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1.
F. Schipp 《Analysis Mathematica》1990,16(2):135-141
H={h
1,I } — , . : , I ¦(I)¦=¦I¦, ¦I¦ — I. H H
={h
(I),I} . , , . L
p
.
Dedicated to Professor B. Szökefalvi-Nagy on his 75th birthday
This research was supported in part by MTA-NSF Grants INT-8400708 and 8620153. 相似文献
Dedicated to Professor B. Szökefalvi-Nagy on his 75th birthday
This research was supported in part by MTA-NSF Grants INT-8400708 and 8620153. 相似文献
2.
A study is presented of the relationship between the topological and uniformity properties of a group G and the spaces (G), (G) of all nonempty closed subsets and closed subgroups of G. A base for the neighborhood system of a closed subset X of G is formed by the sets S(X, U)={Y Y XU, X YU}, where U ranges over all neighborhoods of the identity in G. Criteria are obtained for the space (G) and some of its subspaces to be totally bounded and locally totally bounded. Some classes of groups with compact spaces (G) are described. It is proved that the spaces (G), (G) are complete in the case of projective metrizable groups G.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 4, pp. 542–549, April, 1990. 相似文献
3.
, [0, 1], (n+1) n-. . [2]. — (. 5.4 5.6). . 6.4 2 [5]. , [4]. , , [6] [7]. [1]. 相似文献
4.
M. Kh. Khafizov 《Mathematical Notes》1978,23(6):469-473
Let be a ring of sets, X a normed space, : X ( ) a bounded family of triangular functions. The following generalized Nikodym theorem is established: the family {} is uniformly bounded on if and only if it is bounded on every sequence of pairwise disjoint sets of which the union is a part of some set in . An analogous criterion is established also for semiadditive functions. In addition, it is shown that uniform boundedness of a family of triangular functions is preserved in passing from a ring to the -ring it generates.Translated from Matematicheskie Zametki, Vol. 23, No. 6, pp. 855–861, June, 1978. 相似文献
5.
Nieminen Juhani 《manuscripta mathematica》1972,7(1):13-21
Let L be a distributive lattice characterized by a ternary operation (, ,), where (a,b,c)=(ab)(bc)(ac)=(ab)(ac)(bc), a,b,cL. The note considers convex sublattices of L, called generalized ideals of L generated by the operation (, ,). Some remarks have been stated about the graph of a distributive lattice. 相似文献
6.
Summary In this paper we study the noncharacteristic Cauchy problem, ut–(a(x)ux)x=0, x(0, l), t.(0, T], u(0, t)=(t), ux(0,t)=0, 0tT, assuming only L for a. In the case of weak a priori bounds on u, we derive stability estimates on u of Hölder type in the interior and of logarithmic type at the boundary. Also the continuous dependence on a is considered.
Sunto Nel presente lavoro consideriamo il problema di Cauchy non ben posto ut= (a(x)ux)x, x(0, l), t(0, T), u(0, t)=(t), ux(0, t)=0, 0tT. Supponiamo che a sia misurabile e limitato inferiormente e superiormente da constanti positive. Introduciamo delle limitazioni a priori su u e dimostriamo la dipendenza continua di u rispetto al dato sia in (0, l)×(0, T) (di tipo hölderiano) sia per x=l (di tipo logaritmico). Consideriamo, inoltre, la dipendenza continua di u da a.相似文献
7.
V. N. Sudakov 《Mathematical Notes》1973,14(4):886-888
Let X and Y be locally compact-compact topological spaces, F X×Y is closed, and P(F) is the set of all Borel probability measures on F. For us to find, for the pair of probability measures (x, y P (X)×P(Y), a probability measure P(F) such that
X
=
X
–1
,
Y
=
Y
–1
it is necessary and sufficient that, for any pair of Borel sets A X, B Y for which (A× B) F=Ø, the condition
XA+
YB 1 holds.Translated from Matematicheskie Zametki, Vol. 14, No. 4, pp. 573–576, October, 1973. 相似文献
8.
Summary We show that there exist infinitely many positive integers m not of the form n -&ohgr;(n ) for any positive integer n . Here, &ohgr;(n ) stands for the number of distinct prime factors of n . A similar result holds with &ohgr;(n ) replaced by the total number of prime factors of n (counting multiplicities), or by the number of divisors of n . 相似文献
9.
This paper deals with the following Dirichlet problem Lu = 1A ( Au – qu = – f ( , u ) on ] 0, [ , u, ( 0 ) = 0, u ( ) = 0, where ] 0, + ], q 0 is continuous on [ 0, [ × ] 0, + [ ] 0, + [ is continuous and A satisfies some appropriate conditions. The main result is the existence and the uniqueness of a strictly positive regular solution of the problem ( ). Moreover, we study the behaviour of this solution in a neighbourhood of . Our approach is based on the use of the Green's function of the homogeneous equation and Schauder's fixed point theorem. 相似文献
10.
A. V. Ivanov 《Journal of Mathematical Sciences》1987,37(1):823-837
One considers singular parabolic equations of the form (u)/t–u0,where sign u is a multivalued function, equal to -I for u<0, to 1 for u>0, and to the segment [-I,I] for u=0. Such a class of equations contains, in particular, the model for the two-phase Stefan problem, the porous medium equation, and the plasma equation. For the bounded generalized solutions u(x,t) of the indicated equations (without the assumption u/L2one has established a qualified local estimate of the modulus of continuity.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Ins'tituta im. V. A. Steklova AN SSSR, Vol. 147, pp. 49–71, 1985. 相似文献
11.
