conglomerability of probability measures on boolean algebras for the case where b is a boolean algebra of events and p is a probability finitely additive definetti 1972 considered the question of conglomerability of p and found that in many circumstances this natural notion was equivalent to countable additivity of p schervish seidenfeld and kadane 1984 pursued these investigations on the connection between countable additivity and conglomerability in greater detail for the case where b is a algebra hill and lane 1985 and zame 1988 give alternative proofs this article is an extension for the most part of schervish seidenfeld and kadane s work to the case where b is an arbitrary boolean algebra the more restrictive notion of positive conglomerability for a class of algebras including the countable algebras complete algebras and inifinite product algebras is treated completely this class is described by the requirement that a 0 1 valued measure be countably additive if every countable family of negligible sets is contained within a negligible set i e corresponds to a p point of of the stone space in general positive conglomerability fails to be equivalent to countable additivity though the degree of failure is minor building on techniques of hill lane and zame we obtain partial results on conglomerability for non complete algebras

convergence of the fractional step lax friedrichs scheme and godunov scheme for the isentropic system of gas dynamics a convergence theorem of the fractional step lax friedrichs scheme and godunov scheme for an inhomogeneous system of isentropic gas dynamics 1 5 3 is established by using the framework of compensated compactness meanwhile a corresponding existence theorem of global solutions with large data containing the vacuum is obtained

differentiability of the metric projection in hilbert space a study is made of differentiability of the metric projection p onto a closed convex subset k of a hilbert space h when k has nonempty interior the gateaux or fr het smoothness of its boundary can be related with some precision to gateaux or frechet differentiability properties of p for instance combining results in 3 with earlier work of r d holmes shows that k has a c2 boundary if and only if p is cl in h k and its derivative p has a certain invertibility property at each point an example in 5 shows that if the c2 condition is relaxed even slightly then p can be nondifferentiable fr het in h k

on the initial boundary value problem for the bipolar hydrodynamic model for semiconductors abstract the global existence and zero relaxation limit results of weak solutions of the initial boundary value problem to the bipolar hydrodynamic model for semiconductors are established by the theory of compensated compactness the boundary conditions of weak solutions in the sense of traces are discussed

the relaxation of the hydrodynamic model for semiconductors to the drift diffusion equations abstract we establish the convergence and consistency of approximate solutions derived by the modified godunov scheme for the initial boundary value problem to a simplified one dimensional hydrodynamic model for semiconductors using the compensated compactness method the traces of weak solutions are introduced and then the weak solutions are proved to satisfy the natural boundary conditions the zero relaxation limit of the hydrodynamic model to the drift diffusion model is proved when the momentum relaxation time tends to zero

spectrum and analytical indices of the c algebra of wiener hopf operators we study multivariate generalisations of the classical wiener hopf algebra which is the c algebra generated by the wiener hopf operators given by convolutions restricted to convex cones by the work of muhly and renault this c algebra is known to be isomorphic to the reduced c algebra of a certain restricted action groupoid given by the action of euclidean space on a certain compactification using groupoid methods we construct composition series for the wiener hopf c algebra by a detailed study of this compactification we compute the spectrum and express homomorphisms in k theory induced by the symbol maps which arise by the subquotients of the composition series in analytical terms namely these symbols maps turn out to be given by an analytical family index of a continuous family of fredholm operators in a subsequent paper we also obtain a topological expression of these indices

existence and some limits of stationary solutions to a one dimensional bipolar euler poisson system abstract in this paper we study the stationary flow for a one dimensional isentropic bipolar euler poisson system hydrodynamic model for semiconductor devices this model consists of the continuous equations for the electron and hole densities and their current densities coupled the poisson equation of the electrostatic potential in a bounded interval supplemented by the proper boundary conditions we first show the unique existence of stationary solutions of the one dimensional isentropic hydrodynamic model based on the schauder fixed point principle and the careful energy estimates next we investigate the zero electron mass limit combined zero electron mass and zero hole mass limit the zero relaxation time limit and the debye length quasi neutral limit respectively we also show the strong convergence of the sequence of solutions and give the associated convergence rates

