a numerical solution of a one dimensional blood flow model moving grid approach we consider a one dimensional blood flow model suitable for larger arteries it consists of a hyperbolic system of two coupled nonlinear equations the model has already been successfully used in practice its numerical solution is usually achieved by means of an explicit taylor galerkin scheme we have proposed a different approach the system can be transformed to characteristic directions emphasizing the physical nature of the problem we solved this system by using an operator splitting on a moving grid

a method for determining exact solutions to a class of nonlinear models based on introduction of differential constraints a nonhomogeneous system of partial differential equations of first order involving two dependent and two independent variables is considered the introduction of suitable differential constraint equations permits to develop an approach to determining exact solutions to the model in point based on the use of the hodograph transformation within the present theoretical framework the governing systems of rate type materials and flows in fluid filled elastic tubes are investigated

the perturbed riemann problem and delta contact discontinuity in chromatography equations abstract in this paper we discuss the perturbed riemann problem for the nonlinear chromatography equations the solutions to the problem are constructed with the method of the splitting delta function in solutions we find another kind of delta contact discontinuity on which both state variables simultaneously contain the dirac delta functions it is quite different from the previous ones on which only one state variable contains the dirac delta function this phenomenon is also predicted theoretically by mazzotti 2009 and mazzotti et al 2010 moreover by studying the limits of the solutions as the perturbed parameter e 0 it can be found that the riemann solutions are stable for such perturbations with the initial data

duality theorems for graded algebras and coalgebras the concepts of smash product and smash coproduct have been proved to be extremely useful tools in the theory of graded rings and graded coalgebras and more recently in the theory of action and coactions of a hopf algebra on an algebra or on a coalgebra once these concepts were defined a natural question appeared how can the smash product resp the smash coproduct be related to a matrix algebra resp to a matrix w x coalgebra the answer is given by the duality theorems proved in 3 for w x graded rings and in 5 for graded coalgebras various duality theorems w x w x for algebras have been proved during the last ten years cf 2 or 10 the purpose of this paper is to study duality for the smash product resp the smash coproduct associated to a g set and a g graded ring resp a g graded coalgebra the mentioned smash product and smash coproduct w x w x w x have been constructed in 10 and 6 it is shown by an example in 12 that for a g graded ring r and a left g set a we do not have a duality

minimal cones and self expanding solutions for mean curvature flows in this paper we study self expanding solutions for mean curvature flows and their relationship to minimal cones in euclidean space ilmanen lectures on mean curvature flow and related equations trieste notes 1995 proved the existence of self expanding hypersurfaces with prescribed tangent cones at infinity if the cone is c 3 alpha regular and mean convex but not area minimizing we can prove that the corresponding self expanding hypersurfaces are smooth embedded and have positive mean curvature everywhere see theorem 1 1 as a result for regular minimal but not area minimizing cones we can give an affirmative answer to a problem arisen by lawson brothers in proc sympos pure math 44 441 464 1986

application of space time ce se method to shallow water magnetohydrodynamic equations in this article we apply a space time conservation element and solution element ce se method for the approximate solution of shallow water magnetohydrodynamic smhd equations in one and two space dimensions these equations model the dynamics of nearly incompressible conducting fluids for which the evolution is nearly two dimensional with magnetic equilibrium in the third direction in this article we are using a variant of the ce se method developed by zhang et al a space time conservation element and solution element method for solving the two dimensional unsteady euler equations using quadrilateral and hexahedral meshes j comput phys 175 2002 168 199 this method uses structured and unstructured quadrilateral and hexahedral meshes in two and three space dimensions respectively in this method a single conservation element at each grid point is employed for solving conservation laws no matter in one two and three space dimensions the present scheme use the conservation element to calculate flow variables only while the gradients of flow variables are calculated by central differencing reconstruction procedure we give both one and two dimensional test computations a qualitative comparison reveals an excellent agreement with previous published results of wave propagation method and evolution galerkin schemes the one and two dimensional computations reported in this paper demonstrate the remarkable versatility of the present ce se scheme

differential calculus on compact matrix pseudogroups quantum groups the paper deals with non commutative differential geometry the general theory of differential calculus on quantum groups is developed bicovariant bimodules as objects analogous to tensor bundles over lie groups are studied tensor algebra and external algebra constructions are described it is shown that any bicovariant first order differential calculus admits a natural lifting to the external algebra so the external derivative of higher order differential forms is well defined and obeys the usual properties the proper form of the cartan maurer formula is found the vector space dual to the space of left invariant differential forms is endowed with a bilinear operation playing the role of the lie bracket commutator generalized antisymmetry relation and jacobi identity are proved