, (n), - (P
n
), P
n
(A
n
)>0P
n
(A
n
)0,n. [15] - , . , P
n
P
n
T
n
T
n
. 相似文献
12.
Fan Xianling 《数学学报(英文版)》1996,12(3):254-261
In this paper the regularity of the Lagrangiansf(x, )=||(x)(1<
1(x)2< +) is studied. Our main result: If(x) is Holder continuous, then the Lagrangianf(x, )=f(x, )=||(x) is regular. This result gives a negative answer to a conjecture of V. Zhikov.Supported by the National Natural Science Foundation of China. 相似文献
13.
N. M. Ivochkina 《Journal of Mathematical Sciences》1984,26(6):2349-2359
One proves that a priori boundedness of the norm
of the solution of the problem det(Uxx)=f(x,u,ux)>>0,u¦=0. The magnitudes of the exponents,() depends on whether the arguments u p occur or not in f (x,u,p).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 125, pp. 74–90, 1983. 相似文献
14.
Dr. Alexander Kovačec 《Monatshefte für Mathematik》1981,92(1):19-35
We shall develop a method to prove inequalities in a unified manner. The idea is as follows: It is quite often possible to find a continuous functional :
n
, such that the left- and the right-hand side of a given inequality can be written in the form (u)(v) for suitable points,v=v(u). If one now constructs a map
n
n
, which is functional increasing (i.e. for each x
n
(which is not a fixed point of ) the inequality (x)<((x)) should hold) one specially gets the chain (u)(
u))(
2(u))...
n
(u)). Under quite general conditions one finds that the sequence {
n
(u)}
n converges tov=v(u). As a consequence one obtains the inequality (u)(v). 相似文献
15.
Paul Terwilliger 《Journal of Algebraic Combinatorics》2004,19(2):143-172
Let denote a distance-regular graph with diameter D 3, valency k, and intersection numbers a
i, b
i, c
i. Let X denote the vertex set of and fix x X. Let denote the vertex-subgraph of induced on the set of vertices in X adjacent X. Observe has k vertices and is regular with valency a
1. Let 1 2 ···
k
denote the eigenvalues of and observe 1 = a
1. Let denote the set of distinct scalars among 2, 3, ...,
k
. For let mult denote the number of times appears among 2, 3,...,
k
. Let denote an indeterminate, and let p
0, p1, ...,p
D denote the polynomials in
[] satisfying p
0 = 1 andp
i = c
i+1
p
i+1 + (a
i – c
i+1 + c
i)p
i + b
i
p
i–1 (0 i D – 1),where p
–1 = 0. We show
where we abbreviate
= –1 – b
1(1+)–1. Concerning the case of equality we obtain the following result. Let T = T(x) denote the subalgebra of Mat
X
(
) generated by A, E*0, E*1, ..., E*
D
, where A denotes the adjacency matrix of and E*
i
denotes the projection onto the ith subconstituent of with respect to X. T is called the subconstituent algebra or the Terwilliger algebra. An irreducible T-module W is said to be thin whenever dimE*
i
W 1 for 0 i D. By the endpoint of W we mean min{i|E*
i
W 0}. We show the following are equivalent: (i) Equality holds in the above inequality for 1 i D – 1; (ii) Equality holds in the above inequality for i = D – 1; (iii) Every irreducible T-module with endpoint 1 is thin. 相似文献
16.
Klaus Schmidt 《Probability Theory and Related Fields》1984,68(1):75-95
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.
Mario Bonk 《Aequationes Mathematicae》1997,53(1-2):54-72
Summary In this paper we solve the functional equationx(u + v)(u – v) = f
1(u)g1(v) + f2(u)g2(v) under the assumption thatx, , f
1, f2, g1, g2 are complex-valued functions onR
n
,n N arbitrary, and 0 and 0 are continuous. Our main result shows that, apart from degeneracy and some obvious modifications, theta functions of one complex variable are the only continuous solutions of this functional equation. 相似文献
18.
A. M. Sedletskii 《Mathematical Notes》1977,22(6):941-947
Conditions on the closeness of real sequences {n} and {n} are studied which imply the equality of the excesses of the systems {exp(inx)} and {exp(inx)} in the space L2(–a, a). A theorem is formulated in terms of the difference of the sequences {n} and {n} enumerating the functions. In the corollaries of the theorem, conditions are given in terms of the behavior of the difference n–n0. An example is constructed showing that the condition n–n0 alone is not sufficient for equality of the excesses.Translated from Matematicheskie Zametki, Vol. 22, No. 6, pp. 803–814, December, 1977. 相似文献
19.
Norbert?Hegyvri 《Acta Mathematica Hungarica》2005,106(3):187-195
20.
Let A be a set, and let E be the Banach space of bounded functions : A R, equipped with its natural order. With a rectangle R = (a,b) × (0,T] let F(x,t,) : R × E E be a bounded, continuous function satisfying a local Hölder condition and being quasimonotone increasing with respect to . Then there exists a solution u: [a,b] × [0,T] E of the problem ut(x,t) – uxx(x,t) = F(x,t,u(x,t)) ((x,t) R), u(x,t) = 0 ((x,t) R R). 相似文献