quantum corrected drift diffusion models solution fixed point map and finite element approximation this article deals with the analysis of the functional iteration denoted generalized gummel map ggm proposed in c de falco a l lacaita e gatti r sacco quantum corrected drift diffusion models for transport in semiconductor devices j comp phys 204 2 2005 533 561 for the decoupled solution of the quantum drift diffusion qdd model the solution of the problem is characterized as being a fixed point of the ggm which permits the establishment of a close link between the theoretical existence analysis and the implementation of a numerical tool which was lacking in previous non constructive proofs n b abdallah a unterreiter on the stationary quantum drift diffusion model z angew math phys 49 1998 251 275 r pinnau a unterreiter the stationary current voltage characteristics of the quantum drift diffusion model siam j numer anal 37 1 1999 211 245 the finite element approximation of the ggm is illustrated and the main properties of the numerical fixed point map discrete maximum principle and order of convergence are discussed numerical results on realistic nanoscale devices are included to support the theoretical conclusions

stark heegner points and the cohomology of quaternionic shimura varieties let f be a totally real field of narrow class number one and let e f be a modular semistable elliptic curve of conductor n 1 l etk f be a non cm quadratic extension with disc k n 1 such that the sign in the functional equation of l e k s is 1 suppose further that there is a prime p n that is inert in k w e describe a p adic construction of points on e which we conjecture to be rational over ring class fields of k f and satisfy a shimura reciprocity law these points are expected to behave like classical heegner points and can be viewed as new instances of the stark heegner point construction of 5 the key idea in our construction is a reinterpretation of darmon s theory of modular symbols and mixed period integrals in terms of group cohomology

the weber problem with regional demand abstract this paper is devoted to the study of the regional weber problem an extension of the weber problem which allows the demand not be concentrated onto a finite set of points the most serious drawback of this formulation from a resolution viewpoint is the high computational cost involved in the evaluation of the objective function a new approach is proposed which requires a low amount of computation and where it is possible to control the error on the approximation this approximation suggests a new methodology to solve the problem this methodology is compared with the existing ones showing its relevance from a practical point of view

collisions and phase vortex interactions in dissipative ginzburg landau dynamics in this paper we describe a natural framework for the vortex dynamics in the parabolic complex ginzburg landau equation in r this general setting does not rely on any assumption of well preparedness and has the advantage to be valid even after collision times we analyze carefully collisions leading to annihilation a new phenomenon is identified the phase vortex interaction related to persistence of low frequency oscillations and leading to an unexpected drift in the motion of vortices

analytical and numerical study of photocurrent transients in organic polymer solar cells abstract this article is an attempt to provide a self consistent picture including existence analysis and numerical solution algorithms of the mathematical problems arising from modeling photocurrent transients in organic polymer solar cells oscs the mathematical model for oscs consists of a system of nonlinear diffusion reaction partial differential equations pdes with electrostatic convection coupled to a kinetic ordinary differential equation ode we propose a suitable reformulation of the model that allows us to prove the existence of a solution in both stationary and transient conditions and to better highlight the role of exciton dynamics in determining the device turn on time for the numerical treatment of the problem we carry out a temporal semi discretization using an implicit adaptive method and the resulting sequence of differential subproblems is linearized using the newton raphson method with inexact evaluation of the jacobian then we use exponentially fitted finite elements for the spatial discretization and we carry out a thorough validation of the computational model by extensively investigating the impact of the model parameters on photocurrent transient times

minimum spanning trees with neighborhoods mathematical programming formulations and solution methods this paper studies minimum spanning trees under incomplete information assuming that it is only known that vertices belong to some neighborhoods that are second order cone representable and distances are measured with a lq norm two mixed integer non linear mathematical programming formulations are presented based on alternative representations of subtour elimination constraints a solution scheme is also proposed resulting from a reformulation suitable for a benders like decomposition which is embedded within an exact branch and cut framework furthermore a mathheuristic is developed which alternates in solving convex subproblems in different solution spaces and is able to solve larger instances the results of extensive computational experiments are reported and analyzed

