共查询到20条相似文献,搜索用时 46 毫秒
1.
Branko Dragovich Zoran Rakić 《P-Adic Numbers, Ultrametric Analysis, and Applications》2010,2(4):322-340
Feynman’s path integrals in ordinary, p-adic and adelic quantum mechanics are considered. The corresponding probability amplitudes K(x″, t″; x′, t′) for two-dimensional systems with quadratic Lagrangians are evaluated analytically and obtained expressions are generalized
to any finite-dimensional spaces. These general formulas are presented in the form which is invariant under interchange of
the number fields ℝ ↔ ℚ
p
and ℚ ↔ ℚ
p
, p ≠ p′. According to this invariance we have that adelic path integral is a fundamental object in mathematical physics of quantum
phenomena. 相似文献
2.
We study prime and composite numbers in the sequence of integer parts of powers of a fixed real number. We first prove a result
which implies that there is a transcendental number ξ>1 for which the numbers [ξn
!], n =2,3, ..., are all prime. Then, following an idea of Huxley who did it for cubics, we construct Pisot numbers of arbitrary
degree such that all integer parts of their powers are composite. Finally, we give an example of an explicit transcendental
number ζ (obtained as the limit of a certain recurrent sequence) for which the sequence [ζn], n =1,2,..., has infinitely many elements in an arbitrary integer arithmetical progression.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
3.
V. S. Vladimirov 《Theoretical and Mathematical Physics》2010,164(3):1101-1109
We obtain regularized adelic formulas for gamma and beta functions for fields of rational numbers and the one-class quadratic
fields and arbitrary quasicharacters (ramified or not). We consider applications to four-tachyon tree string amplitudes, generalized
Veneziano amplitudes (open string), perturbed Virasoro amplitudes (closed string), massless four-particle tree open and closed
superstring amplitudes, Ramond-Neveu-Schwarz superstring amplitudes, and charged heterotic superstring amplitudes. We establish
certain relations between different string and superstring amplitudes. 相似文献
4.
We say that A has fractional powers {A
t
}
t≥0 if there exists a nondegenerate C-regularized semigroup {W(t)}
t≥0 such that A=C
−1
W(1); then A
t
≡C
−1
W(t). We show that this generalizes the usual definition of fractional powers for nonnegative operators, and enables many operators
with spectrum containing the entire unit disc to have fractional powers. Our definition gives clear, simple proofs of the
basic properties of fractional powers. We show that, for nonnegative operators, the fractional powers with the property that,
if A is of type θ, then A
t
is of type t
θ, whenever t
θ<π, are unique. More generally, for injective G∈B(X) commuting with A, we show that an operator A of G-regularized type θ has a unique family of fractional powers with the property that A
t
is of G-regularized type t
θ whenever t
θ<π. This leads to a construction of fractional powers of operators with polynomially bounded resolvent outside of an appropriate
sector. We show that an operator is of regularized type if and only if it has exponentially bounded regularized imaginary
powers.
This work was done while the second author was visiting Ohio University, with funding from Universitat de València. He would
like to thank Ohio University and Professor deLaubenfels for their hospitality and support. 相似文献
5.
6.
Andrea Lucchini 《Israel Journal of Mathematics》2011,181(1):53-64
It has been conjectured by Mann that the infinite sum Σ
H
μ(H,G)/|G:H|
s
, where H ranges over all open subgroups of a finitely generated profinite group G, converges absolutely in some half right plane if G is positively finitely generated. We prove that the conjecture is true if the nonabelian crowns of G have bounded rank. In particular Mann’s conjecture holds if G has polynomial subgroup growth or is an adelic profinite group. 相似文献
7.
René Schmidt 《P-Adic Numbers, Ultrametric Analysis, and Applications》2009,1(4):338-351
In this paper we present an approach to adelic physics via algebraic spaces. Relative algebraic spaces X → S are considered as fundamental objects which describe space-time. This yields a number field invariant formulation of general
relativity which, in the special case S = Spec ℂ, may be translated back into the language of manifolds. With regard to adelic physics the case of an excellent Dedekind
scheme S as base scheme is of interest (e.g. S = Spec ℤ). Some solutions of the arithmetic Einstein equations are studied. 相似文献
8.
