degenerate diffusion and the stefan problem on etudie le probleme i u t u xx f x u dans 0 1 r u 0 t 0 u 1 t 0 dans r u x 0 u 0 x dans 0 1 avec certaines hypotheses sur f et u 0 on etudie le caractere des solutions quand s annule sur un intervalle

dirichlet conditions at infinity for parabolic and elliptic equations we investigate existence and uniqueness of bounded solutions of parabolic equations with unbounded coefficients in rn r under specific assumptions we establish existence of solutions satisfying prescribed conditions at infinity depending on the direction along which infinity is approached moreover the large time behavior of such solutions is addressed we consider also elliptic equations in rn with similar conditions at infinity

the first sign change of fourier coefficients of cusp forms let f sum no a n q n a n real be an arbitrary nonzero cusp form of even integral weight k geq 2 on gamma 0 n square free n we obtain an effective bound that the first sign change of a n occurs

on multiple fixed sign solutions of a discrete system with hermite boundary conditions abstract we consider the discrete system m u i k p i k u 1 k u 2 k u n k k 0 1 n 1 i n together with hermite boundary conditions j u i k 0 j 0 m 1 1 r 1 i n where r 2 m 1 for 1 r 1rm m and k s are integers such that 0 k1

blow up for a porous medium equation with a localized source in this paper we investigate the blow up properties of the positive solutions to a localized porous medium equation v t dv m av p 1v q 1 x 0 t subject to homogeneous dirichlet condition and positive initial datum v 0 x under appropriate hypotheses we establish the local existence and obtain that in the case of p 1 q 1m the solution of the above problem blows up for large initial datum while it admits a global solution for small initial datum moreover for the special case p 1 0 q 1 m and a is large under an additional hypothesis on the initial datum we can also obtain the asymptotic behavior of the blow up solution

splitting dense columns in sparse linear systems abstract we consider systems of equations of the form aa t x b where a is a sparse matrix having a small number of columns which are much denser than the other columns these dense columns in a cause aat to be very or even completely dense which greatly limits the effectiveness of sparse matrix techniques for directly solving the above system of equations in the literature on interior point methods for linear programming the usual technique for dealing with this problem is to split a into a sparse part s and a dense part d a s d and to solve systems involving aat in terms of the solution of systems involving sst using either conjugate gradient techniques or the sherman morrison woodbury formula this approach has the difficulty that sst is often rank deficient even when aat has full rank in this paper we propose an alternative method which avoids the rank deficiency problem and at the same time allows for the effective use of sparse matrix techniques the resulting algorithm is both efficient and robust

quenching for solutions of a plasma type equation here 0 l the so called slow diffusion case the analysis will be carried out in the manner of 5 in which levine gave a complete qualitative study of problem i with m 1 the plan of our paper is as follows in the next section we present the comparison theorem and local existence of solutions for i in the third section we characterize the set of stationary solutions of i finally in the last section we establish stability and quenching results for problem i

an active set method for single cone second order cone programs we develop an active set method for solving second order cone programs that may have an arbitrary number of linear constraints but are restricted to having only one second order cone constraint problems of this form arise in the context of robust optimization and trust region methods the proposed active set method exploits the fact that a second order cone program with only one second order cone constraint and no inequality constraints can be solved in closed form

universal bounds for global solutions of a forced porous medium equation we show that in a smooth bounded domain rn n 2 all global nonnegative solutions of ut um up with zero boundary data are uniformly bounded in by a constant depending on p and but not on u0 provided that 1 m p n 1 n 1 m furthermore we prove an a priori bound in l 0 depending on u0 l under the optimal condition 1 m p n 2 n 2 m

the blow up rate for a degenerate parabolic equation with a non local source abstract in this paper we establish the local existence of the solution and the finite time blow up result for the equation v v m xx a l l v q dx x l l 0 moreover it is proved that the solution has global blow up and there exist constants c 1 c 2 such that c 1 t 1 1 q 1 max x l l v x c 2 t 1 1 q 1 where t 1 is the blow up time