asymptotic behavior of solutions to euler poisson equations for bipolar hydrodynamic model of semiconductors abstract in this paper we study the cauchy problem for 1 d euler poisson system which represents a physically relevant hydrodynamic model but also a challenging case for a bipolar semiconductor device by considering two different pressure functions and a non flat doping profile different from the previous studies gasser et al 2003 7 huang et al 2011 12 huang et al 2012 13 for the case with two identical pressure functions and zero doping profile we realize that the asymptotic profiles of this more physical model are their corresponding stationary waves steady state solutions rather than the diffusion waves furthermore we prove that when the flow is fully subsonic by means of a technical energy method with some new development the smooth solutions of the system are unique exist globally and time algebraically converge to the corresponding stationary solutions the optimal algebraic convergence rates are obtained

strong singularity disjointness and strong finite additivity of finitely additive measures abstract the most striking difference between finitely additive measures and countably additive measures is that the hahn decomposition theorem may be only approximate if countable additivity fails a corollary is that whereas two singular countably additive measures are disjoint in giving full measure to disjoint sets this is usually only approximately true without countable additivity one natural question is which finitely additive measures are disjoint from all singular measures in the stone space setting the question becomes which radon measures have support disjoint from all singular radon measures if so the support is a p1 set of atalla which is more general than a p set construction of such measures is considered at length existence of nonmolecular nonatomic measures based on p1 points with support a p1 set is equivalent to the existence of a p1 homeomorph of n in the stone space if x is a positive localizable measure space then ba has l x as a band and and l1 x as a subband it is shown that the band complementary to l x consists of measures disjoint to so supp is a p1 set in the stone space of a notion of strong singularity to intermediate to disjointness and singularity is shown to be equivalent to strong finite additivity admitting countable partitions by null sets for elements of l x the band of l x orthogonal to l1 x consists of strongly finitely additive measures precisely when the measure algebra satisfies the chain condition for a nonreal valued measurable cardinal or when the maximal ideal space of l x does not have real valued measurable cellularity a in ba has a countably additive ideal of negligible sets iff it is not strongly finitely additive on any set of positive measure on the stone space this corresponds to radon measures with p sets as supports even for purely finitely additive measures of this type much of countable additive measure theory holds for null functions are precisely those with null support it is not known for 2x whether purely finitely additive measures of this type exist their existence may be independent of zfc and or other axioms such as martin s real valued measurable cardinal or measurable cardinal a locally compact space y is sham compact so that c x cb x cc x precisely when its remainder in any compactification is a p set in this case m x mb x mc x the latter strong of identities is the definition of sham sham compact spaces these are characterized by having a p1 set as remainder in any compactification new examples of sham compact open subsets of the maximal ideal space z of a positive localizable measure space x are given based on maharam s homogeneity character however no open subset of z can be sham sham compact without being sham compact this is true when z is replaced by any compact space which locally the support of a radon measure

subsonic flow for the multidimensional euler poisson system we establish the existence and stability of subsonic potential flow for the steady euler poisson system in a multidimensional nozzle of a finite length when prescribing the electric potential difference on a non insulated boundary from a fixed point at the exit and prescribing the pressure at the exit of the nozzle the euler poisson system for subsonic potential flow can be reduced to a nonlinear elliptic system of second order in this paper we develop a technique to achieve a priori c 1 alpha estimates of solutions to a quasi linear second order elliptic system with mixed boundary conditions in a multidimensional domain enclosed by a lipschitz continuous boundary in particular we discovered a special structure of the euler poisson system which enables us to obtain c 1 alpha estimates of the velocity potential and the electric potential functions and this leads us to establish structural stability of subsonic flows for the euler poisson system under perturbations of various data

on a quasilinear degenerate system arising in semiconductor theory part ii localization of vacuum solutions the temporal and spatial localization of vacuum sets of the solutions to the drift diffusion equations for semiconductors is studied in this paper it is shown that if there are vacuum sets initially then there are vacuum sets for a small time which shows the finite propagation speed of the support of the densities it is also shown that for a certain recombination generation rate there is no dilation of the initial support and under some condition on the recombination generation rate the vacuum will develop after a certain time even if there is no vacuum initially these results are proved based on a local energy method for free boundary problems

