共查询到20条相似文献,搜索用时 31 毫秒
1.
A. M. Arkhipov 《Journal of Mathematical Sciences》2006,139(6):7013-7024
In this paper, we consider the Kuramoto-Sivashinskii equation on the multidimensional torus with a Riemannian metric:
where
. For this equation the theorem on energy transfer holds. It is formulated in the following way. Let
be the Fourier expansion of the function u. Denote by P
N
and P
N
⊥
the operators of rejection of the “leading” and, respectively, “lowest” terms of the Fourier expansion (harmonics), i.e.,
.
For any ρ > 0,N ∈ ℕ, s ≥ n/2+5, and λ ∈ (0, 1), there exists R such that for any function. ϕ ∈
lying outside the ball
in the ball
, there exists an instant of time t ∈ (0, 1) such that g
KS
t
ϕ=ψ and
. Here, R is a constant depending on the metric (g), n
s
is the sth Sobolev norm, and
is the C
1-norm.
__________
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 24, Dynamical
Systems and Optimization, 2005. 相似文献
2.
V. D. Lyakhovsky 《Journal of Mathematical Sciences》2006,136(1):3596-3606
Using a graphic presentation of the dual Lie algebra
# (r) for a simple algebra
, it is possible to show that there always exist solutions rech of the classical Yang—Baxter equation with a parabolic carrier. To get a closed-form expression for rech, we find dual coordinates in which the adjoint action of the carrier
c
is reducible. This allows us to find the structure of Jordanian r-matrices rJ which are candidates for enlarging the initial full chain rfch and realize the desired solution rech in the factorized form rech ≈ rfch + rJ. We obtain a unique transformation: the canonical chain has to be replaced by a special kind of peripheric r-matrices, rfch → rrfch. To illustrate the method, the case of
=sl(11) is considered in the full detail. Bibliography: 11 titles.
To my friend Petr Petrovich Kulish
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 317, 2004, pp. 122–141. 相似文献
3.
O. V. Sarafanov 《Journal of Mathematical Sciences》2004,120(2):1195-1239
The C
*-algebra
generated by the operators of pseudodifferential boundary value problems on a manifold
with smooth closed disjoint edges and boundary
is studied. The operators act in the space L
2(
)
L
2(
). The goal of this paper is to describe all (up to an equivalence) irreducible representations of the algebra
Bibliography: 12 titles. 相似文献
4.
N. V. Smorodina 《Journal of Mathematical Sciences》2007,145(2):4914-4922
Let ξ(t), t ∈ [0, 1], be a strictly stable process with an index of stability α ∈ (0, 2). By
we denote the law of ξ in the Skorokhod space
[0,1]. For arbitrary strictly stable process ξ, we construct a semigroup of transformations of
[0, 1] for which the measure
is quasi-invariant. For strictly stable processes with positive and negative jumps, we construct a group of transformations
of
[0, 1] for which the measure
is quasi-invariant. In the symmetric case, this group is a group of invariant transformations. Bibliography: 10 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 339, 2006, pp. 135–149. 相似文献
5.
N. A. Shirokov 《Journal of Mathematical Sciences》2005,129(4):4083-4086
Let
n be the unit ball in ℂn, n ≥ 2. Let Tα = {z ∈
n : (z, a) = |a|2} for a ∈
n and denote
for a discrete set A in
n. We find a sharp necessary condition for a set A to be a part of the zero-set for a function in H∞(
n). Bibliography 4 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 303, 2003, pp. 272–278. 相似文献
6.
We solve a problem, which appears in functional analysis and geometry, on the group of symmetries of functions of several
arguments. Let
be a measurable function defined on the product of finitely many standard probability spaces (Xi,
, μi), 1 ≤ i ≤ n, that takes values in any standard Borel space Z. We consider the Borel group of all n-tuples (g1, ..., gn) of measure preserving automorphisms of the respective spaces (Xi,
, μi) such that f(g1
x
1, ..., gnxn) = f(x1, ..., xn) almost everywhere and prove that this group is compact, provided that its “trivial” symmetries are factored out. As a consequence,
we are able to characterize all groups that result in such a way. This problem appears with the question of classifying measurable
functions in several variables, which was solved by the first author but is interesting in itself. Bibliography: 5 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 334, 2006, pp. 57–67. 相似文献
7.