reaction diffusion equations in one dimension particular solutions and relaxation abstract reaction diffusion equations for the concentration of one species in one spatial dimension are considered where the diffusion coefficient as well as creation and annihilation terms are monomials when the exponent of the annihilation term is smaller than the one of the creation term unstable equilibrium solutions may exist in the opposite case travelling wave solutions are found in phase space yielding the value of speed even when the wave form cannot be written in closed form the stability of some solutions is studied numerically showing their robustness in the case of nonlinear diffusion it is found that localized initial conditions evolve to the stable steady state via the travelling waves the invasion of the stable state into the unstable one is via a travelling front with the largest possible gradient this front can be interpreted as the final result of the growth of the most unstable mode the exact solutions allow a modulation approach to study the problem with slowly varying coefficients it is shown that when the creation term is of compact support in space equilibria of compact support are also obtained

computational experience with exterior point algorithms for the transportation problem an experimental computational study to compare the classical primal simplex algorithm and the exterior point algorithms for the transportation problem tp is presented totally four algorithms are compared on uniformly randomly generated test problems the results are very encouraging for one of the competitive algorithms in particular a dual forest exterior point algorithm is on average up to 4 5 times faster than network simplex algorithm on tps of size 300x300 and for all classes this result leads into corresponding savings in computational time from the computational performance we conclude that as the problem size increases exterior point algorithm get relatively faster

product form cholesky factorization in interior point methods for second order cone programming second order cone programming socp problems are typically solved by interior point methods as in linear programming lp interior point methods can in theory solve socps in polynomial time and can in practice exploit sparsity in the problem data specifically when cones of large dimension are present the density that results in the normal equations that are solved at each iteration can be remedied in a manner similar to the treatment of dense columns in an lp here we propose a product form cholesky factorization pfcf approach and show that it is more numerically stable than the alternative sherman morrison woodbury approach we derive several pfcf variants and compare their theoretical perfomance finally we prove that the elements of l in the cholesky factorizations ldlt that arise in interior point methods for socp are uniformly bounded as the duality gap tends to zero as long as the iterates remain is some conic neighborhood of the cental path

the augmented system variant of ipms in two stage stochastic linear programming computation abstract the application of interior point methods ipm to solve the deterministic equivalent of two stage stochastic linear programming problems is a known and natural idea experiments have proved that among the interior point methods the augmented system approach gives the best performance on these problems however most of their implementations encounter numerical difficulties in certain cases which can result in loss of efficiency we present a new approach for the decomposition of the augmented system which automatically exploits the special behavior of the problems we show that the suggested approach can be implemented in a fast and numerically robust way by solving a number of large scale two stage stochastic linear programming problems the comparison of our solver with fo1aug which is considered as a state of the art augmented system implementation of interior point methods is also given

modified cholesky factorizations in interior point algorithms for linear programming we investigate a modified cholesky algorithm typical of those used in most interior point codes for linear programming cholesky based interior point codes are popular for three reasons their implementation requires only minimal changes to standard sparse cholesky algorithms allowing us to take full advantage of software written by specialists in that area they tend to be more efficient than competing approaches that use alternative factorizations and they perform robustly on most practical problems yielding good interior point steps even when the coefficient matrix of the main linear system to be solved for the step components is ill conditioned we investigate this surprisingly robust performance by using analytical tools from matrix perturbation theory and error analysis illustrating our results with computational experiments finally we point out the potential limitations of this approach

on geometrical properties of preconditioners in ipms for classes of block angular problems one of the most efficient interior point methods for some classes of block angular structured problems solves the normal equations by a combination of cholesky factorizations and preconditioned conjugate gradient for respectively the block and linking constraints in this work we show that the choice of a good preconditioner depends on geometrical properties of the constraint structure in particular the principal angles between the subspaces generated by the diagonal blocks and the linking constraints can be used to estimate ex ante the efficiency of the preconditioner numerical validation is provided with some generated optimization problems an application to the solution of multicommodity network flow problems with nodal capacities and equal flows of up to 64 million variables and up to 7 9 million constraints is also presented these computational results also show that predictor corrector directions combined with iterative system solves can be a competitive option for large instances

new preconditioners for kkt systems of network flow problems we propose a new set of preconditioners for the iterative solution via a preconditioned conjugate gradient pcg method of the kkt systems that must be solved at each iteration of an interior point ip algorithm for the solution of linear min cost flow mcf problems these preconditioners are based on the idea of extracting a proper triangulated subgraph of the original graph which strictly contains a spanning tree we define a new class of triangulated graphs called brother connected trees bcts and discuss some fast heuristics for finding bcts of large weight computational experience shows that the new preconditioners can complement tree preconditioners outperforming them both in iterations count and in running time on some classes of graphs

