共查询到20条相似文献,搜索用时 31 毫秒
1.
We consider, for maps in H1/2(S1;S1), a family of (semi)norms equivalent to the standard one. We ask whether, for such a norm, there is some map in H1/2(S1;S1) of prescribed topological degree equal to 1 and minimal norm. In general, the answer is no, due to concentration phenomena. The existence of a minimal map is sensitive to small perturbations of the norm. We derive a sufficient condition for the existence of minimal maps. In particular, we prove that, for every given norm, there are arbitrarily small perturbations of it for which the minimum is attained. In case there is no minimizer, we determine the asymptotic behavior of minimizing sequences. We prove that, for such minimizing sequences, the energy concentrates near a point of S1. We describe this concentration in terms of bubbling-off of circles. 相似文献
2.
Jean-Pierre Gabardo 《Acta Appl Math》2009,107(1-3):49-73
We consider Gabor systems generated by a window given by the hyperbolic secant function. We show that such a system forms a Parseval frame for L 2(?) when the translations and modulations of the window are associated with certain non-separable lattices in ?2 which we explicitly describe. We also study the more general problem of characterizing the positive Borel measures μ on ?2n with the property that the short-time Fourier transform defines an isometric embedding from L 2(? n ) to L μ 2 (?2n ) when the window belongs to the Schwartz class and, in particular, we characterize the extreme points of this set. In the case where the window is the hyperbolic secant function, we consider the situation where the measure is discrete with constant weights and supported on a non-separable lattice yielding a Parseval frame. We provide arithmetic conditions on the parameters defining the lattice characterizing when the associated measure is an extreme point. 相似文献
3.
Alan Dow 《Topology and its Applications》1985,21(2):193-207
For an infinite cardinal κ, we call a compact zero-dimensional space a κ-Parovicenko space if its boolean algebra of clopen sets is κ-saturated and has cardinality κ<κ. We answer some questions about these spaces which were posed in [14]. For instance, it is shown that a κ+-Parovicenko spacé can be a Stone-Cech remainder in a natural way. We show that some of the results in [14] which used the assumption κ<κ=κ, do indeed require this assumption. We also show that if 2κ=κ+ then each compact Fκ+-space with weight κ+ can be embedded into a κ+-Parovicenko space (and so into an extremally disconnected space). 相似文献
4.
A. S. Gorsky 《Theoretical and Mathematical Physics》2012,171(2):616-628
We consider the gravimagnetization of the N=2 supersymmetric vacuum in the presence of the ??-deformation. We argue that the Seiberg-Witten prepotential is related to the vacuum density of the angular momentum in the Euclidean space ? 4 . We conjecture the possible role of the dyonic instantons as the microscopic angular momentum carriers that could yield a spontaneous vacuum gravimagnetization. We interpret the dyonic instanton as an analogue of the Euclidean bounce in ? 4 . Such a bounce is related to the Schwinger pair production. We also briefly discuss the induced angular momentum in ? 4 in the dual Liouville formulation of the SU(2) theory in terms of the hypothesis of the Alday-Gaiotto-Tachikawa correspondence. 相似文献
5.
Sk. Safique Ahmad 《Linear algebra and its applications》2009,430(4):1171-2221
We develop a general framework for perturbation analysis of matrix polynomials. More specifically, we show that the normed linear space Lm(Cn×n) of n-by-n matrix polynomials of degree at most m provides a natural framework for perturbation analysis of matrix polynomials in Lm(Cn×n). We present a family of natural norms on the space Lm(Cn×n) and show that the norms on the spaces Cm+1 and Cn×n play a crucial role in the perturbation analysis of matrix polynomials. We define pseudospectra of matrix polynomials in the general framework of the normed space Lm(Cn×n) and show that the pseudospectra of matrix polynomials well known in the literature follow as special cases. We analyze various properties of pseudospectra in the unified framework of the normed space Lm(Cn×n). We analyze critical points of backward errors of approximate eigenvalues of matrix polynomials and show that each critical point is a multiple eigenvalue of an appropriately perturbed polynomial. We show that common boundary points of components of pseudospectra of matrix polynomials are critical points. As a consequence, we show that a solution of Wilkinson’s problem for matrix polynomials can be read off from the pseudospectra of matrix polynomials. 相似文献
6.
