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1.
Let V be a finite-dimensional real vector space on which a root system is given. Consider a meromorphic function on V =V+iV, the singular locus of which is a locally finite union of hyperplanes of the form V , = s, , s . Assume is of suitable decay in the imaginary directions, so that integrals of the form +iV , d make sense for generic V. A residue calculus is developed that allows shifting . This residue calculus can be used to obtain Plancherel and Paley–Wiener theorems on semisimple symmetric spaces.  相似文献   

2.
Rovira  Carles  Tindel  Samy 《Potential Analysis》2001,14(4):409-435
We consider the family {X , 0} of solution to the heat equation on [0,T]×[0,1] perturbed by a small space-time white noise, that is t X = X +b({X })+({X }) . Then, for a large class of Borelian subsets of the continuous functions on [0,T]×[0,1], we get an asymptotic expansion of P({X }A) as 0. This kind of expansion has been handled for several stochastic systems, ranging from Wiener integrals to diffusion processes.  相似文献   

3.
We consider the maximum function f resulting from a finite number of smooth functions. The logarithmic barrier function of the epigraph of f gives rise to a smooth approximation g of f itself, where >0 denotes the approximation parameter. The one-parametric family g converges – relative to a compact subset – uniformly to the function f as tends to zero. Under nondegeneracy assumptions we show that the stationary points of g and f correspond to each other, and that their respective Morse indices coincide. The latter correspondence is obtained by establishing smooth curves x() of stationary points for g , where each x() converges to the corresponding stationary point of f as tends to zero. In case of a strongly unique local minimizer, we show that the nondegeneracy assumption may be relaxed in order to obtain a smooth curve x().  相似文献   

4.
The problem of scheduling n nonpreemptive jobs having a common due date d on m, m 2, parallel identical machines to minimize total tardiness is studied. Approximability issues are discussed and two families of algorithms {A } and {B } are presented such that (T 0T*)/(T* + d) holds for any problem instance and any given > 0, where T* is the optimal solution value and T 0 is the value of the solution delivered by A or B . Algorithms A and B run in O(n 2m / m–1) and O(n m+1/ m ) time, respectively, if m is a constant. For m = 2, algorithm A can be improved to run in O(n 3/) time.  相似文献   

5.
We prove a convergence theorem and obtain asymptotic (as 0) estimates for a solution of a parabolic initial boundary-value problem in a junction that consists of a domain 0 and a large number N 2 of -periodically located thin cylinders whose thickness is of order = O(N –1).  相似文献   

6.
Consider a one parameter family of diffeomorphisms f such that f 0 is an Anosov element in a standard abelian Anosov action having sufficiently strong mixing properties. Let be any u-Gibbs state for f . We prove (Theorem 1) that for any C function A the map (A) is differentiable at =0. This implies (Corollary 2.2) that the difference of Birkhoff averages of the perturbed and unperturbed systems is proportional to . We apply this result (Corollary 3.3) to show that a generic perturbation of the time one map of geodesic flow on the unit tangent bundle over a surface of negative curvature has a unique SRB measure with good statistical properties.  相似文献   

7.
First, in joint work with S. Bodine of the University of Puget Sound, Tacoma, Washington, USA, we consider the second-order differential equation 2 y'=(1+2 (x, ))y with a small parameter , where is analytic and even with respect to . It is well known that it has two formal solutions of the form y±(x,)=e±x/h±(x,), where h±(x,) is a formal series in powers of whose coefficients are functions of x. It has been shown that one (resp. both) of these solutions are 1-summable in certain directions if satisfies certain conditions, in particular concerning its x-domain. We show that these conditions are essentially necessary for 1-summability of one (resp. both) of the above formal solutions. In the proof, we solve a certain inverse problem: constructing a differential equation corresponding to a certain Stokes phenomenon. The second part of the paper presents joint work with Augustin Fruchard of the University of La Rochelle, France, concerning inverse problems for the general (analytic) linear equations r y' = A(x,) y in the neighborhood of a nonturning point and for second-order (analytic) equations y' - 2xy'-g(x,) y=0 exhibiting resonance in the sense of Ackerberg-O'Malley, i.e., satisfying the Matkowsky condition: there exists a nontrivial formal solution such that the coefficients have no poles at x=0.  相似文献   

8.
We use an instantonic approach to calculate the asymptotic behavior of higher orders of the (4–)-expansion for the scaling function of the pair correlator of the O(n)-symmetric 4-theory in the minimal subtraction scheme. Our results differ substantially from the known exact expression for the 3 order of the expansion of the scaling function in the small- domain.  相似文献   

9.
Out of a right, circular cylinder of height H and cross-section a disc of radius R+ one removes a stack of nH/ parallel, equi-spaced cylinders Cj,j=1,2,...,n, each of radius R and height . Here , are fixed positive numbers and is a positive parameter to be allowed to go to zero. The union of the Cj almost fills in the sense that any two contiguous cylinders Cj are at a mutual distance of the order of and that the outer shell, i.e., the gap S=-o has thickness of the order of (o is obtained from by formally setting =0). The cylinder from which the Cj are removed, is an almost disconnected structure, it is denoted by , and it arises in the mathematical theory of phototransduction.For each >0 we consider the heat equation in the almost disconnected structure , for the unknown function u, with variational boundary data on the faces of the removed cylinders Cj. The limit of this family of problems as 0 is computed by concentrating heat capacity and diffusivity on the outer shell, and by homogenizing the u within the limiting cylinder o.It is shown that the limiting problem consists of an interior diffusion in o and a boundary diffusion on the lateral boundary S of o. The interior diffusion is governed by the 2-dimensional heat equation in o, for an interior limiting function u. The boundary diffusion is governed by the Laplace–Beltrami heat equation on S, for a boundary limiting function uS. Moreover the exterior flux of the interior limit u provides the source term for the boundary diffusion on S. Finally the interior limit u, computed on S in the sense of the traces, coincides with the boundary limit uS. As a consequence of the geometry of , local arguments do not suffice to prove convergence in o, and also we have to take into account the behavior of the solution in S. A key, novel idea consists in extending equi-bounded and equi-Hölder continuous functions in -dependent domains, into equi-bounded and equi-Hölder continuous functions in the whole N, by means of the Kirzbraun–Pucci extension technique.The biological origin of this problem is traced, and its application to signal transduction in the retina rod cells of vertebrates is discussed. Mathematics Subject Classification (2000) 35B27, 35K50, 92C37  相似文献   

10.
In this paper we study spaces of level sets of holomorphic mappings. We give an elementary (i.e. we are using elementary means) proof of a theorem a special case of which is the following statement: Let : XY be a holomorphic mapping of the irreducible normal complex space into the reduced complex space Y, which degenerates nowhere; the last condition means in the present case all -level sets having the same dimension; a -level set is a connected component of a fibre –1(Q), Q (X). Then the space Z of -level sets is a quasicomplex space and the natural mapping : XZ which maps each P X onto the -level set to which P belongs is open. If we substitute the assumption degenerating nowhere by the assumption having compact level sets, we get a space Z of level sets, which is a complex space. - The first part of this statement is a generalisation of a theorem of K. Stein, the second part is a special case of a theorem of H. Cartan and a well known theorem of H. Grauert on proper mappings. We will use our theorem in order to give a new proof of Grauert's theorem in a subsequent paper.  相似文献   

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