riemann problem and wave interactions for the one dimensional relativistic string equation in minkowski space abstract in this paper we consider the riemann problem for the one dimensional relativistic string equation in minkowski space it is shown that the delta shock wave will be constructed in the riemann solutions in some certain situations furthermore the interactions of elementary waves including contact discontinuity and delta shock wave are obtained

interactions of delta shock waves for the transport equations with split delta functions this paper is concerned with the interactions of shock waves and the vacuum states between the two contact discontinuities for the transport equations the solutions are obtained constructively when the initial data are three piecewise constant states the global structure and large time asymptotic behaviors of the solutions are analyzed case by case moreover it can be found that the riemann solutions are stable for such small perturbations with initial data by studying the limits of the solutions when the perturbed parameter e tends to zero

galois extensions for co frobenius hopf algebras abstract forhan infinite dimensional co frobenius hopf algebra over a fieldk andaanh comodule algebra the smash producta h ratis linked to the ring of coinvariantsacohby a morita context we use the morita setting to show that for co frobeniush equivalent conditions fora acohto be galois parallel the case ofhfinite dimensional

on the fundamental diagram of traffic flow we present a new fluid dynamical model of traffic flow this model generalizes the model of aw and rascle siam j appl math 60 2000 pp 916 938 and greenberg siam j appl math 62 2001 pp 729 745 by prescribing a more general source term to the velocity equation this source term can be physically motivated by experimental data when taking into account relaxation and reaction time in particular the new model has a linearly unstable regime as observed in traffic dynamics we develop a numerical code that solves the corresponding system of balance laws applying our code to a wide variety of initial data we find the observed inverse lambda shape of the fundamental diagram of traffic flow

exact description of simple wave interactions in multicomponent chromatography nonlinear wave interaction processes for a quasilinear hyperbolic homogeneous system of first order partial differential equations multicomponent chromatography are investigated the wave analysis is worked out by extending to the present multicomponent case the leading ideas of a well established method of approach that was developed for solving initial value wave problems in terms of exact solutions to 2 2 hyperbolic homogeneous systems these interaction processes may model different situations concerning the separation of a mixture into its chemical components several numerical plots are also given in order to illustrate the behavior of the exact wave solutions arising from the analysis that is accomplished

systems of conservation laws with invariant submanifolds systems of conservation laws with coinciding shock and rarefaction curves arise in the study of oil reservoir simulation multicomponent chromatogra phy as well as in the study of nonlinear motion in elastic strings here we characterize this phenomenon by deriving necessary and sufficient conditions on the geometry of a wave curve in order that the shock wave curve coincide with its associated rarefaction wave curve for a system of conservation laws this coinci dence is the one dimensional case of a submanifold of the state variables being invariant for the system of equations and the necessary and sufficient conditions are derived for invariant submanifolds of arbitrary dimension in the case of 2 x 2 systems we derive explicit formulas for the class of flux functions that give rise to the coupled nonlinear conservation laws for which the shock and rarefaction wave curves coincide introduction systems of conservation laws which have coinciding shock and rarefaction curves arise in the study of oil reservoir simulation nonlinear wave motion in elastic strings as well as in multicomponent chromatography 1 4 5 6 9 11 12 these systems have many interesting features the riemann problem for these equations can be explicitly solved in the large and wave interactions have a simplified structure even in the presence of a nonconvex flux function for this reason these systems represent some of the few examples for which the cauchy problem has been solved for arbitrary data of bounded variation also hyperbolic degeneracies appear in each of these systems in the present paper we are concerned with characterizing the phenomenon of coinciding shock and rarefaction curves this phenomenon turns out to be a special case of the general phenomenon of a submanifold of r being invariant for weak solutions of a given system of n conservation laws invariant manifolds of higher dimension also appear in physical conservation equations in which the conserved quantities represent concentrations i e when the concentrations c of any of the species vanish the system must reduce to a lower order system that expresses the conservation of the remaining species thus c 0 defines a manifold which is invariant in the sense that solutions that start on the manifold remain there for all time moreover such an invariant manifold of dimension n 1 is the boundary of an dimensional invariant region in the sense of chueh conley and smoller 14 in the case of

