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1.
Summary We study the equation (A – ) x + (B–)x=y, with unknown x, in a Banach space X. y Xis the datum, > 0, A and B are linear closed unbounded operators in X with domains DA, DB. In the non commutative case, under assumptions already considered in the literature (see [7]), we show that for large values of any solution x DA DB satisfies an a priori estimate ¦|x¦|c–1¦|y||and we prove that for any y X there exists a unique strong solution x, i.e. there exist xnDA DB such that xn x, (A–) xn+(B–) xny in X. We also study regularity properties of strong solutions and we show that they belong to suitable interpolation spaces between DA (or DB) and X.  相似文献   

2.
It is proved that for anyf(x, y) L(R), where R=[-,,-, ], a function (x, y), exists such that ¦(x, y) ¦=¦f(x, y) ¦ for almost all (x, y) R. The Fourier series of the function (x, y) and all conjugate trigonometric series are A*-summable almost everywhere.Translated from Matematicheskie Zametki, Vol. 11, No. 2, pp. 145–150, February, 1972.  相似文献   

3.
Zusammenfassung Gegeben seien endliche MengenX, Y undZ X × Y, Z x ={y¦(x,y) Z},Z y ={x¦(x,y) Z}.Man nenntA X (bzw.B Y)zuordenbar, wenn es eine Injektion:A Y (bzw.: B X) mit(x) Z x (bzw.(y) Z y ) gibt, und (A, B) mit #A=#B > 0 einZuordnungspaar, wenn eine Bijektionf:A B mitf(x)Z x B (bzw.f –1 (y) Z y A) existiert. Die Bijektionf heißtZuordnungsplan fürA, B.In der vorliegenden Arbeit werden Fragen nach der Existenz von optimal zuordenbaren Mengen und optimalen Zuordnungspaaren behandelt, wenn man auf den MengenX undY Ordnungen vorgibt, wobei auch Nebenbedingungen berücksichtigt werden. In manchen Fällen lassen sich anhand der Beweise Zuordnungspläne oder ihre Berechnungsvorschrift explizit angeben.Zum Schluß werden die Aussagen an konkreten, dem Bereich der Wirtschaftswissenschaften entnommenen Beispielen erläutert.
Summary LetX, Y be finite sets andZ X × Y, Z x ={y¦(x,y) Z},Z y ={x¦(x,y)Z}. A X (resp.B Y) is calledassignable if there is an injection: A Y (resp.: B X) with (x) Z x (resp.(y) Z y ), (A, B) with #A=#B > 0 anassigned pair if there is a bijection f:A B withf (x) Z x B (resp.f –1(y) Z y A). The bijectionf is called aplan forA andB.In this paper problems are discussed concerning the existence of optimal assignable sets and optimal assigned pairs ifX andY are totally ordered, additional constraints are also considered. In some cases the proofs give explicit constructions of plans. The results are illustrated by application to problems occurring in Operations Research.


Diese Arbeit ist mit Unterstützung des Sonderforschungsbereiches 72 an der Universität Bonn entstanden.  相似文献   

4.
The solution of the following problems is offered. Suppose a multiset J (¦J¦=p) is given. For each pair of elements and J, a number 1 P is given. Moreover, if 1 < x<p then x is undefined. If x=1, then x=p. Problem 1. Find the permutation 1...F of elements of the multiset J satisfying the following conditions. Let i, i=. If i,j < x, thenj <i. If i,j > x, then i<j. Such a permutation is called a PC-schedule. Problem 2. Find a PC-schedule in which the following property holds: if i < x < j, i=, j=, then. Such a PC-schedule is called an SC-schedule. The conditions under which these problems have solutions are studied. For their solution an algorithm of shifts is used with the complexity O(¦B(J)¦2¦J¦).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 124, pp. 44–72, 1983.  相似文献   

5.
Thewidth (chain number) of a partial order P, < is the smallest cardinal such that ¦A¦< 1 + whenever A is an antichain (chain) in P. We prove that, if a partial order (P, <) has width and cf()=, then P contains antichains An (n<) such that ¦A 0¦<¦A1¦ <...<={¦An¦: n < < } and either A01 A2< ... or A0>A1 >A2> ... A similar structure result is obtained for partial orders with chain number if cf()=. As an application we solve a problem of van Douwen, Monk and Rubin [1] by showing that if a Boolean algebra has width , thencf() .This work has been partially supported by NATO grant No. 339/84.Presented by Bjarni Jonsson.  相似文献   

