes, the field of all algebraic numbers, and Z the set of square-free natural numbers. We consider partially ordered sets of interpretability types such as , and , where AD is a variety of -divisible Abelian groups with unique taking of the pth root p(x) for every p , is a variety of -modules over a normal field , contained in , and Gn is a variety of n-groupoids defined by a cyclic permutation (12 ...n). We prove that , and are distributive lattices, with and where ub and ubf are lattices (w.r.t. inclusion) of all subsets of the set and of finite subsets of , respectively.Deceased.__________Translated from Algebra i Logika, Vol. 44, No. 2, pp. 198–210, March–April, 2005.  相似文献   

19.
Let f be holomorphic on a domain G C¯ and n be the error in best approximation of f in the supremum norm on a compact set E G by rational functions of order n. We obtain results characterizing the degree of decrease of the best approximation n in terms connected with the condenser (E,F), F=C¯ \ G¯, and the rate of growth of the maximum modulus of f(z). In particular, if f has a generalized order (, , f) in the domain G, thenlim supn (n)/ (log (1/log+((0 1 ....... n)1/n(n+1) ))) (, , f),where = exp (1/C(E,F)), C(E,F) is the capacity of the condenser (E,F).  相似文献   

20.
Let X and Y be two Hilbert spaces, and the space of bounded linear transformations from X into Y. Let {A } be a weakly periodic sequence of period T. Spectral theory of weakly periodic sequences in a Hilbert space is studied by H. L. Hurd and V. Mandrekar (1991). In this work we proceed further to characterize {A n} by a positive measure and a number T of -valued functions a 0, . . . ,a T–1; in the spectral form , where and is an -valued Borel set function on [0, 2) such that   相似文献   

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