摘要:

AbstractLetXbe a smooth complex projective curve of genusgover an algebraically closed fieldkof charcteristic 0. In this paper we prove that given two general stable bundlesFandGsuch thatthere exists an extensionofGbyFwithEstable.Moreover, such extension also exists for any general stable bundles ofFandGof degree even andXeither a double covering of a curve of genus 2 or a curve of genusg≥ 3 + 4(rankG+ rankF) + max {rankG, rankF).That solves Lange's conjecture ([L2], p. 455) for such case

ISSN:0025-584X    

DOI:10.1002/mana.19981940102

出版商:WILEY‐VCH Verlag    

年代:1998

数据来源: WILEY

摘要:

AbstractZu jeder Konfiguration des IR3, welche aus einem Ellipsoid in Hauptachsenform und einem Punktepaar besteht, wird eine vierdimensionale reelle Divisionsalgebra konstruiert. Diese Konstruktion induziert eine Bijektion zwischen den Äquivalenzklassen von Konfigurationen und den Isomorphieklassen vierdimensionaler potenzassoziativer reeller Divisionsalgebren. Hierbei sind zwei Konfigurationen genau dann äquivalent, wenn ihre Ellipsoide übereinstimmen und ihre Punktepaare in derselben Bahn unter der Operation der eigentlichen Symmetriegruppe des Ellipsoids liegen. Ein Querschnitt für die Äquivalenzklassen von Konfigurationen wird angeg

ISSN:0025-584X    

DOI:10.1002/mana.19981940103

出版商:WILEY‐VCH Verlag    

年代:1998

数据来源: WILEY

摘要:

AbstractWe show that certain Hardy‐ type inequalities hold in plump domains and domains with a Whitney cube #‐condit

ISSN:0025-584X    

DOI:10.1002/mana.19981940104

出版商:WILEY‐VCH Verlag    

年代:1998

数据来源: WILEY

摘要:

AbstractWe prove a general embedding theorem for Sobolev spaces on open manifolds of bounded geometry and infer from this the module structure theorem. Thereafter we apply this to weighted Sobolev spaces.

ISSN:0025-584X    

DOI:10.1002/mana.19981940105

出版商:WILEY‐VCH Verlag    

年代:1998

数据来源: WILEY

摘要:

AbstractWe obtain a nonexistence result and an anti‐maximum principle for weak solutions u = (u1,…, un) to the following strictly cooperative elliptic system,Here, Ω CIRNis a bounded domain with aC2,α‐ boundary δΩ, for some α ∈ (0,1), Δpdenotes thep‐Laplacian defined by Δpu = div (|∇u|p‐2∇u) for p 6 (1,∞), and the coefficients aij(1 ≤ i,j ≤ n)are assumed to be constants satisfying aij>0 for i ≠ j (a strictly cooperative system). We assume 0 ≤fi, ∈ L∞(Ω) (1 ≤ i ≤ n). For ∇+= ∇‐∇‐= ∈ IR and f = (f1,…,fn) 0 in Ω, let μ1denote the first eigenvalue of the (p ‐ 1)‐homogeneous system(S).Assuming f ≠ 0 in Ω, we show: (i) if ∧+= ∧‐= μ1, then (S) has no solution; and (ii) if ∧+, ∧‐∧ (μ1,μ1+ δ), for some δ>0 small enough, then ui0 on δΩ (1 ≤ i ≤ n). Our methods for the system (S) are completely different from the casen= 1 (a single equation)

ISSN:0025-584X    

DOI:10.1002/mana.19981940106

出版商:WILEY‐VCH Verlag    

年代:1998

数据来源: WILEY

摘要:

AbstractLetXC PN=P NKbe a subvariety of dimensionnand ∧PNbe a generic linear subspace of dimensionNk ‐ 1 withk≥n.Then the linear projection π∧:X→ Pkis a finite map. LetR(π∧) be its ramification locus. In this paper we study the map from the GrassmannianG(N‐ k ‐ 1,N) of planes of dimensionN‐ k ‐ 1 inPNto the Hilbert moduli space given by ∧R(π∧). We wish to compute in particular the dimension, say,nof the image of this map. The motivation of this question comes from the fact that these ramification cycles are closely related to the Stückrad ‐ Vogel cycle. We show thatnis just the transcendence degree of a certain part of this cycle. The main result is that, under some mild hypothesis, in case of a projectionX→ Pn, i.e., k = n, the map ∧ →R(π∧) is generically finite and sontakes its maximal possible value. Moreover, we show that in the case of smooth surfacesX∇ P4and generic projections onto P3this map is again generically finite if the norm

ISSN:0025-584X    

DOI:10.1002/mana.19981940107

出版商:WILEY‐VCH Verlag    

年代:1998

数据来源: WILEY

摘要:

AbstractThis paper solves explicitly the direct spectral problem of canonical differential systems for a special class of potentials. For a potential from this class the corresponding spectral function may have jumps and its absolutely continuous part has a rational derivative possibly with zeros on the real line. A direct and self‐contained proof of the diagonalization of the associated differential operator is given, including explicit formulas for the diagonalizing operator and the spectral function. This proof also yields an explicit formula for the solution of the inverse problem. As an application new representations are derived for a large class of solutions of nonlinear integrable partial differential equations. The method employed is based on state space techniques and uses the idea of realization from mathematical system theor

ISSN:0025-584X    

DOI:10.1002/mana.19981940108

出版商:WILEY‐VCH Verlag    

年代:1998

数据来源: WILEY

摘要:

AbstractDie Fragestellung dieser Arbeit ist motiviert durch ein allgemeines Existenzprinzip für Lösungen nichtlinearer Gleichungen in metrischen Räumen, welches folgendermaßen formuliert werden k

ISSN:0025-584X    

DOI:10.1002/mana.19981940109

出版商:WILEY‐VCH Verlag    

年代:1998

数据来源: WILEY

摘要:

AbstractWe consider a regular singular Sturm‐Liouville operatoron the line segment (0,1]. We impose certain boundary conditions such that we obtain a semi‐bounded self‐adjoint operator. It is known (cf. Theorem 1.1 below) that the ζ‐function of this operatorhas a meromorphic continuation to the whole complex plane with 0 being a regular point. Then, according to [RS] the ζ ‐ regularized determinant ofLis defined byIn this paper we are going to express this determinant in terms of the solutions of the homogeneous differential equationLy= 0 generalizing earlier work of S. Levit and U. Smilansky [LS], T. Dreyfus and H. Dym [DD], and D. Burghelea, L. Friedlander and T. Kappeler [BFK1, BFK2). More precisely we prove the formulaHere ϕ ψ is a certain fundamental system of solutions for the homogeneous equationLy= 0,W(ϕ ψ), denotes their Wronski determinant, and v0, v1are numbers related to the characteristic roots of the regular singu

ISSN:0025-584X    

DOI:10.1002/mana.19981940110

出版商:WILEY‐VCH Verlag    

年代:1998

数据来源: WILEY

摘要:

AbstractOscillation and nonoscillation criteria are established for the second order linear differential equationunder the hypothesis thatp(t)>0 andwhere a(t) ∈ C2([t0,∞);(0,∞)) is a given function. These results improve some well‐known oscillation and nonoscillation c

ISSN:0025-584X    

DOI:10.1002/mana.19981940111

出版商:WILEY‐VCH Verlag    

年代:1998

数据来源: WILEY