6.
In this paper we study particular sets of a Steiner systemS. More precisely, we study the setsA such that ¦A ¦ d modh for all lines ofS, withd andh integers satisfyingd 0,h 2.Dedicated to Professor M. Scafati Tallini on the occasion of her sixtyfifth birthday  相似文献   

7.
Error bounds are derived for the Lagrange interpolation formula and for the k-th derivative of the residual term of this formula in terms of the Lipschitz constant of the n-th derivative for the case with (n+1) nodes and also for the case when the functions satisfy a special condition: G x, y, z [a, b]: ¦ (x)(z–y) +(y)(x–z)+(z)(y–x)¦G¦(x–y)(y–z)(z–x)¦.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 73, pp. 27–32, 1992.  相似文献   

8.
For the multidimensional heat equation in a parallelepiped, optimal error estimates inL 2(Q) are derived. The error is of the order of +¦h¦2 for any right-hand sidef L 2(Q) and any initial function ; for appropriate classes of less regularf andu 0, the error is of the order of ((+¦h¦2 ), 1/2<1.Translated fromMatematicheskie Zametki, Vol. 60, No. 2, pp. 185–197, August, 1996.  相似文献   

9.
Summary This work deals with theH 1 condition numbers and the distribution of theB h singular values of the preconditioned operators {B h –1 A h }0, whereA h andB h are finite element discretizations of second order elliptic operators,A andB respectively.B is also assumed to be self-adjoint and positive definite. For conforming finite elements, Parter and Wong have shown that the singular values cluster in a positive finite interval. Goldstein also has derived results on the spectral distribution ofB h –1 A h using a different approach. As a generalization of the results of Parter and Wong, the current work includes nonconforming finite element methods which deal with Dirichlet boundary conditions. It will be shown that, in this more general setting, the singular values also cluster in a positive finite interval. In particular, if the leading part ofB is the same as the leading part ofA, then the singular values cluster about the point {1}. Two specific methods are given as applications of this theory. They are the penalty method of Babuka and the method of nearly zero boundary conditions of Nitsche. Finally, it will be shown that the same results can be proven by an approach generalized from the work of Goldstein.This research was supported by the National Science Foundation under grant number DMS-8913091.  相似文献   

10.
A-design is a family B 1,B 2,...,B v of subsets of X={1, 2,..., v} such that B i B j = for all i jand not all B i are of the same size. Ryser's andWoodall's -design conjecture states thateach -design can be obtained from a symmetricblock design by a certain complementation procedure. Our mainresult is that the conjecture is true when is twice a prime number.  相似文献   

11.
Necessary and sufficient conditions are given on a familyA r r>0 of subsets of a real linear space X under which infr > 0 x A r is a quasinorm [l] on X. It is shown that for any symmetric (about zero) closed set A in a normed space X containing the ball {x X: x l there exists a quasinorm ¦·¦ on X such that A = {x X ¦x¦ 1}. Examples are constructed of linear metric spaces in which there exists a Chebyshev line which is not an approximately compact set.Translated from Matematicheskie Zametki, Vol. 19, No. 2, pp. 237–246, February, 1976.  相似文献   

12.
Summary LetX 1,X 2,..., be i.i.d. random variables andS n=X 1+X 2+. +X n. In this paper we simplify Rogozin's condition forS n/B n ±1for someB n+, which generalises Hinin's condition for relative stability ofS n. We also consider convergence of subsequences ofS n/B n. As an application of our methods, we extend a result of Chow and Robbins to show thatS n/B n±1 a.s. for someB n + if and only if 0<¦EX¦E¦X¦<+ .  相似文献   