positive solutions for a higher order four point boundary value problem with a p laplacian in this paper we study the existence of positive solutions of the following nth order four point boundary value problem with one dimensional p laplacian f p u n 1 h t f t u t u t u n 2 t 0 0 3 u i 0 0 0 i n 3 u n 1 0 au n 2 x 0 n 3 u n 1 1 bu n 2 h 0 n 3 where f p s s p 2s p 1 0 a 1 x 0 b 11 h 0 x h 1 by using a fixed point theorem in cones the existence of a positive solution and multiple positive solutions is obtained also at the end of this paper we present a generalization of this problem

an investigation of interior point algorithms for the linear transportation problem recently resende and veiga it siam j optim 3 1993 pp 516 537 proposed an efficient implementation of the dual affine da interior point algorithm for the solution of linear transportation models with integer costs and right hand side coefficients this procedure incorporates a preconditioned conjugate gradient pcg method for solving the linear system that is required in each iteration of the da algorithm in this paper we introduce an incomplete qr decomposition iqrd preconditioning for the pcg algorithm computational experience shows that the iqrd preconditioning is appropriate in this instance and is more efficient than the preconditioning introduced by resende and veiga we also show that the primal dual pd and the predictor corrector pc interior point algorithms can also be implemented by using the same type of technique a comparison among these three algorithms is included and indicates that the pd and pc algorithms are more appropriate for the solution of transportation problems with well scaled cost and right hand side coefficients and assignment problems with poorly scaled cost coefficients on the other hand the da algorithm seems to be more efficient for assignment problems with well scaled cost coefficients and transportation problems whose cost coefficients are badly scaled

stabilization of solutions of a degenerate nonlinear diffusion problem i 4 u f u in l l x r u tl t o in r u x 0 uo x in l l where m 1 is a parameter f is locally lipschitz continuous f 0 0 and u is bounded problems of this form arise in a number of areas of science for instance in models for gas or fluid flow in porous media 2 and for the spread of certain biological populations 13 161 this paper is divided into two parts in part i we consider what may be called the motivating example problem i which consists of problem i with the special choice f u u 1 u u a 1 for suitably restricted parameters a we begin by describing in detail the set l of nonnegative equilibrium solutions of problem i clearly 8 l contains the trivial solution u 0 for all l 0 write 8 l e l o in the description of z l there are two critical parameter values lo and l1 with 0 lo l1 j we show that i g l 4 for 0 l lo

blow up for a degenerate reaction diffusion system with nonlinear nonlocal sources this paper investigates the global existence and blow up of nonnegative solution of the systemu email protected m u p email protected wv q 1dx v email protected n v p email protected wu q 2dx x t email protected 0 t with homogeneous dirichlet boundary conditions where email protected r n is a bounded domain with smooth boundary email protected m n 1 p 1 p 2 q 1 q 2 0 the results depend crucially on the number p i q i m n the domain w and the initial data u 0 x v 0 x moreover we obtain the blow up rate of the blow up solution under some appropriate hypotheses

triple positive solutions of conjugate boundary value problems ii we consider the following boundary value problems 1 n py n a t h y n 2 t 0 1 y i 0 0 0 i p 1 y i 1 0 0 i n p 1 and 1 n p ny f k y y n 1y n 2 0 k m iy 0 0 i p 1 iy m p 1 0 0 i n p 1 where 1 p n 1 is fixed by employing fixed point theorems for operators on a cone existence criteria are developed for multiple at least three positive solutions of the boundary value problems as an application we also establish the existence of radial solutions of certain partial difference equations several examples are included to dwell upon the importance of the results obtained

simple linear time algorithms to test chordality of graphs test acyclicity of hypergraphs and selectively reduce acyclic hypergraphs chordal graphs arise naturally in the study of gaussian elimination on sparse symmetric matrices acyclic hypergraphs arise in the study of relational data bases rose tarjan and lueker siam j c

coefficient of maass forms and the siegel zero with an appendix by dorian goldfeld jeffrey hoffstein and daniel lieman

