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991.
Sisto Baldo Giandomenico Orlandi 《Calculus of Variations and Partial Differential Equations》1996,4(4):369-384
We define a class
p
(M,N) of Sobolev maps from a manifoldM into a manifoldN, in such a way that each mapu
p
(M, N) has a well defined [p]-homotopy type, providedN satisfies a topological hypothesis. Using this, we prove the existence of minimizers in [p]-homotopy classes for some polyconvex variational problems. 相似文献
992.
This paper considers the prescribed scalar curvature problem onS
n
forn>-3. We consider the limits of solutions of the regularization obtained by decreasing the critical exponent. We characterize those subcritical solutions which blow up at the least possible energy level, determining the points at which they can concentrate, and their Morse indices. We then show that forn=3 this is the only blow up which can occur for solutions. We use this in combination with the Morse inequalities for the subcritical problem to obtain a general existence theorem for the prescribed scalar curvature problem onS
3.This article was processed by the author using the
style filepljourlm from Springer-Verlag. 相似文献
993.
Inclusion-exclusion: Exact and approximate 总被引:1,自引:0,他引:1
It is often required to find the probability of the union of givenn eventsA
1
,...,A
n
. The answer is provided, of course, by the inclusion-exclusion formula: Pr(A
i
)=
i
–
i<j
Pr(A
i
A
j
)±.... Unfortunately, this formula has exponentially many terms, and only rarely does one manage to carry out the exact calculation. From a computational point of view, finding the probability of the union is an intractable, #P-hard problem, even in very restricted cases. This state of affairs makes it reasonable to seek approximate solutions that are computationally feasible. Attempts to find such approximate solutions have a long history starting already with Boole [1]. A recent step in this direction was taken by Linial and Nisan [4] who sought approximations to the probability of the union, given the probabilities of allj-wise intersections of the events forj=1,...k. The developed a method to approximate Pr(A
i
), from the above data with an additive error of exp
. In the present article we develop an expression that can be computed in polynomial time, that, given the sums |S|=j
Pr(
iS
A
i
) forj=1,...k, approximates Pr(A
i
) with an additive error of exp
. This error is optimal, up to the logarithmic factor implicit in the
notation.The problem of enumerating satisfying assignments of a boolean formula in DNF formF=v
l
m
C
i
is an instance of the general problem that had been extensively studied [7]. HereA
i
is the set of assignments that satisfyC
i
, and Pr(
iS
A
i
)=a
S
/2n where
iS
C
i
is satisfied bya
S
assignments. Judging from the general results, it is hard to expect a decent approximation ofF's number of satisfying assignments, without knowledge of the numbersa
S
for, say, all cardinalities
. Quite surprisingly, already the numbersa
S
over |S|log(n+1)uniquely determine the number of satisfying assignments for F.We point out a connection between our work and the edge-reconstruction conjecture. Finally we discuss other special instances of the problem, e.g., computing permanents of 0,1 matrices, evaluating chromatic polynomials of graphs and for families of events whose VC dimension is bounded.Work supported in part by a grant of the Binational Israel-US Science Foundation.Work supported in part by a grant of the Binational Israel-US Science Foundation and by the Israel Science Foundation. 相似文献
994.
We describe an algorithm for selecting the n-th largest element (where 0<<1), from a totally ordered set ofn elements, using at most (1+(1+o(1))H())·n comparisons whereH() is the binary entropy function and theo(1) stands for a function that tends to 0 as tends to 0. For small values of this is almost the best possible as there is a lower bound of about (1+H())·n comparisons. The algorithm obtained beats the global 3n upper bound of Schönhage, Paterson and Pippenger for <1/3. 相似文献
995.
F. A. Sukochev 《Integral Equations and Operator Theory》1996,26(1):102-124
If is a surjective isometry of the separable symmetric operator spaceE(M, ) associated with the approximately finite-dimensional semifinite factorM and if ·
E(M,)
is not proportional to ·
L
2, then there exist a unitary operatorUM and a Jordan automorphismJ ofM such that(x)=UJ(x) for allxME(M, ). We characterize also surjective isometries of vector-valued symmetric spacesF((0, 1), E(M, )).Research supported by the Australian Research Council 相似文献
996.
Ryszard Rudnicki 《Integral Equations and Operator Theory》1996,24(3):320-327
A class of Markov operators appearing in biomathematics is investigated. It is proved that these operators are asymptotic stable inL
1, i.e. lim
n
P
n f=0 forfL
1 and f(x) dx=0. 相似文献
997.
Christiane Tretter 《Integral Equations and Operator Theory》1996,26(2):222-248
We study nonselfadjoint spectral problems for ordinary differential equationsN(y)–P(y)=0 with -linear boundary conditions where the orderp of the differential operatorP is less than the ordern ofN. The present paper addresses the question of the completeness of the eigenfunctions and associated functions in the Sobolev spacesW
2
k
(0,1) fork=0,1,...,n. To this end we associate a pencil
– of operators acting fromL
2(0,1) to the larger spaceL
2x(0,1)
n
with the given problem. We establish completeness results for normal problems in certain finite codimensional subspaces ofW
2
k
(0,1) which are characterized by means of Jordan chains in 0 of the adjoint of the compact operator
=
–1.Dedicated to Professor Heinz Langer on the occasion of his 60th birthday 相似文献
998.
V. Suresh 《K-Theory》1996,10(6):597-610
Let X be a smooth projective surface over a number field k. Let (CH0(X)) denote the Chow group of zero-cyles modulo rational equivalence on X. Let CH0(X) be the subgroup of CH
0(X) consisting of classes which vanish when going over to an arbitrary completion of k. Bloch put forward a conjecture asserting that this group is isomorphic to the Tate-Shafarevich group of a certain Galois module atttached to X. In this paper, we disprove this general conjecture. We produce a conic bundle X over an elliptic curve, for which the group (CH0(X) is not zero, but the Galois-theoretic Tate-Shafarevich group vanishes. 相似文献
999.
Ayelet Lindenstrauss 《K-Theory》1996,10(3):239-265
Topological Hochschild homology is calculated for the rings /p[x]/(f(x)) (where p is prime and f(x) /p[x] any polynomial), [x]/(x
n) and [x]/(x
n–1). A spectral sequence argument is used for calculating the homology of the topological Hochschild homology spectrum, from which its stable homotopy structure can be read off since the spectrum is known for a priori reasons to be a restricted product of Eilenberg-MacLane spectra. 相似文献
1000.
Let be a product order on [n]
p
i.e. for A, B [n]
p
, 1a
1<a
2<...<a
p
º-n and 1<-b
1<b
2<...<b
p
<-n we have AB iff a
i<-b
i for all i=1, 2,..., p. For a linear extension < of (ordering [n]
p
as
) let F
<
[n],p
(m) count the number of A
i
's, i<-m such that 1A
i. Clearly,
for every m and <, where <l denotes the lexicographic order on [n]
p
. In this note we prove that the colexicographical order, <c, provides a corresponding lower bound i.e. that
holds for any linear extension < of .This project together with [2] was initiated by the first author and continued in colaboration with the second author. After the death of the first author the work was continued and finalized by the second and the third author.Research supported by NSF grant DMS 9011850. 相似文献