global uniqueness in the inverse scattering problem for the schrodinger operator with external yang mills potentials we consider the schrodinger equation in r n n 3 with external yang mills potentials having compact supports we prove the uniqueness modulo a gauge transformation of the solution of the inverse boundary value problem in a bounded convex domain a similar uniqueness result holds for the inverse scattering problem at a fixed energy

an inverse problem for a semi linear elliptic equation in riemannian geometries abstract we study the inverse problem of unique recovery of a complex valued scalar function v m c c defined over a smooth compact riemannian manifold m g with smooth boundary given the dirichlet to neumann map in a suitable sense for the elliptic semi linear equation g u v x u 0 we show that uniqueness holds for a large class of non linearities when the manifold is conformally transversally anisotropic the proof is constructive and is based on a multiple fold linearization of the semi linear equation near complex geometric optic solutions for the linearized operator and the resulting non linear interactions these interactions result in the study of a weighted integral transform along geodesics that we call the jacobi weighted ray transform

computing the coefficients in laplace s method laplace s method is a preeminent technique in the asymptotic approximation of integrals its utility was enhanced enormously in 1956 when erdelyi found a way to apply watson s lemma and thereby obtain an infinite asymptotic expansion valid in principle for any integral of laplace type erdelyi s formulation requires tedious computation of coefficients c s for each specific application of the method and traditionally this has involved reverting a series recently it was shown that the coefficients c s can be computed via a simple explicit expression that is probably computationally optimal which avoids the reversion approach altogether the formula is made possible by recognizing the central role of faa di bruno s formula alongside watson s lemma in erdelyi s formulation of laplace s classical method laplace s method can now be implemented cleanly and relatively quickly provided one has the luck and the patience to get to the point where implementation becomes automatic the present paper outlines the recent discovery of the role of faa di bruno s formula in laplace s method gives examples of the application of the explicit expression for the coefficients c s and provides grounds for a possible generalization of the result

on the coefficients that arise from laplace s method laplace s method is one of the best known techniques in the asymptotic approximation of integrals the salient step in the technique s historical development was erdelyi s use of watson s lemma to obtain an infinite asymptotic expansion valid for any laplace type integral published in 1956 erdelyi s expansion contains coefficients cs that must be calculated in each application of laplace s method a tedious process that has traditionally involved the reversion of a series this paper shows that the coefficients cs in fact have a very simple general form in effect we extend erdelyi s theorem our results greatly simplify calculation of the cs in any particular application and clarify the theoretical basis of erdelyi s expansion it turns out that faa di bruno s formula has always played a central role in it we prove or derive the following the correct dimensionless groups erdelyi s expansion is properly expressed in terms of scaled coefficientscs two explicit expressions for cs in terms of combinatorial objects called partial ordinary bell polynomials this form is probably computationally optimal and makes checking for correctness a relatively straightforward process a recursive expression for cs each coefficient cs can be expressed as a polynomial in s where and are quantities in erdelyi s formulation the main insight that emerges is that the traditional approach to laplace s method involving reversion of a series is less efficient and need only be invoked if one is interested in the role of the reversion coefficients in erdelyi s expansion a point which erdelyi himself alluded to we consider as an example an integral that occurs in a variational approach to finding the binding energy of helium dimers we also present a three line computer code to generate the coefficients cs exactly in the general case in a sequel paper to be published in siam review a new representation for the gamma function is obtained and the link with faa di bruno s formula is explained

inverse viscosity problem for the navier stokes equation abstract we consider an inverse problem of determining a viscosity coefficient in the navier stokes equation by observation data in a neighborhood of the boundary we prove the lipschitz stability by the carleman estimates in sobolev spaces of negative order

stable determination of a semilinear term in a parabolic equation in 5 the flrst and third authors establish holder type stability estimates for the inverse problem consisting in the determination of a semilinear term of a parabolic equation from a single boundary measurement when the domain is a rectangle in the present paper we extend the results in 5 for a general smooth domain