irrotational approximation to the one dimensional bipolar euler poisson system abstract under the assumptions that initial data have sufficiently small total variation and that the initial data are supersonic or are subsonic respectively we prove that in any bounded domain the l 1 norm of the difference between the local solutions of the one dimensional bipolar euler poisson system and the potential flow system of the one dimensional bipolar euler poisson system with the same initial data can be bounded by the cube of the total variation of the initial data

diffusion relaxation limit of a bipolar hydrodynamic model for semiconductors in the paper we discuss the relaxation limit of a bipolar isentropic hydrodynamical models for semiconductors with small momentum relaxation time with the help of the maxwell iteration we prove that as the relaxation time tends to zero periodic initial value problems of a scaled bipolar isentropic hydrodynamic model have unique smooth solutions existing in the time interval where the classical drift diffusion model has smooth solutions meanwhile we justify a formal derivation of the corresponding drift diffusion model from the bipolar hydrodynamic model

an index theorem for wiener hopf operators abstract we study the multivariate generalisation of the classical wiener hopf algebra which is the c algebra generated by the wiener hopf operators given by convolutions restricted to convex cones by the work of muhly and renault this c algebra is known to be isomorphic to the reduced c algebra of a certain restricted action groupoid it admits a composition series and therefore a symbol calculus using groupoid methods we obtain in the framework of kasparov s bivariant kk theory a topological expression of the index maps associated to these symbol maps in terms of geometric topological data of the underlying convex cone this generalises an index theorem by upmeier concerning wiener hopf operators on symmetric cones our result covers a wide class of cones containing polyhedral and homogeneous cones

large time behavior of solution to the three dimensional quantum bipolar drift diffusion model from semiconductors abstract in this study we consider the three dimensional quantum bipolar drift diffusion model arising from the semiconductor device simulation which consists of the coupled nonlinear fourth order parabolic equation and poisson equation based on the results of the self similar stability for the one dimensional quantum bipolar drift diffusion equation we show the stability of planar self similar wave for the three dimensional quantum bipolar drift diffusion model using the energy methods we present the global existence of smooth solutions for the initial value problem of the three dimensional quantum bipolar drift diffusion equation when the initial data are close to the planar self similar wave we also show that in large time the solution of the three dimensional quantum bipolar drift diffusion equations tends to the planar self similar wave at an algebraic time decay rate

convergence of the viscosity method for isentropic gas dynamics a convergence theorem for the method of artificial viscosity applied to the isentropic equations of gas dynamics is established convergence of a subsequence in the strong topology is proved without uniform estimates on the derivatives using the theory of compensated compactness and an analysis of progressing entropy waves

zero electron mass limit and zero relaxation time limit in a multi dimensional stationary bipolar euler poisson system in this paper we discuss a two and three dimensional stationary bipolar euler poisson system from plasmas and semiconductor devices we study the zero electron mass limit and the zero relaxation time limit of smooth subsonic solutions for the equations with proper boundary value conditions by using the method of matched asymptotic expansions for each limit we show the existence and uniqueness of profiles and justify the asymptotic expansions up to any order

solutions for a hydrodynamic model of semiconductors we study a three dimensional isothermal hydrodynamic model of semiconductors and prove the existence of local solutions to the initial boundary value problem corresponding to an insulated boundary

global existence and asymptotic behavior of the solutions to the three dimensional bipolar euler poisson systems abstract in this paper the global existence of smooth solutions for the three dimensional bipolar hydrodynamic model is studied when the initial data are close to a constant state the l 2 decay rate of the solutions is also obtained our approach is based on the detailed analysis of the green function of the linearized system and the elaborate energy estimates as far as we known it is the first result about the existence and l 2 decay rate of global smooth solutions to the multi dimensional bipolar hydrodynamic model