existence of global solution for reaction diffusion systems with density dependent diffusion on demontre l existence de solutions globales pour un systeme de reaction diffusion a diffusion dependant de la densite du type u id t u i mi f i u x t 0 i 1 2 m u u 1 u 2 u m avec des conditions aux limites de derichlet

fourier coefficients of harmonic weak maass forms and the partition function in a recent paper bruinier and ono proved that certain harmonic weak maass forms have the property that the fourier coefficients of their holomorphic parts are algebraic traces of weak maass forms evaluated on heegner points as a special case they obtained a remarkable finite algebraic formula for the hardy ramanujan partition function p n which counts the number of partitions of a positive integer n we establish an asymptotic formula with a power saving error term for the fourier coefficients in the bruinier ono formula as a consequence we obtain a new asymptotic formula for p n one interesting feature of this formula is that the main term contains essentially 3 cdot h 24n 1 fewer terms than the truncated main term in rademacher s exact formula for p n where h 24n 1 is the class number of the imaginary quadratic field bbb q sqrt 24n 1

branches of positive and free boundary solutions for some singular quasilinear elliptic problems we study the existence and multiplicity of solutions strictly positive or nonnegative having a free boundary the boundary of the set where the solution vanishes of some one dimensional quasilinear problems of eigenvalue type with possibly singular nonlinear terms

global bifurcation of steady state solutions in this paper we study the bifurcation of steady state solutions of a reaction diffusion equation in one space variable the steady state solutions satisfy the equation a f u 0 on the interval l 0 or 0 for some nonzero function c c a for the neumann problem we use entirely different techniques to prove that s is never critical for any cubic polynomial j this implies at once that the neumann problem can have at most one nonconstant solution having a given number of maxima or minima this solution is necessarily strongly nondegenerate in the sense that zero is not contained in the spectrum of the linearized operator see 2 for the dirichlet problem the situation is far more complicated and the bifurcation diagrams undergo qualitative changes depending on the positions of the roots off for example fig 1 shows the bifurcation diagram for the positive solutions for two different cubic functions of the form f u a u u b u c it is interesting to note however that in every case we study there are at most three solutions to the dirichlet problem for each

the stefan problem with heating appearance and disappearance of a mushy region on considere un materiau qui est initialement dans l etat solide et qui sous l action de la chaleur commence la fusion on decrit la region dans laquelle le materiau n est ni un solide ni un liquide

second order cone programming second order cone programming socp problems are convex optimization problems in which a linear function is minimized over the intersection of an affine linear manifold with the cartesian product of second order lorentz cones linear programs convex quadratic programs and quadratically constrained convex quadratic programs can all be formulated as socp problems as can many other problems that do not fall into these three categories these latter problems model applications from a broad range of fields from engineering control and finance to robust optimization and combinatorial optimization on the other hand semidefinite programming sdp that is the optimization problem over the intersection of an affine set and the cone of positive semidefinite matrices includes socp as a special case therefore socp falls between linear lp and quadratic qp programming and sdp like lp qp and sdp problems socp problems can be solved in polynomial time by interior point methods the computational effort per iteration required by these methods to solve socp problems is greater than that required to solve lp and qp problems but less than that required to solve sdp s of similar size and structure because the set of feasible solutions for an socp problem is not polyhedral as it is for lp and qp problems it is not readily apparent how to develop a simplex or simplex like method for socp while socp problems can be solved as sdp problems doing so is not advisable both on numerical grounds and computational complexity concerns for instance many of the problems presented in the survey paper of vandenberghe and boyd vb96 as examples of sdps can in fact be formulated as socps and should be solved as such in 2 3 below we give socp formulations for four of these examples the convex quadratically constrained quadratic programming qcqp problem problems involving fractional quadratic functions rutcor rutgers university e mail alizadeh rutcor rutgers edu research supported in part by the u s national science foundation grant ccr 9901991 ieor columbia university e mail gold ieor columbia edu research supported in part by the department of energy grant de fg02 92er25126 national science foundation grants dms 94 14438 cda 97 26385 and dms 01 04282

