nonexistence and uniqueness of positive solutions of yamabe type equations on nonpositively curved manifolds we prove nonexistence and uniqueness of positive c2 solutions of the elliptic equation u a x u k x u 0 1 on a nonpositively curved complete manifold m g 0 introduction let m g be a complete noncompact riemannian manifold of dimension m 3 and let a x k x be assigned continuous functions on m the aim of this paper is to determine conditions involving the asymptotic behavior of a k and the geometry of m g in order to guarantee nonexistence and eventually uniqueness of positive c solutions of the elliptic equation u a x u k x u 0 0 1 on m for some constant 1 this problem has geometrical roots indeed up to an inessential multiplicative positive constant in front of the choice m 2 m 2 in 0 1 produces the well known yamabe equation relating the scalar curvature a x of g to that k x of the conformally deformed metric gu u 4 m 2 g u 0 in this case a fairly accurate general existence result satisfying the further request of completeness of gu has been given in rrv1 for negative scalar curvatures in the present investigation as naturally expected on a riemannian manifold the geometry is controlled via curvature conditions to be more precise we have fixed our attention on the two most typical cases i riem m g 0 and ii riem m g b2 for some constant b 0 here riem m g denotes the sectional curvature thus r with its canonical metric pertains to case i and in this special setting under the further assumption a x 0 a number of results have been obtained for instance by ni n lin l and more recently by cheng and lin c l however our methods beside having a geometrical flavor differ from those of the above authors mainly because while in r standard symmetrization techniques are at hand on a general manifold such an approach is obviously not feasible furthermore the appearance of the linear term in 0 1 plays a role in connection with k x which to our knowledge has not been thoroughly analysed even in euclidean space as received by the editors march 6 1995 1991 mathematics subject classification primary 53c21 58g03

a framework for the adaptive finite element solution of large scale inverse problems since problems involving the estimation of distributed coefficients in partial differential equations are numerically very challenging efficient methods are indispensable in this paper we will introduce a framework for the efficient solution of such problems this comprises the use of adaptive finite element schemes solvers for the large linear systems arising from discretization and methods to treat additional information in the form of inequality constraints on the parameter to be recovered the methods to be developed will be based on an all at once approach in which the inverse problem is solved through a lagrangian formulation the main feature of the paper is the use of a continuous function space setting to formulate algorithms in order to allow for discretizations that are adaptively refined as nonlinear iterations proceed this entails that steps such as the description of a newton step or a line search are first formulated on continuous functions and only then evaluated for discrete functions on the other hand this approach avoids the dependence of finite dimensional norms on the mesh size making individual steps of the algorithm comparable even if they used differently refined meshes numerical examples will demonstrate the applicability and efficiency of the method for problems with several million unknowns and more than 10 000 parameters

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

frechet differentiability for a damped sine gordon equation abstract we consider a damped sine gordon equation with a variable diffusion coefficient the goal is to derive necessary conditions for the optimal set of parameters minimizing the objective function j first we show that the solution map is continuous under a weak assumption on the topology of the admissible set p then the solution map is shown to be weakly g teux differentiable on p implying the g teux differentiability of the objective function finally we show the frechet differentiability of j the optimal set of parameters is shown to satisfy a bang bang control law

a petrov galerkin spectral element technique for heterogeneous porous media flow abstract a novel spectral element technique is examined in which the test functions are different from the approximating elements examples are given for a simple 1 d helmholtz equation burger s equation with a small viscosity and for darcy s equation with a discontinuous hydraulic conductivity

on the number of positive solutions of weakly non linear elliptic equations when a parameter is large on etudie les solutions positives du probleme u f u dans u 0 sur ou est un domaine borne lisse de r n f r r est c 1 et est grand

convergence of an iterative method for total variation denoising in total variation denoising one attempts to remove noise from a signal or image by solving a nonlinear minimization problem involving a total variation criterion several approaches based on this idea have recently been shown to be very effective particularly for denoising functions with discontinuities this paper analyzes the convergence of an iterative method for solving such problems the iterative method involves a lagged diffusivity approach in which a sequence of linear diffusion problems are solved global convergence in a finite dimensional setting is established and local convergence properties including rates and their dependence on various parameters are examined

