共查询到20条相似文献,搜索用时 31 毫秒
1.
An asymptotic formula for the voltage potential in the case of a near-surface conductivity inclusion
Habib Ammari Hyeonbae Kang Karim Touibi 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(2):234-243
We rigorously derive an asymptotic expansion of the steady-state voltage potentials in the presence of a conductivity inclusion
of small volume that is close to a planar surface. This new formula is motivated by the practically important inverse problem
of imaging a conductivity inclusion near a planar interface.
Partly supported by ACI Jeunes Chercheurs (0693) from the Ministry of Education and Scientific Research, France.
Partially supported by grant R02-2003-000-10012-0 from the Korea Science and Engineering Foundation.
Received: December 2, 2003; revised: January 18, 2004 相似文献
2.
A. Boumenir 《Proceedings of the American Mathematical Society》2003,131(11):3553-3557
Using an operator theoretic framework and pseudo-spectral methods, we provide a simple and explicit formula for the conductivity coefficient in terms of the Dirichlet to Neumann map and the eigenvalues of the Laplacian operator.
3.
The finite-dimensional irreducible representations of the Yangian of sl2 are parametrized by their highest weights, which are monic polynomials in one variable. In this paper, we give a formula for the character of such a representation which depends only on its highest weight, and is an analogue of the classical Weyl character formula. 相似文献
4.
We give an interpolation-free proof of the known fact that a dyadic paraproduct is of Schatten-von Neumann class Sp, if and only if its symbol is in the dyadic Besov space Bpd. Our main tools are a product formula for paraproducts and a “p-John-Nirenberg-Theorem” due to Rochberg and Semmes.We use the same technique to prove a corresponding result for dyadic paraproducts with operator symbols.Using an averaging technique by Petermichl, we retrieve Peller's characterizations of scalar and vector Hankel operators of Schatten-von Neumann class Sp for 1<p<∞. We then employ vector techniques to characterise little Hankel operators of Schatten-von Neumann class, answering a question by Bonami and Peloso.Furthermore, using a bilinear version of our product formula, we obtain characterizations for boundedness, compactness and Schatten class membership of products of dyadic paraproducts. 相似文献
5.
On the concepts of intertwining operator and tensor product module in vertex operator algebra theory
Yi-Zhi Huang James Lepowsky Haisheng Li Lin Zhang 《Journal of Pure and Applied Algebra》2006,204(3):507-535
We produce counterexamples to show that in the definition of the notion of intertwining operator for modules for a vertex operator algebra, the commutator formula cannot in general be used as a replacement axiom for the Jacobi identity. We further give a sufficient condition for the commutator formula to imply the Jacobi identity in this definition. Using these results we illuminate the crucial role of the condition called the “compatibility condition” in the construction of the tensor product module in vertex operator algebra theory, as carried out in work of Huang and Lepowsky. In particular, we prove by means of suitable counterexamples that the compatibility condition was indeed needed in this theory. 相似文献
6.
Yuming Wei Patricia J.Y. Wong 《Journal of Computational and Applied Mathematics》2010,233(9):2189-2199
In this paper, we consider the existence of countably many positive solutions to a boundary value problem of a nonlinear delay differential equation with countably many singularities on infinite interval
7.
《Quaestiones Mathematicae》2013,36(4):553-562
AbstractIn this paper, we study the formula for a product of two Euler poly-nomials. From this study, we derive some formulae for the integral of the product of two or more Euler polynomials. 相似文献
8.
Consider an insurer who is allowed to make risk-free and risky investments. The price process of the investment portfolio is described as a geometric Lévy process. We study the tail probability of the stochastic present value of future aggregate claims. When the claim-size distribution is of Pareto type, we obtain a simple asymptotic formula which holds uniformly for all time horizons. The same asymptotic formula holds for the finite-time and infinite-time ruin probabilities. Restricting our attention to the so-called constant investment strategy, we show how the insurer adjusts his investment portfolio to maximize the expected terminal wealth subject to a constraint on the ruin probability. 相似文献
9.
In the framework of the Mermin approach, we obtain formulas for the longitudinal electric conductivity in a quantum collisional plasma with a collision frequency depending on the momentum. We use a kinetic equation in the momentum space in the relaxation approximation. We show that as the Planck constant tends to zero, the derived formula transforms into the corresponding formula for a classical plasma. We also show that as the frequency of collisions between plasma particles tends to zero (the plasma transforms into a collisionless plasma), the derived formula transforms into the well-known Klimontovich-Silin formula for the collisionless plasma. We show that if the collision frequency is constant, then the derived formula for the permittivity transforms into the well-known Mermin formula. 相似文献
10.
We provide a rigorous derivation of an asymptotic formula for perturbations in the eigenvalues caused by the presence of a finite number of inhomogeneities of small diameter with conductivity different from the background conductivity. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
11.