accelerated multigrid for graph laplacian operators we consider multigrid type techniques for the numerical solution of large linear systems whose coefficient matrices show the structure of weighted graph laplacian operators we combine ad hoc coarser grid operators with iterative techniques used as smoothers empirical tests suggest that the most effective smoothers have to be of krylov type with subgraph preconditioners while the projectors which define the coarser grid operators have to be designed for maintaining as much as possible the graph structure of the projected matrix at the inner levels the main theoretical contribution of the paper is the characterization of necessary and sufficient conditions for preserving the graph structure in this framework it is possible to explain why the classical projectors inherited from differential equations are good in the differential context and why they may behave unsatisfactorily for unstructured graphs furthermore we report and discuss several numerical experiments showing that our approach is effective even in very difficult cases where the known approaches are rather slow as a conclusion the main advantage of the proposed approach is the robustness since our multigrid type technique behaves uniformly well in all cases without requiring either the setting or the knowledge of critical parameters as it happens when using the best known preconditioned krylov methods

an infeasible exterior point simplex algorithm for assignment problems the so called modified hung rom algorithm based upon theoretical considerations of hirsch paths seems to be one of the most efficient algorithms for assignment problems since any two basic feasible solutions to a linear problem can always be connected with a short simplex path passing through the infeasible region development of algorithms based upon theoretical considerations on infeasible paths seems to be of great practical interest this paper presents an algorithm of this kind for assignment problems

artificial free simplex algorithm based on the non acute constraint relaxation solving a general linear programming problem using the simplex algorithm relies on introducing artificial variables that creates a large search space this paper presents the non acute constraint relaxation technique that not only eliminates the need for artificial variables but also reduces the start up time to solve the initial relaxation problem to guarantee the optimal solution or infeasibility or unboundedness of a linear programming problem the algorithm reinserts the non acute constraints back to the relaxation problem the results of this algorithm are superior than the original simplex algorithm with artificial variables for a linear programming problem with a large number of acute constraints

a product form cholesky factorization method for handling dense columns in interior point methods for linear programming cholesky factorization has become the method of choice for solving the symmetric system of linear equations arising in interior point methods ipms for linear programming lp its main advantages being numerical stability and efficiency for sparse systems however in the presence of dense columns there is dramatic loss of efficiency a typical approach to remedy this problem is to apply the sherman morrison woodbury smw update formula to the dense part this approach while being very efficient is not numerically stable here we propose using product form cholesky factorization to handle dense columns the proposed approach is essentially as stable as the original cholesky factorization and nearly as efficient as the smw approach we demonstrate these properties both theoretically and computationally a key part of our theoretical analysis is the proof that the elements of the cholesky factors of the matrices that arise in ipms for lp are uniformly bounded as the duality gap converges to zero

improving an interior point approach for large block angular problems by hybrid preconditioners abstract the computational time required by interior point methods is often dominated by the solution of linear systems of equations an efficient specialized interior point algorithm for primal block angular problems has been used to solve these systems by combining cholesky factorizations for the block constraints and a conjugate gradient based on a power series preconditioner for the linking constraints in some problems this power series preconditioner resulted to be inefficient on the last interior point iterations when the systems became ill conditioned in this work this approach is combined with a splitting preconditioner based on lu factorization which works well for the last interior point iterations computational results are provided for three classes of problems multicommodity flows oriented and nonoriented minimum distance controlled tabular adjustment for statistical data protection and the minimum congestion problem the results show that in most cases the hybrid preconditioner improves the performance and robustness of the interior point solver in particular for some block angular problems the solution time is reduced by a factor of 10

a specialized interior point algorithm for multicommodity network flows despite the efficiency shown by interior point methods in large scale linear programming they usually perform poorly when applied to multicommodity flow problems the new specialized interior point algorithm presented here overcomes this drawback this specialization uses both a preconditioned conjugate gradient solver and a sparse cholesky factorization to solve a linear system of equations at each iteration of the algorithm the ad hoc preconditioner developed by exploiting the structure of the problem is instrumental in ensuring the efficiency of the method an implementation of the algorithm is compared to state of the art packages for multicommodity flows the computational experiments were carried out using an extensive set of test problems with sizes of up to 700 000 variables and 150 000 constraints the results show the effectiveness of the algorithm

asymptotic analysis for a localized nonlinear diffusion equation in this paper we study a localized nonlinear diffusion equation u t du m l 1u p l 2u q 0 t subject to null dirichlet boundary condition with p q 0 max p q m 1 and l 1 l 2 0 we investigate interactions among the localized and local sources nonlinear diffusion with the zero boundary value condition to establish blow up rates and uniform blow up profiles of solutions under different dominations in addition as results of the interactions of multiple nonlinearities the blow up sets of solutions namely total versus single point blow up of solutions are also determined

