reconstructing an unknown time dependent function in the boundary conditions of a parabolic pde this work investigates the parabolic inverse problem of reconstructing an unknown time dependent function in the boundary conditions from additional terminal integral or point observations a numerical scheme is developed for obtaining an approximate solution for this problem the method consists of reducing the solution of the inverse problem to a system of integral equations the properties of sinc function are then utilized for replacing the resulting integral equations by a system of linear algebraic equations several numerical examples are presented to demonstrate the efficiency and accuracy of the numerical method

on the integral cohomology of wreath products we use the techniques pioneered by nakaoka to study the integral cohomology of wreath products the situation is considerably more complicated than for field coefficients we describe the cohomology of h wr c for c cyclic of prime order and any h whose cohomology is finitely generated in each degree we discuss various related results and conjectures concerning the exponent of integral cohomology of finite groups these include a conjecture of a adem recently solved by j pakianathan conjectures of j carlson one solved in this work and some of our own one example given is a 2 group whose index four subgroups have non trivial intersection but whose integral cohomology has exponent four answering a question posed in 8

identifying the diffusion coefficient by optimization from the final observation this paper deals with the inverse problem of determining a pair a u in the reaction diffusion equationu t au x x f x t with initial and boundary conditionsu x 0 email protected x u x x 0 u x x 1 0 from the final measurement data u x t z x which has important application in a large fields of applied science based on the optimal control framework the existence uniqueness and stability of the minimizer for the cost functional are established a necessary condition which is a couple system of a parabolic equation and a parabolic variational inequality is deduced the gradient iteration algorithm is applied to the inverse problem and some numerical results are presented for various typical test examples

stratified transversality by isotopy for x an abstract stratified set or a w regular stratification hence for any b c or l regular stratification we prove that after stratified isotopy of x a stratified subspace w of x or a stratified map h z x can be made transverse to a fixed stratified map g y x

optimization method for an evolutional type inverse heat conduction problem this paper deals with the determination of a pair q u in the heat conduction equation with initial and boundary conditions from the overspecified data u x t g x t by the time semi discrete scheme the problem is transformed into a sequence of inverse problems in which the unknown coefficients are purely space dependent based on the optimal control framework the existence uniqueness and stability of the solution q u are proved a necessary condition which is a couple system of a parabolic equation and parabolic variational inequality is deduced

coefficient identification in euler bernoulli equation from over posed data a method for solving the inverse problem for coefficient identification in the euler bernoulli equation from over posed data is presented the original inverse problem is replaced by a minimization problem the method is applied to the problem for identifying the coefficient in the case when it is a piece wise polynomial function several examples are elaborated and the numerical results confirm that the solution of the imbedding problem coincides with the direct simulation of the original problem within the second order of approximation

integral grothendieck riemann roch theorem we show that in characteristic zero the obvious integral version of the grothendieck riemann roch formula obtained by clearing the denominators of the todd and chern characters is true without having to divide the chow groups by their torsion subgroups the proof introduces an alternative to grothendieck s strategy we use resolution of singularities and the weak factorization theorem for birational maps

meshfree and finite element nodal integration methods nodal integration can be applied to the galerkin weak form to yield a particle type method where stress and material history are located exclusively at the nodes and can be employed when using meshless or finite element shape functions this particle feature of nodal integration is desirable for large deformation settings because it avoids the remapping or advection of the state variables required in other methods to a lesser degree nodal integration can be desirable because it relies on fewer stress point evaluations than most other methods in this work aspects regarding stability consistency efficiency and explicit time integration are explored within the context of nodal integration both small and large deformation numerical examples are provided copyright 2007 john wiley sons ltd

an inverse problem of identifying the coefficient in a nonlinear parabolic equation abstract this paper deals with the determination of a pair p u in the nonlinear parabolic equation u t u x x p x f u 0 with initial and boundary conditions u x 0 x u x 0 u x 1 0 from the overspecified data u x t g x based on the optimal control framework the problem is transformed into a nonlinear optimization problem and the existence of the minimizer for the control functional is established the necessary condition which is a couple system of a parabolic equation and a parabolic variational inequality is deduced since the optimal control problem is nonconvex one may not expect a unique solution in general however the local uniqueness and stability of the solution are proved which is also the main contribution of the paper

