共查询到20条相似文献,搜索用时 31 毫秒
1.
G. A. Tolstikhina 《Journal of Mathematical Sciences》2011,177(4):623-632
In this paper, we present the main results of the study of multidimensional three-websW(p, q, r) obtained by the method of external forms and moving Cartan frame. The method was developed by the Russian mathematicians
S. P. Finikov, G. F. Laptev, and A. M. Vasiliev, while fundamentals of differential-geometric (p, q, r)-webs theory were described by M. A. Akivis and V. V. Goldberg. Investigation of (p, q, r)-webs, including algebraic and geometric theory aspects, has been continued in our papers, in particular, we found the structure
equations of a three-web W(p, q, r), where p = λl, q = λm, and r = λ(l + m − 1). For such webs, we define the notion of a generalized Reidemeister configuration and proved that a three-web W(λl, λm, λ(l + m − 1)), on which all sufficiently small generalized Reidemeister configurations are closed, is generated by a λ-dimensional Lie group G. The structure equations of the web are connected with the Maurer–Cartan equations of the group G. We define generalized Reidemeister and Bol configurations for three-webs W(p, q, q). It is proved that a web W(p, q, q) on which generalized Reidemeister or Bol configurations are closed is generated, respectively, by the action of a local
smooth q-parametric Lie group or a Bol quasigroup on a smooth p-dimensional manifold. For such webs, the structure equations are found and their differential-geometric properties are studied. 相似文献
2.
G. A. Tolstikhina 《Journal of Mathematical Sciences》2011,177(5):725-734
The notion of the factor-web [`(W)] \bar{W} (ρ, r, r) (1 ≤ ρ < r) is defined for the three-web W(r, r, r) formed on a 2r-dimensional differentiable manifold by three r-dimensional smooth foliations. Embedding of the factor-web in the initial web W(r, r, r) is constructed. This construction is a well-known geometric analog of the canonical extension of a Lie group of transformations
to its parameter group. 相似文献
3.
Xiaoping Xu 《Algebras and Representation Theory》2012,15(2):211-231
Given a weight of sl(n,
\mathbb C{\mathbb C}), we derive a system of variable-coefficient second-order linear partial differential equations that determines the singular
vectors in the corresponding Verma module, and a differential-operator representation of the symmetric group S
n
on the related space of truncated power series. We prove that the solution space of the system of partial differential equations
is exactly spanned by {σ(1)|σ ∈ S
n
}. Moreover, the singular vectors of sl(n,
\mathbb C{\mathbb C}) in the Verma module are given by those σ(1) that are polynomials. The well-known results of Verma, Bernstein–Gel’fand–Gel’fand and Jantzen for the case of sl(n,
\mathbb C{\mathbb C}) are naturally included in our almost elementary approach of partial differential equations. 相似文献
4.
A. A. Duyunova 《Russian Mathematics (Iz VUZ)》2012,56(2):37-49
We consider a three-web on a smooth manifold formed by two n-parameter families of curves and a one-parameter family of hypersurfaces. For such webs, we define a family of adapted frames,
find the systemof structure equations, and study the differential-geometric objects that arise in differential neighborhoods
up to the third order. We prove that each system of ordinary differential equations (SODE) uniquely defines a three-web. This
allows us to describe properties of a SODE in terms of the corresponding three-web. In particular, we characterize autonomous
SODE. 相似文献
5.
We show how the Cartan–Laptev method that generalizes Elie Cartan’s method of external forms and moving frames is applied
to the study of closed G-structures defined by multidimensional three-webs formed on a C
s
-smooth manifold of dimension 2r, r ≥ 1, s ≥ 3, by a triple of foliations of codimension r. We say that a tensor T belonging to a differential-geometric object of order s of a three-web W is closed if it can be expressed in terms of components of objects of lower order s. We find all closed tensors of a three-web and the geometric sense of one of relations connecting three-web tensors. We also
point out some sufficient conditions for the web to have a closed G-structure. It follows from our results that the G-structure associated with a hexagonal three-web W is a closed G-structure of class 4. It is proved that basic tensors of a three-web W belonging to a differential-geometric object of order s of the web can be expressed in terms of an s-jet of the canonical expansion of its coordinate loop, and conversely. This implies that the canonical expansion of every
coordinate loop of a three-web W with closed G-structure of class s is completely defined by an s-jet of this expansion. We also consider webs with one-digit identities of kth order in their coordinate loops and find the conditions for these webs to have the closed G-structure. 相似文献
6.
We prove a “unique crossed product decomposition” result for group measure space II1 factors L ∞(X)⋊Γ arising from arbitrary free ergodic probability measure preserving (p.m.p.) actions of groups Γ in a fairly large family
G\mathcal{G}, which contains all free products of a Kazhdan group and a non-trivial group, as well as certain amalgamated free products
over an amenable subgroup. We deduce that if T
n
denotes the group of upper triangular matrices in PSL (n,ℤ), then any free, mixing p.m.p. action of
G = \operatornamePSL(n,\mathbbZ)*Tn\operatornamePSL(n,\mathbbZ)\Gamma=\operatorname{PSL}(n,\mathbb{Z})*_{T_{n}}\operatorname{PSL}(n,\mathbb{Z}) is W∗-superrigid, i.e. any isomorphism between L ∞(X)⋊Γ and an arbitrary group measure space factor L ∞(Y)⋊Λ, comes from a conjugacy of the actions. We also prove that for many groups Γ in the family G\mathcal{G}, the Bernoulli actions of Γ are W∗-superrigid. 相似文献
7.