distribution of mass of holomorphic cusp forms we prove an upper bound for the l4 norm and for the l2 norm restricted to the vertical geodesic of a holomorphic hecke cusp form f of large weight k the method is based on watson s formula and estimating a mean value of certain l functions of degree 6 further applications to restriction problems of siegel modular forms and subconvexity bounds of degree 8 l functions are given

mollification of the fourth moment of automorphic l functions and arithmetic applications we compute the asymptotics of twisted fourth power moments of modular l functions of large prime level near the critical line this allows us to prove some new non vanishing results on the central values of automorphic l functions in particular those obtained by base change from gl 2 q to gl 2 k for k a cyclic field of low degree

a generalized cubic moment and the petersson formula for newforms using a cubic moment we prove a weyl type subconvexity bound for the quadratic twists of a holomorphic newform of square free level trivial nebentypus and arbitrary even weight this generalizes work of conrey and iwaniec in that the newform that is being twisted may have arbitrary square free level and also that the quadratic character may have even conductor one of the new tools developed in this paper is a more general petersson formula for newforms of square free level

a dantzig wolfe like variant of karmarkar s interior point linear programming algorithm we show that a variant of karmarkar s projective algorithm for linear programming can be viewed as following the approach of dantzig wolfe decomposition at each iteration the current primal feasible solution generates prices which are used to form a simple subproblem the solution to the subproblem is then incorporated into the current feasible solution with a suitable choice of stepsize a constant reduction in potential function is achieved at each iteration we also use our analysis to motivate a new primal simplex pivot rule that is closely related to rules used by e klotz and l schrage

boundary regularity for the porous medium equation we study the boundary regularity of solutions to the porous medium equation u t delta u m in the degenerate range m 1 in particular we show that in cylinders the dirichlet problem with positive continuous boundary data on the parabolic boundary has a solution which attains the boundary values provided that the spatial domain satisfies the elliptic wiener criterion this condition is known to be optimal and it is a consequence of our main theorem which establishes a barrier characterization of regular boundary points for general not necessarily cylindrical domains in bf r n 1 one of our fundamental tools is a new strict comparison principle between sub and superparabolic functions which makes it essential for us to study both nonstrict and strict perron solutions to be able to develop a fruitful boundary regularity theory several other comparison principles and pasting lemmas are also obtained in the process we obtain a rather complete picture of the relation between sub superparabolic functions and weak sub supersolutions

the characterization of reaction convection diffusion processes by travelling waves it has long been known that the heat equation displays infinite speed of propagation this is to say that if the initial data are nonnegative and have nonempty compact support the solution of an initial value problem is positive everywhere after any infinitesimal time however since the nineteen fifties it has also been known that certain nonlinear diffusion equations of degenerate parabolic type do not display this phenomenon for these equations the generalized solution of an initial value problem with compactly supported initial data will have bounded support with respect to the spatial variable at all times in this paper the necessary and sufficient criterion for finite speed of propagation for the general nonlinear reaction convection diffusion equation formula is determined the assumptions on the coefficientsa bandcare such that the classification unifies and generalizes previously known results the technique employed is comparision of an arbitrary solution of the equation with suitably constructed travelling wave solutions and subsolutions basically the central conclusion is that the equation exhibits finite speed of propagation if and only if it admits a travelling wave solution with bounded support concurrently the search for a travelling wave solution with bounded support can be reduced to the study of a singular nonlinear integral equation whose solution must satisfy a certain constraint

efficient svm training using low rank kernel representations svm training is a convex optimization problem which scales with the training set size rather than the feature space dimension while this is usually considered to be a desired quality in large scale problems it may cause training to be impractical the common techniques to handle this difficulty basically build a solution by solving a sequence of small scale subproblems our current effort is concentrated on the rank of the kernel matrix as a source for further enhancement of the training procedure we first show that for a low rank kernel matrix it is possible to design a better interior point method ipm in terms of storage requirements as well as computational complexity we then suggest an efficient use of a known factorization technique to approximate a given kernel matrix by a low rank matrix which in turn will be used to feed the optimizer finally we derive an upper bound on the change in the objective function value based on the approximation error and the number of active constraints support vectors this bound is general in the sense that it holds regardless of the approximation method