Michael Lau 《Advances in Mathematics》2005,194(2):225-245
Given any representation of an arbitrary Lie algebra g over a field K of characteristic 0, we construct representations of a central extension of g on bosonic and fermionic Fock space. The method gives an explicit formula for a (sometimes trivial) 2-cocycle in H2(g;K). We illustrate these techniques with several concrete examples. 相似文献
12.
Bernt Ivar Utstøl Nødland 《Journal of Pure and Applied Algebra》2018,222(3):508-533
We use Matsui and Takeuchi's formula for toric A-discriminants to give algorithms for computing local Euler obstructions and dual degrees of toric surfaces and 3-folds. In particular, we consider weighted projective spaces. As an application we give counterexamples to a conjecture by Matsui and Takeuchi. As another application we recover the well-known fact that the only defective normal toric surfaces are cones. 相似文献
13.
A monadic formula ψ(Y) is a selector for a monadic formula φ(Y) in a structure M if ψ defines in M a unique subset P of the domain and this P also satisfies φ in M. If C is a class of structures and φ is a selector for ψ in every M∈C, we say that φ is a selector for φ over C.For a monadic formula φ(X,Y) and ordinals α≤ω1 and δ<ωω, we decide whether there exists a monadic formula ψ(X,Y) such that for every P⊆αof order-type smaller thanδ, ψ(P,Y) selects φ(P,Y) in (α,<). If so, we construct such a ψ.We introduce a criterion for a class C of ordinals to have the property that every monadic formula φ has a selector over it. We deduce the existence of S⊆ωω such that in the structure (ωω,<,S) every formula has a selector.Given a monadic sentence π and a monadic formula φ(Y), we decide whether φ has a selector over the class of countable ordinals satisfying π, and if so, construct one for it. 相似文献
14.
We show that the sum of the series formed by the so-called hyperharmonic numbers can be expressed in terms of the Riemann zeta function. These results enable us to reformulate Euler's formula involving the Hurwitz zeta function. In additon, we improve Conway and Guy's formula for hyperharmonic numbers. 相似文献
15.
Congquan Yan 《Integral Equations and Operator Theory》2006,56(4):587-595
In this paper, we obtain a Fredholm index formula for Toeplitz operators whose symbols are certain piecewise continuous function
matrices on the unit ball. Moreover, using this formula, we discuss the automorphisms on the corresponding Toeplitz algebra 相似文献
16.
17.
We revisit the computation of (2-modified) Fredholm determinants
for operators with matrix-valued semi-separable integral kernels. The latter
occur, for instance, in the form of Greens functions associated with closed
ordinary differential operators on arbitrary intervals on the real line. Our
approach determines the (2-modified) Fredholm determinants in terms of solutions
of closely associated Volterra integral equations, and as a result offers
a natural way to compute such determinants.We illustrate our approach by identifying classical objects such as the
Jost function for half-line Schrödinger operators and the inverse transmission
coe.cient for Schrödinger operators on the real line as Fredholm determinants,
and rederiving the well-known expressions for them in due course.
We also apply our formalism to Floquet theory of Schrödinger operators, and
upon identifying the connection between the Floquet discriminant and underlying
Fredholm determinants, we derive new representations of the Floquet
discriminant.Finally, we rederive the explicit formula for the 2-modified Fredholm
determinant corresponding to a convolution integral operator, whose kernel
is associated with a symbol given by a rational function, in a straghtforward
manner. This determinant formula represents a Wiener-Hopf analog of Days
formula for the determinant associated with finite Toeplitz matrices generated
by the Laurent expansion of a rational function. 相似文献
18.
We derive formulas for the transverse electrical conductivity and the permittivity in a quantum collisional plasma using the kinetic equation for the density matrix in the relaxation approximation in the momentum space. We show that the derived formula becomes the classical formula when the Planck constant tends to zero and that when the electron collision rate tends to zero (i.e., the plasma becomes collisionless), the derived formulas become the previously obtained Lindhard formulas. We also show that when the wave number tends to zero, the quantum conductivity becomes classical. We compare the obtained conductivity with the conductivity obtained by Lindhard and with the classical conductivity 相似文献
19.
20.
In this paper, we consider the usual and generalized order-k Fibonacci and Pell recurrences, then we define a new recurrence, which we call generalized order-k F–P sequence. Also we present a systematic investigation of the generalized order-k F–P sequence. We give the generalized Binet formula, some identities and an explicit formula for sums of the generalized order-k F–P sequence by matrix methods. Further, we give the generating function and combinatorial representations of these numbers. Also we present an algorithm for computing the sums of the generalized order-k Pell numbers, as well as the Pell numbers themselves. 相似文献