We study the numerical solution procedure for two-dimensional Laplace’s equation subjecting to non-linear boundary conditions.
Based on the potential theory, the problem can be converted into a nonlinear boundary integral equations. Mechanical quadrature
methods are presented for solving the equations, which possess high accuracy order O(h
3) and low computing complexities. Moreover, the algorithms of the mechanical quadrature methods are simple without any integration
computation. Harnessing the asymptotical compact theory and Stepleman theorem, an asymptotic expansion of the errors with
odd powers is shown. Based on the asymptotic expansion, the h
3 −Richardson extrapolation algorithms are used and the accuracy order is improved to O(h
5). The efficiency of the algorithms is illustrated by numerical examples. 相似文献
9.
Christof Külske 《Probability Theory and Related Fields》2003,126(1):29-50
We consider diffraction at random point scatterers on general discrete point sets in ℝν, restricted to a finite volume. We allow for random amplitudes and random dislocations of the scatterers. We investigate
the speed of convergence of the random scattering measures applied to an observable towards its mean, when the finite volume
tends to infinity. We give an explicit universal large deviation upper bound that is exponential in the number of scatterers.
The rate is given in terms of a universal function that depends on the point set only through the minimal distance between
points, and on the observable only through a suitable Sobolev-norm. Our proof uses a cluster expansion and also provides a
central limit theorem.
Received: 10 October 2001 / Revised version: 26 January 2003 /
Published online: 15 April 2003
Work supported by the DFG
Mathematics Subject Classification (2000): 78A45, 82B44, 60F10, 82B20
Key words or phrases: Diffraction theory – Random scatterers – Random point sets – Quasicrystals – Large deviations – Cluster expansions 相似文献
10.
K. O. Buryachenko 《Ukrainian Mathematical Journal》2012,63(8):1165-1175
We consider a Cauchy-type boundary-value problem, a problem with three boundary conditions, and the Dirichlet problem for
a general typeless fourth-order differential equation with constant complex coefficients and nonzero right-hand side in a
bounded domain Ω ⊂ R
2 with smooth boundary. By the method of the Green formula, the theory of extensions of differential operators, and the theory
of L-traces (i.e., traces associated with the differential operation L), we establish necessary and sufficient (for elliptic operators) conditions of the solvability of each of these problems
in the space H
m
(Ω), m ≥ 4. 相似文献
11.
G. A. Martynov 《Theoretical and Mathematical Physics》2000,123(3):833-845
We show that the general solution of the Ornstein-Zernike system of equations for multicomponent solutions has the form hαβ=∑A
αβ
j
exp(-λjr)/r, where λj are the roots of the transcendental equation 1-ρΔ(λj)=0 and the amplitudes Aαβ
j can be calculated if the direct correlation functions are given. We investigate the properties of this solution including
the behavior of the roots A
αβ
j
and amplitudes Aαβ
j in both the low-density limit and the vicinity of the critical point. Several relations on Aαβ
j and Cαβ are found. In the vicinity of the critical point, we find the state equation for a liquid, which confirms the Van der Waals
similarity hypothesis. The expansion under consideration is asymptotic because we expand functions in series in eigenfunctions
of the asymptotic Ornstein-Zernike equation valid at r→∞.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 123, No. 3, pp. 500–515, June, 2000. 相似文献
12.
Jean Louis Woukeng 《Applications of Mathematics》2009,54(6):465-489
This paper is devoted to the homogenization beyond the periodic setting, of nonlinear monotone operators in a domain in ℝ
N
with isolated holes of size ɛ2 (ɛ > 0 a small parameter). The order of the size of the holes is twice that of the oscillations of the coefficients of the
operator, so that the problem under consideration is a reiterated homogenization problem in perforated domains. The usual
periodic perforation of the domain and the classical periodicity hypothesis on the coefficients of the operator are here replaced
by an abstract assumption covering a great variety of behaviors such as the periodicity, the almost periodicity and many more
besides. We illustrate this abstract setting by working out a few concrete homogenization problems. Our main tool is the recent
theory of homogenization structures. 相似文献
13.