V.G. Osmolovskii 《Journal of Mathematical Sciences》2004,122(3):3278-3289
We consider the energy functional of a two-phase elastic medium
with quadratic energy densities
defined for
such that
,where
is a measurable characteristic function. Under some natural conditions on the data of the problem, we prove the existence of an interval (t
-,t
+) of the change of temperature
such that the energy functional has only a minimizer
such that
for
or
such that
t^ + $$
" align="middle" border="0">
. The energy functional has no minimizers
such that
or
if
. We derive two-sided estimates for the numbers
in terms of the characteristics of the two-phase elastic medium and the boundary condition. Bibliography: 3 titles. 相似文献
8.
P. M. Akhmet'ev 《Journal of Mathematical Sciences》2004,119(1):5-9
Pairs B,
of divergence-free vector fields with compact support in
are considered higher-order analog M(B,
c (of order 3) of the Gauss helicity number H(B,
)=
, curl(A)=B; (of order 1) is constructed, which is invariant under volume-preserving diffeomorphisms. An integral expression for M is given. A degree-four polynomial m(B(x1), B(x2),
(
1),
(
2)), x1, x2,
1
2
, is defined, which is symmetric in the first and second pairs of variables separately. M is the average value of m over arbitrary configurations of points. Several conjectures clarifying the geometric meaning of the invariant and relating it to invariants of knots and links are stated. Bibliography: 11 titles. 相似文献
9.
N. V. Smorodina 《Journal of Mathematical Sciences》2007,147(4):6950-6957
Let ξ(t), t ∈ [0, 1], be a jump Lévy process. We denote by
the law of ξ in the Skorokhod space
[0, 1]. Under some nondegeneracy condition on the Lévy measure Λ of the process, we construct a group of
-preserving transformations of the space
[0, 1]. Bibliography: 11 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 341, 2007, pp. 175–188. 相似文献
10.
We observe an unknown function of infinitely many variables f = f(t), t = (t1, ..., tn, ... ) ∈, [0, 1]∞, in the Gaussian white noise of level ε > 0. We suppose that in each variable there exists a 1-periodical σ-smooth extension
of the function f(t) to IR
∞. Taking a quantity σ > 0 and a positive sequence a = {ak}, we consider the set
that consists of functions f such that
. We consider the cases ak = kα and ak = exp(λk), α > 0, λ > 0. We would like to estimate a function f ∈
or to test the null hypothesis H0: f = 0 against the alternatives f ∈
, where the set
consists of functions f ∈
such that ∥f∥2 ≥ r. In the estimation problem, we obtain the asymptotics (as ε → 0) of the minimax quadratic risk. In the detection problem,
we study the sharp asymptotics of minimax separation rates f
ɛ
*
that provide distiguishability in the problems. Bibliography: 12 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 328, 2005, pp. 91–113. 相似文献
11.
The paper deals with the problem of recovering the parameters (functions)
and
of the Maxwell dynamical system
(tan is the tangent component;
is a solution) by the response operator
(
is the normal). The parameters determine the velocity
, the c-metric
, and the time
. It is shown that for any fixed
, the operator
determines
and
in
uniquely. Bibliography: 15 titles. 相似文献
12.
E. G. Emel'yanov 《Journal of Mathematical Sciences》2002,110(6):3078-3090
An extension of a theorem on extremal decomposition of a Riemann surface is obtained. The problem of extremal decomposition is extended from the case of a Riemann surface
with a prescribed set
of distinguished points to the case of the Teichmüller space
corresponding to
under quasiconformal homeomorphisms f. For the functional
of our problem on extremal decomposition of a surface
, we consider a function
expressing the dependence of the extremal value of
on a point
. Differentiation formulas for the function
are derived. These formulas are different and depend on the genus g of the surface
. The case where the function
is pluriharmonic is considered. Bibliography: 8 titles. 相似文献
13.
V. L. Oleînik 《Journal of Mathematical Sciences》2000,101(3):3133-3138
Let {
}, where {
} is the open unit disk on the complex plane {
}. In G, we consider analytic solutions u(t, z) ({
}, {
}) of the heat equation 2ut=uzz with initial data f(z)=u(0, z) belonging to the Fock space F, i.e., to the space of entire functions square summable with
the weight e−|z|2.Conditions on a nonnegative measure μ on G are described under which for all f ∈ F we have {
} Bibliography: 17 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 247, 1997, pp. 146–155.
Translated by S. V. Kislyakov. 相似文献
14.
