共查询到20条相似文献,搜索用时 15 毫秒
1.
In this article we prove that if , , is a bounded pseudoconvex domain with real analytic boundary, then for each , there exists a fixed open neighborhood of and an open neighborhood of in such that any can be extended holomorphically to , and that the action defined by
is real analytic in joint variables. This extends H. Cartan's theorem beyond the boundary. Some applications are also discussed here.
2.
Jeanne N. Clelland Thomas A. Ivey 《Transactions of the American Mathematical Society》2005,357(3):1061-1093
We begin an exploration of parametric Bäcklund transformations for hyperbolic Monge-Ampère systems. (The appearance of an arbitrary parameter in the transformation is a feature of several well-known completely integrable PDEs.) We compute invariants for such transformations and explore the behavior of four examples, two of which are new, in terms of their invariants, symmetries, and conservation laws. We prove some preliminary results and indicate directions for further research.
3.
James E. Tener 《Journal of Mathematical Analysis and Applications》2008,341(1):640-648
We present a necessary and sufficient condition for a 3×3 matrix to be unitarily equivalent to a symmetric matrix with complex entries, and an algorithm whereby an arbitrary 3×3 matrix can be tested. This test generalizes to a necessary and sufficient condition that applies to almost every n×n matrix. The test is constructive in that it explicitly exhibits the unitary equivalence to a complex symmetric matrix. 相似文献
4.
In this paper Rothe’s classical method is extended so that it can be used to solve some linear parabolic boundary value problems
in non-cylindrical domains. The corresponding existence and uniqueness theorems are proved and some further results and generalizations
are discussed and applied. 相似文献
5.
Yu. R. Romanovskii 《Mathematical Notes》1996,60(1):56-67
The Cartan equivalence method is used to find out if a given equation has a nontrivial Lie group of point symmetries. In particular,
we compute invariants that permit one to recognize equations with a three-dimensional symmetry group. An effective method
to transform the Lie system (the system of partial differential equations to be satisfied by the infinitesimal point symmetries)
into a formally integrable form is given. For equations with a three-dimensional symmetry group, the formally integrable form
of the Lie system is found explicitly.
Translated fromMatematicheskie Zametki, Vol. 60, No. 1, pp. 75–91, July, 1996. 相似文献
6.
Dean S. Clark 《Stochastic Processes and their Applications》1984,17(2):359-367
This paper examines the relation between convergence of the Robbins-Monro iterates , and the laws of large numbers Sn=anΣn?1j=0ξj→0 as n→+∞. If an is decreasing at least as rapidly as c/n, then Xn→θw.p. 1 (resp. in Lp, p?1) implies Sn→0 w.p. 1 (resp. in Lp, p?1) as n→+∞. If an is decreasing at least as slowly as c?n and limn→+∞an=0, then Sn→0 w.p. 1 (resp. in Lp, p?2) implies Xn→θw.p. 1 (resp. in Lp, p?2) as n →+∞. Thus, there is equivalence in the frequently examined case . Counter examples show that the LLN must have the form of Sn, that the rate of decrease conditions are sharp, that the weak LLN is neither necessary nor sufficient for the convergence in probability of Xn to θ when . 相似文献
7.
I. A. Tel’nykh 《Mathematical Notes》2000,68(3):397-404
In this paper a topological invariant is introduced for the class of supertransitive flows on closed nonorientable surfacesM of negative Euler characteristic. We describe properties of this invariant and prove that it provides necessary conditions
for the topological equivalence of flows belonging to the above-mentioned class of supertransitive flows.
Translated fromMatematicheskie Zametki, Vol. 68, No. 3, pp. 461–470, September, 2000. 相似文献
8.
In this paper we apply the contragredient equivalence to solve two matrix systems. Firstly, we characterize and build all possible solutions of the matrix system P = XY, Q = YX, giving a recursive formula for the number of contragrediently nonequivalent solutions. And, secondly, we find the solution of the matrix system AX = YC, BY = XD. 相似文献
9.
V. Lakshmikantham 《Journal of Optimization Theory and Applications》1994,82(2):315-321
In this paper, the question of whether it is possible to develop monotone sequences that converge to the solution quadratically, when the function involved in the initial-value problem admits a decomposition into a difference of two convex functions, is answered positively. This extends the method of quasilinearization to a larger class. 相似文献
10.
Geno Nikolov 《Mathematische Nachrichten》2005,278(10):1190-1208
Denote by πn the set of all algebraic polynomials of degree at most n with complex coefficients. An inequality of I. Schur asserts that the first derivative of the transformed Tchebycheff polynomial has the greatest uniform norm in [?1, 1] among all f ∈ ??n, where (1) Here we show that this extremal property of persists in the wider class of polynomials f ∈ πn which vanish at ±1, and for which there exist n ? 1 points separating the zeros of and such that for j = 1, …, n ? 1. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
11.