zero relaxation time limits to a hydrodynamic model of two carrier types for semiconductors in this paper we study the zero relaxation time limits to a one dimensional hydrodynamic model of two carrier types for semiconductors first we introduce the flux approximation coupled with the classical viscosity method to obtain the uniform l loc p p ge 1 bound of the approximation solutions rho i varepsilon delta and other estimates of u i varepsilon delta e varepsilon delta with the help of the high energy estimates jungel and peng comm partial differ equ 58 1007 1033 1999 then we apply the compensated compactness method coupled with the scaled variables technique marcati and natalini arch ration mech anal 129 129 145 1995 to prove the zero relaxation time limits with arbitrarily large initial data and arbitrary adiabatic exponents gamma i 1

global smooth solutions to the multidimensional hydrodynamic model for plasmas with insulating boundary conditions the existence of global smooth solutions to the multidimensional hydrodynamic model for plasmas of electrons and positively charged ions with insulating boundary conditions is shown under the assumption that the initial densities are close to a constant furthermore it is proved that the particle densities converge exponentially fast to the constant steady state

stability of steady state solutions for an isentropic hydrodynamic model of semiconductors of two species abstract we discuss the stability of the steady state solutions for an isentropic hydrodynamic model of semiconductors of two species we consider not only the mass and momentum equations for electrons but also those two equations for holes the recombination effects between electrons and holes are taken into consideration as well we study the case where the doping profile is close to zero and depends on the spacial variable x we shall show that steady state solutions are asymptotically stable

stability of steady states of the compressible euler poisson system in r 3 abstract we investigate the global existence and asymptotic behavior of smooth solutions near a non flat steady state to the compressible euler poisson system in r 3 using some concise energy estimates and an interpolation trick we refine the global existence and show that the solution converges to the stationary solution exponentially fast we assume that the h 3 norms of the initial density and velocity are small but the higher derivatives can be arbitrarily large in this sense our method simplifies the proof of hsiao et al 2003 17 and improves the results of it

toeplitz c algebras on bounded symmetric domains in this paper we develop a structure theory for the toeplitz c algebra y for an arbitrary bounded symmetric domain d in c classical or exceptional as the main result it is shown that 5y is a c algebra of type i which is solvable i e admits a finite composition sequence of closed ideals sk in 7 such that the subquotients fk i k are continuous fields of elementary c algebras of compact operators the length of this composition sequence coincides with the rank r of d as a hermitian symmetric space for 0 k r the spectral components sk of ay parametrizing the irreducible representations of y are realized in terms of the boundary components complex analytic faces of d the structure theory for y is based on the fact that the tangent space z c c of d carries a jordan algebraic structure z is a jordan triple system with triple product uv w describing the geometry of d in algebraic terms for example d is the open unit ball with respect to the so called spectral norm on z and the boundary components of d are in 1 1 correspondence with the tripotents e e z partial isometries satisfying ee e 4 e in particular the shilov boundary s of d consists of all tripotents of maximal rank r the jordan theoretic description of d was used in 17 to determine an explicit peter weyl decomposition of the hardy space h2 s cf 15 in terms of the norm functions generalized determinants associated with the jordan triple

relaxation time limit of the multidimensional bipolar hydrodynamic model in besov space abstract in this paper we study a multidimensional bipolar hydrodynamic model for semiconductors or plasmas this system takes the form of the bipolar euler poisson model with electric field and frictional damping added to the momentum equations in the framework of the besov space theory we establish the global existence of smooth solutions for cauchy problems when the initial data are sufficiently close to the constant equilibrium next based on the special structure of the nonlinear system we also show the uniform estimate of solutions with respect to the relaxation time by the high and low frequency decomposition methods finally we discuss the relaxation time limit by compact arguments that is it is shown that the scaled classical solution strongly converges towards that of the corresponding bipolar drift diffusion model as the relaxation time tends to zero

global existence and asymptotic behavior for a multidimensional nonisentropic hydrodynamic semiconductor model with the heat source abstract in this paper a multidimensional nonisentropic hydrodynamic model for semiconductors with the nonconstant lattice temperature is studied the model is self consistent in the sense that the electric field which forms a forcing term in the momentum equation is determined by the coupled poisson equation global existence to the cauchy problem for the multidimensional nonisentropic hydrodynamic semiconductor model with the small perturbed initial data is established and the asymptotic behavior of these smooth solutions is investigated namely that the solutions converge to the general steady state solution exponentially fast as t is obtained moreover the existence and uniqueness of the stationary solutions are investigated