existence results for inverse problems associated with a nonlinear parabolic equation this paper deals with the determination of a pair p u in the nonlinear parabolic equation ut u p x f u 0 with initial and boundary conditions u x 0 0 u 0 t g from the overspecified data u t q the problem is reduced to a nonlinear operator equation and solved by taking advantage of a fixed point theory in ordered banach spaces similarly another form of overspecified data is considered

a study on the performance of natural neighbour based galerkin methods in this paper we address the problem of improving natural element simulations in terms of computational cost several problems are discussed that include an efficient natural neighbour search algorithm and a comparison of different natural neighbour based interpolation algorithms in particular we review the so called pseudo nem a moving least squares like approximation scheme that employs natural neighbours and compare it with traditional sibson and laplace interpolation schemes in terms of both accuracy and computational cost some examples in linear elasticity and visco plasticity are analysed in order to test the proposed schemes in engineering problems

unramified cohomology of degree 3 and noether s problem let g be a finite group and w be a faithful representation of g over c the group g acts on the field of rational functions c w the question whether the field of invariant functions c w g is purely transcendental over c goes back to emmy noether using the unramified cohomology group of degree 2 of this field as an invariant saltman gave the first examples for which c w g is not rational over c around 1986 bogomolov gave a formula which expresses this cohomology group in terms of the cohomology of the group g

simultaneous reconstruction of the spatially distributed reaction coefficient initial temperature and heat source from temperature measurements at different times abstract in many practical situations concerned with high temperatures pressures loads and or hostile environments certain properties of the physical medium geometry boundary and or initial conditions are not known and their direct measurement can be very inaccurate or even inaccessible in such situations one can adopt an inverse approach and try to infer the unknowns from some extra accessible measurements of other quantities that may be available however the simultaneous identification of several non constant physical properties along with initial and or boundary conditions is very challenging especially when it cannot be decoupled as it combines both nonlinear as well as ill posedness features one such new inverse problem concerning the identification of the space dependent reaction coefficient the initial temperature and the source term from measured temperatures at two instants t 1 t 2 and at the final time t where 0 t 1 t 2 t is investigated in this paper insight into the uniqueness of solution is gained by considering various particular cases moreover as in practice the input temperature data are usually noise polluted due to the errors that are inherently present their influence on the solution of inversion has to be assessed as such the least squares objective functional modelling the gap between the measured and computed data is minimized to obtain the quasi solution to the inverse problem and the frechet gradients are obtained the conjugate gradient method cgm with the fletcher reeves formula is applied to estimate the three unknown coefficients numerically numerical examples are illustrated to show that accurate and stable numerical solutions are obtained using the cgm regularized by the discrepancy principle

riemann roch for tensor powers mapping a locally free module on a scheme to its l th tensor power gives rise to a natural map from the grothendieck group of all locally free modules to the grothendieck group of all locally free representations of the l th symmetric group in this paper we prove some formulas of riemann roch type for the behavior of this tensor power operation with respect to the push forward homomorphism associated with a projective morphism between schemes we furthermore establish analogous formulas for higher k groups

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

finding a control parameter in one dimensional parabolic equations an inverse problem concerning diffusion equation with source control parameter is considered several finite difference schemes are presented for identifying the control parameter which produces at each time a desired temperature at a given point in a spatial domain these schemes are based on the second order 3 point forward time centred space ftcs explicit formula and the fourth order 5 point ftcs explicit scheme and the second order 3 point backward time centred space btcs implicit technique and the fourth order 3 3 crandall s implicit formula the 5 point ftcs scheme has a bounded range of stability but its fourth order accuracy is significant the 3 point btcs method uses less central processor cpu time than the 3 3 crandall s technique but it is only second order accurate the basis of analysis of the finite difference equations considered here is the modified equivalent partial differential equation approach developed from the 1974 work of warming and hyett this allows direct and simple comparison of the errors associated with the equations as well as providing a means to develop more accurate finite difference schemes the results of a numerical experiment are presented and accuracy and the cpu time needed for the parabolic inverse problem are discussed

an inverse problem of finding a parameter in a semi linear heat equation we consider the following inverse problem of finding the pair u p which satisfies the following u1 uxx p t u f x t u ux p t 0 x 1 0 t t u x 0 u0 x 0 x 1 ux 0 t f t ux 1 t g t 0 t t and 01 x t u x t dx e t 0 t t where u0 f g f and e are known functions the existence uniqueness regularity and the continuous dependence of the solution upon the data are demonstrated

