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1.
Jiakun Liu 《Calculus of Variations and Partial Differential Equations》2009,34(4):435-451
It is known that optimal mappings in optimal transportation problems are uniquely determined by corresponding potential functions.
In this paper we prove various local properties of potential functions. In particular we obtain the C
1,α
regularity of potential functions with optimal exponent α, which improves previous regularity results of Loeper. 相似文献
2.
We consider the M/G/1 queue with an arrival rate λ that depends weakly upon time, as λ = λ(εt) where ε is a small parameter. In the asymptotic limit ε → 0, we construct approximations to the probability p
n(t)that η customers are present at time t. We show that the asymptotics are different for several ranges of the (slow) time scale Τ= εt. We employ singular perturbation techniques and relate the various time scales by asymptotic matching.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
3.
In this paper we define the radical ϱ
k
(k∈Z
+) of a relation ϱ on an arbitrary semigroup. Also, we define various types of k-regularity of semigroups and various types of k-Archimedness of semigroups. Using these notions we describe the structure of semigroups in which ρ
k
is a band (semilattice) congruence for some Green’s relation. 相似文献
4.
The purpose of the paper is to find explicit formulas describing the joint distributions of the first hitting time and place
for half-spaces of codimension one for a diffusion in ℝ
n + 1, composed of one-dimensional Bessel process and independent n-dimensional Brownian motion. The most important argument is carried out for the two-dimensional situation. We show that this
amounts to computation of distributions of various integral functionals with respect to a two-dimensional process with independent
Bessel components. As a result, we provide a formula for the Poisson kernel of a half-space or of a strip for the operator (I − Δ)
α/2, 0 < α < 2. In the case of a half-space, this result was recently found, by different methods, in Byczkowski et al. (Trans Am Math Soc 361:4871–4900, 2009). As an application of our method we also compute various formulas for first hitting places for the isotropic stable Lévy process. 相似文献
5.
6.
We use a method recently devised by Bolle to establish the existence of an infinite number of solutions for various non-homogeneous
boundary value problems. In particular, we consider second order systems, Hamiltonian systems as well as semi-linear partial
differential equations. The non-homogeneity can originate in the equation but also from the boundary conditions. The results
are more satisfactory than those obtained by the standard “Perturbation from Symmetry” method that was developed – in various forms – in the early eighties by Bahri–Berestycki, Struwe and Rabinowitz.
Received: 13 August 1998 / Revised version: 6 July 1999 相似文献
7.
Multiplicatively large sets are defined in (ℕ, ·) by an analogy to sets of positive upper density in (ℕ, +). By utilizing
various ergodic multiple recurrence theorems, we show that multiplicatively large sets have a rich combinatorial structure.
In particular, it is proved that for any multiplicatively large setE ⊂ ℕ and anyk ∈ ℕ, there existsa,b,c,d,e,q ∈ ℕ such that {fx23-1}
Dedicated to MORI VAHAVERI Hillel Furstenberg on the occasion of his retirement
The author acknowledges support received from the National Science Foundation (USA) via grants DMS-0070566 and DMS-0345350. 相似文献
8.
Don Zagier 《Proceedings Mathematical Sciences》1994,104(1):57-75
In 1956, Rankin described which polynomials in the derivatives of modular forms are again modular forms, and in 1977, H Cohen
defined for eachn ≥ 0 a bilinear operation which assigns to two modular formsf andg of weightk andl a modular form [f, g]n of weightk +l + 2n. In the present paper we study these “Rankin-Cohen brackets” from two points of view. On the one hand we give various explanations
of their modularity and various algebraic relations among them by relating the modular form theory to the theories of theta
series, of Jacobi forms, and of pseudodifferential operators. In a different direction, we study the abstract algebraic structure
(“RC algebra”) consisting of a graded vector space together with a collection of bilinear operations [,]n of degree + 2n satisfying all of the axioms of the Rankin-Cohen brackets. Under certain hypotheses, these turn out to be
equivalent to commutative graded algebras together with a derivationS of degree 2 and an element Φ of degree 4, up to the equivalence relation (∂,Φ) ~ (∂ - ϕE, Φ - ϕ2 + ∂(ϕ)) where ϕ is an element of degree 2 andE is the Fuler operator (= multiplication by the degree).
Dedicated to the memory of Professor K G Ramanathan 相似文献
9.
Gary M. Lieberman 《Journal d'Analyse Mathématique》2011,115(1):213-249
In this paper, we study the asymptotic behavior of solutions of the problem Δ
p
u = f (u) in Ω, u = ∞ on ∂Ω, under general conditions on the function f, where Ω
p
is the p-Laplace operator. We show that the technique used by the author for the special case p = 2 works in this more general setting, and that the behavior described by various authors for the case p = 2 is easily derived from this technique for the general case. 相似文献
10.
Suppose Ω is a smooth domain in Rm,N is a compact smooth Riemannian manifold, andZ is a fixed compact subset of Ω having finite (m − 3)-dimensional Minkowski content (e.g.,Z ism − 3 rectifiable). We consider various spaces of harmonic mapsu: Ω →N that have a singular setZ and controlled behavior nearZ. We study the structure of such spacesH and questions of existence, uniqueness, stability, and minimality under perturbation. In caseZ = 0,H is a Banach manifold locally diffeomorphic to a submanifold of the product of the boundary data space with a finite-dimensional
space of Jacobi fields with controlled singular behavior. In this smooth case, the projection ofu εH tou |ϖΩ is Fredholm of index 0.
