determination of a spacewise dependent heat source this paper investigates the inverse problem of determining a spacewise dependent heat source in the parabolic heat equation using the usual conditions of the direct problem and information from a supplementary temperature measurement at a given single instant of time the spacewise dependent temperature measurement ensures that the inverse problem has a unique solution but this solution is unstable hence the problem is ill posed for this inverse problem we propose an iterative algorithm based on a sequence of well posed direct problems which are solved at each iteration step using the boundary element method bem the instability is overcome by stopping the iterations at the first iteration for which the discrepancy principle is satisfied numerical results are presented for various typical benchmark test examples which have the input measured data perturbed by increasing amounts of random noise

error analysis of an equation error method for the identification of the diffusion coefficient in a quasi linear parabolic differential equation we consider the inverse problem of reconstructing the diffusion coefficient in a quasi linear parabolic differential equation in divergence form from measurements of the solution at a finite number of points in the interior of the domain an equation error method is developed which transforms the inverse problem into a system of linear operator equations for the diffusion coefficient and which can be solved by the conjugate gradient method in a very efficient and stable manner a detailed error analysis relates the required number of measurements with their accuracy numerical results illustrate the performance of the method

identification of the pollution source from one dimensional parabolic equation models abstract consider an inverse source problem modeling the pollution source detection in a watershed the diffusion process due to the point source pollution is governed by a one dimensional linear parabolic equation with unknown source of the form t x s where s is the location and t the amplitude of point source applying a priori information about the source location and the analytic extension theory we prove the uniqueness from two interior measurements for the two kinds of boundary state one is a finite watershed model with zero neumann boundary data and the other is an infinite watershed model finally an implementable inversion algorithm together with some numerical examples are presented which shows the validity of our inversion scheme

a meshless method for solving an inverse spacewise dependent heat source problem in this paper an effective meshless and integration free numerical scheme for solving an inverse spacewise dependent heat source problem is proposed due to the use of the fundamental solution as basis functions the method leads to a global approximation scheme in both spatial and time domains the standard tikhonov regularization technique with the generalized cross validation criterion for choosing the regularization parameter is adopted for solving the resulting ill conditioned system of linear algebraic equations the effectiveness of the algorithm is illustrated by several numerical examples

simultaneous inversion of the fractional order and the space dependent source term for the time fractional diffusion equation abstract in this paper a simultaneous identification problem of the spacewise source term and the fractional order for a time fractional diffusion equation is considered firstly under some assumption and with two different kinds of observation data for one dimensional and two dimensional time fractional diffusion equation the unique results of the inverse problem are proven by the laplace transformation method and analytic continuation technique then the inverse problems are transformed into tikhonov type optimization problems the existence of optimal solutions to the tikhonov functional is proven finally we adopt an alternating minimization algorithm to solve the optimization problems the efficiency and stability of the inversion algorithm are tested by several one and two dimensional examples

solving an inverse parabolic problem by optimization from final measurement data we consider an inverse problem of reconstructing the coefficient q in the parabolic equation ut u q x u 0 from the final measurement u x t where q is in some subset of l1 the optimization method combined with the finite element method is applied to get the numerical solution under some assumption on q the existence of minimizer as well as the convergence of approximate solution in finite dimensional space is proven the new ingredient in this paper is that we do not need uniformly a priori bounds of h1 norm on q numerical implementations are also presented

differentiation by integration with jacobi polynomials in this paper the numerical differentiation by integration method based on jacobi polynomials originally introduced by mboup et al 19 20 is revisited in the central case where the used integration window is centered such a method based on jacobi polynomials was introduced through an algebraic approach 19 20 and extends the numerical differentiation by integration method introduced by lanczos 1956 21 the method proposed here rooted in 19 20 is used to estimate the nth email protected n order derivative from noisy data of a smooth function belonging to at least c n 1 q email protected n in 19 20 where the causal and anti causal cases were investigated the mismodelling due to the truncation of the taylor expansion was investigated and improved allowing a small time delay in the derivative estimation here for the central case we show that the bias error is o h q 2 where h is the integration window length for email protected c n q 2 in the noise free case and the corresponding convergence rate is o d q 1 n 1 q where d is the noise level for a well chosen integration window length numerical examples show that this proposed method is stable and effective

some properties of h extendible domains in cn 1 abstract the purpose of this article is twofold the first aim is to characterize h extendibility of smoothly bounded pseudoconvex domains in c n 1 by their noncompact automorphism groups our second goal is to show that if the squeezing function tends to 1 at an h extendible boundary point of a smooth pseudoconvex domain in c n 1 then this point must be strongly pseudoconvex

causal independence and the energy level density of states in local quantum field theory within the general framework of local quantum field theory a physically motivated condition on the energy level density of well localized states is proposed and discussed it is shown that any model satisfying this condition obeys a strong form of the principle of causal statistical independence which manifests itself in a specific algebraic structure of the local algebras split property it is also shown that the proposed condition holds in a free field theory