numerical identification of a nonlinear diffusion coefficient by discrete mollification the discrete mollification method is a convolution based filtering procedure suitable for the regularization of ill posed problems combined with explicit space marching finite difference schemes it provides stability and convergence for a variety of coefficient identification problems in linear parabolic equations in this paper we extend such a technique to identify some nonlinear diffusion coefficients depending on an unknown space dependent function in one dimensional parabolic models for the coefficient recovery process we present detailed error estimates and to illustrate the performance of the algorithms several numerical examples are included

an inverse problem of identifying the coefficient of first order in a degenerate parabolic equation this work studies an inverse problem of determining the first order coefficient of degenerate parabolic equations using the measurement data specified at a fixed internal point being different from other ordinary parameter identification problems in parabolic equations in our mathematical model there exists degeneracy on the lateral boundaries of the domain which may cause the corresponding boundary conditions to go missing by the contraction mapping principle the uniqueness of the solution for the inverse problem is proved a numerical algorithm on the basis of the predictor corrector method is designed to obtain the numerical solution and some typical numerical experiments are also performed in the paper the numerical results show that the proposed method is stable and the unknown function is recovered very well the results obtained in the paper are interesting and useful and can be extended to other more general inverse coefficient problems of degenerate pdes

analysis of a reaction diffusion system modeling man environment man epidemics in this paper an old model for the temporal and spatial evolution of orofecal transmitted disease is reexamined it consists of a system of two coupled reaction diffusion equations for the concentration of bacteria and infective humans under the assumptions that the total population of humans is unaffected by the disease and only a small proportion of the population is affected at any one time the force of infection on healthy humans is assumed to be a sigmoidal function of bacterial concentration tending to some finite limit and with zero gradient at zero this last feature models an immune response to low concentrations of the infectious agent in practice the diffusion coefficient for infective humans ismuch smaller than that of bacteria and is therefore set to zero a detailed analysis of the steady state bifurcation pattern is then performed for the case of homogeneous dirichlet boundary conditions applied at the endpoints of a one dimensional interval particular attention is paid to the limiti

classes de stiefel whitney de formes quadratiques et de representations galoisiennes reelles i u n peu de t o p o l o g i e a l g6b r ique 226 1 1 le fonc t eu r 226 1 2 le t rans fe r t mu l t i p l i c a t i f 228 1 3 t rans f e r t et c lasses de s t ie fe l whi tney 233 1 4 le cas d u n g r o u p e d iscre t t r a d u c t i o n s 238

simultaneous reconstruction of space dependent heat transfer coefficients and initial temperature abstract many complex physical phenomena and engineering systems e g in heat exchanges reflux condensers combustion chambers nuclear vessels etc due to the high temperatures high pressures hostile environment involved possess certain properties which are inaccessible to measure and therefore their influence determination using inverse analysis is very important and desirable in this spirit the purpose of this paper is to mathematically formulate and analyse a new inverse problem in which given measurements of temperature at two different instants it is required to obtain the space dependent heat transfer coefficients htcs and the initial temperature this simultaneous identification is challenging since it is both nonlinear and ill posed the uniqueness of solution is established based on the max min principle for parabolic equations and the contraction mapping principle for the existence and uniqueness of a fixed point the novel inverse mathematical model that is proposed offers appropriate scientific guidance to the polymer heat transfer processing industry as to which data to measure provide in order to be able to reliably determine the desirable htcs along with the initial temperature which is in general unknown furthermore for the reconstruction the surface htc is determined separately whilst the variational formulation is introduced for the simultaneous determination of the domain htc and the initial temperature the frechet gradient of the minimizing objective functional is derived the numerical reconstruction process is based on the conjugate gradient method cgm regularized by the discrepancy principle accurate and stable numerical solutions are obtained even in the presence of noise in the input temperature data since noisy data are invented the study models realistic practical situations in which temperature measurements recorded using sensors or thermocouples are inherently contaminated with random noise

the mathematics of infectious diseases many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases threshold theorems involving the basic reproduction number r 0 the contact number sigma and the replacement number r are reviewed for the classic sir epidemic and endemic models similar results with new expressions for r 0 are obtained for mseir and seir endemic models with either continuous age or age groups values of r 0 and sigma are estimated for various diseases including measles in niger and pertussis in the united states previous models with age structure heterogeneity and spatial structure are surveyed