Davide Di Giorgio 《Journal of Mathematical Analysis and Applications》2002,275(1):165-187
We consider two infinitesimal generators A, B of strongly continuous groups in a general Banach space X, such that either the commutator between A and B commutes both with etA and with etB, or the commutator is a multiple of A. We prove that under suitable assumptions the sum A+B and the commutator [A,B] are closable, and their closures generate strongly continuous groups. We give explicit representation formulas for such groups, in terms of etA and etB. 相似文献
7.
A. V. Borovskikh 《Siberian Mathematical Journal》2006,47(5):813-834
We study the two-dimensional eikonal equation ψ x 2 + ψ y 2 = 1/v 2(x, y). We carry out the group analysis of the equation, establish a connection between the group properties and geometric characteristics of the Riemannian space with the metric ds 2 = [dx 2 + dy 2]/v 2(x, y). We select the most important classes of equations and derive some conditions for reducibility of a given equation to an equation of one of those classes. We find a condition for two equations to be equivalent (the theorem of seven invariants). For the equations corresponding to Riemannian spaces of constant curvature, we obtain explicit formulas for the solutions describing the wave front for a point source and also the ray equations. 相似文献
8.
Benton L. Duncan 《Linear algebra and its applications》2007,422(1):67-76
We study a class of matrix function algebras, here denoted T+(Cn). We introduce a notion of point derivations, and classify the point derivations for certain finite dimensional representations of T+(Cn). We use point derivations and information about n×n matrices to show that every T+(Cn)-valued derivation on T+(Cn) is inner. 相似文献
9.
《Annals of Pure and Applied Logic》1988,39(3):273-290
We analyse the trees given by sharps for Π12 sets via inner core models to give a canonical decomposition of such sets when a core model is Σ13 absolute. This is by way of analogy with Solovay's analysis of Π11 sets into ω1 Borel sets — Borel in codes for wellorders. We find that Π12 sets are also unions of ω1 Borel sets — but in codes for mice and wellorders. We give an application of this technique in showing that if a core model, K, is Σ13 absolute thenTheorem. Every real is in K iff every Π13 set of reals contains a Π13 singleton. 相似文献
10.
Moubariz Z. Garaev 《Journal of Combinatorial Theory, Series A》2006,113(5):851-865
We estimate character sums with Catalan numbers and middle binomial coefficients modulo a prime p. We use this bound to show that the first at most p13/2(logp)6 elements of each sequence already fall in all residue classes modulo every sufficiently large p, which improves the previously known result requiring pO(p) elements. We also study, using a different technique, similar questions for sequences satisfying polynomial recurrence relations like the Apéry numbers. We show that such sequences form a finite additive basis modulo p for every sufficiently large prime p. 相似文献
11.
《Journal of Complexity》1994,10(1):96-128
Linear multivariate problems are defined as the approximation of linear operators on functions of d variables. We study the complexity of computing an ϵ-approximation in different settings. We are particularly interested in large d and/or large ϵ−1. Tractability means that the complexity is bounded by c(d) K(d, ϵ), where c(d) is the cost of one information operation and K(d, ϵ) is a polynomial in d and/or in ϵ−1. Strong tractability means that K(d, ϵ) is a polynomial in ϵ−1, independent of d. We provide necessary and sufficient conditions for linear multivariate problems to be tractable or strongly tractable in the worst case, average case, randomized, and probabilistic settings. This is done for the class Λall where an information operation is defined as the computation of any continuous linear functional. We also consider the class Λstd where an information operation is defined as the computation of a function value. We show under mild assumptions that tractability in the class Λall is equivalent to tractability in the class Λstd. The proof is, however, not constructive. Finally, we consider linear multivariate problems over reproducing kernel Hilbert spaces, showing that such problems are strongly tractable even in the worst case setting. 相似文献
12.
We study nonlinear Schrödinger equations, posed on a three dimensional Riemannian manifold M. We prove global existence of strong H1 solutions on M=S3 and M=S2×S1 as far as the nonlinearity is defocusing and sub-quintic and thus we extend results of Ginibre, Velo and Bourgain who treated the cases of the Euclidean space R3 and the torus T3=R3/Z3 respectively. The main ingredient in our argument is a new set of multilinear estimates for spherical harmonics. 相似文献
13.