morphisms of relative hopf modules smash products and duality the aim of this paper is to extend a result of h j schneider on endomorphism rings of relative hopf modules 17 theorem 3 2 to the case of projective hopf algebras with bijective antipode and to show the connection between this extension and several duality theorems for hopf algebras a consequence of this generalization is the following if h is a co frobenius hopf algebra over the field k a b is a hopf galois extension and m is a right a h hopf module then considering the usual ring embeddings

elementary wave interactions in blood flow through artery in this paper we consider the riemann problem and interaction of elementary waves for the quasilinear hyperbolic system of conservation laws that arises in blood flow through arteries we study the properties of solution involving shocks and rarefaction waves and establish the existence and uniqueness conditions we show that the riemann problem is solvable for arbitrary initial data under certain condition and construct the condition for no feasible solution finally we present numerical examples with different initial data and discuss all possible interactions of elementary waves

numerical method of characteristics for one dimensional blood flow mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one dimensional nonlinear hyperbolic system describing flow in a single vessel this model is often simulated by computationally intensive methods like finite elements and discontinuous galerkin while some recent applications require more efficient approaches e g for real time clinical decision support phenomena occurring over multiple cardiac cycles iterative solutions to optimization inverse problems and uncertainty quantification further the high speed of pressure waves in blood vessels greatly restricts the time step needed for stability in explicit schemes we address both cost and stability by presenting an efficient and unconditionally stable method for approximating solutions to diagonal nonlinear hyperbolic systems theoretical analysis of the algorithm is given along with a comparison of our method to a discontinuous galerkin implementation lastly we demonstrate the utility of the proposed method by implementing it on small and large arterial networks of vessels whose elastic and geometrical parameters are physiologically relevant

a duality theorem for hopf module algebras let g be a locally compact abelian group acting continuously on a von neumann algebra a via a homomorphism ci of g into aut a in 1973 takesaki showed how an action oi of the dual group g could be naturally defined on the von neumann algebra crossed product d x g and proved that the double crossed product 4 x a g x ti g was naturally isomorphic to where 6 is the ring of all bounded operators on l g this duality theorem for group actions was extended to arbitrary locally compact groups g independently by nakagami landstad and stratilavoiculescu zsido in the mid 1970s this extension required replacing the action of g on x r g by a coaction of g on x a g indeed coactions of g are defined in general and it is proved that jl e x rr g x d g n y 0 6 for any action c of g on and corresponding coaction oi of g on x g a similar theorem is proved reversing the roles of c1 and oi an exposition of this theorem may be found in nakagami takesaki 7 where complete references to the literature may also be found nakagami and takesaki phrase things in a dual fashion to handle the topological subtleties more easily in 2 cohen and montgomery recognized that for finite groups g a coaction of g on an f algebra a where f is a field is just a g grading of a it was known that a g grading of an algebra a is the same as an fg module algebra action of fg the hopf algebra dual to fg on a given these facts they were able to prove the following duality theorems

wave interactions and stability of the riemann solutions for the chromatography equations we prove that the riemann solutions are stable for the chromatography system under the local small perturbations of the riemann initial data the proof is based on the detailed analysis of the wave interactions by applying the method of characteristic analysis it is noteworthy that both the propagation directions of the shock wave s and rarefaction wave r are unchanged when they interact with the contact discontinuity j moreover the global structures and large time asymptotic behaviors of the perturbed riemann solutions are constructed and analyzed case by case c 2009 elsevier inc all rights reserved

a reduction procedure for generalized riemann problems with application to nonlinear transmission lines generalized simple wave solutions to quasilinear hyperbolic nonhomogeneous systems of pdes are obtained through the differential constraint method these solutions prove to be flexible enough to solve generalized riemann problems where discontinuous initial data are involved within such a theoretical framework the governing model of nonlinear transmission lines is investigated throughout

a note on front tracking for the keyfitz kranzer system abstract a front tracking method is developed for the n n symmetric keyfitz kranzer system and convergence of the approximations to the strong generalized entropy solution of the system as defined by panov e y panov on the theory of generalized entropy solutions of the cauchy problem for a class of nonstrictly hyperbolic systems of conservation laws sb math 191 2000 121 150 is proved we also present numerical examples and compare the front tracking approximation with the approximations computed by two finite difference upwind schemes

