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1.
G. V. Kuz'mina 《Journal of Mathematical Sciences》1978,10(2):241-256
We obtain a complete solution of the problem of the maximum of the fourth diameter in the family of continua with capacity 1. Let E(o, ei, e–i). 0<2, be a continuum of minimum capacity containing the points o, ei, e–i; H(=cap E(o, ei, e–i). Let C() be the common point of three analytic arcs which form E(o, ei, e–i). One shows that the indicated maximum is realized by the continuum ={z:H(0)z
2E(o, ei, e–i)} where
0, o<02, is a solution of the equation. Any other extremal continuum of the gives problem is an image of under the mappingz ei
z+C ( is a real and C is a complex constant). One finds the value of the required maximum. The paper contains a brief exposition of the proof of this result.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 59, pp. 60–79, 1976. 相似文献
2.
Torben Maack Bisgaard 《Analysis Mathematica》2001,27(1):37-54
For >2, let Q
+() be the infimum of those q>0 for which the function n epn is positive definite on N
0 for every pq. We shall prove that Q
+()0 as 2. 相似文献
3.
Bernard Badzioch 《K-Theory》1999,16(1):29-34
We prove that for an arbitrary endomorphism of a ring R the group K1(R[t]) splits into the direct sum of K1(R) and Ñil (r;). Moreover, for any such R and Ñil (R; ) is isomorphic to Ñil (R ; ) for some ring R with : R R – an isomorphism. 相似文献
4.
D. Leladze 《Georgian Mathematical Journal》1994,1(3):287-302
We have obtained an estimate, in terms of partial and mixed moduli, of the continuity of deviation of the Cesáro (C, ) means ( = (1,...,n),i , 1 > –1,
) of the sequence of rectangular partial sums ofn-multiple (n>1) conjugate trigonometric series from then-multiple truncated conjugate function. This estimate implies the result on them
-convergence (1) of (C, ) means (1 > 0,
) provided that the essential conditions are imposed on the partial moduli of continuity. Finally, it is shown that them
-convergence cannot be replaced by ordinary convergence. 相似文献
5.
V. A. Belonogov 《Algebra and Logic》2005,44(1):13-24
In the representation theory of symmetric groups, for each partition of a natural number n, the partition h() of n is defined so as to obtain a certain set of zeros in the table of characters for Sn. Namely, h() is the greatest (under the lexicographic ordering ) partition among P(n) such that (g) 0. Here, is an irreducible character of Sn, indexed by a partition , and g is a conjugacy class of elements in Sn, indexed by a partition . We point out an extra set of zeros in the table that we are dealing with. For every non self-associated partition P(n), the partition f() of n is defined so that f() is greatest among the partitions of n which are opposite in sign to h() and are such that (g) 0 (Thm. 1). Also, for any self-associated partition of n > 1, we construct a partition
() P(n) such that
() is greatest among the partitions of n which are distinct from h() and are such that (g) 0 (Thm. 2).Supported by RFBR grant No. 04-01-00463 and by RFBR-BRFBR grant No. 04-01-81001.Translated from Algebra i Logika, Vol. 44, No. 1, pp. 24–43, January–February, 2005. 相似文献
6.
Jean-François Le Gall 《Probability Theory and Related Fields》1987,76(4):587-627
Summary LetW=(W
t, t0) denote a two-dimensional Brownian motion starting at 0 and, for 0<<, letC
be a wedge in 2 with vertex 0 and angle 2. We consider the set of timest's such that the path ofW, up to timet, stays inside the translated wedgeW
t-C. It follows from recent results of Burdzy and Shimura that this set, which we denote byH
, contains nonzero times if, and only if, >/4. Here we construct a measure, a local time, supported onH
. For /42, the Brownian motionW, time-changed by the inverse of this local time, is shown to be a two-dimensional stable process with index 2-/2. This results extends Spitzer's construction of the Cauchy process, which is recovered by taking =/2. A formula which describes the behaviour ofW before a timetH
is established and applied to the proof of a conjecture of Burdzy. We also obtain a two-dimensional version of the famous theorem of Lévy concerning the maximum process of linear Brownian motion. Precisely, for 0<2, letS
t denote the vertex of the smallest wedge of the typez-C
which contains the path ofW up to timet. The processS
t-Wt is shown to be a reflected Brownian motion in the wedgeC
, with oblique reflection on the sides. Finally, we investigate various extensions of the previous results to Brownian motion inR
d, d3. LetC
be the cone associated with an open subset of the sphereS
d-1, and letH
be defined asH
above. Sufficient conditions are given forH
to contain nonzero times, in terms of the first eigenvalue of the Dirichlet Laplacian on . 相似文献
7.
It is proved for an arbitrary commutative ring A with identity and any integer n3 that if H is a subgroup of GLn(A) normalized by E
n(A,q), then there is an ideal of A such that E
n(A,) H GL
n
(A, (:q40).Furthermore, is uniquely determined up to a certain equivalence relation on the set of ideals of A. The result extends a theorem of Bak, by removing a stability condition he uses on A. 相似文献
8.
L. I. Bausov 《Mathematical Notes》1968,4(2):612-617
Let Cn (, ) be the upper bound for deviations of periodic functions which form the Zygmund class Z,0 0<<2 from a class of positive linear operators. A study is made of the conditions under which there exists a limit
nCn(, )=C(, ). An explicit expression is given for the functions C(,).Translated from Matematicheskie Zametki, Vol. 4, No. 2, pp. 201–210, August, 1968. 相似文献
9.
