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1.
Yu. N. Bibikov 《Mathematical Notes》1997,61(1):29-37
We consider small perturbations with respect to a small parameter ε≥0 of a smooth vector field in ℝn+m possessing an invariant torusT
m. The flow on the torusT
m is assumed to be quasiperiodic withm basic frequencies satisfying certain conditions of Diophantine type; the matrix Ω of the variational equation with respect
to the invariant torus is assumed to be constant. We investigate the existence problem for invariant tori of different dimensions
for the case in which Ω is a nonsingular matrix that can have purely imaginary eigenvalues.
Translated fromMatematicheskie Zametki, Vol. 61, No. 1, pp. 34–44, January, 1997.
Translated by S. K. Lando 相似文献
2.
Let (K, μ) be a measurable space with μ(K)=1. Let Ip,q: Lp (K, μ)→Lq (K, μ) be the embedding operator. The Bernstein widths of Ip, q are considered. Bibliography: 5 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 247, 1997, pp. 166–169.
Translated by S. V. Kislyakov. 相似文献
3.
In the present paper, the embedding problem is considered for number fields with p-groups whose kernel is either of two groups
with two generators α and β and with the following relations: (1) αρ=1, αρ=1, [α,β,β]=1, [α,β,α,α]=1, or (2) αρ=[α, β α], βρ=1, [α,β,β]=1. It is shown that for the solvability of the original embedding problem it is necessary and sufficient to have the solvability
of the associated Abelian and local problems for all completions of the base fields. Bibliography: 7 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 211, 1994, pp. 120–126.
Translated by V. V. Ishkhanov. 相似文献
4.
D. V. Gorbachev 《Mathematical Notes》1997,61(4):430-439
For a functional on the classH
ω
(n)
,n≥3, we construct the extremal function on which the upper bound obtained by A. I. Stepanets is attained.
Translated fromMatematicheskie Zametki, Vol. 61, No. 4, pp. 519–529, April, 1997.
Translated by N. K. Kulman 相似文献
5.
N. M. Timofeev 《Mathematical Notes》1997,61(3):321-332
Let τk(n) be the number of representations ofn as the product ofk positive factors, τ(n)=τ(n). The asymptotics of Σ
n≤x
τ
k
(n)τ(n+1) for 80k
10 (lnlnx)3≤lnx is shown to be uniform with respect tok.
Translated fromMatematicheskie Zametki, Vol. 61, No. 3, pp. 391–406, March, 1997.
Translated by N. K. Kulman 相似文献
6.
A. P. Oskolkov 《Journal of Mathematical Sciences》1997,83(2):320-326
In this paper, we study some nonlocal problems for the Kelvin-Voight equations (1) and the penalized Kelvin-Voight equations
(2): the first and second initial boundary-value problems and the first and second time periodic boundary problems. We prove
that these problems have global smooth solutions of the classW
∞
1
(ℝ+;W
2
2+k
(Ω)),k=1,2,...;Ω⊂ℝ3. Bibliography: 25 titles.
Dedicated to N. N. Uraltseva on her jubilee
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 221, 1995, pp. 185–207.
Translated by N. A. Karazeeva. 相似文献
7.
V. N. Karpushkin 《Mathematical Notes》1997,62(6):697-700
In this paperk-harmonic polynomials in ℝ
n
, i.e. polynomials satisfying the Laplace equation with respect tok variables: ∂2/∂x
1
2
+...+∂2/∂x
k
2
F=0 are considered; here 1≤k≤n andn≥2. For a polynomialF (of degreem) of this type, it is proved that the number of components of the complements of its level sets does not exceed 2m
n−1+O(m
n−2). Under the assumptions that the singular set of the level surface is compact or that the leading homogeneous part of thek-harmonic polynomialF is nondegenerate, sharper estimates are also established.
Translated fromMatematicheskie Zametki, Vol. 62, No. 6, pp. 831–835, December, 1997
Translated by S. S. Anisov 相似文献
8.
Y. V. Kurylev 《Journal of Mathematical Sciences》1996,79(4):1231-1246
In this paper a uniqueness theorem is proved for the wave equation in the domain Q2T=Ω×(0,2T), where Ω is a piecewise analytic Riemannian manifold (Riemannian polyhedron). Initial data are assumed to be given
on a part Γ0 × (0, 2T) of the space-time boundary of the cylinder Q2T, Γ0. The uniqueness of a weak solution is proved “in the large,” in a domain formed by the corresponding characteristics of the
wave equation. Bibliography:24 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 203, 1992, pp. 113–136.
Translated by T. N. Surkova. 相似文献
9.
D. A. Labutin 《Mathematical Notes》1997,61(2):164-179
Some classes of cuspidal domainsG ⊂ ℝ
n
are introduced, and embeddings of the formW
p
(l)
(G)↪Lq(G),l ∈ ℕ, for sobolev spaces are established. To this end, estimates of some integral operators are needed. These operators cannot
be estimated via Riesz potentials or their anisotropic analogs.
Translated fromMatematicheskie Zametki, Vol. 61, No. 2, pp. 201–219, February, 1997.
Translated by V. E. Nazaikinskii 相似文献
10.
N. G. Moshchevitin 《Mathematical Notes》1997,61(5):590-599
For any monotone functionψ(y)=O(y
1/s), we prove the existence of a continual family of vectors (α1...,αs) admitting infinitely many simultaneous ψ-approximations, but nocψ-approximations with some constantc>0.
Translated fromMatematicheskie Zametki, Vol. 61, No. 5, pp. 706–716, May, 1997.
Translated by S. K. Lando 相似文献
11.