existence uniqueness and qualitative properties of the solution of a degenerate nonlinear parabolic system abstract in this paper we are concerned with the study of the existence of solutions of a nonlinear parabolic system with density dependent diffusion subject to homogeneous third type boundary conditions a comparison result is shown that allows the study of the asymptotic behavior of the solutions via the same methods used for systems with classical diffusion finally an application of the results to an epidemic system is presented sufficient conditions are given for the positivity of the solution of this system

blowup in diffusion equations a survey this paper deals with quasilinear reaction diffusion equations for which a solution local in time exists if the solution ceases to exist for some finite time we say that it blows up in contrast to linear equations blowup can occur even if the data are smooth and well defined for all times depending on the equation either the solution or some of its derivatives become singular we shall concentrate on those cases where the solution becomes unbounded in finite time this can occur in quasilinear equations if the heat source is strong enough there exist many theoretical studies on the question on the occurrence of blowup in this paper we shall recount some of the most interesting criteria and most important methods for analyzing blowup the asymptotic behavior of solutions near their singularities is only completely understood in the special case where the source is a power a better knowledge would be useful also for their numerical treatment thus not surprisingly the numerical analysis of this type of problems is still at a rather early stage the goal of this paper is to collect some of the known results and algorithms and to direct the attention to some open problems

solving symmetric indefinite systems in an interior point method for linear programming we describe an implementation of a primal dual path following method for linear programming that solves symmetric indefinite augmented systems directly by bunch parlett factorization rather than reducing these systems to the positive definite normal equations that are solved by cholesky factorization in many existing implementations the augmented system approach is seen to avoid difficulties of numerical instability and inefficiency associated with free variables and with dense columns in the normal equations approach solving the indefinite systems does incur an extra overhead whose median is about 40 in our tests but the augmented system approach proves to be faster for a minority of cases in which the normal equations have relatively dense cholesky factors a detailed analysis shows that the augmented system factorization is reliable over a fairly large range of the parameter settings that control the tradeoff between sparsity and numerical stability

the asymptotic distribution of traces of maass poincare series abstract we establish an asymptotic formula with a power savings in the error term for traces of cm values of a family of maass poincare series which contains the modular j function as a special case by work of borcherds 1998 2 zagier 2002 31 and bringmann and ono 2007 4 these traces are fourier coefficients of half integral weight weakly holomorphic modular forms and maass forms

on the waldspurger formula and the metaplectic ramanujan conjecture over number fields abstract in this paper by inputting the bessel identities over the complex field in previous work of the authors the waldspurger formula of baruch and mao is extended from totally real fields to arbitrary number fields this is applied to give a non trivial bound towards the ramanujan conjecture for automorphic forms on the metaplectic group sl 2 for the first time in the generality of arbitrary number fields

existence and iteration of n symmetric positive solutions for a singular two point boundary value problem let n be an arbitrary natural number in this paper we consider the existence of n symmetric positive solutions and establish a corresponding iterative scheme for the two point boundary value problem w t h t f w t 0 0 t 1 w 0 w 0 0 1 w 1 0 the main tool is the monotone iterative technique here the coefficient h t is symmetric on 0 1 and may be singular at both end points t 0 and t 1

global bifurcation of positive radial solutions for an elliptic system in reactor dynamics in this paper we are concerned with the existence of positive radial solutions of the elliptic system email protected email protected f x u r 1 0 is a constant m 0 is a parameter and 0 0 is continuous and f t s 0 for all t s r 1 r 2 x 0 under some appropriate conditions on the nonlinearity f we show that the above system possesses at least one positive radial solution for any email protected 0 the proof of our main results is based upon bifurcation techniques

integral moments of l functions we give a new heuristic for all of the main terms in the integral moments of various families of primitive l functions the results agree with previous conjectures for the leading order terms our conjectures also have an almost identical form to exact expressions for the corresponding moments of the characteristic polynomials of either unitary orthogonal or symplectic matrices where the moments are defined by the appropriate group averages this lends support to the idea that arithmetical l functions have a spectral interpretation and that their value distributions can be modelled using random matrix theory numerical examples show good agreement with our conjectures