the global dimension of schur algebras for gl2 and gl3 abstract we first define the notion of good filtration dimension and weyl filtration dimension in a quasi hereditary algebra we calculate these dimensions explicitly for all irreducible modules in sl 2 and sl 3 we use these to show that the global dimension of a schur algebra for gl 2 and gl 3 is twice the good filtration dimension to do this for sl 3 we give an explicit filtration of the modules by modules of the form f l where is a dominant weight and is p restricted

bounding and unbounding higher extensions for sl2 we analyse the recursive formula found for various ext groups for sl2 k k a field of characteristic p and derive various generating functions for these groups we use this to show that the growth rate for the cohomology of sl2 k is at least exponential in particular max dimextsl2 k i k a a i n has at least exponential growth for all p we also show that max dimextsl2 k i k a a n for a fixed i is bounded

an augmented lagrangian method for identifying discontinuous parameters in elliptic systems the identification of discontinuous parameters in elliptic systems is formulated as a constrained minimization problem combining the output least squares and the equation error method the minimization problem is then proved to be equivalent to the saddle point problem of an augmented lagrangian the finite element method is used to discretize the saddle point problem and the convergence of the discretization is also proved finally an uzawa algorithm is suggested for solving the discrete saddle point problem and is shown to be globally convergent

identification of the reaction coefficient in time fractional diffusion equations abstract in this paper we present an inverse problem of identifying the reaction coefficient for time fractional diffusion equations in two dimensional spaces by using boundary neumann data it is proved that the forward operator is continuous with respect to the unknown parameter because the inverse problem is often ill posed regularization strategies are imposed on the least fit to data functional to overcome the stability issue there may exist various kinds of functions to reconstruct it is crucial to choose a suitable regularization method we present a multi parameter regularization l 2 b v method for the inverse problem this can extend the applicability for reconstructing the unknown functions rigorous analysis is carried out for the inverse problem in particular we analyze the existence and stability of regularized variational problem and the convergence to reduce the dimension in the inversion for numerical simulation the unknown coefficient is represented by a suitable set of basis functions based on a priori information a few numerical examples are presented for the inverse problem in time fractional diffusion equations to confirm the theoretic analysis and the efficacy of the different regularization methods

bounding ext for modules for algebraic groups finite groups and quantum groups given a finite root system we show that there is an integer c c such that dimextg1 l l c for any reductive algebraic group g with root system and any irreducible rational g modules l l there also is such a bound in the case of finite groups of lie type depending only on the root system and not on the underlying field for quantum groups a similar result holds for extn for any integer n 0 using a constant depending only on n and the root system when l is the trivial module the same result is proved in the algebraic group case thus giving similar bounded properties independent of characteristic for algebraic and generic cohomology a similar result holds for any choice of l l even allowing to vary provided the p adic expansion of lambda is limited to a fixed number of terms in particular because of the interpretation of generic cohomology as a limit for underlying families of finite groups the same boundedness properties hold asymptotically for finite groups of lie type the results both use and have consequences for kazhdan lusztig polynomials appendix a proves a stable version needed for small prime arguments of donkin s tilting module conjecture

r almost newton ricci solitons immersed into a riemannian manifold abstract we establish the new concept of r almost newton ricci soliton for hypersurfaces immersed in a riemannian manifold which involves the r th newton and the ricci tensors and extends in a natural way the notion of immersed almost ricci solitons introduced by barros et al 3 in this setting our purpose is to investigate the existence of these geometric objects after exhibit some examples of r almost newton ricci solitons we obtain sufficient conditions to guarantee that they must be totally geodesic under suitable constraints on the potential function and using appropriate maximum principles furthermore a particular study of 1 almost newton ricci solitons immersed in a locally symmetric einstein manifold is also made

on the scalar curvature of constant mean curvature hypersurfaces in space forms abstract in this paper we study the behavior of the scalar curvature s of a complete hypersurface immersed with constant mean curvature into a riemannian space form of constant curvature deriving a sharp estimate for the infimum of s our results will be an application of a weak omori yau maximum principle due to pigola rigoli setti 2005 17

