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1.
We establish conditions under which the relation M(x, F) (x, F) m(x, F) holds except for a small set, as ¦x¦ + for an entire function F(z) of several complex variables z (p2) represented by a Dirichlet series, where M(x, F) = sup{¦F(x+iy¦: y p}, m(x, F) = inf{¦F(x+iy)¦: y p} (x, F) being the maximal term of the Dirichlet series, and x p.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 4, 1997, pp. 21–25. 相似文献
2.
K. Koncz 《Analysis Mathematica》1987,13(1):75-91
, (1). 3, , ()=, (8) (16). [1], . (28) (31) ( 5), - (. [3]).
The author thanks Professor M.Arató for having pointed out this problem, and for his valuable suggestions. 相似文献
The author thanks Professor M.Arató for having pointed out this problem, and for his valuable suggestions. 相似文献
3.
A. V. Tushev 《Ukrainian Mathematical Journal》1995,47(4):663-664
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
4.
E. A. Mikhailyuk 《Ukrainian Mathematical Journal》1991,43(7-8):1047-1051
With each subgroup A of a free group F there is associated a number FA called the quasi-index. It is proved that FA=ªA¦ if ¦FA¦ is finite. Some properties of the quasi-index are also established, in particular that the analog of Lagrange's theorem is valid for it: FB FA AB if A B as well as generalizations of Howson's and Byrnes' theorems.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, Nos. 7 and 8, pp. 1115–1119, July–August, 1991. 相似文献
5.
Let (n) be the sum of unitary divisors of n, and k(n) be its k-fold iterate. We prove that (n) ¦ 2(n) 1 as n on a set of density one. 相似文献
6.
E. Csáki 《Probability Theory and Related Fields》1980,54(3):287-301
Summary Let W(t) be a standard Wiener process and let f(x) be a function from the compact class in Strassen's law of the iterated logarithm. We investigate the lim inf behavior of the variable sup ¦W(xT)(2T loglog T)–1/2–f(x)¦, 0x1 suitably normalized as T.This extends Chung's result valid for f(x)0, stating that lim inf.[ sup ¦(2T loglogT)–1/2
W(xT)¦(loglog T)–1]=/4 a.s. T 0x1 相似文献
7.
A. V. Sobolev 《Journal of Mathematical Sciences》1988,40(5):652-672
One considers the total scattering cross section on the potential gV(x), xm, m3, for large values of the coupling constant g and of the wave number k. One assumes that V(x)(x/|1x|)|x|–, 2>m+1, as ¦x¦. It is shown that for gk–1 , g3–ak2(a–2) the scattering cross section is equal asymptotically to a(gk–1), x=(m–1)(–1)–1. Here the coefficient a is determined only by the function and the number . Under the additional conditions >0, V>0, the indicated asymptotic behavior holds in the large domain gk–1 , gka–z c(gk–1), >0.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 152, pp. 105–136, 1986. 相似文献
8.
Yu. Lyubich 《Integral Equations and Operator Theory》1995,23(2):232-244
If X is a real Banach space, then the inequality x defines so-called hyperbolic cone in E=X. We develop a relevant version of Perron-Frobenius-Krein-Rutman theory. 相似文献
9.
Existence for the Cahn-Hilliard phase separation model with a nondifferentiable energy 总被引:3,自引:0,他引:3
Summary The Cahn-Hilliard model for phase separation in a binary alloy leads to the equations (I) ut=w, (II) w= (u)– u with an associated energy functional F(u)=f [(u)+ +¦u¦2/2] dx. In this paper we discuss the existence theory for initial bounday value problems arising from modifications to the Cahn-Hilliard model due to the addition of the non-differentiable term ¦u¦dx to the energy F(u). 相似文献
10.
М. Г. Григорян 《Analysis Mathematica》1985,11(3):201-216
, . . Q
k
[0,2],k=1,2, — . F(x, y)L(T), T=[0, 2]2, G(x, y)L(T) , G(x,y)=F(x,y) Q=Q
1
×Q
2
- . 相似文献
11.
V. F. Gapoškin 《Analysis Mathematica》1980,6(2):105-119
a
k
f
k
, f
k
L
2, w-, (2), w(n) — .
a
k
f
k
N {a
k
}l
2, {a
k
}l
2 ( 1, 2, 1a, 2a). ( 2) [8]. , {a
k
} w-. 相似文献
12.
( qP. ) 相似文献
13.
V. V. Kurta 《Ukrainian Mathematical Journal》1992,44(10):1262-1268
Analogues are formulated of the well-known, in the theory of analytic functions, Phragmen-Lindelöf theorem for the gradients of solutions of a broad class of quasilinear equations of elliptic type. Examples are given illustrating the accuracy of the results obtained for the gradients of solutions of the equations of the form div(|U|–2u)=f(x, u, u), where f(x, u, u) is a function locally bounded in 2n+1. f(x, 0, u)=0, uf(x, u, u) c¦u¦1+q(1+ ¦u|), > 1, c > 0, q > 0, is an arbitrary real number, and n >- 2. The basic role in the technique employed in the paper is played by the apparatus of capacitary characteristics.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 10, pp. 1376–1381, October, 1992.The author sincerely appreciates E. M. Landis's permanent attention and numerous useful discussions. 相似文献
14.
Graham R. Brightwell 《Order》1985,2(2):129-144
Posets A, BX×X, with X finite, are said to be universally correlated (AB) if, for all posets R over X, (i.e., all posets RY×Y with XY), we have P(RA) P(RB)P(RAB) P(R). Here P(RA), for instance, is the probability that a randomly chosen bijection from Y to the totally ordered set with |Y| elements is a linear extension of RA. We show that AB iff, for all posets R over X, P(RA) P(RB)P(RAB) P(R(AB)).Winkler proved a theorem giving a necessary and sufficient condition for AB. We suggest an alteration to his proof, and give another condition equivalent to AB.Daykin defined the pair (A, B) to be universally negatively correlated (A B) if, for all posets R over X, P(RA) P(RB)P(RAB) P(R(AB)). He suggested a condition for AB. We give a counterexample to that conjecture, and establish the correct condition. We write AB if, for all posets R over X, P(RA) P(RB)P(RAB) P(R). We give a necessary and sufficient condition for AB.We also give constructive techniques for listing all pairs (A, B) satisfying each of the relations AB, AB, and AB. 相似文献
15.
Gianni Dal Maso 《Annali di Matematica Pura ed Applicata》1981,129(1):327-366
Summary In this paper we study the asymptotic behaviour (as h) of the solutions of minimum problems for the functional [¦Du¦2+g(x, u)]dx with bilateral obstacles of the type huh, where h and h are sequences of arbitrary functions fromR
n into ¯R. 相似文献
16.
Liu Yongping 《Analysis Mathematica》1995,21(2):107-124
17.
18.
The problem
is considered on the N-dimensional torus with ai and g a continuous function satisfying a growth condition as ¦u¦. We show the existence of bounded solutions that are continuous if g is strictly increasing in u. 相似文献
19.
G. P. Golovach 《Journal of Mathematical Sciences》1994,71(5):2645-2649
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
20.
. . 相似文献