wiener hopf operators on ordered homogeneous spaces i abstract the c algebra w p of wiener hopf operators related to an ordered homogeneous space g h is shown to be the homomorphic image of a groupoid c algebra to obtain this groupoid c algebra we construct an ordered compactification of g h the regularity of this compactification permits to show that w p contains the ideal of compact operators

convergence of the godunov scheme for a simplified one dimensional hydrodynamic model for semiconductor devices convergence of approximate solutions derived by the godunov scheme for a simplified one dimensional hydrodynamic model for semiconductor devices is established by using the compensated compactness method a global existence theorem is shown and a numerical method for the computation of the physical global solution of this model is provided by this approach

exact controllability of scalar conservation laws with an additional control in the context of entropy solutions in this paper we study the exact controllability problem for nonlinear scalar conservation laws on a compact interval with a regular convex flux and in the framework of entropy solutions with the boundary data and a source term depending only on the time as controls we provide sufficient conditions for a state to be reachable in arbitrary small time to do so we introduce a slightly modified wave front tracking algorithm

symmetries of supersymmetric integrable hierarchies of kp type this article is devoted to the systematic study of additional non isospectral symmetries of constrained reduced supersymmetric integrable hierarchies of kp type the so called skp r mb mf models the latter are supersymmetric extensions of ordinary constrained kp hierarchies which contain as special cases basic integrable systems such as m kdv akns fordy kulish yajima oikawa etc as a first main result it is shown that any skp r mb mf hierarchy possesses two different mutually anti commuting types of superloop superalgebra additional symmetries corresponding to the positive and negative grade parts of certain superloop superalgebras the second main result is the systematic construction of the full algebra of additional virasoro symmetries of skp r mb mf hierarchies which requires nontrivial modifications of the virasoro flows known from the general case of unconstrained manin radul super kp hierarchies the latter flows do not define symmetries for constrained skp r mb mf hierarchies as

optimal convergence rates to nonlinear diffusion waves for the compressible euler poisson system with damping abstract in this work we study the 1 d isentropic bipolar hydrodynamic model this model takes the form of compressible euler poisson system with nonlinear damping added to the momentum equations under some smallness conditions the solutions to the cauchy problem of the system globally exist and convergence to the nonlinear diffusion waves which are the corresponding solutions of nonlinear parabolic equations given by the darcy s law with a specified initial data the optimal convergence rates are obtained by green function method when the initial perturbation is in l 1 space

a note on asymptotic behavior of solutions for the one dimensional bipolar euler poisson system abstract in this note we consider a one dimensional bipolar euler poisson system hydrodynamic model this system takes the form of euler poisson with electric field and frictional damping added to the momentum equations when n n paper i gasser l hsiao h l li large time behavior of solutions of the bipolar hydrodynamical model for semiconductors j differential equations 192 2003 326 359 discussed the asymptotic behavior of small smooth solutions to the cauchy problem of the one dimensional bipolar euler poisson system subsequent to i gasser l hsiao h l li large time behavior of solutions of the bipolar hydrodynamical model for semiconductors j differential equations 192 2003 326 359 we investigate the asymptotic behavior of solutions to the cauchy problem with n n n and obtain the optimal convergence rate toward the constant state n 0 n 0 we accomplish the proofs by energy estimates and the decay rates of fundamental solutions of the heat type equations

asymptotic convergence to planar stationary waves for multi dimensional unipolar hydrodynamic model of semiconductors abstract in this study we consider the high dimensional unipolar hydrodynamic model for semiconductors in the form of euler poisson equations based on the results that we have obtained in the first part huang et al 2011 16 for the 1 d case we can further show the stability of planar stationary waves in multi dimensional case utilizing the energy method we obtain the global existence of the solutions of high dimensional euler poisson equations for the unipolar hydrodynamic model and prove that the solutions converge to the planar stationary waves time exponentially