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

free skew fields have many orderings abstract the notion of a ordering on a skew field with involution was introduced by s holland in j algebra 101 1986 16 46 as an analogue to the notion of a total ordering on a skew field and developed further in a series of papers of t craven i idris m marshall and t smith while it is well known that every free skew field has a total ordering see j lewin trans amer math soc 192 1974 339 346 it has not been known so far whether every free skew field with some natural involution has a ordering the aim of this paper is to give an explicit construction of a class of orderings on free associative algebras and to prove that orderings from this class extend uniquely to the corresponding free skew fields the problem was posed by t craven and t smith in j algebra 238 2001 314 327

identification of nonlinearity in k approximate periodic parabolic equations abstract this work is concerned with the identification of nonlinearities in k approximate periodic parabolic equations with observations on a subdomain of the physical domain some approximation processes for the identification problems are given

higher order mean curvature estimates for bounded complete hypersurfaces abstract we obtain sharp estimates involving the mean curvatures of higher order of a complete bounded hypersurface immersed in a complete riemannian manifold similar results are also given for complete spacelike hypersurfaces in lorentzian ambient spaces

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

strong approximation property for baer orderings on fields abstract let d be a field with d z d being finite our main objective is to show that the space of all baer orderings resp weak orderings of d satisfies the strong approximation property iff every baer ordering of d is in fact a weak ordering this shows that the notions of baer orderings and weak orderings are respectively the correct analogues for semiorderings and orderings we also intro duce the concept of baer formally real fields and baer preorderings we prove that a field admits a baer ordering iff it is baer formally real in addition some new results on weak orderings are also discussed

hermitian forms over ordered fields abstract letdbe a division ring with an involution assuming thatdadmits baer orderings we can study the witt group of hermitian forms overdby observing its image in the ring of continuous functions on the space of orderings we are led to define a new class of rings which when viewed in an abstract setting provide a natural generalization of the spaces of orderings and real spectra studied in real algebraic geometry

a liouville type result for quasi linear elliptic equations on complete riemannian manifolds we extend a liouville type result of d g aronson and h f weinberger and e n dancer and y du concerning solutions to the equation pu b x f u to the case of a class of singular elliptic operators on riemannian manifolds which include the laplacian and are the natural generalization to manifolds of the operators studied by j serrin and collaborators in euclidean setting in the process we obtain an a priori lower bound for positive solutions of the equation in consideration which complements an upper bound previously obtained by the authors in the same context

estimation of discontinuous coefficients in parabolic systems applications to reservoir simulation we present spline based techniques for estimating spatially varying parameters that appear in parabolic distributed systems typical of those found in reservoir simulation problems in particular we discuss the problem of determining discontinuous coefficients estimating both the functional shape and points of discontinuity for such parameters in addition our ideas may also be applied to problems with unknown initial conditions and unknown parameters appearing in terms representing external forces convergence results and a summary of numerical performance of the resulting algorithms are given

the estimation of l diffusion coefficients in the parabolic equations abstract the estimation of diffusion coefficients having only l bounds in parabolic equations is considered existence is obtained within a more general class of parabolic operators by means of g convergence the corresponding semi discrete problems are related to the original problem

positive solutions of yamabe type equations on complete manifolds and applications we study the semilinear equation u a x u b x u 1 on a complete riemannian manifold we determine conditions on the coefficients that guarantee existence and nonexistence of positive solutions a very general uniqueness result is also established our main results are valid without explicit curvature assumptions and appear to be new even in rm