hodograph transformation and differential constraints for wave solutions to 2 2 quasilinear hyperbolic nonhomogeneous systems the differential constraint method is used to work out a reduction approach to determine solutions in a closed form to the highly nonlinear hodograph system arising from 2 2 hyperbolic nonhomogeneous models these solutions inherit all of the features of the standard wave solutions obtainable via the classical hodograph transformation and in the meantime incorporate the dissipative effects induced on wave processes by the source like term involved in the governing equations within such a theoretical framework the problem of integrating the standard linear hodograph system associated with 2 2 homogeneous models is also revisited and a number of results obtained elsewhere of relevant interest in wave problems are recovered as a particular case along the lines of the proposed reduction approach different examples of 2 2 governing models are analysed thoroughly in order to highlight the flexibility of the provided solutions to describe hyperbolic dissipative wave processes

riemann problem and wave interactions in magnetogasdynamics abstract this paper is mainly concerned with the riemann problem for one dimensional ideal isentropic magnetogasdynamics with transverse magnetic field the existence and uniqueness of the solutions of the riemann problem are obtained constructively with the characteristic method furthermore we investigate the interactions of the elementary waves

on the wave interactions in the drift flux equations of two phase flows abstract in the present work we investigate the riemann problem and interaction of weak shocks for the widely used isentropic drift flux equations of two phase flows the complete structure of solution is analyzed and with the help of rankine hugoniot jump condition and lax entropy conditions we establish the existence and uniqueness condition for elementary waves the explicit form of the shock waves contact discontinuities and rarefaction waves are derived analytically within this respect we develop an exact riemann solver to present the complete solution structure a necessary and sufficient condition for the existence of solution to the riemann problem is derived and presented in terms of initial data furthermore we present a necessary and sufficient condition on initial data which provides the information about the existence of a rarefaction wave or a shock wave for one or three family of waves to validate the performance and the efficiency of the developed exact riemann solver a series of test problems selected from the open literature are presented and compared with independent numerical methods simulation results demonstrate that the present exact solver is capable of reproducing the complete wave propagation using the current drift flux equations as the numerical resolution the provided computations indicate that accurate results be accomplished efficiently and in a satisfactory agreement with the exact solution

riemann problems and exact solutions to a traffic flow model within the theoretical framework of differential constraints method a nonhomogeneous model describing traffic flows is considered classes of exact solutions to the governing equations under interest are determined furthermore riemann problems and generalized riemann problems which model situations of interest for traffic flows are solved

stable solutions of the allen cahn equation in dimension 8 and minimal cones abstract for all n 1 we are interested in bounded solutions of the allen cahn equation u u u 3 0 which are defined in all r n 1 and whose zero set is asymptotic to a given minimal cone in particular in dimension n 1 8 we prove the existence of stable solutions of the allen cahn equation whose zero sets are not hyperplanes

the constant astigmatism equation new exact solution in this paper we present a new solution for the constant astigmatism equation this solution is parameterized by an arbitrary function of a single variable

delta shock waves in chromatography equations abstract the previous investigations on delta shock waves were mostly focused on those with dirac delta function in only one state variable in this paper we obtain another kind from the nonlinear chromatography equations in which the dirac delta functions develop simultaneously in both state variables it is strictly proved to satisfy the system in the sense of distributions the generalized rankine hugoniot relation and entropy condition are clarified the numerical results completely coinciding with the theoretical analysis are presented

a duality theorem for crossed products of hopf algebras several variations have appeared recently see l 5 8 101 among the best are 2 2 1 3 2 2 but the former is restricted to the case of a trivial cocycle 0 and the latter to the case of finite dimensional h the main purpose of this paper is to prove a common generalization of these two theorems in section 2 we first recall preliminaries about crossed products then we introduce some new algebra constructions and we prove related useful results in particular we define an algebra a h op u that will replace a h u in the main theorem and we show a relationship between the two algebras in the new construction u is allowed to be more general for example we may take u h section 3 introduces a subalgebra h of h with a comodule structure co h h h they are our tools to formulate and handle certain awkward assumptions in the main theorem these can be regarded as finiteness conditions and they correspond to the u local finiteness and rl condition of 2 section 4 contains the duality theorem and its proof in section 5 we draw some corollaries in particular we show that 2 2 1 3 2 2 do follow from our theorem 153 0021 8693 92 3 00