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101.
We study the exact multiplicity and ordering properties of positive solutions of the p-Laplacian Dirichlet problem
102.
In several complex variables, the multivariate Padé-type approximation theory is based on the polynomial interpolation of the multidimensional Cauchy kernel and leads to complicated computations. In this paper, we replace the multidimensional Cauchy kernel by the Bergman kernel function K
(z,x) into an open bounded subset of C
n
and, by using interpolating generalized polynomials for K
(z,x), we define generalized Padé-type approximants to any f in the space OL
2() of all analytic functions on which are of class L
2. The characteristic property of such an approximant is that its Fourier series representation with respect to an orthonormal basis for OL
2() matches the Fourier series expansion of f as far as possible. After studying the error formula and the convergence problem, we show that the generalized Padé-type approximants have integral representations which give rise to the consideration of an integral operator – the so-called generalized Padé-type operator – which maps every f
OL
2() to a generalized Padé-type approximant to f. By the continuity of this operator, we obtain some convergence results about series of analytic functions of class L
2. Our study concludes with the extension of these ideas into every functional Hilbert space H and also with the definition and properties of the generalized Padé-type approximants to a linear operator of H into itself. As an application we prove a Painlevé-type theorem in C
n
and we give two examples making use of generalized Padé-type approximants. 相似文献
103.
Rein van der Hout 《Journal of Differential Equations》2003,192(1):188-201
Let and be the unit disk and the unit sphere, and let be a radially symmetric harmonic map heat flow, whose singularities coincide with downward energy jumps. Then its finite time singularities are simple in the sense that precisely one harmonic sphere separates at a time. 相似文献
104.
Giuseppe Marino 《Journal of Mathematical Analysis and Applications》2003,284(2):775-778
Let X be a real Banach space. Let be a family of closed, convex subsets of X. We show that either the intersection ?γ∈Γ(Gγ)? of the ?-neighborhood of the sets Gγ is bounded for each ?>0, or it is unbounded for each ?>0. From this we derive a fixed point theorem for suitable maps that move some points along a bounded direction in Hilbert spaces. 相似文献
105.
A. S. Tikhomirov 《Acta Appl Math》2003,75(1-3):271-279
We study the moduli scheme M(2;0,n) of rank-2 stable vector bundles with Chern classes c
1=0, c
2=n, on the Fano threefold X – the double space P
3 of index two. New component of this scheme is produced via the Serre construction using certain families of curves on X. In particular, we show that the Abel–Jacobi map :HJ(X) of any irreducible component H of the Hilbert scheme of X containing smooth elliptic quintics on X into the intermediate Jacobian J(X) of X factors by Stein through the quasi-finite (probably birational) map g:M of (an open part of) a component M of the scheme M(2;0,3) to a translate of the theta-divisor of J(X). 相似文献
106.
C. Boldrighini L. A. Bunimovich G. Cosimi S. Frigio A. Pellegrinotti 《Journal of statistical physics》2001,102(5-6):1271-1283
We consider a one-dimensional lattice of expanding antisymmetric maps [–1, 1][–1, 1] with nearest neighbor diffusive coupling. For such systems it is known that if the coupling parameter is small there is unique stationary (in time) state, which is chaotic in space-time. A disputed question is whether such systems can exhibit Ising-type phase transitions as grows beyond some critical value c. We present results from computer experiments which give definite indication that such a transition takes place: the mean square magnetization appears to diverge as approaches some critical value, with a critical exponent around 0.9. We also study other properties of the coupled map system. 相似文献
107.
Cindy de Volder 《Geometriae Dedicata》2001,85(1-3):237-251
We consider the blowing-up Y
k
of the projective plane along k general points P
1,...,P
k
. Let
k
: Y
k
2 be the projection map and E
i
the exceptional divisor corresponding to P
i
for 1ik. For m2 and km(m+3)/2–4 let
k
be the invertible sheaf
k
*(
2(m))
Y
k
(–E
1–···–E
k
) on Y
k
, and let k: Y
k
N
be the morphism corresponding to
k
. As
k
is a local embedding, the Gauss map
k
corresponding to
k
is defined on Y
k
by
k
(x)=(d
x
k
)(T
x
(Y
k
)) for all xY
k
. We prove that this Gauss map
k
is injective. 相似文献
108.
V. E. Slyusarchuk 《Mathematical Notes》2000,68(3):386-391
Necessary and sufficient conditions for the Lipschitzian invertibility of the difference map
, wheref: ℝ → ℝ is a continuous function, in the spacesl
p
(ℤ, ℝ), where 1≤p≤∞, of two-sided numerical sequences are obtained.
Translated fromMatematicheskie Zametki, Vol. 68, No. 3, pp. 448–454, September, 2000. 相似文献
109.
Let P
k be a path on k vertices. In an earlier paper we have proved that each polyhedral map G on any compact 2-manifold
with Euler characteristic
contains a path P
k such that each vertex of this path has, in G, degree
. Moreover, this bound is attained for k = 1 or k 2, k even. In this paper we prove that for each odd
, this bound is the best possible on infinitely many compact 2-manifolds, but on infinitely many other compact 2-manifolds the upper bound can be lowered to
. 相似文献
110.
We give a minimal triangulation : S
12
3
S
4
2
of the Hopf map h:S
3S
2 and use it to obtain a new construction of the 9-vertex complex projective plane. 相似文献