geometry of domains with the uniform squeezing property abstract we introduce the notion of domains with uniform squeezing property study various analytic and geometric properties of such domains and show that they cover many interesting examples including teichmuller spaces and hermitian symmetric spaces of non compact type the properties supported by such manifolds include pseudoconvexity hyperconvexity kahler hyperbolicity vanishing of cohomology groups and quasi isometry of various invariant metrics it also leads to nice geometric properties for manifolds covered by bounded domains and a simple criterion to provide positive examples to a problem of serre about stein properties of holomorphic fiber bundles

numerical differentiation for the second order derivatives of functions of two variables a regularized optimization problem for computing numerical differentiation for the second order derivatives of functions with two variables from noisy values at scattered points is discussed in this article we prove the existence and uniqueness of the solution to this problem provide a constructive scheme for the solution which is based on bi harmonic green s function and give a convergence estimate of the regularized solution to the exact solution for the problem under a simple choice of regularization parameter the efficiency of the constructive scheme is shown by some numerical examples

discrete mollification and automatic numerical differentiation abstract an automatic method for numerical differentiation based on discrete mollification and the principle of generalized cross validation is presented with data measured at a discrete set of points of a given interval the method allows for the approximate recovery of the derivative function on the entire domain no information about the noise is assumed error estimates are included together with several numerical examples of interest

canonical metrics on the moduli space of riemann surfaces i in this paper we continue our study of the canonical metrics on the moduli space of curves we first prove the bounded geometry of the ricci and perturbed ricci metrics by carefully choosing the pertubation constant and by studying the asymptotics we show that the ricci and holomorphic sectional curvatures of the perturbed ricci metric are bounded from above and below by negative constants based on our understanding of the kahler einstein metric we show that the logarithmic cotangent bundle over the deligne mumford moduli space is stable with respect to the canonical polarization finally in the last section we prove the strongly bounded geometry of the kahler einstein metric by using the kahler ricci flow and a priori estimates of the complex monge ampere equation

nuclear maps and modular structures ii applications to quantum field theory a correspondence between spectral properties of modular operators appearing in quantum field theory and the hamiltonian is established it allows to prove the distal split property for a wide class of models conversely any model having this property is shown to satisfy the haag swieca compactness criterion the results lead to a new type of nuclearity condition which can be applied to quantum field theories on arbitrary space time manifolds

properties of squeezing functions and global transformations of bounded domains the central purpose of the present paper is to study boundary behavior of squeezing functions on bounded domains we prove that the squeezing function of a strongly pseudoconvex domain tends to 1 near the boundary in fact such an estimate is proved for the squeezing function on any domain near its globally strongly convex boundary points we also study the stability of squeezing functions on a sequence of bounded domains and give comparisons of intrinsic measures and metrics on bounded domains in terms of squeezing functions as applications we give new and simple proofs of several well known results about geometry of strongly pseudoconvex do mains and prove that all cartan hartogs domains are homogenous regular finally some related problems that ask for further study are proposed

estimation of boundary condition of two dimensional nonlinear pde with application to continuous casting abstract solidification heat transfer process of billet is described by nonlinear partial differential equation pde due to the poor productive environment the boundary condition of this nonlinear pde is difficult to be fixed therefore the identification of boundary condition of two dimensional nonlinear pde is considered this paper transforms the identification of boundary condition into a pde optimization problem the lipchitz continuous of the gradient of cost function is proved based on the dual equation in order to solve this optimization problem this paper presents a modified conjugate gradient algorithm and the global convergence of which is analyzed the results of the simulation experiment show that the modified conjugate gradient algorithm obviously reduces the iterative number and running time due to the ill posedness of the identification of boundary condition this paper combines regularization method with the modified conjugate gradient algorithm the simulation experiment illustrates that regularization method can eliminate the ill posedness of this problem finally the experimental data of a steel plant illustrate the validity of this paper s method

characterizing strong pseudoconvexity obstructions to biholomorphisms and lyapunov exponents in this paper we consider the following question for bounded domains with smooth boundary can strong pseudoconvexity be characterized in terms of the intrinsic complex geometry of the domain our approach to answering this question is based on understanding the dynamical behavior of real geodesics in the kobayashi metric and allows us to prove a number of results for domains with low regularity for instance we show that for convex domains with c 2 epsilon boundary strong pseudoconvexity can be characterized in terms of the behavior of the squeezing function near the boundary the behavior of the holomorphic sectional curvature of the bergman metric near the boundary or any other reasonable measure of the complex geometry near the boundary the first characterization gives a partial answer to a question of fornaess and wold as an application of these characterizations we show that a convex domain with c 2 epsilon boundary which is biholomorphic to a strongly pseudoconvex domain is also strongly pseudoconvex