For a family F{{\cal F}} of subsets of [n] = {1, 2, ..., n} ordered by inclusion, and a partially ordered set P, we say that F{{\cal F}} is P-free if it does not contain a subposet isomorphic to P. Let ex(n, P) be the largest size of a P-free family of subsets of [n]. Let Q
2 be the poset with distinct elements a, b, c, d, a < b,c < d; i.e., the 2-dimensional Boolean lattice. We show that 2N − o(N) ≤ ex(n, Q
2) ≤ 2.283261N + o(N), where
N = \binomn?n/2 ?N = \binom{n}{\lfloor n/2 \rfloor}. We also prove that the largest Q
2-free family of subsets of [n] having at most three different sizes has at most 2.20711N members. 相似文献
8.
In this work we study a system of M( ≥ 2) first-order singularly perturbed ordinary differential equations with given initial conditions. The leading term of
each equation is multiplied by a distinct small positive parameter, which induces overlapping layers. A maximum principle
does not, in general, hold for this system. It is discretized using backward Euler difference scheme for which a general convergence
result is derived that allows to establish nodal convergence of O(N
− 1ln N) on the Shishkin mesh and O(N
− 1) on the Bakhvalov mesh, where N is the number of mesh intervals and the convergence is robust in all of the parameters. Numerical experiments are performed
to support the theoretical results. 相似文献
9.
Summary. Let (W, H, μ) be an abstract Wiener space and let Tw = w + u (w), where u is an H-valued random variable, be a measurable transformation on W. A Sard type lemma and a degree theorem for this setup are presented and applied to derive existence of solutions to elliptic
stochastic partial differential equations.
Received: 19 March 1996 / In revised form: 7 January 1997 相似文献
10.
D. Çakmak 《Ukrainian Mathematical Journal》2008,60(5):799-809
Some new oscillation criteria are given for general nonlinear second-order ordinary differential equations with damping of
the form x″+ p ( t ) x′+ q ( t ) f ( x ) = 0, where f is monotone or nonmonotone. Our results generalize and extend some earlier results of Deng.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 5, pp. 694–700, May, 2008. 相似文献
11.
Sigurd Assing 《Probability Theory and Related Fields》2001,120(2):143-167
The paper deals with the infinite-dimensional stochastic equation dX= B(t, X) dt + dW driven by a Wiener process which may also cover stochastic partial differential equations. We study a certain finite dimensional
approximation of B(t, X) and give a qualitative bound for its rate of convergence to be high enough to ensure the weak uniqueness for solutions of
our equation. Examples are given demonstrating the force of the new condition.
Received: 6 November 1999 / Revised version: 21 August 2000 / Published online: 6 April 2001 相似文献
12.
V. B. Levenshtam 《Journal of Mathematical Sciences》2009,163(1):89-110
A complete asymptotic expansion is constructed for solutions of the Cauchy problem for nth order linear ordinary differential
equations with rapidly oscillating coefficients, some of which may be proportional to ω
n/2, where ω is oscillation frequency. A similar problem is solved for a class of systems of n linear first-order ordinary differential
equations with coefficients of the same type. Attention is also given to some classes of first-order nonlinear equations with
rapidly oscillating terms proportional to powers ω
d
. For such equations with d ∈ (1/2, 1], conditions are found that allow for the construction (and strict justification) of the leading asymptotic term
and, in some cases, a complete asymptotic expansion of the solution of the Cauchy problem. 相似文献
13.
In this paper we investigate the degree and the homotopy theory of Orlicz–Sobolev mappings W
1,P
(M,N) between manifolds, where the Young function P satisfies a divergence condition and forms a slightly larger space than W
1,n
, n=dim M. In particular, we prove that if M and N are compact oriented manifolds without boundary and dim M=dim N=n, then the degree is well defined in W
1,P
(M,N) if and only if the universal cover of N is not a rational homology sphere, and in the case n=4, if and only if N is not homeomorphic to S
4. 相似文献
14.
I. V. Karnaukh 《Journal of Mathematical Sciences》1993,67(3):3104-3108
A new method is proposed for formulating a boundary-value problem for a fourth-order ordinary differential equation with a solution in W2
1(0, 1). This generalized formulation is based on a system of second-order equations with coefficients in W2
–1 (0, 1). The existence and uniqueness of the indicated solution in this class is proven.Translated fromVychislitel'naya i Prikladnaya Matematika, No. 69, pp. 90–96, 1989. 相似文献
15.
