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1.
A necessary and sufficient condition for regularity of the
-Neumann operator on (0,q)-forms in a smooth bounded pseudoconvex domain in Cn is that the orthogonal projections onto
-closed forms of degrees (0,q−1), (0,q), and (0,q+1) all be regular.
The first author partially supported by NSF Grant DMS-8701038 相似文献
2.
The classical factorization method reduces the study of a system of ordinary differential equations Ut=[U+, U] to solving algebraic equations. Here U(t) belongs to a Lie algebra
which is the direct sum of its subalgebras
and
, where “+” signifies the projection on
. We generalize this method to the case
. The corresponding quadratic systems are reducible to a linear system with variable coefficients. It is shown that the generalized
version of the factorization method can also be applied to Liouville equation-type systems of partial differential equations.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 110, No. 3, pp. 339–350, March, 1997. 相似文献
3.
Let
denote the class of ergodic probability preserving transformations which are disjoint from every weakly mixing system. Let
be the class of multipliers for
, i.e. ergodic transformations whose all ergodic joinings with any element of
are also in
. Fix an ergodic rotationT, a mildly mixing actionS of a locally compact second countable groupG and an ergodic cocycle ϕ forT with values inG. The main result of the paper is a sufficient (and also necessary by [LeP] whenG is countable Abelian andS is Bernoullian) condition for the skew product build fromT, ϕ andS to be an element of
. Moreover, the self-joinings of such extensions ofT are described with an application to study semisimple extensions of rotations.
Dedicated to Hillel Furstenberg on the occasion of his retirement
The first-named author was supported in part by CRDF, grant UM1-2546-KH-03.
The second-named author was supported in part by KBN grant 1P03A 03826. 相似文献
4.
V. D. Lyakhovsky 《Theoretical and Mathematical Physics》2006,148(1):968-979
In accordance with the quantum duality principle, the twisted algebra
is equivalent to the quantum group
and has two preferred bases: one inherited from the universal enveloping algebra
and the other generated by coordinate functions of the dual Lie group
. We show howthe transformation
can be explicitly obtained for any simple Lie algebra and a factorable chain
of extended Jordanian twists. In the algebra
, we introduce a natural vector grading
, compatible with the adjoint representation of the algebra. Passing to the dual-group coordinates allows essentially simplifying
the costructure of the deformed Hopf algebra
, considered as a quantum group
. The transformation
can be used to construct new solutions of the twist equations. We construct a parameterized family of extended Jordanian
deformations
and study it in terms of
; we find new realizations of the parabolic twist.
Dedicated to the birthday of my teacher, Yurii Novozhilov
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 148, No. 1, pp. 112–125, July, 2006. 相似文献
5.
LetW be an open Riemann surface and
ap-sheeted (1<p<∞) unlimited covering surface ofW. Denote by Δ1 (resp.,
) the minimal Martin boundary ofW (resp.,
). For ζ ∈ Δ, let
ζ be the (cardinal) number of the set of pionts
which lie over ζ and
the class of open connected subsetsM ofW such thatM∪{ζ} is a minimal fine neighborhood of ζ. Our main result is the following:
, where
is the number of components of π-1
M and π is the projection of
ontoW. Moreover, some applications of the above results are discussed whenW is the unit disc. 相似文献
6.
A. M. Semikhatov 《Theoretical and Mathematical Physics》1997,112(2):949-987
We review several constructions that are realized in bosonic and N = 2 strings and which relate the affine Lie algebra
(2), affine superalgebra
(2|1), and the superconformal N = 2 algebra.
This paper was written at the request of the Editorial Board.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 112, No. 2, pp. 195–240, August, 1997. 相似文献
7.
J. Mossino 《Israel Journal of Mathematics》1978,30(1-2):14-50
This paper deals with some problems arising in plasma physics. The typical example is the following:
where
is the (neither local, nor monotone, nor continuous) operator:
. Using a quasi-variational approach, we prove the existence of minimal and maximal solutions for a weak form of this problem,
involving a multi-valued operator β. Various generalizations are treated.
相似文献
8.
A. S. Fedorenko 《Ukrainian Mathematical Journal》2000,52(6):981-986
We consider the approximation of functions of the classes of
by Zygmund sums. In papticular, we present asymptotic equalities for the quantities
under various conditions imposed on functions ψ1(·) and ψ2(·).
Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 52,
No. 6, pp. 856–860, June, 2000. 相似文献
9.
V. R. Kogan 《Theoretical and Mathematical Physics》2000,122(3):380-389
We study the distribution of the distance R(t) between two Lagrangian trajectories in a spatially smooth turbulent velocity
field with an arbitrary correlation time and a non-Gaussian distribution. There are two dimensionless parameters, the degree
of deviation from the Gaussian distribution α and β=τD, where τ is the velocity correlation time and D is a characteristic
velocity gradient. Asymptotically, R(t) has a lognormal distribution characterized by the mean runaway velocity
and the dispersion Δ. We use the method of higher space dimensions d to estimate
and Δ for different values of α and β. It was shown previously that
for β≪ 1 and
for β≫ 1. The estimate of Δ is then nonuniversal and depends on details of the two-point velocity correlator. Higher-order
velocity correlators give an additional contribution to Δ estimated as αD2τ for β≪1 and αβ/τ for β≫1. For α above some critical value σcr, the values of
and Δ are determined by higher irreducible correlators of the velocity gradient, and our approach loses its applicability.
This critical value can be estimated as
for β≪1 and
for β≫1.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 122, No. 3, pp. 456–467, March, 2000. 相似文献
10.