Tiziana Giorgi Robert Smits 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,124(1):600-618
We consider the principal eigenvalue λ
1Ω(α) corresponding to Δu = λ (α) u in
W, \frac?u?v = au \Omega, \frac{\partial u}{\partial v} = \alpha u on ∂Ω, with α a fixed real, and W ì Rn\Omega \subset {\mathcal{R}}^n a C
0,1 bounded domain. If α > 0 and small, we derive bounds for λ
1Ω(α) in terms of a Stekloff-type eigenvalue; while for α > 0 large we study the behavior of its growth in terms of maximum curvature.
We analyze how domain monotonicity of the principal eigenvalue depends on the geometry of the domain, and prove that domains
which exhibit domain monotonicity for every α are calibrable. We conjecture that a domain has the domain monotonicity property for some α if and only if it is calibrable. 相似文献
14.
María del Mar González 《Calculus of Variations and Partial Differential Equations》2009,36(2):173-210
We prove a Γ-convergence result for an energy functional related to some fractional powers of the Laplacian operator, (−Δ)
s
for 1/2 < s < 1, with two singular perturbations, that leads to a two-phase problem. The case (−Δ)1/2 was considered by Alberti–Bouchitté–Seppecher in relation to a model in capillarity with line tension effect. However, the
proof in our setting requires some new ingredients such as the Caffarelli–Silvestre extension for the fractional Laplacian
and new trace inequalities for weighted Sobolev spaces. 相似文献
15.
Oliver Dragičević 《Archiv der Mathematik》2011,96(5):463-471
We provide a proof of sharp lower L
p
bounds for powers of the Ahlfors–Beurling operator T and improve the numerical constant in their asymptotic estimates. We also discuss the possibilities of applying de Branges’
theorem in the p − 1 problem. 相似文献
16.
Abstract. On a Banach space X consider an equibounded (C_0)-semigroup of linear operators { T(t): t ≥ 0} with infinitesimal generator A . We introduce fractional powers (-A)
α
, α >0 , of A with domain D((-A)
α
)) and characterize the K -functionals with respect to (X,D((-A)
α
)) via fractional differences [I-T(t)]
α
, via appropriate truncated hypersingular integrals and via some type of fractional integral over the resolvent of A . Immediate consequences are an abstract Marchaud-type inequality for moduli of smoothness arising from (semi-) groups of
operators as well as optimal and nonoptimal approximation results. 相似文献
17.
M. Yu. Nalimov 《Theoretical and Mathematical Physics》1995,102(2):163-172
The On-symmetric 4 theory in a half-space is investigated. The propagators of the theory in the ordered phase for zero external field are obtained, and the dependence of these propagators on the boundary conditions is studied. The general form of the Goldstone asymptotics of the various correlation functions, as functions of weak external fields and small momenta and large distances from the boundary of the system, is determined.State University, St. Petersburg. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 102, No. 2, pp. 223–236, February, 1995. 相似文献
18.
Exact propagators are obtained for the degenerate second order hyperbolic operators ∂2
t
-t
2l
Δ
x
, l=1,2,..., by analytic continuation from the degenerate elliptic operators ∂2
t
+t
2l
Δ
x
. The partial Fourier transforms are also obtained in closed form, leading to integral transform formulas for certain combinations
of Bessel functions and modified Bessel functions. 相似文献
19.
Let −A be a linear, injective operator, on a Banach spaceX. We show that ∃ anH
∞ functional calculus forA if and only if −A generates a bouned strongly continuous holomorphic semigroup of uniform weak bounded variation, if and only ifA(ζ+A)
−1 is of uniform weak bounded variation. This provides a sufficient condition for the imaginary powers ofA, {A−is} sεR, to extend to a strongly continuous group of bounded operators; we also give similar necessary conditions. 相似文献
20.
We determine the simplicial complexes Δ whose Stanley-Reisner ideals I
Δ have the following property: for all n ≥ 1 the powers I
Δ
n
have linear resolutions and finite length local cohomologies.
Received: 10 July 2007 相似文献