stiefel whitney classes of real representations of finite groups abstract we prove the existence and uniqueness of stiefel whitney classes of real representations subject to the hirzebruch axioms within the category of finite groups we also give a method of constructing and computing with these classes using multiplicative transfer and induced representations and apply our formulae in certain simple cases

an inverse problem of determining the implied volatility in option pricing in the black scholes world there is the important quantity of volatility which cannot be observed directly but has a major impact on the option value in practice traders usually work with what is known as implied volatility which is implied by option prices observed in the market in this paper we use an optimal control framework to discuss an inverse problem of determining the implied volatility when the average option premium namely the average value of option premium corresponding with a fixed strike price and all possible maturities from the current time to a chosen future time is known the issue is converted into a terminal control problem by green function method the existence and uniqueness of the minimum of the control functional are addressed by the optimal control method and the necessary condition which must be satisfied by the minimum is also given the results obtained in the paper may be useful for those who engage in risk management or volatility trading

identification of discontinuous parameters in flow equations a problem of identifying possibly discontinuous diffusion coefficients in parabolic equations is considered general theorems on existence and convergence of galerkin approximations are proved in l 1 setting classes of functions of bounded variation are discussed and the variation estimates are obtained a double discretization method with the variations constraints is used in two and three dimensional problems and the numerical experiments are presented

a note on the existence and stability of an inverse problem for a sis model abstract in this note we discuss the existence and stability of an inverse problem arising from the determination of the reaction coefficients for an sis model the study is motivated by a remark regarding the final discussion of the recent paper by xiang and liu 2015 the weak assumption of the work of h xiang and b liu is that the proofs of existence and stability results are valid only for the one dimensional case here we introduce an appropriate framework which is also valid in the multidimensional case and that generalizes the previous results

an inverse problem for computing a leading coefficient in the sturm liouville operator by using the boundary data abstract we consider an inverse problem for identifying a leading coefficient x in x y x q x y x h x which is known as an inverse coefficient problem for the sturm liouville operator we transform y x to u x t 1 t y x and derive a parabolic type pde in a fictitious time domain of t then we develop a lie group adaptive method lgam to find the coefficient function x when x is a continuous function of x we can identify it very well by giving boundary data of y y and the efficiency of lgam is confirmed by comparing the numerical results with exact solutions although the data used in the identification are limited we can provide a rather accurate solution of x

cup and cap products in intersection co homology abstract we construct cup and cap products in intersection co homology with field coefficients the existence of the cap product allows us to give a new proof of poincare duality in intersection co homology which is similar in spirit to the usual proof for ordinary co homology of manifolds

inverse problem for coefficient identification in the euler bernoulli equation a special technique has been developed for the identification of the solution and the unknown coefficient in the euler bernoulli equation the original problem of the unknown coefficient identification from over posed data is transferred into a higher order well posed problem following the idea of the method of variational imbedding the new boundary value problem is solved by means of an iterative finite difference scheme the scheme is thoroughly validated and is shown to have a second order truncation error

a three dimensional computational procedure for reproducing meshless methods and the finite element method a flexible computational procedure for solving 3d linear elastic structural mechanics problems is presented that currently uses three forms of approximation function natural neighbour moving least squares using a new nearest neighbour weight function and lagrange polynomial and three types of integration grids to reproduce the natural element method and the finite element method the addition of more approximation functions which is not difficult given the structure of the code will allow reproduction of other popular meshless methods results are presented that demonstrate the ability of the first order meshless approximations to capture solutions more accurately than first order finite elements also the quality of integration for the three types of integration grids is compared the concept of a region is introduced which allows the splitting of a domain into different sections each with its own type of approximation function and spatial integration scheme copyright 2004 john wiley sons ltd

an inverse radiative coefficient problem arising in a two dimensional heat conduction equation with a homogeneous dirichlet boundary condition in a circular section abstract in this study we investigate the well posedness of the solution of an optimal control problem related to a nonlinear inverse coefficient problem problems of this type have important applications in several fields of applied science unlike other terminal control problems the observation data are only given for a fixed direction rather than for the whole domain which may make the conjugate theory for parabolic equations ineffective moreover the coefficients in our model are singular so we propose some weighted sobolev spaces based on the optimal control framework the problem is transformed into an optimization problem and the existence of the minimizer is established after deducing the necessary conditions that must be satisfied by the minimizer we prove the uniqueness and stability of the minimizer following a minor modification of the cost functional and imposing some a priori regularity conditions on the forward operator we obtain the convergence of the minimizer for the noisy input data considered in this study the results obtained in this study are interesting and useful and they can be extended to more general parabolic equations with singular coefficients