completeness of products of solutions and some inverse problems for pde abstract in this paper we give conditions which guarantee that products of solutions of partial differential equations pu au 0 are complete in l 2 here p is a linear partial differential operator with constant coefficients and a is a function in l we check these conditions for elliptic parabolic and hyperbolic equations of second order and give applications to inverse problems for related equations where a is to be found

inverse boundary value problem for the stokes and the navier stokes equations in the plane in this paper we prove in two dimensions the global identifiability of the viscosity in an incompressible fluid by making boundary measurements the main contribution of this work is to use more natural boundary measurements the cauchy forces than the dirichlet to neumann map previously considered in imanuvilov and yamamoto global uniqueness in inverse boundary value problems for navier stokes equations and lame ststem in two dimensions arxiv 1309 1694 2013 to prove the uniqueness of the viscosity for the stokes equations and for the navier stokes equations

laplace s method on a computer algebra system with an application to the real valued modified bessel functions we examine a maple implementation of two distinct approaches to laplace s method used to obtain asymptotic expansions of laplace type integrals one algorithm uses power series reversion whereas the other expands all quantities in taylor or puiseux series these algorithms are used to derive asymptotic expansions for the real valued modified bessel functions of pure imaginary order and real argument that mimic the well known corresponding expansions for the unmodified bessel functions

determination of viscosity in the stationary navier stokes equations abstract in this paper we consider the stationary navier stokes equations in a bounded domain with a variable viscosity we prove that one can uniquely determine the viscosity function from the knowledge of boundary data

global uniqueness for a two dimensional semilinear elliptic inverse problem for a general class of nonlinear schrodinger equations au a x u 0 in a bounded planar domain 2 we show that the function a x u can be recovered from knowledge of the corresponding dirichlet to neumann map on the boundary dq

global uniqueness for an inverse boundary value problem arising in elasticity we prove that we can determine the lame parameters of an elastic isotropic inhomogeneous medium in dimensionsn 3 by making measurements of the displacements and corresponding stresses at the boundary of the medium

inverse problems in quasilinear anisotropic media we consider the question of whether one can determine the anisotropic quasilinear conductivity of a medium by making voltage and current measurements at the boundary we prove that all the known results for the linear case also hold in the quasilinear case

the resurgence properties of the hankel and bessel functions of nearly equal order and argument the aim of this paper is to derive new representations for the hankel functions the bessel functions and their derivatives exploiting the reformulation of the method of steepest descents by berry and howls proc roy soc london ser a 434 657 675 1991 using these representations we obtain a number of properties of the asymptotic expansions of the hankel and bessel functions and their derivatives of nearly equal order and argument including explicit and numerically computable error bounds asymptotics for the late coefficients exponentially improved asymptotic expansions and the smooth transition of the stokes discontinuities

adaptive dual boundary element method for solving oblique incident wave passing a submerged breakwater in this paper an adaptive mesh scheme in boundary element computations for solving the propagation of oblique incident wave passing a breakwater is developed the purpose is to demonstrate cost savings engendered through adaptivity the computation is performed on meshes of constant boundary elements and are adapted to the solution by locally changing element sizes h version two error indicators obtained from the dual integral equations are used as local error norm which are essential ingredients for all adaptive mesh schemes in boundary element method bem the evaluation of two local error norms is the norm between the obtained boundary condition and the given boundary condition the two error tracking curves are in good agreement with their shapes two examples show that the adaptive mesh based on the error indicators converge to the solution more efficiently using the same number of elements than does uniform mesh discretization for each segment of the boundary to check the validity of the present formulation the transmission and reflection coefficients are determined by using the developed dual bem program and are compared well with those of experiment and analytical solution using the eigenfunction expansion method

absorbing boundary conditions for free surface waves in this paper the use of absorbing boundary conditions is investigated for the numerical simulation of gravity waves on an incompressible inviscid fluid in three dimensions a review of existing methods is given for linear and nonlinear waves after which first and second order partial differential equations are introduced as absorbing boundary conditions for the linearized model well posedness is investigated and it is shown that the reflection properties of the second order equation are superior to those of the first order equation