K. L. Avetisyan 《Potential Analysis》2008,29(1):49-63
We study anisotropic mixed norm spaces h(p,q,α) consisting of n-harmonic functions on the unit polydisc of by means of fractional integro-differentiation including small 0 < p < 1 and multi-indices α = (α
1,...,α
n
) with non-positive α
j
≤ 0. As an application, two different Bloch spaces of n-harmonic functions are characterized.
相似文献
16.
E. G. Goluzina 《Journal of Mathematical Sciences》2009,157(4):560-567
The paper continues the studies of the well-known class T of typically real functions f(z) in the disk U = {z:|z| < 1}. The region of values of the system {f(z
0), f(z
0), f(r
1), f(r
2),…, f(r
n
)} in the class T is investigated. Here, z
0 ∈ U, Im z
0 ≠ 0, 0 < r
j
< 1 for j = 1,…, n, n ≥ 2. As a corollary, the region of values of f′(z
0) in the class of functions f ∈ T with fixed values f(z
0) and f(r
j
) (j = 1,…, n) is determined. The proof is based on the criterion of solvability of the power problem of moments. Bibliography: 10 titles.
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 357, 2008, pp. 33–45. 相似文献
17.
We study additive representability of orders on multisets (of size k drawn from a set of size n) which satisfy the condition of independence of equal submultisets (IES) introduced by Sertel and Slinko (Ranking committees,
words or multisets. Nota di Laboro 50.2002. Center of Operation Research and Economics. The Fundazione Eni Enrico Mattei,
Milan, 2002, Econ. Theory 30(2):265–287, 2007). Here we take a geometric view of those orders, and relate them to certain combinatorial objects which we call discrete
cones. Following Fishburn (J. Math. Psychol., 40:64–77, 1996) and Conder and Slinko (J. Math. Psychol., 48(6):425–431, 2004), we define functions f(n,k) and g(n,k) which measure the maximal possible deviation of an arbitrary order satisfying the IES and an arbitrary almost representable
order satisfying the IES, respectively, from a representable order. We prove that g(n,k) = n − 1 whenever n ≥ 3 and (n, k) ≠ (5, 2). In the exceptional case, g(5,2) = 3. We also prove that g(n,k) ≤ f(n,k) ≤ n and establish that for small n and k the functions g(n,k) and f(n,k) coincide.
相似文献
18.
Extremes of independent Gaussian processes 总被引:1,自引:0,他引:1
Zakhar Kabluchko 《Extremes》2011,14(3):285-310
For every n ∈ ℕ, let X
1n
,..., X
nn
be independent copies of a zero-mean Gaussian process X
n
= {X
n
(t), t ∈ T}. We describe all processes which can be obtained as limits, as n→ ∞, of the process a
n
(M
n
− b
n
), where M
n
(t) = max
i = 1,...,n
X
in
(t), and a
n
, b
n
are normalizing constants. We also provide an analogous characterization for the limits of the process a
n
L
n
, where L
n
(t) = min
i = 1,...,n
|X
in
(t)|. 相似文献
19.
LetW be an algebraically closed filed of characteristic zero, letK be an algebraically closed field of characteristic zero, complete for an ultrametric absolute value, and letA(K) (resp. ℳ(K)) be the set of entire (resp. meromorphic) functions inK. For everyn≥7, we show that the setS
n(b) of zeros of the polynomialx
n−b (b≠0) is such that, iff, g ∈W[x] or iff, g ∈A(K), satisfyf
−1(S
n(b))=g
−1(S
n(b)), thenf
n=g
n. For everyn≥14, we show thatS
n(b) is such that iff, g ∈W({tx}) or iff, g ∈ ℳ(K) satisfyf
−1(S
n(b))=g
−1(S
n(b)), then eitherf
n=g
n, orfg is a constant. Analogous properties are true for complex entire and meromorphic functions withn≥8 andn≥15, respectively.
For everyn≥9, we show that the setY
n(c) of zeros of the polynomial
, (withc≠0 and 1) is an ursim ofn points forW[x], and forA(K). For everyn≥16, we show thatY
n(c) is an ursim ofn points forW(x), and for ℳ(K). We follow a method based on thep-adic Nevanlinna Theory and use certain improvement of a lemma obtained by Frank and Reinders. 相似文献
20.
Let Ω and Π be two finitely connected hyperbolic domains in the complex plane
\Bbb C{\Bbb C}
and let R(z, Ω) denote the hyperbolic radius of Ω at z and R(w, Π) the hyperbolic radius of Π at w. We consider functions f that are analytic in Ω and such that all values f(z) lie in the domain Π. This set of analytic functions is denoted by A(Ω, Π). We prove among other things that the quantities
Cn(W,P) := supf ? A(W,P)supz ? W\frac|f(n)(z)| R(f(z),P)n! (R(z,W))nC_n(\Omega,\Pi)\,:=\,\sup_{f\in A(\Omega,\Pi)}\sup_{z\in \Omega}\frac{\vert f^{(n)}(z)\vert\,R(f(z),\Pi)}{n!\,(R(z,\Omega))^n}
are finite for all
n ? \Bbb N{n \in {\Bbb N}}
if and only if ∂Ω and ∂Π do not contain isolated points. 相似文献