multi parameters identification problem for a degenerate parabolic equation abstract this paper investigates an inverse problem of simultaneously reconstructing the initial value and source coefficient in a degenerate parabolic equation problems of this type have important applications in several fields of applied science being different from other inverse coefficient problems in classical parabolic equations non degenerate the principal coefficient in the mathematical model discussed in the paper may vanish on both extremities of the domain on the basis of carleman estimate the uniqueness and conditional stability of solution for the original problem are established then an iteration algorithm of landweber type is designed to obtain the numerical solution and some typical numerical experiments are also performed numerical results show that the proposed method is stable and the unknown coefficients are recovered quite well

intersection homology ii in 19 20 we introduced topological invariants ih x called intersection homology groups for the study of singular spaces x these groups depend on the choice of a perversity p a perversity is a function from 2 3 to the non negative integers such that both c and c 2 c are positive and increasing functions of c 2 1 the group ihr is defined for spaces x called pseudomanifolds a pseudomanifold of dimension n is a space that admits a stratification x x n x n z x n 3 x 1 x 0

chern classes of automorphic vector bundles 1 1 suppose x is a compact n dimensional complex manifold each partition i i1 i2 ir of n corresponds to a chern number c x ci1 x ci2 x cir x x z where c x h x z are the chern classes of the tangent bundle x h2n x z is the fundamental class and h0 x z z is the augmentation many invariants of x such as its complex cobordism class may be expressed in terms of its chern numbers mi st during the last 25 years characteristic classes of singular spaces have been defined in a variety of contexts whitney classes of euler spaces su h t ak todd classes of singular varieties bfm chern classes of singular algebraic varieties mac l classes of stratified spaces with even codimension strata gm1 wu classes of singular spaces go2 gp to name a few however these characteristic classes are invariably homology classes and as such they cannot be multiplied with each other in some cases it has been found possible to lift these classes from homology to intersection homology where some characteristic numbers may be formed bbf bw go2 gp t the case of locally symmetric spaces is particularly interesting suppose is a torsionfree arithmetic group acting on a complex n dimensional hermitian symmetric domain d g k where g is the group of real points of a semisimple algebraic group g defined over q with g q and where k g is a maximal compact subgroup then x d is a hermitian locally symmetric space when x is compact hirzebruch s proportionality theorem hr1 says that there is a number v q so that for every partition i i1 i2 ir of n the chern number satisfies c x v c where gu k is the compact dual symmetric space and gu is a compact real form of g c containing k if x d is noncompact it has a canonical baily borel satake compactification x this is a usually highly singular complex projective algebraic variety to formulate a proportionality theorem in the noncompact case one might hope that the tangent bundle tx extends as a complex vector bundle over x but this is false in mu1 d mumford showed that tx has a particular extension e x over any toroidal resolution x x of the baily borel compactification and that for any partition i of n the resulting chern numbers c e c e c e c e x 1 1 1

determination of the source parameter in a heat equation with a non local boundary condition in this article we consider the inverse problem of identifying a time dependent unknown coefficient in a parabolic problem subject to initial and non local boundary conditions along with an overspecified condition defined at a specific point in the spatial domain due to the non local boundary condition the system of linear equations resulting from the backward euler approximation have a coefficient matrix that is a quasi tridiagonal matrix we consider an efficient method for solving the linear system and the predictor corrector method for calculating the solution and updating the estimate of the unknown coefficient two model problems are solved to demonstrate the performance of the methods

uniqueness and stability of the minimizer for a binary functional arising in an inverse heat conduction problem abstract the local well posedness of the minimizer of an optimal control problem is studied in this paper the optimization problem concerns an inverse problem of simultaneously reconstructing the initial temperature and heat radiative coefficient in a heat conduction equation being different from other ordinary optimization problems the cost functional constructed in the paper is a binary functional which contains two independent variables and two independent regularization parameters particularly since the status of the two unknown coefficients in the cost functional are different the conjugate theory which is extensively used in single parameter optimization problems cannot be applied for our problem the necessary condition which must be satisfied by the minimizer is deduced by assuming the terminal time t is relatively small an l 2 estimate regarding the minimizer is obtained from which the uniqueness and stability of the minimizer can be deduced immediately