Detlef Müller 《Mathematische Annalen》2008,340(1):23-75
This is a the first in a series of two articles devoted to the question of local solvability of doubly characteristic differential operators L, defined, say, in an open set $\Omega \subset \mathbb{R}^n.This is a the first in a series of two articles devoted to the question of local solvability of doubly characteristic differential
operators L, defined, say, in an open set Suppose the principal symbol p
k
of L vanishes to second order at , and denote by the Hessian form associated to p
k
on . As the main result of this paper, we show (under some rank conditions and some mild additional conditions) that a necessary
condition for local solvability of L at x
0 is the existence of some such that . We apply this result in particular to operators of the form
where the X
j
are smooth real vector fields and the α
jk
are smooth complex coefficients forming a symmetric matrix . We say that L is essentially dissipative at x
0, if there is some such that e
iθ
L is dissipative at x
0, in the sense that . For a large class of doubly characteristic operators L of this form, our main result implies that a necessary condition for local solvability at x
0 is essential dissipativity of L at x
0. By means of H?rmander’s classical necessary condition for local solvability, the proof of the main result can be reduced
to the following question: suppose that Q
A
and Q
B
are two real quadratic forms on a finite dimensional symplectic vector space, and let Q
C
: = {Q
A
,Q
B
} be given by the Poisson bracket of Q
A
and Q
B
. Then Q
C
is again a quadratic form, and we may ask: when can we find a common zero of Q
A
and Q
B
at which Q
C
does not vanish? The study of this question occupies most of the paper, and the answers may be of independent interest. In
the second paper of this series, building on joint work with F. Ricci, M. Peloso and others, we shall study local solvability
of essentially dissipative left-invariant operators of the form (0.1) on Heisenberg groups in a fairly comprehensive way.
Various examples exhibiting a kind of exceptional behaviour from previous joint works, e.g., with G. Karadzhov, have shown
that there is little hope for a complete characterization of locally solvable operators on Heisenberg groups. However, the
“generic” scheme of what rules local solvability of second order operators on Heisenberg groups becomes evident from our work.
相似文献
12.
Christopher A. Okpoti Gord Sinnamon 《Journal of Mathematical Analysis and Applications》2007,326(1):398-413
It is proved that, besides the usual Muckenhoupt condition, there exist four different scales of conditions for characterizing the Hardy type inequality with general measures for the case 1<p?q<∞. In fact, an even more general equivalence theorem of independent interest is proved and discussed. 相似文献
13.
van der WOUDE J. W. 《中国科学 数学(英文版)》2011,(5)
We in this paper give a decomposition concerning the general matrix triplet over an arbitrary divisionring F with the same row or column numbers. We also design a practical algorithm for the decomposition of thematrix triplet. As applications, we present necessary and suficient conditions for the existence of the generalsolutions to the system of matrix equations DXA = C1, EXB = C2, F XC = C3 and the matrix equation AXD + BY E + CZF = Gover F. We give the expressions of the general solutions to the system a... 相似文献
14.
Christopher A. Okpoti Gord Sinnamon 《Journal of Mathematical Analysis and Applications》2008,337(1):219-230
Scales of equivalent weight characterizations for the Hardy type inequality with general measures are proved. The conditions are valid in the case of indices 0<q<p<∞, p>1. We also include a reduction theorem for transferring a three-measure Hardy inequality to the case with two measures. 相似文献
15.
In this paper, an entropy-like proximal method for the minimization of a convex function subject to positivity constraints is extended to an interior algorithm in two directions. First, to general linearly constrained convex minimization problems and second, to variational inequalities on polyhedra. For linear programming, numerical results are presented and quadratic convergence is established.Corresponding author. His research has been supported by C.E.E grants: CI1* CT 92-0046. 相似文献
16.
Aron Pinker 《International Journal of Mathematical Education in Science & Technology》2013,44(3):299-301
This paper provides a graphical (technical) exhaustive search algorithm for elements which belong to expressions containing cross products of sets. Initial tests suggest that this technique, an extension of the truth table technique, is superior to the currently employed method of verbal (symbolic) inclusion check. The method allows routine treatment of complicated expressions which contain cross products, utilizing the basic table 相似文献
17.
M. B. Subrahmanyam 《Journal of Optimization Theory and Applications》1989,62(2):311-319
The simplex algorithm of Nelder and Mead is extended to handle nonlinear optimization problems with constraints. To prevent the simplex from collapsing into a subspace near the constraints, a delayed reflection is introduced for those points moving into the infeasible region. Numerical experience indicates that the proposed algorithm yields good results in the presence of both inequality and equality constraints, even when the constraint region is narrow. We note that it may be possible to modify and improve the algorithm by trying out variants. 相似文献
18.
Yu. A. Chernyaev 《Computational Mathematics and Mathematical Physics》2006,46(4):548-553
The conditional gradient method is extended to the case when the feasible set is the set-the-oretic difference of a certain convex set and the union of several convex sets. Necessary extremum conditions are used to prove the convergence of the method. 相似文献
19.
The Conjugate Gradient (CG) method and the Conjugate Residual (CR) method are Krylov subspace methods for solving symmetric (positive definite) linear systems. To solve nonsymmetric linear systems, the Bi-Conjugate Gradient (Bi-CG) method has been proposed as an extension of CG. Bi-CG has attractive short-term recurrences, and it is the basis for the successful variants such as Bi-CGSTAB. In this paper, we extend CR to nonsymmetric linear systems with the aim of finding an alternative basic solver. Numerical experiments show that the resulting algorithm with short-term recurrences often gives smoother convergence behavior than Bi-CG. Hence, it may take the place of Bi-CG for the successful variants. 相似文献
20.
A. Luisa Elgueta Melitta Fiebig-Wittmaack Maria Teresa Villacran 《Applicable analysis》2013,92(3-4):359-367
We approximate a Duffing equation by an averaged system. We solve the system explicitely and draw bifurcation diagrams in dependence of the forcing term. We discuss the goodness of the averaging method, relative to the behavior of the solutions in dependence of involved parameters, by comparing with results obtained in [6,10] for the original Duffing equation. 相似文献