R. H.’s research partially supported by the National Science Foundation. 相似文献
11.
Jan Brinkhuis 《manuscripta mathematica》1992,75(1):333-347
In this paper we make a contribution to the problem of the existence of a normal integral basis. Our main result is that unramified
realizations of a given finite abelian group Δ as a Galois group Gal (N/K) of an extensionN of a givenCM-fieldK are invariant under the involution on the set of all realizations of Δ overK which is induced by complex conjugation onK and by inversion on Δ. We give various implications of this result. For example, we show that the tame realizations of a
finite abelian group Δ of odd order over a totally real number fieldK are completely characterized by ramification and Galois module structure. 相似文献
12.
In this paper, we introduce the classes of (B, ρ)-type I and generalized (B, ρ)-type I, and derive various sufficient optimality conditions and mixed type duality results for multiobjective control problems
under (B, ρ)-type I and generalized (B, ρ)-type I assumptions. 相似文献
13.
B. F. Melnikov 《Journal of Applied Mathematics and Computing》1999,6(3):565-574
Nondeterministic finite Rabin-Scott’s automata without initial and final states (2ω-FA) are considered. In this paper, they are used to define so called sets of obstructions, used also in various algebraic systems, and to consider similar problems for the formal languages theory. Thus, we define sets of obstructions of languages (or, rather, 2ω-languages) of such automata. We obtain that each 2ω-language defined by 2 ω-FA has the set of obstruction being a regular language. And, vice versa, for each regular languageL (containing no proper subword of its another word), there exists a 2ω-FA havingL as the set of obstructions. 相似文献
14.
Péter Csorba 《Combinatorica》2007,27(6):669-682
In [14] Matoušek and Ziegler compared various topological lower bounds for the chromatic number. They proved that Lovász’s
original bound [9] can be restated as X(G) ≥ ind(B(G)) + 2. Sarkaria’s bound [15] can be formulated as X(G) ≥ ind(B0(G)) + 1. It is known that these lower bounds are close to each other, namely the difference between them is at most 1. In this
paper we study these lower bounds, and the homotopy types of box complexes. The most interesting result is that up to ℤ2-homotopy the box complex B(G) can be any ℤ2-space. This together with topological constructions allows us to construct graphs showing that the mentioned two bounds are
different. Some of the results were announced in [14].
Supported by the joint Berlin/Zürich graduate program Combinatorics, Geometry, and Computation, financed by ETH Zürich and
the German Science Foundation (DFG). 相似文献
15.
The Grunsky coefficient inequalities play a crucial role in various problems and are intrinsically connected with the integrable
holomorphic quadratic differentials having only zeros of even order. For the functions with quasi-conformal extensions, the
Grunsky constant ℵ(f) and the extremal dilatationk(f) are related by ℵ(f)≤k(f). In 1985, Jürgen Moser conjectured that any univalent functionf(z)=z+b
0+b
1
z
−1+… on Δ*={|z|>1} can be approximated locally uniformly by functions with ℵ(f)<k(f). In this paper, we prove a theorem confirming Moser’s conjecture, which sheds new light on the features of Grunsky coefficients.
In memory of Jürgen Moser
The research was supported by the RiP program of the Volkswagen-Stiftung in the Mathematisches Forschungsinstitut Oberwolfach. 相似文献
16.
Nancy Childress 《manuscripta mathematica》1990,68(1):447-453
In this paper, we will examine some of the implications of the results in [C1] for the Iwasawa invariants, λ
p
, of the cyclotomic fields Q(ζ
n
), wherep + n. In particular, a number of examples, for various primesp, are given. 相似文献
17.
In this paper we consider various aspects of generalized invertibility of the operator matrix acting on a Banach space X⊕Y. 相似文献
18.
Given a multiplicative band of idempotents S in a ring R, for all e,f∈S the ∇-product e
∇
f=e+f+fe−efe−fef is an idempotent that lies roughly above e and f in R just as ef and fe lie roughly below e and f. In this paper we study ∇-bands in rings, that is, bands in rings that are closed under ∇, giving various criteria for ∇ to be associative, thus making the band a skew lattice. We also consider when a given band S in R generates a ∇-band. 相似文献
19.
G.J. Zalmai Qing-hong Zhang 《应用数学学报(英文版)》2007,23(2):217-234
In this paper,we discuss a large number of sets of global parametric sufficient optimality condi-tions under various gcneralized (η,ρ)-invexity assumptions for a semi-infinite minmax fractional programmingproblem. 相似文献
20.
Eugenia Cheng 《Applied Categorical Structures》2007,15(4):439-453
We make a definition of ω-precategory which should underlie any definition of weak ω-category. We make a precise definition of pseudo-invertible cells in this setting. We show that in an ω-precategory with all weak duals, every cell is pseudo-invertible. We deduce that in any “sensible” theory of ω-categories, an ω-category with all weak duals is an ω-groupoid. We discuss various examples and open questions involving higher-dimensional tangles and cobordisms.
相似文献