asymptotic profiles of the positive steady state for an sis epidemic reaction diffusion model part i abstract to capture the impact of spatial heterogeneity of environment and movement of individuals on the persistence and extinction of a disease allen et al in l j s allen b m bolker y lou a l nevai asymptotic profiles of the steady states for an sis epidemic reaction diffusion model discrete contin dyn syst ser a 21 1 2008 1 20 proposed a spatial sis susceptible infected susceptible reaction diffusion model and studied the existence uniqueness and particularly the asymptotic behavior of the endemic equilibrium as the diffusion rate of the susceptible individuals goes to zero in the case where a so called low risk subhabitat is created in this work we shall provide further understanding of the impacts of large and small diffusion rates of the susceptible and infected population on the persistence and extinction of the disease which leads us to determine the asymptotic behaviors of the endemic equilibrium when the diffusion rate of either the susceptible or infected population approaches to infinity or zero in the remaining cases consequently our results reveal that in order to eliminate the infected population at least in low risk area it is necessary that one will have to create a low risk subhabitat and reduce at least one of the diffusion rates to zero in this case our results also show that different strategies of controlling the diffusion rates of individuals may lead to very different spatial distributions of the population moreover once the spatial environment is modified to include a low risk subhabitat the optimal strategy of eradicating the epidemic disease is to restrict the diffusion rate of the susceptible individuals rather than that of the infected ones

inverse problem for coefficient identification in sir epidemic models abstract this work deals with the development of a numerical method for solving an inverse problem for identifying coefficients from over posed data in an sir mathematical model of infectious diseases spread through a population the parameters are identified using a generalized least squares method which is similar to the technique called method of variational imbedding where the original inverse problem is replaced by a minimization problem a difference scheme and a numerical algorithm for solving the parameter identification problem are developed the correctness of the embedded problem is discussed numerical results of the parameters representing the solution to the inverse problem are presented

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

reconstruction of the space dependent perfusion coefficient from final time or time average temperature measurements abstract knowledge of the blood perfusion in biomedicine is of crucial importance in applications related to hypothermia in this paper we consider the inverse bio heat transfer nonlinear problem to determine the space dependent perfusion coefficient from final time or time average temperature measurements which are themselves space dependent quantities in other applications this coefficient multiplying the temperature function represents a reaction rate uniqueness of solution holds but continuous dependence on the input data is violated the problem is reformulated as a least squares minimization whose gradient is obtained by solving the sensitivity and adjoint problems the newly obtained gradient formula is used in the conjugate gradient method cgm this is the first time that the cgm is applied to solve the inverse problems under investigation for exact data we investigate the convergence of the iterative cgm we also test that the iterative algorithm is semi convergent under noisy data by stopping the iteration using the discrepancy principle criterion to produce a stable solution furthermore because the search step size is computed using an optimization scheme at each iteration the cgm is very efficient three examples are investigated to verify the accuracy and stability of the numerical method

a high order meshless method with compact support abstract in spite of their advantages in handling complex geometries meshless methods have been restricted very much to applications at low spatial order typically of the second order this is because the conventional meshless methods would require a very large supporting set of nodes when high order interpolants are used and this could pose problems for neighborhood and nodal selection in complex domains in this work a new meshless method is proposed for obtaining high order approximation on a highly compact nodal set whereas conventional meshless methods utilize the lowest order solution data to reconstruct the solution and its derivatives in the neighborhood of the reference node the present method increases the usage of available information at the nodes by interpolating over nodal set of vector data the utilization of the increased degrees of freedom and corresponding high order information at nodes results in a significant reduction in the number of support nodes needed for solution reconstruction high order accuracy of up to the 6th order is demonstrated for problems in linear advection diffusion and poisson equation the scheme is also applied to incompressible viscous fluid flows governed by the nonlinear system of navier stokes equations in all cases nine support nodes including the reference node are used for data interpolation and spatial reconstruction