a twisted motohashi formula and weyl subconvexity for functions of weight two cusp forms we derive a motohashi type formula for the cubic moment of central values of l functions of level q cusp forms twisted by quadratic characters of conductor q previously studied by conrey and iwaniec and young corollaries of this formula include weyl subconvex bounds for l functions of weight two cusp forms twisted by quadratic characters and estimates towards the ramanujan petersson conjecture for fourier coefficients of weight 3 2 cusp forms

solving mixed sparse dense linear least squares problems by preconditioned iterative methods the efficient solution of large linear least squares problems in which the system matrix a contains rows with very different densities is challenging previous work has focused on direct methods for problems in which a has a few relatively dense rows these rows are initially ignored a factorization of the sparse part is computed using a sparse direct solver and then the solution is updated to take account of the omitted dense rows in some practical applications the number of dense rows can be significant and for very large problems using a direct solver may not be feasible we propose processing rows that are identified as dense separately within a conjugate gradient method using an incomplete factorization preconditioner combined with the factorization of a dense matrix of size equal to the number of dense rows numerical experiments on large scale problems from real applications are used to illustrate the effectiveness of our approach the results demonstrate that we can efficiently solve prob

positive solutions of singular differential equations on measure chains this paper is concerned with singular differential equations on measure chains theorems on the existence of positive solutions and eigenvalue intervals are obtained which extend some existing results

on scaled projections and pseudoinverses abstract let x be a matrix of full column rank and let d be a diagonal matrix with positive diagonal elements the weighted pseudoinverse defined by x d x t dx 1 x t d and the associated oblique projection p d xx d arise in many applications in this paper we show that the norms of both matrices are bounded by numbers that are independent of d

hybrid bounds for twisted l functions the aim of this paper is to derive bounds on the critical line s 1 for l functions attached to twists f of a primitive cusp form f of level n and a primitive character modulo q that break convexity simultaneously in the s and q aspects if f has trivial nebentypus it is shown that

a combinatorial interior point method for network flow problems for solving minimum cost flow problems we develop a combinatorial interior point method based on a variant of the algorithm of karmarkar described in gonzaga 3 4 gonzaga proposes search directions generated by projecting certain directions onto the nullspace ofa by the special combinatorial structure of networks any projection onto the nullspace ofa can be interpreted as a flow in the incremental graph ofg in particular to evaluate the new search direction it is sufficient to choose a negative circuit subject to costs on the arcs depending on the current solution that approach results in an o mn2l algorithm wherem denotes the number of vertices n denotes the number of arcs andl denotes the total length of the input data

positive solutions for multi point boundary value problem on the half line this paper presents a variety of existence results for nonlinear multi point boundary value problem on the half line in particular we consider x t px t qx t f t x t 0 t 0 x 0 x 0 i 1nkix i a limt x t ert b r 0 p p2 4q2 existence results are established using fixed point theorems on cone

short time behaviour of a singular solution to the heat equation with absorption on considere l evolution aux temps petits de l interface qui apparait dans le probleme aux limites u t u xx u p u o t 1 t 0 u x o 0 x 0 pour p 1 on construit une solution interieure d ordre zero consistante avec une interface mobile ou u est zero

a decision support system for a real vehicle routing problem abstract the vehicle routing problem has been widely studied in the literature mainly because of the real world logistics and transportation problems related to it in the present paper a new two stage exact approach for solving a real problem is shown along with decision making software in the first stage all the feasible routes are generated by means of an implicit enumeration algorithm afterwards an integer programming model is designed to select in the second stage the optimum routes from the set of feasible routes the integer model uses a number of 0 1 variables ranging from 2000 to 15 000 and gives optimum solutions in an average time of 60 seconds for instances up to 60 clients an interactive decision support system was also developed the system was tested with a set of real instances and in a worst case scenario up to 60 clients the routes obtained ranged from a 7 to 12 reduction in the distance travelled and from a 9 to 11 reduction in operational costs

the stefan problem with mushy regions continuity of the interface on considere un probleme de stefan a une dimension avec un terme source sous l hypothese que le profil initial est monotone on obtient la continuite des frontieres libres le solide le melange et la region liquide

stabilization of solutions of nonlinear and degenerate evolution equations on etudie le comportement asymptotique des solutions bornees des equations de la forme u t u f x u dans r u x o u 0 x dans u x t u 1 x t dans r ou est un domaine borne de r n avec de classe c 2 0 1