hida families and rational points on elliptic curves let e be an elliptic curve over q of conductor n mp having a prime p n of multiplicative reduction because e is modular it corresponds to a normalised weight two eigenform on 0 n whose q expansion is denoted f n anq letx hom z p z p z p 1 z zp which contains z as a dense subset by associating to k z the character x xk 2 denote by a u the ring of cp valued p adic analytic functions on a compact open subset u of x hida s theory associates to f a neighborhood u of 2 x which can be assumed for simplicity to be contained in the residue class of 2 modulo p 1 and a formal q expansion

on symmetric power l invariants of iwahori level hilbert modular forms we compute the arithmetic cal l invariants of greenberg benois of twists of symmetric powers of p adic galois representations attached to iwahori level hilbert modular forms under some technical conditions our method uses the automorphy of symmetric powers and the study of analytic galois representations on p adic families of automorphic forms over symplectic and unitary groups combining these families with some explicit plethysm in the representation theory of rm gl 2 we construct global galois cohomology classes with coefficients in the symmetric powers and provide formulae for the cal l invariants in terms of logarithmic derivatives of hecke eigenvalues

the iwasawa main conjecture for semistable abelian varieties over function fields we prove the iwasawa main conjecture over the arithmetic mathbb z p extension for semistable abelian varieties over function fields of characteristic p 0

the p median problem under uncertainty abstract consider the need to currently locate p facilities but it is possible that up to q additional facilities will have to be located in the future there are known probabilities that 0 r q facilities will need to be located the p median problem under uncertainty is to find the location of p facilities such that the expected value of the objective function in the future is minimized the problem is formulated on a graph properties of it are proven an integer programming formulation is constructed and heuristic algorithms are suggested for its solution the heuristic algorithms are modified to reduce the run time by about two orders of magnitude with minimal effect on the quality of the solution optimal solutions for many problems are found effectively by cplex computational results using the heuristic algorithms are presented

a monotone finite element scheme for convection diffusion equations a simple technique is given in this paper for the construction and analysis of a class of finite element discretizations for convection diffusion problems in any spatial dimension by properly averaging the pde coefficients on element edges the resulting finite element stiffness matrix is an m matrix under some mild assumption for the underlying generally unstructured finite element grids as a consequence the proposed edge averaged finite element scheme is particularly interesting for the discretization of convection dominated problems this scheme admits a simple variational formulation it is easy to analyze and it is also suitable for problems with a relatively smooth flux variable some simple numerical examples are given to demonstrate its effectiveness for convection dominated problems

derivative of the standard p adic l function associated with a siegel form this work has greatly bene ted from an excellent long stay at columbia university founded by a fwo travel grant v4 260 14n while the author was a fwo phd fellow at ku leuven

technical note bounds in the generalized weber problem under locational uncertainty an existing analysis of the bounds on the weber problem solution under uncertainty is incorrect for the generalized problem with arbitrary measures of distance we give easily computable ranges on the bounds and state the conditions under which the exact values of the bounds can be found with little computational effort numerical examples illustrate the analysis

a conservative and monotone mixed hybridized finite element approximation of transport problems in heterogeneous domains in this article we discuss the numerical approximation of transport phenomena occurring at material interfaces between physical subdomains with heterogenous properties the model in each subdomain consists of a partial differential equation with diffusive convective and reactive terms the coupling between each subdomain being realized through an interface transmission condition of robin type the numerical approximation of the problem in the two dimensional case is carried out through a dual mixed hybridized finite element method with numerical quadrature of the mass flux matrix the resulting method is a conservative finite volume scheme over triangular grids for which a discrete maximum principle is proved under the assumption that the mesh is of delaunay type in the interior of the domain and of weakly acute type along the domain external boundary and internal interface the stability accuracy and robustness of the proposed method are validated on several numerical examples motivated by applications in biology electrophysiology and neuroelectronics

the iwasawa main conjectures for gl2 we prove the one two and three variable iwasawa greenberg main conjectures for a large class of modular forms that are ordinary with respect to an odd prime p the method of proof involves an analysis of an eisenstein ideal for ordinary hida families for gu 2 2

on the feasible set for the squared euclidean weber problem and applications abstract in this paper we find the set of feasible solution points to the weber location problem with squared euclidean distances when the weights can be at any point in a given set of intervals we prove that this set is a convex polygon the result is then used to solve the minimax regret objective when individual scenarios can be any set of weights in a given set of intervals