an iterative scheme for a class of quasi variational inequalities an iterative scheme is given to obtain the approximate solution of a class of quasi variational inequalities it is shown that the approximate solution obtained by the iterative scheme converges strongly in the hilbert space to the exact solution as a special case we obtain the corresponding iterative scheme for variational inequalities

lattice preserving maps on lattices of continuous functions abstract lattice preserving maps between sublattices of continuous functions on locally compact spaces e g the functions with compact support are studied these maps though not necessarily linear are related to continuous functions between the underlying locally compact spaces consequences for first countable spaces including an automatic continuity for these lattice maps are provided

existence and uniqueness of solutions for the couette problem we study existence and uniqueness results for the one dimensional boltzmann equation with inflow and diffusive boundary conditions our focus partly encompasses some of the properties of the boltzmann collision gain term which play a significant role in existence and uniqueness results a series of estimates are proven on the collision term which is shown to produce a suitable function space in which the contraction mapping arguments are available

on diffuse reflection at the boundary for the boltzmann equation and related equations the paper considers diffuse reflection at the boundary with nonconstant boundary temperature and unbounded velocities the solutions obtained are proved to conserve mass at the boundary after a preliminary study of the collisionless case the main results obtained are existence for the boltzmann equation in a diperna lions framework with the above boundary conditions in a bounded measure sense and existence together with uniqueness for the bgk equation with maxwellian diffusion on the boundary in anl framework

algorithm for generalized co complementarity problems in banach spaces abstract in this paper we introduce a new class of generalized co complementarity problems in banach spaces an iterative algorithm for finding approximate solutions of these problems is considered some convergence results for this iterative algorithm are derived and several existence results are obtained

sequential quantum measurements a quantum effect is an operator a on a complex hilbert space h that satisfies 0 a i we denote the set of quantum effects by e h the set of self adjoint projection operators on h corresponds to sharp effects and is denoted by p h we define the sequential product of a b e h by a b a1 2ba1 2 the main purpose of this article is to study some of the algebraic properties of the sequential product many of our results show that algebraic conditions on a b imply that a and b commute for the usual operator product for example if a b satisfies certain distributive or associative laws then ab ba moreover if a b p h then ab ba and a b b or b a b if and only if ab ba b a natural definition of stochastic independence is introduced and briefly studied

projection methods isotone projection cones and the complementarity problem one studies some iterative methods for solving complementarity problems explicit or implicit in hilbert spaces the iterative methods presented are based on the fixed point theory on the coincidence equations on convex cones and on some properties of projection operators onto a special cone named the isotone projection cone the ordering defined by the cone is essential for the complementarity theory the idea is to use systematically the ordering in the iterative methods for solving complementarity problems in this sense one shows that the isotone projection cone is a good instrument

algorithm for generalized multivalued variational inequalities in hilbert spaces abstract we introduce a new class of generalized multivalued variational inequality problems 1 1 which contain several existing variational inequality problems as special cases an iterative algorithm for finding approximate solutions of problem 1 1 is considered several convergence results for this algorithm are derived and in particular several existence results of problems 1 1 are obtained we also introduce a new class of generalized multivalued complementarity problems 5 1 which also contain several known complementarity problems as special cases it is shown that problem 5 1 is equivalent to problem 1 1 of special type from which several existence results of problem 5 1 are obtained

stationary solutions for the ellipsoidal bgk model in a slab abstract we address the boundary value problem for the ellipsoidal bgk model of the boltzmann equation posed in a bounded interval the existence of a unique mild solution is established under the assumption that the inflow boundary data does not concentrate too much around the zero velocity and the gas is sufficiently rarefied

comparability preserving maps on hilbert space effect algebras we describe the general form of bijective comparability preserving transformations of the hilbert space effect algebra thus improving several known characterizations of ortho order automorphisms

a note on the infimum problem of hilbert space effects the quantum effects for a physical system can be described by the set e h of positive operators on a complex hilbert space h that are bounded above by the identity operator i the infimum problem of hilbert space effects is to find under what condition the infimum a b exists for two quantum effects a and b e h the problem has been studied in different contexts by kadison gudder moreland and ando in this note using the method of the spectral theory of operators we give a affirmative answer of a conjecture of s gudder j math phys 37 2637 2642 1996 in addition some properties of generalized infimum a b were considered

simulation of boundary value problems for the boltzmann equation the paper presents numerical results on the simulation of boundary value problems for the boltzmann equation in one and two dimensions in the one dimensional case we use prescribed fluxes at the left and diffusive conditions on the right end of a slab to study the resulting steady state solution moreover we compute the numerical density function in velocity space and compare the result with the chapman enskog distribution obtained in the limit for continuous media the aim of the two dimensional simulations is to investigate the possibility of a symmetry break in the numerical solution

linear preserver problems a brief introduction and some special techniques abstract linear preserver problems concern the characterization of linear operators on matrix spaces that leave certain functions subsets relations etc invariant the earliest papers on linear preserver problems date back to 1897 and a great deal of effort has been devoted to the study of this type of question since then we present a brief picture of the subject aiming at giving a gentle introduction to the reader then we describe some techniques used in our recent papers on this type of problem