Hiroshi Suzuki 《Graphs and Combinatorics》1991,7(4):363-375
Let be a distance regular graph with diameterd, and
d
() the set of vertices at distanced from. is said to be thin if the induced subgraph on
d
() is a union of cliques for every vertex. We show that the diameterd is bounded above by a function depending only onk
d, which is the cardinality of
d
(), if is not thin. We also investigate thin distance regular graphs witha
d 0. 相似文献
10.
Thomas Stehling 《Combinatorica》1992,12(4):475-479
We consider the numberN
A
(r) of subgroups of orderp
r
ofA, whereA is a finite Abelianp-group of type =1,2,...,
l
()), i.e. the direct sum of cyclic groups of order ii. Formulas for computingN
A
(r) are well known. Here we derive a recurrence relation forN
A
(r), which enables us to prove a conjecture of P. E. Dyubyuk about congruences betweenN
A
(r) and the Gaussian binomial coefficient
. 相似文献
11.
We describe an algorithm for selecting the n-th largest element (where 0<<1), from a totally ordered set ofn elements, using at most (1+(1+o(1))H())·n comparisons whereH() is the binary entropy function and theo(1) stands for a function that tends to 0 as tends to 0. For small values of this is almost the best possible as there is a lower bound of about (1+H())·n comparisons. The algorithm obtained beats the global 3n upper bound of Schönhage, Paterson and Pippenger for <1/3. 相似文献
12.
Choosing the maximum value from a sequence ofN independent values is a well known problem often called the candidate problem or secretary problem. This paper treats the above problem with a discount penalty (0<<1) for each additional observation taken. It is shown that asN increases indefinitely, the optimal stopping policy is bounded although the maximum expected payoff goes to zero, and that there exists a sequence 0=
0<1<2<<1, such that the asymptotic optimal stopping rule is the same for all
i–1<i. 相似文献
13.
S. V. Solov'ev 《Journal of Mathematical Sciences》1982,20(4):2367-2369
We consider the (&, )-fragment of the intuitionistic propositional calculus. It is proved that under the standard transformation of a Gentzen derivation into a natural derivation(), the length of (())22·length(
). There is constructed a sequence of Gentzen derivations of length i, for which the length of ((
i))21/3·length(i), which shows that the upper bound obtained is not too weak.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 88, pp. 192–196, 1979. 相似文献
14.
G. S. Karkarashvili 《Journal of Mathematical Sciences》1993,66(3):2236-2242
We consider numerical solution of an integro-differential equation with nonsmooth initspaial values. Unique solvability in Sobolev spaceW
2
(0, 1), =1,2, is proved. We establish the rate of convergence of the approximate solution to the exact solution in fractional spacesW
2
+1
, 01, with approximation order O(h
++1/2
) for 01/2 andO(h
+1
|ln h|1/2, for 1/2 #x2264;1.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 64, pp. 8–16, 1988. 相似文献
15.
We consider the boundary-value problem u
tt + u
t + (1 + cos2)sin u =2
u
xx, u
x|x=0=ux|x==0, where 0<1, =(1+)t, ,> 0, and the sign of is arbitrary. It is proved that for an appropriate choice of the external parameters and and for sufficiently small the number of exponentially stable solutions 2-periodic in can be made equal to an arbitrary predefined number. 相似文献
16.
Summary We prove the following theorem: «Given 0<1, the (C, )-means of a sequence of i.i.d. random variables X
n converge a.s. iff E|X
n|1/<.» For 1/2<1 and 0<<1/2 this result is essentially known. We give here a proof of the case =1/2; an important tool is a theorem of Hsu and Robbins [5]. 相似文献
17.
Wilhelm Niethammer 《Numerische Mathematik》1980,34(3):271-283
Summary A nonlinear generalizationÊ
z
of Euler's series transformation is compared with the (linear) Euler-Knopp transformationE
z
and a twoparametric methodE
. It is shown how to applyE
orE
, to compute the valuef(zo) of a functionf from the power series at 0 iff is holomorphic in a half plane or in the cut plane. BothE
andE
, are superior toÊ
z
. A compact recursive algorithm is given for computingE
andE
,. 相似文献
18.
Adams Peter Bryant Darryn El-Zanati Saad I. Gavlas Heather 《Graphs and Combinatorics》2003,19(3):289-296
In this paper, we show that K10n can be factored into C5-factors and 1-factors for all non-negative integers and satisfying 2+=10n–1.Research partially supported by an NSF-AWM Mentoring Travel Grant 相似文献
19.
Given a setX and subsetsX
1,...,X
m, we consider the problem of finding a graphG with vertex setX and the minimum number of edges such that fori=1,...,m, the subgraphG
i; induced byX
i is connected. Suppose that for any pointsx
1,...,x
X, there are at mostX
i 's containing the set {x1,...,x
}. In the paper, we show that the problem is polynomial-time solvable for ( 2, 2) and is NP-hard for (3,=1), (=l,6), and (2,3).Support in part by the NSF under grant CCR-9208913 and CCR-8920505.Part work was done while this author was visiting at DIMACS and on leave from Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing. 相似文献
20.
Lurdes Sousa 《Applied Categorical Structures》1996,4(1):87-95
Each ordinal equipped with the upper topology is a T
0-space. It is well known that for =2 the reflective hull of in Top0 is the subcategory of sober spaces. Here, we define -sober space for each 2 in such a way that the reflective hull of in Top0 is the subcategory of -sober spaces. Moreover, we obtain an order-preserving bijective correspondence between a proper class of ordinals and the corresponding (epi)reflective hulls. Our main tool is the concept of orthogonal closure operator, first introduced in [12].The author acknowledges financial support from Instituto Politécnico de Viseu and from Centro de Matemática da Universidade de Coimbra. 相似文献