characterizations of linear weingarten submanifolds abstract in this paper we deal with complete linear weingarten submanifolds m n immersed with parallel normalized mean curvature vector field in a riemannian space form q c n p of constant sectional curvature c and with n 4 we recall that a submanifold is called linear weingarten when its mean and scalar curvatures are linearly related in this setting we establish a suitable extension of the generalized maximum principle of omori yau in order to show that such a submanifold m n must be either totally umbilical or isometric to a clifford torus s 1 1 r 2 s n 1 r when c 1 a circular cylinder r s n 1 r when c 0 or a hyperbolic cylinder h 1 1 r 2 s n 1 r when c 1 we also study the parabolicity of these submanifolds with respect to a cheng yau modified operator

on the good filtration dimension of weyl modules for a linear algebraic group let g be a linear algebraic group over an algebraically closed field of characteristic p whose corresponding root system is irreducible in this paper we calculate the weyl filtration di mension of the induced g modules and the simple g modules l fora regular weight we use this to calculate some ext groups of the form ext extl l and ext where are regular and is the weyl module of highest weight we then deduce the projective dimensions and injective dimensions for l and for a regular weight in associated generalised schur algebras we also deduce the global dimension of the schur algebras for gln s n r when p n and for s mp p with m an integer

higher extensions between modules for abstract we calculate ext sl 2 k ext sl 2 k l ext sl 2 k l ext sl 2 k l l where is the weyl module of highest weight l is the simple sl 2 k module of highest weight and our field k is algebraically closed of positive characteristic we also get analogous results for the dipper donkin quantisation to do thus we construct the lyndon hochschild serre spectral sequence in a new way and find a new condition for the e 2 page of any spectral sequence to be the same as the e page

submanifolds with constant scalar curvature in a space form abstract we deal with complete submanifolds m n having constant positive scalar curvature and immersed with parallel normalized mean curvature vector field in a riemannian space form q c n p of constant sectional curvature c 1 0 1 in this setting we show that such a submanifold m n must be either totally umbilical or isometric to a clifford torus s 1 1 r 2 s n 1 r when c 1 a circular cylinder r s n 1 r when c 0 or a hyperbolic cylinder h 1 1 r 2 s n 1 r when c 1 this characterization theorem corresponds to a natural improvement of previous ones due to alias garcia martinez and rigoli 2 cheng 4 and guo and li 6

approximate periodic solutions of a nonlinear parabolic system and an identification problem this work continues our study in l lei identification of parameters through the approximate periodic solutions of a linear parabolic system preprint 2005 on the identification problem for the coefficients for the lower order terms in a parabolic system through its approximate periodic solutions different from the work in l lei identification of parameters through the approximate periodic solutions of a linear parabolic system preprint 2005 our system now is nonlinear and the coefficients to be detected are from the first order term from the application point of view we now try to determine the diffusion coefficients for the system by the observation over a subregion of the physical domain the existence and uniqueness problem of the approximate periodic solutions is studied in the first part of the paper

uniqueness of entire graphs in warped products abstract under suitable restrictions on the higher order mean curvatures we establish uniqueness results for entire graphs in a warped product space satisfying a standard convergence condition consequences are given for such graphs to be slices by using comparison inequalities of their higher order mean curvatures applications to the study of the rigidity of minimal and radial graphs in the euclidean space are also given

identifiability of piecewise constant conductivity in a heat conduction process we study the identification and identifiability problems for heat conduction in a nonhomogeneous rod the identifiability results are established for two different sets of observations given a sequence of distributed type observations the identifiability is proved for conductivities in a piecewise smooth class of functions in the case of observations taken at finitely many points the identifiability is established for piecewise constant conductivities such conductivities can be uniquely identified using the proposed marching algorithm

propagation and extinction of fronts for semilinear parabolic equations on riemannian manifolds abstract we study the cauchy problem for the semilinear heat equation on riemannian manifolds propagation and extinction of solutions are addressed supposing that the nonlinear forcing term is either of kpp type or of bistable type in particular we highlight the influence both of sectional curvatures and of ricci curvature on such phenomena

on the omori yau maximum principle and its applications to differential equations and geometry abstract in this paper we prove a generalised version of the omori yau maximum principle and describe some applications to problems in geometry and differential equations

approximation properties for orderings on fields the goal of this paper is to extend the main theorems on approximation properties of the topological space of orderings from formally real fields to skew fields with an involution to accomplish this the concept of semiordering is developed and new theorems are obtained for lifting orderings from the residue class field of a real valuation