We construct a strong Laplacian D * D by using the third operator in the basis {d,d *,D} of the space of natural first-order operators acting on the differential forms of a Riemannian manifold (M,g). We study the properties of the Laplacian D * D and obtain Weitzenbock's formula relating the three strong Laplacians dd *, d * d, and D * D to the curvature of the manifold (M,g). 相似文献
14.
《Journal of Computational and Applied Mathematics》2002,142(1):173-184
We prove a local limit theorem for the length of the side of the Durfee square in a random partition of a positive integer n as n→∞. We rely our asymptotic analysis on the power series expansion of xm2∏j=1m(1−xj)−2 whose coefficient of xn equals the number of partitions of n in which the Durfee square is m2. 相似文献
15.
Nicolas Bedaride 《Discrete Mathematics》2009,309(8):2053-2066
We consider a minimal rotation on the torus Td of direction ω. A natural cellular decomposition of the torus is associated to this map. We consider an infinite orbit for this map. We compute the complexity of the associated word. Under some hypothesis on the direction, we obtain an exact formula which shows that the order of magnitude is nd. This result is related to the billiard map inside a hypercube of Rd+1. 相似文献
16.
Heather Russell 《Advances in Mathematics》2003,179(1):38-58
We give a method of counting the number of curves with a given type of singularity in a suitably ample linear series on a smooth surface using punctual Hilbert schemes. The types of singularities for which our results suffice include the topological type with local equation xa+yb with ?a?3b. We work out the example of curves with the analytic type of singularity with local equation x2+yn for 1<n<9. 相似文献
17.
We illustrate the connection between homogeneous perturbations of homogeneous Gaussian random fields over Rn or Zn, with values in Rm, and classical as well as quantum statistical mechanics. In particular we construct homogeneous non-Gaussian random fields as weak limits of perturbed Gaussian random fields and study the infinite volume limit of correlation functions for a classical continuous gas of particles with inner degrees of freedom. We also exhibit the relation between quantum statistical mechanics of lattice systems (anharmonic crystals) at temperature β?1 and homogeneous random fields over Zn × Sβ, where Sβ is the circle of length β, which then provides a connection also with classical statistical mechanics. We obtain the infinite volume limit of real and imaginary times Green's functions and establish its properties. We also give similar results for the Gibbs state of the correspondent classical lattice systems and show that it is the limit as h → 0 of the quantum statistical Gibbs state. 相似文献
18.
We study the problem of acute triangulations of convex polyhedra and the space ? n . Here an acute triangulation is a triangulation into simplices whose dihedral angles are acute. We prove that acute triangulations of the n-cube do not exist for n≥4. Further, we prove that acute triangulations of the space ? n do not exist for n≥5. In the opposite direction, in ?3, we present a construction of an acute triangulation of the cube, the regular octahedron and a non-trivial acute triangulation of the regular tetrahedron. We also prove nonexistence of an acute triangulation of ?4 if all dihedral angles are bounded away from π/2. 相似文献
19.
Davide Penazzi 《Archive for Mathematical Logic》2011,50(7-8):743-758
We initiate a geometric stability study of groups of the form G/G 00, where G is a 1-dimensional definably compact, definably connected, definable group in a real closed field M. We consider an enriched structure M?? with a predicate for G 00 and check 1-basedness or non-1-basedness for G/G 00, where G is an additive truncation of M, a multiplicative truncation of M, SO 2(M) or one of its truncations; such groups G/G 00 are now interpretable in M??. We prove that the only 1-based groups are those where G is a sufficiently ??big?? multiplicative truncation, and we relate the results obtained to valuation theory. In the last section we extend our results to ind-hyperdefinable groups constructed from those above. 相似文献
20.
Mieko Yamada 《Designs, Codes and Cryptography》2013,67(1):37-57
We construct an infinite family of (2 ns , 2 ns/2 -1(2 ns/2?1), 2 ns/2 -1(2 ns/2 -1 ?1)) difference sets over a Galois ring GR(2 n , s) with characteristic an even power n of 2 and an odd extension degree s. It makes a chain of difference sets preserving the structures when n increases and s is fixed. We introduce a new operation into GR(2 n , s). The Gauss sum associated with the multiplicative character defined by the subgroup with respect to the new operation plays an important role in the construction. 相似文献