V. G. Krotov 《Mathematical Notes》1997,62(4):439-448
In the critical case αp=n functions from the Hardy-Sobolev spacesH
α
p
(B
n
) have a limit almost everywhere on the boundary along certain regions of exponential contact with the boundary. It is proved
in the paper that the maximal operator associated with these regions is bounded as an operator fromH
α
p
(B
n
) toL
p
(ϖB
n
).
Translated fromMatematicheskie Zametki, Vol. 62, No. 4, pp. 527–539, October, 1997.
Translated by N. K. Kulman 相似文献
12.
We prove a strengthenedC
r
-closing lemma (r≥1) for wandering chain recurrent trajectories of flows without equilibrium states on the two-dimensional torus and for wandering
chain recurrent orbits of a diffeomorphism of the circle. The strengthenedC
r
-closing lemma (r≥1) is proved for a special class of infinitely smooth actions of the integer lattice ℤ
k
on the circle. The result is applied to foliations of codimension one with trivial holonomy group on the three-dimensional
torus.
Translated fromMatematicheskie Zametki, Vol. 61, No. 3, pp. 323–331, March, 1997.
Translated by S. K. Lando 相似文献
13.
M. -B. A. Babaev 《Mathematical Notes》1997,62(1):15-29
We study the approximation of functions of several variables by bilinear forms that are the pairwise products of functions
of fewer variables. The order of approximation of Sobolev classesW
q
r
by bilinear forms inL
p
for 2≤q≤p≤∞ is found.
Translated by N. K. Kulman
Translated fromMatematicheskie Zametki, Vol. 62, No. 1, pp. 18–34, July, 1997. 相似文献
14.
For a system of n identical particles in a homogeneous magnetic field, the discrete spectrum of the Hamiltonian Hα, m on the subspaces of functions with permutational symmetry α and rotational (SO(2)) symmetry m is studied as m→∞. It is proved
that the discrete spectrum of the operator Hα,m contains only one eigenvalue if certain conditions are satisfied. The asymptotic behavior of this eigenvalue as m→∞ is found.
Bibliography: 7 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 197, pp. 28–41, 1992.
Translated by A. V. Lyakhovskaya 相似文献
15.
V. A. Bykovskii 《Functional Analysis and Its Applications》2000,34(2):98-105
The Dirichlet (Hecke-Maass) series associated with the eigenfuctionsf andg of the invariant differential operator Δk=−y2(∂2/∂x2)+iky∂/∂x of weightk are investigated. It is proved that any relation of the form (f/kM)=g for thek-action of the groupSL
2
SL
2(ℝ) is equivalent to a pair of functional equations relating the Hecke-Maass series forf andg and involving only traditional gamma factors.
This work was supported by the Russian Foundation for Basic Research (grant No. 96-01-10439).
Institute of Applied Mathematics, Far East Division of Russian Academy of Sciences. Translated from Funktional'nyi Analiz
i Ego Prilozheniya, Vol. 34, No. 2, pp. 23–32, April–June, 2000.
Translated by V. M. Volosov 相似文献
16.
A projective m-configuration is a collection of m nonoriented pairwise disjoint lines in ℝP
3. An isotopy consisting of projective m-configurations is called a rigid isotopy. In the paper, the rigid isotopy classification
of ordered projective m-configurations is obtained for m≤7. Bibliography: 11 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 231, 1995, pp. 269–285.
Translated by V. F. Mazurovskii. 相似文献
17.
S. E. Kozlov 《Journal of Mathematical Sciences》2000,100(3):2239-2253
The paper deals with the properties of the exterior algebra ℝ(Λn) related to the Euclidean structure on ℝ(Λn) induced by the scalar product in ℝ(Λn). A geometric interpretation of inner multiplication for simple p-vectors is given. An invariant form of the Cartan criterion
for the simplicity of a p-vector is given. The Plücker model realizing the real Grassmann manifold as a submanifold of the
Euclidean space ℝ(Λn), and an isometry of this submanifold onto the classical Grassmann manifold with SO(n)-invariant metric are described. A
canonical decomposition of bivectors is given. Bibliography: 12 titles.
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 246, 1997, pp. 84–107.
Translated by N. Yu: Netsvetaev. 相似文献
18.
A bounded linear operatorA:X→X in a linear topological spaceX is called ap-involution operator,p≥2, ifA
p=I, whereI is the identity operator. In this paper, we describe linearp-involution operators in a linear topological space over the field ℂ and prove that linear operators can be continued to involution
operators.
Translated fromMatematicheskie Zametki, Vol. 61, No. 5, pp. 671–676, May, 1997.
Translated by M. A. Shishkova 相似文献
19.
It is proved that the equation (x
2−1)(y
2−1)=(z
2−1)2, |x|≠|y|, |z|≠1, is not solvable in integersx,y,z under the conditionx−y=kz, wherek is a positive integer different from 2.
Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 181–187, August, 1999. 相似文献
20.
M. A. Vsemirnov 《Journal of Mathematical Sciences》2000,98(4):427-441
Direct constructions of Diophantine representations for linear recurrent sequences are considered. Diophantine representations
of the sets of values for third-order sequences with negative discriminants are found. As an auxiliary problem, we study the
structure of the multiplicative group of the ringZ[λ], where λ is an invertible algebraic integer (unit) in a real quadratic field or in a cubic field of negative discriminant.
The index of the subgroup {±λ
n
∣n ∈Z} in the group (Z[λ])* and the generator of (Z[λ])* are evaluated explicitly. Bibliography: 14 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 241, 1997, pp. 5–29.
This research was supported in part by the ISSEP, grants a96-1965 and a97-2261.
Translated by M. A. Vsemirnov 相似文献