homomorphisms between weyl modules for sl3 k we classify all homomorphisms between weyl modules for sl3 k when k is an algebraically closed field of characteristic at least three and show that the hom spaces are all at most one dimensional as a corollary we obtain all homomorphisms between specht modules for the symmetric group when the labelling partitions have at most three parts and the prime is at least three we conclude by showing how a result of fayers and lyle on hom spaces for specht modules is related to earlier work of donkin for algebraic groups let g be a reductive algebraic group over an algebraically closed field of characteristic p 0 an important class of modules for such a group are the weyl modules labelled by dominant weights these can be constructed relatively explicitly and their heads provide a full set of simple modules for g equivalently one can study the duals of these modules denoted which have the advantage of being induced from one dimensional modules for a borel subgroup in determining the structure of such modules or indeed their cohomology the calculation of hom spaces between them is a useful tool relatively little is known in general about such hom spaces in type a when andare related by a suitable single reflection explicit non zero homomorphisms from to were constructed with some restrictions by carter and lusztig 3 and more generally by carter and payne 4 the corresponding cases in other types were considered by franklin 14 while it is clear that there should be a hierarchy of families of homomorphisms corresponding to different powers of p the only case where the above results provide a complete classification is when g is sl2 where it is relatively easy to determine all hom spaces exactly 6 the only other general results in this area by andersen 1 and koppinen 18 concern homo morphisms between modules labelled by weights which are close together typically such results show that certain hom spaces are non zero or in some cases one dimensional for weights which are far apart and not related by a single reflection almost nothing is known in this paper we will determine all homomorphisms between weyl modules for sl3 when p 3 and provide a recursive procedure for determining the composition factors arising in the image or kernel of such maps in most cases from these results we will also classify all homomorphisms between specht modules for the symmetric groups corresponding to three part partitions when p 3 after a section of preliminaries we review the sl3 data concerning p filtrations that we will need from 21 this describes certain filtrations of induced modules which will allow us to proceed by induction together with the set of p good homomorphisms which will be fundamental in our later constructions we also recall a theorem of carter and payne 4 on the existence of certain homomorphisms these will be the two key sets of data which we need to determine all possible homomorphisms with the notation developed up to that point in place in section 4 we can give the strategy to be followed in the remainder of the paper and in particular the translation functor arguments

an augmented lagrangian method for parameter identifications in parabolic systems the identification of parameters in parabolic systems is formulated as a constrained minimization problem combining the output least squares and the equation error method the minimization problem is then proved to be equivalent to the saddle point problem of an augmented lagrangian

hypersurfaces with constant scalar curvature in space forms let rn l c be an n 1 dimensional riemannian manifold with constant sectional curvature c we also call it space form when c 1 r l c s l i e n 1 dimensional unit sphere space when c o rn t c e n l i e n 1 dimensional euclidean space let m be an n dimensional compact hypersurface in rn l c and el e a local orthonormal frame field on m col con its dual coframe field then the second fundamental form of m is

convergence rates for total variation regularization of coefficient identification problems in elliptic equations ii abstract we investigate the convergence rates for total variation regularization of the problem of identifying i the coefficient q in the neumann problem for the elliptic equation div q u f in q u n g on ii the coefficient a in the neumann problem for the elliptic equation u a u f in u n g on r d d 1 when u is imprecisely given by z h 1 u z h 1 0 we regularize these problems by correspondingly minimizing the strictly convex functionals 1 2 q u q z 2 d x 1 2 q l 2 2 q and 1 2 u a z 2 d x 1 2 a u a z 2 d x 1 2 a l 2 2 a over admissible sets where u q u a is the solution of the first second neumann boundary value problem 0 is the regularization parameter taking the solutions of these optimization problems as the regularized solutions to the corresponding identification problems we obtain the convergence rates of them to the solution of the inverse problem in the sense of the bregman distance and in the l 2 norm under relatively simple source conditions without the smallness requirement on the source functions