normal product states for fermions and twisted duality for ccr and car type algebras with application to the yukawa2 quantum field model we present sufficient conditions that imply duality for the algebras of local observables in all abelian sectors of all locally normal irreducible representations of a field algebra if twisted duality obtains in one of these representations it is verified that the yukawa2 model satisfies these conditions yielding the first proof of duality for the observable algebra in all coherent charge sectors in this model this paper also constitutes the first verification of the assumptions of the axiomatic study of the structure of superselection sectors by doplicher haag and roberts in an interacting model with nontrivial sectors the existence of normal product states for the free fermi field algebra and thus the verification of the funnel property for the associated net of local algebras are demonstrated

a tikhonov type method for solving a multidimensional inverse heat source problem in an unbounded domain in this study we prove a stability estimate for an inverse heat source problem in the n dimensional case we present a revised generalized tikhonov regularization and obtain an error estimate numerical experiments for the one dimensional and two dimensional cases show that the revised generalized tikhonov regularization works well

the squeezing function on doubly connected domains via the loewner differential equation for any bounded domains varomega in mathbb c n deng guan and zhang introduced the squeezing function s varomega z which is a biholomorphic invariant of bounded domains we show that for n 1 the squeezing function on an annulus a r lbrace z in mathbb c r z 1 rbrace is given by s a r z max left z frac r z right for all 0 r 1 this disproves the conjectured formula for the squeezing function proposed by deng guan and zhang and establishes up to biholomorphisms the squeezing function for all doubly connected domains in mathbb c other than the punctured plane it provides the first non trivial formula for the squeezing function for a wide class of plane domains and answers a question of wold our main tools used to prove this result are the schottky klein prime function following the work of crowdy and a version of the loewner differential equation on annuli due to komatu we also show that these results can be used to obtain lower bounds on the squeezing function for certain product domains in mathbb c n

a regularized optimization method for identifying the space dependent source and the initial value simultaneously in a parabolic equation in this paper a regularized optimization method is proposed for identifying the space dependent source and the initial value simultaneously in an inverse parabolic equation problem from two over specified measurements at different instants of time the solvability of the direct problem is presented and then the inverse problem is formulated into a regularized optimization problem for the stable identification of both the source term and the initial value based on a sequence of well posed direct problems solved by the finite element method a numerical scheme formulated into a linear system is proposed to implement the regularized optimization problem numerical results of three examples show that the proposed method is efficient and robust with respect to data noise

letter to the editor numerical differentiation for high orders by an integration method this paper mainly studies the numerical differentiation by integration method proposed first by lanczos new schemes of the lanczos derivatives are put forward for reconstructing numerical derivatives for high orders from noise data the convergence rate of these proposed methods is o d 4 n 4 as the noise level d 0 numerical examples show that the proposed methods are stable and efficient

a proof of haag swieca s compactness property for elastic scattering states it is proved that in any massive relativistic quantum field theory satisfying two particle asymptotic completeness all the bounded energy components in the elastic two particle range of all subsets of states which are excitations of the vacuum state by uniformly bounded observables localized in a given finite region of spacetime are compact in the hilbert space of states this result which is in agreement with haag swieca s conjecture is also given a more precise form in terms of the rate of decrease of the n dimensional thickness or approximation number of such sets of states when n tends to infinity a similar computation valid at arbitrarily high energies is also given for the massive free field case

linear time derivative trackers the design of an ideal differentiator is a difficult and a challenging task in this paper we discuss the properties and the limitations of two different structures of linear differentiation systems the first time derivative observer is formulated as a high gain observer where the observer gain is calculated through a lyapunov like dynamical equation the second one is given in brunovski form in which the output to be differentiated appears as a control input and the differentiation gain is calculated from the dual lyapunov equation of the first differentiation observer a discrete time version of the second form is given finally illustrative examples are presented to show their strengths and weaknesses

numerical reconstruction of heat fluxes this paper studies the reconstruction of heat fluxes on an inner boundary of a heat conductive system when the measurement of temperature in a small subregion near the outer boundary of the physical domain is available we will first consider two different regularization formulations for this severely ill posed inverse problem and justify their well posedness then we will propose two fully discrete finite element methods to approximate the resultant nonlinear minimization problems the existence and uniqueness of the discrete minimizers and convergence of the finite element solution are rigorously demonstrated a conjugate gradient method is formulated to solve the nonlinear finite element optimization problems numerical experiments are given to demonstrate the stability and effectiveness of the proposed reconstruction methods

gromov hyperbolicity and the kobayashi metric on convex domains of finite type in this paper we prove necessary and sufficient conditions for the kobayashi metric on a convex domain to be gromov hyperbolic in particular we show that for convex domains with c infty boundary being of finite type in the sense of d angelo is equivalent to the gromov hyperbolicity of the kobayashi metric we also show that bounded domains which are locally convexifiable and have finite type in the sense of d angelo have gromov hyperbolic kobayashi metric the proofs use ideas from the theory of the hilbert metric