13.
Strict upper bounds are determined for ¦s(z)¦, ¦Re s(z)¦, and ¦Im s(z) ¦ in the class of functions s(z)=a nzn+an+1zn+1+... (n1) regular in ¦z¦<1 and satisfying the condition ¦u (1) –u (2) ¦K¦ 1- 2¦, where U()=Re s (ei ), K>0, and 1 and 2 are arbitrary real numbers. These bounds are used in the determination of radii of convexity and close-to-convexity of certain integral representations.Translated from Matematicheskie Zametki, Vol. 7, No. 5, pp. 581–592, May, 1970.The author wishes to thank L. A. Aksent'ev for his guidance in this work.  相似文献   

14.
A closed subset E of the unit circumference T is said to be a peak set for the analytic Hölder class A, 0 < < 1 there exists a functionf,fA such that f¦E1 and ¦f(z)¦<1 for. It is shown that the set E is a peak set of the algebra A if and only if there exists a nonnegative Borel measure on T such that the function coincides almost everywhere with a function of the Hölder class , equal to zero on E. A sufficient condition in order that a closed set E should belong to the family of peak sets is obtained.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 157, pp. 129–136, 1987.  相似文献   

15.
Summary In this note we observe that for independent symmetric random variables X and Y, when the pdf of X is PF, the conditional distributions of ¦Y¦ given S = X + Y form a MLR family. We then show that for a function : R nR that is symmetric in each coordinate and increasing on (0, )n, E((S1,...,Sn)¦Sn = s) is even and increasing in ¦s¦. Here S1,...,Sn are partial sums with independent symmetric PF summands. Application is made to sequential tests that minimize the maximum expected sample size when the model is a one-parameter exponential family generated by a symmetric PF density.Work supported by NSF grants MPS 72-05082 AO2 and MCS 75-23344  相似文献   

16.
In this paper, we prove the existence of an element of the group algebra A=F of a free groupF with two generatorsx andy over the field of complex numbersC such that, for any complexa andb for which ¦a¦=¦b¦=1, we haveA a,b ()A=0, where a,b ( is an automorphism ofA that mapsx,y intoax, by, respectively. Thus, we give a negative answer to question 12.46 of P. A. Linnel from Kourovka Notebook.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No.4, pp. 571–572, April, 1995.  相似文献   

17.
In this paper we examine for which Witt classes ,..., n over a number field or a function fieldF there exist a finite extensionL/F and 2,..., n L* such thatT L/F ()=1 andTr L/F (i)=i fori=2,...n.  相似文献   

18.
The imaginary powersA it of a closed linear operatorA, with inverse, in a Banach spaceX are considered as aC 0-group {exp(itlogA);t R} of bounded linear operators onX, with generatori logA. Here logA is defined as the closure of log(1+A) – log(1+A –1). LetA be a linearm-sectorial operator of typeS(tan ), 0(/2), in a Hilbert spaceX. That is, |Im(Au, u)| (tan )Re(Au, u) foru D(A). Then ±ilog(1+A) ism-accretive inX andilog(1+A) is the generator of aC 0-group {(1+A) it ;t R} of bounded imaginary powers, satisfying the estimate (1+A) it exp(|t|),t R. In particular, ifA is invertible, then ±ilogA ism-accretive inX, where logA is exactly given by logA=log(1+A)–log(1+A –1), and {A it;t R} forms aC 0-group onX, with the estimate A it exp(|t|),t R. This yields a slight improvement of the Heinz-Kato inequality.  相似文献   

19.
One considers the differential equation dx/dt=f(t, x) with the impulse action ¦t=ti=Hi(ti,x) in the space of bounded numerical sequences, where f(t, x), Hi(t, x) are T-periodic, countable-dimensional vector-valued functions, is a positive parameter. One gives conditions for the existence of a control (1,2) such that the solution of the equation dx/dt=f(t, x)–1 with impulse action x¦t=ti=Hi(ti,x)–2 assuming for t= the value x=x0, be T-periodic.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 2, pp. 271–275, February, 1990.  相似文献   

20.
It is shown that the axiom of choice AC is equivalent to the statements: (1)For every Boolean ring (B, +, ·)and every subset H B which is closed under + there exists amaximal ideal QB such that H Q={0} and, (2)For every Boolean ring (B,+,·),for every A B, the infinite system:X i + yi=bi,iI, b i B has a solution in A iff each of its equations has a solution in A.Presented by G. Grätzer  相似文献   

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