identifying the radiative coefficient of an evolutional type heat conduction equation by optimization method this paper studies an evolutional type inverse problem of identifying the radiative coefficient of heat conduction equation when the over specified data is given problems of this type have important applications in several fields of applied science being different from other ordinary inverse coefficient problems the unknown coefficient in this paper depends on both the space variable x and the time t based on the optimal control framework the inverse problem is transformed into an optimization problem and a new cost functional is constructed in the paper the existence uniqueness and stability of the minimizer of the cost functional are proved and the necessary conditions which must be satisfied by the minimizer are also given the results obtained in the paper are interesting and useful and can be extended to more general parabolic equations

application of the restrained optimal perturbation method to study the backward heat conduction problem in this paper a restrained optimal perturbation method is firstly proposed to solve the backward heat conduction problem the initial temperature distribution will be identified from the overspecified data a regularization term is introduced in the objective functional for overcoming the ill posedness of this problem spectral projected gradient algorithm is used to solve the optimal problem and we give the sensitivity analysis of the initial value the results of numerical experiments are also presented

holomorphic flexibility properties of complex manifolds we obtain results on approximation of holomorphic maps by algebraic maps the jet transversality theorem for holomorphic and algebraic maps between certain classes of manifolds and the homotopy principle for holomorphic submersions of stein manifolds to certain algebraic manifolds

inverse problem for a coupling model of reaction diffusion and ordinary differential equations systems application to an epidemiological model abstract this paper investigates an identifiability method for a class of systems of reaction diffusion equations in the l2 framework this class is composed of a master system of ordinary differential equations coupled with a slave system of diffusion equations it can model two populations the second one being diffusive contrary to the first one the identifiability method is based on an elimination procedure providing relations called input output polynomials and linking the unknown parameters the inputs and the outputs of the model these polynomials can also be used to estimate the parameters as shown in this article to our best knowledge such an identifiability method and a parameter estimation procedure have not yet been explored for such a system in the l2 framework this work is applied on an epidemiological model describing the propagation of the chikungunya in a local population

solving the inverse problem of an sis epidemic reaction diffusion model by optimal control methods in this contribution a novel inverse problem on an sis epidemic reaction diffusion model is investigated by employing the optimal control methods by setting a proper regular cost functional and choosing the coefficients to be identified as control variables we embed the original inverse problem which is very difficult to solve into an optimal control problem the existence of the optimal controls and the first order necessary optimality condition satisfied by the optimal controls are established respectively in particular the local uniqueness and stability of the identification of the coefficients are proved by using analytical techniques

identification of parameters in distributed parameter systems by regularization identification of spatially varying parameters in distributed parameter systems from noisy data is an ill posed problem the concept of regularization widely used in solving linear fredholm integral equations is developed for the identification of parameters in distributed parameter systems a general regularization identification theory is first presented and then applied to the identification of parabolic systems the performance of the regularization identification method is evaluated by numerical experiments on the identification of a spatially varying diffusivity in the diffusion equation

identification of time dependent source terms and control parameters in parabolic equations from overspecified boundary data abstract this paper presents a semigroup approach for inverse source problems for the abstract heat equation when the measured output data is given in subject to the integral overspecification over the spatial domain the existence of a solution to the inverse source problem is shown in appropriate function spaces and a representation formula for the solution is proposed such representation permits the derivation of sufficient conditions for the uniqueness of the solution also an approximation method based on the optimal homotopy analysis method oham is designed and the error estimates are discussed using graphical analysis moreover we conjecture that our approach can be applied for the determination of a control parameter in an inverse problem with integral overspecialization data the proposed algorithm is examined through various numerical examples for the reconstruction of continuous sources and the determination of a control parameter in parabolic equations the accuracy and stability of the method are discussed and compared with several finite difference techniques computational results show efficiency and high accuracy of the proposed algorithm

schubert calculus on the grassmannian of hermitian lagrangian spaces abstract with an eye towards index theoretic applications we describe a schubert like stratification on the grassmannian of hermitian lagrangian spaces in c n c n this is a natural compactification of the space of hermitian n n matrices the closures of the strata define integral cycles and we investigate their intersection theoretic properties we achieve this by blending morse theoretic ideas with techniques from o minimal or tame geometry and geometric integration theory

whitney stratified chains and cochains this paper contains the technical constructions necessary for a geometric cycle definition of cohomology and homology in the context of whitney stratifications cup and cap products are interpreted as the transverse intersection of geometric cocycles and cycles