Research on finite solvable groups with C-closed invariant subgroups has given rise to groups structured as follows. Let p,
q1, q2, ..., qm be distinct primes, ni be the exponent of p modulo qi, and n be the exponent of p modulo
. Then G = Pλ〈x〉, where P is a group and
; Zi; here, Zi and P/Z(P) are elementary Abelian groups of respective orders
and pn, |x| = r, the element x acts irreducibly on P/Z(P) and on each of the subgroups Zi, and
. We state necessary and sufficient conditions for such groups to exist.
__________
Translated from Algebra i Logika, Vol. 45, No. 4, pp. 379–389, July–August, 2006. 相似文献
15.
M. B. Zvyagina 《Journal of Mathematical Sciences》1998,89(2):1122-1126
Let Λ be an associative ring with identity and let
be the category of left unitary Λ-modules. A subcateqory
of the category
is said to be small if the pairwise nonisomorphic objects of
form a set. The main result of this paper consists of the fact that for every small full subcategory
, there exists a ring Γ such that
is dual to a small full subcategory of the category
. Some applications of this result are indicated. Bibliography: 3 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 227, 1995, pp. 66–73. 相似文献
16.
17.
A. K. Prykarpatsky D. L. Blackmore Ya. V. Mykytyuk 《Journal of Mathematical Sciences》2001,104(5):1411-1421
This article is a continuation of [J. Math. Sci., 99, No.5, 1541–1547 (2000)] devoted to the validity of the Lax formula (cited in the article of Crandall, Ishii, and Lions [Bull. AMS, 27, No.1, 1–67 (2000)])
for a solution to the Hamilton–Jacobi nonlinear partial differential equation
where the Cauchy data
are now a function semicontinuous from below,
is the usual norm in
,
, and
is a positive evolution parameter. We proved that the Lax formula solves the Cauchy problem (2) at all points
,
fixed save for an exceptional set of points R of the F
type, having zero Lebesgue measure. In addition, we formulate a similar Lax-type formula without proof for a solution to a new nonlinear equation of the Hamilton–Jacobi-type:
where
is a diagonal positive-definite matrix, mentioned in Part I and having interesting applications in modern mathematical physics. 相似文献
18.
Let ℂ denote the complex numbers and
denote the ring of complex-valued Laurent polynomial functions on ℂ\{0}. Furthermore, we denote by
the subsets of Laurent polynomials whose restriction to the unit circle is real, nonnegative, respectively. We prove that
for any two Laurent polynomials
, which have no common zeros in ℂ\{0} there exists a pair of Laurent polynomials
satisfying the equation Q
1
P
1 + Q
2
P
2 = 1. We provide some information about the minimal length Laurent polynomials Q
1 and Q
2 with these properties and describe an algorithm to compute them. We apply this result to design a conjugate quadrature filter
whose zeros contain an arbitrary finite subset Λ⊂ℂ\{0} with the property that for every
implies
and
.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
19.
A. V. Demyanov 《Journal of Mathematical Sciences》2006,136(2):3706-3717
The problem of establishing necessary and sufficient conditions for l.s.c. under PDE constraints is studied for a special
class of functionals:
with respect to the convergence un → u in measure, vn ⇀ v in Lp(Ω;ℝd)
in W−1,p(Ω), and χn ⇀ χ in Lp(Ω), where χn ∈ Z:= {χ ∈ L∞(Ω): 0 ≤ χ(x) ≤ 1 for a.e. x}. Here
is a constant-rank partial differential operator. The main result is that if the characteristic cone of
has the full dimension, then the l.s.c. is equivalent to the fact that the F± are both
-quasiconvex and
for a.e. x ∈ Ω and for all u ∈ ℝd. As a corollary, we obtain several results for the functional
with respect to the same convergence. We show that this functional is l.s.c. iff
Bibliography: 14 titles.
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 318, 2004, pp. 100–119. 相似文献
20.
S. Ya. Novikov 《Journal of Mathematical Sciences》2004,120(5):1733-1751
We study operators
(not necessarily linear) defined on a quasi-Bahach space X and taking values in the space of real-valued Lebesgue-measurable functions. Factorization theorems for linear and superlinear operators with values in the space
are proved with the help of the Lorentz sequence spaces
. Sequences of functions belonging to fixed bounded sets in the spaces
are characterized for
and
. The possibility of distinguishing weak type operators (bounded in the space
) from operators factorizable through
is obtained in terms of sequences of independent random variables. A criterion under which an operator is symmetrically bounded in order in
, is established. Some refinements of the above-mentioned results are obtained for translation shift-invariant sets and operators. Bibliography: 30 titles. 相似文献