relaxation limit of the one dimensional bipolar euler poisson system in the bound domain in this paper we present a one dimensional bipolar hydrodynamic model from semiconductor devices and plasmas which takes the form of bipolar isothermal euler poisson with electric field and frictional damping added to the momentum equations from proper scaling when the relaxation time in the bipolar euler poisson system tends to zero we can obtain the bipolar drift diffusion equation first we show that the solutions to the initial boundary value problems of the bipolar euler poisson system and the corresponding drift diffusion equation converge to their stationary solutions as time tends to infinity respectively then it is shown that the solution for the bipolar euler poisson equation converges to that of the corresponding bipolar drift diffusion equations as the relaxation time tends to zero with the initial layer

jordan fields and improper integrals abstract an integral is defined for not necessarily bounded functions with respect to a finitely additive possibly infinite measure in particular this strictly includes the familiar case of absolutely convergent improper riemann integration in euclidean space however the measure need not have a countably additive extension and no topology is assumed on the underlying space the jordan field of sets with integrable characteristic functions is used to characterize the integrable functions as those that are nearly jordan measurable and their integrals are shown to equal the lebesgue integrals of the measures of the appropriate jordan sets

index theory for multivariable wiener hopf operators on montre que les indices de fredholm pour des operateurs de wiener hopf sur des cones homogenes auto duaux dans r n peuvent s exprimer topologiquement en fonction de la formule d indice d atiyah singer sur la variete de toutes les faces de

a viscous approximation for a 2 d steady semiconductor or transonic gas dynamic flow existence theorem for potential flow in this paper we solve a boundary value problem in a two dimensional domain 1 for a system of equations of fluid poisson type that is a viscous approximation to a potential equation for the velocity coupled with an ordinary differential equation along the streamlines for the density and a poisson equation for the electric field a particular case of this system is a viscous approximation of transonic flow models the general case is a model for semiconductors we show existence of a density p velocity potential cp and electric potential in the bounded domain r that are c fi c fi and w2 p 2 functions respectively such that p cp 3 the speed ivlpl and the electric field e v are uniformly bounded in the viscous parameter this is a necessary step in the existing programs in order to show existence of a solution for the transonic flow problem 0 19 john wiley sons inc 1 presentation of the model

notes on jordan fields based on an article by maharam abstract results of maharam on jordan fields associated with a finitely additive measure are extended to take into consideration the natural topology induced by an algebra of sets namely that induced by the stone space based on this the question of when the jordan field is a algebra and the question of the completeness of associated l 1 spaces are answered

the bipolar hydrodynamic model for semiconductors and the drift diffusion equations we establish the existence of entropy solutions for a bipolar hydrodynamic model for semiconductors we show also that the limit as the relaxation time goes to zero of an appropriate scaled sequence of entropy solutions is a solution of the classical drift diffusion equations

asymptotic profile in a one dimensional steady state nonisentropic hydrodynamic model for semiconductors we study the stationary flow for a one dimensional nonisentropic hydrodynamic model for semiconductor devices this model consists of the continuous equations for the electron density the electron current density and electron temperature coupled the poisson equation of the electrostatic potential in a bounded interval supplemented by the proper boundary conditions we investigate the zero electron mass limit the zero relaxation time limit and the debye length quasi neutral limit respectively we show the strong convergence of the sequence of solutions and give the associated convergence rate

global solutions to the isothermal euler poisson system with arbitrarily large data abstract we prove the global existence of a solution to the euler poisson system with arbitrarily large data in a one dimensional geometry the pressure law we consider is deduced from an isothermal assumption for the electrons gas in this case nishida has already pointed out that the linear part of the glimm functional is decreasing with respect to time using a glimm scheme he used this property to construct globally defined weak solutions for the euler system with arbitrary large data we follow his outline of proof here a new difficulty arises with the source term due to the electric field a key point is that the glimm scheme is almost conservative this quasi conservation of charge leads to a uniform estimate of the total variation of the electric field this estimate allows to prove the convergence of the scheme