Zoé Chatzidakis 《Israel Journal of Mathematics》1986,55(2):173-183
LetK be a hilbertian field,G(K) its absolute Galois group. IfK is countable, then for a.a.
inG(K)
e
,
and there is no intermediate field
with
. Let
∈G(K)
e
. Then for a.a.
in
. 相似文献
11.
This paper examines the following question. If
and
are saturated formations then
is defined to be the class of all soluble groups whose
belong to
. In general
is a formation, but need not be a saturated formation. Here the smallest saturated formation containing
is studied. 相似文献
12.
G. E. Arutyunov L. O. Chekhov S. A. Frolov 《Theoretical and Mathematical Physics》1997,111(2):536-562
It is shown that the classical L-operator algebra of the elliptic Ruijsenaars-Schneider model can be realized as a subalgebra
of the algebra of functions on the cotangent bundle over the centrally extended current group in two dimensions. It is governed
by two dynamic τ and
-matrices satisfying a closed system of equations. The corresponding quantum R- and
-matrices are found as solutions to quantum analogues of these equations. We present the quantum L-operator algebra and show
that the system of equations for R and
arises as the compatibility condition for this algebra. It turns out that the R-matrix is twist-equivalent to the Felder
elliptic RF-matrix, with
playing the role of the twist. The simplest representation of the quantum L-operator algebra corresponding to the elliptic
Ruijsenaars-Schneider model is obtained. The connection of the quantum L-operator algebra to the fundamental relation RB LL=LLRB with the Belavin elliptic R-matrix is established. As a by-product of our construction, we find a new N-parameter elliptic
solution to the classical Yang-Baxter equation.
This paper was written at the request of the Editorial Board.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 111, No. 2, pp. 182–217, May, 1997. 相似文献
13.
Jong Taek Cho 《Israel Journal of Mathematics》1999,109(1):299-318
N. Tanaka ([10]) defined the canonical affine connection on a nondegenerate integrable CR manifold. In the present paper,
we introduce a new class of contact Riemannian manifolds satisfying (C) (
for any unit
-geodesic (
, where
is the generalized Tanaka connection. In particular, when the associated CR structure of a given contact Riemannian manifold
is integrable we have a structure theorem and find examples which are neither Sasakian nor locally symmetric but satisfy the
condition (C).
This work was supported in part by BSRI 98-1425. 相似文献
14.
Kyewon Koh Park 《Israel Journal of Mathematics》1982,42(4):343-352
A flow built under a step function with a multi-step Markov partition on the base is a direct product of a Bernoulli flow
with a finite rotation. A
of the flows in this family cannot have two irrationally related rotation factors.
of this family is shown to consist of all direct products of Bernoulli flows and flows of rational pure point spectrum with
respect to some number. 相似文献
15.
A renormalization group transformation R
1 has a single stable point
in the space of the analytic circle homeomorphisms with a single cubic critical point and with the rotation number
(the golden mean). Let a homeomorphism T be the C
1-conjugate of
. We let
denote the sequence of distribution functions of the time of the kth entrance to the nth renormalization interval for the homeomorphism T. We prove that for any
, the sequence
has a finite limiting distribution function
, which is continuous in
, and singular on the interval [0,1]. We also study the sequence
for k>1. 相似文献
16.
The
of the class of multi-step Markov chains is shown to consist of all direct products of Bernoulli processes with processes
of rational pure point spectrum. The class of processes that are approached in
by their canonical multi-step Markov approximations is also studied. It is found to be strictly smaller than the former class,
dense in it, and characterized within it by a certain (noninvariant) property of its rotation factors. 相似文献
17.
We show that for a
-action Ψ being the Kronecker sum of a symbolic strictly ergodic
-actionT and a Chacon
-actionS, the rank (covering number) of Ψ is the same as that forT. Using this result we construct, for a given natural numberr≥2 and a real numberb∈(0,1) withr\b≥1, a
-action with rankr, covering numberb and a simple spectrum. On the other hand, for any positive integersr, m with 1≤m≤r≤∞ we construct a
-action with rankr and spectral multiplicitym. 相似文献
18.
E. I. Timoshenko 《Algebra and Logic》1998,37(6):391-398
Part of any basis of a relatively free group
in the variety
is called a primitive system of elements. We provide a criterion of being primitive for
, where
is a variety of Abelian groups satisfying xm=1, and
a variety generated by a finite group. Let
be a variety of nilpotent groups of class ≤c. It is proved that, for the group
, the property of being primitive for an element g is stronger than the condition of being unimodular on a vector composed
of values of Fox derivatives in the ring
. The group
is not residually finite whenever a system of elements is primitive.
Supported by RFFR grant No. 96-01-01948.
Translated fromAlgebra i Logika, Vol. 37, No. 6, pp. 687–699, November–December, 1998. 相似文献
19.
We consider the problems of three-particle scattering and annihilation in a system of three strongly interacting charged particles
(
pn). We propose a model for the elastic scattering and the breakup process in the nucleon channel as well as for the annihilation
into mesons. The mathematical foundation of the model is the extension theory of symmetrical operators. In the framework of
this model, we construct the modified integral Faddeev equations with energy-dependent interactions taking the annihilation
processes into account. These equations are uniquely resolvable for suitable classes of functions. On this basis, we deduce
the corresponding differential Faddeev equations, construct asymptotic boundary conditions for wave function components, and
formulate boundary problems for a system composed of nucleonic and mesonic channels. The results obtained are applied to scattering
and annihilation processes in the three-particle system
.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 118, No. 1, pp. 74–94, January, 1999. 相似文献
20.
We obtain a set of necessary and sufficient conditions for
to imply
for 1 <k ≤ s < ∞. Using this result we establish several inclusion theorems as well as conditions for the equivalence of
and
. 相似文献