lyapunov functionals and l 1 stability for discrete velocity boltzmann equations we devise lyapunov functionals and prove uniform l 1 stability for one dimensional semilinear hyperbolic systems with quadratic nonlinear source terms these systems encompass a class of discrete velocity models for the boltzmann equation the lyapunov functional is equivalent to the l 1 distance between two weak solutions and non increasing in time they result from computations of two point interactions in the phase space for certain models with only transversal collisional terms there exist generalizations for three and multi point interactions

a discrete velocity stationary wigner equation this paper is concerned with the one dimensional stationary linear wigner equation a kinetic formulation of quantum mechanics specifically we analyze the well posedness of the boundary value problem on a slab of the phase space with given inflow data for a discrete velocity model we find that the problem is uniquely solvable if zero is not a discrete velocity otherwise one obtains a differential algebraic equation of index 2 and hence the inflow data make the system overdetermined

preserving the measure of compatibility between quantum states in this article after defining the abstract concept of compatibility like functions on quantum states we prove that every bijective transformation on the set of all states which preserves such a function is implemented by an either unitary or antiunitary operator

coexistency on hilbert space effect algebras and a characterisation of its symmetry transformations the hilbert space effect algebra is a fundamental mathematical structure which is used to describe unsharp quantum measurements in ludwig s formulation of quantum mechanics each effect represents a quantum fuzzy event the relation of coexistence plays an important role in this theory as it expresses when two quantum events can be measured together by applying a suitable apparatus this paper s first goal is to answer a very natural question about this relation namely when two effects are coexistent with exactly the same effects the other main aim is to describe all automorphisms of the effect algebra with respect to the relation of coexistence in particular we will see that they can differ quite a lot from usual standard automorphisms which appear for instance in ludwig s theorem as a byproduct of our methods we also strengthen a theorem of moln ar

the boltzmann grad limit for a one dimensional boltzmann equation in a stationary state in this paper we consider a one dimensional model of interacting particles in a bounded interval with possibly not homogeneous diffusive boundary conditions we prove that when the number of particlesn goes to infinity and the interaction is suitably rescaled the boltzmann grad limit the one particle distribution function of the unique invariant measure for the particle system converges to the unique solution of the boltzmann equation of the model provided that the mean free path is sufficiently large

generalized quasi complementarity problems abstract in this paper we consider and study a new unified algorithm for obtaining the approximate solution of the generalized quasi complementarity of finding u k u a closed convex set in rn such that f u k u u m u f u 0 where f is a mapping from rn into itself and k u is the polar cone of k u and m is a point to point mapping from rn into itself the algorithm includes as a special case many existing algorithms for solving generalized complementarity problems

strongly nonlinear quasivariational inequalities abstract in this paper we develop the algorithms for finding the approximate solution of a strongly nonlinear quasivariational inequality and a strongly nonlinear quasicomplementarity problem and we include as special cases known results in this area we also observe that these two problems are equivalent if the convex set involved in the formulation of these problem is a convex cone

spectral order of operators and range projections we study the effect algebra i e the positive part of the unit ball of an operator algebra and its relation to the projection lattice from the perspective of the spectral order a spectral orthomorphism is a map between effect algebras which preserves the spectral order and orthogonality of elements we show that if the spectral orthomorphism preserves the multiples of the unit then it is a restriction of a jordan homomorphism between the corresponding algebras this is an optimal extension of the dye s theorem on orthomorphisms of the projection lattices to larger structures containing the projections moreover results on automatic countable additivity of spectral homomorphisms are proved further we study the order properties of the range projection map assigning to each positive contraction in a jbw algebra its range projection it is proved that this map preserves infima of positive contractions in the spectral respectively standard order if and only if the projection lattice of the algebra in question is a modular lattice

iterative algorithms for semi linear quasi complementarity problems abstract in this paper we consider an iterative for a class of quasi complementarity problems of finding u rn such that g u k u mu q k u g u mu q 0 where g is a continuous mapping from rn into itself m rn x n q rn and k u is the polar cone of the convex cone k u in rn the algorithms considered in this paper are general and unifying ones which include many existing algorithms as special cases for solving the complementarity problems we also study the convergence criteria of the general algorithms

maps on states preserving the relative entropy let h be a finite dimensional hilbert space the aim of this short note is to prove that every bijective map on the space s h of all density operators on h which preserves the relative entropy is of the form u u with some unitary or antiunitary operator u on h

sequential endomorphisms of finite dimensional hilbert space effect algebras we describe the structure of all continuous sequential endomorphisms of the effect algebra of a finite dimensional hilbert space

the stationary nonlinear boltzmann equation in a couette setting this paper studies the stationary nonlinear boltzmann equation for hard forces in a couette setting between two coaxial rotating cylinders with given indata of maxwellian type on the cylinders a priori estimates are obtained mainly in l2 leading to multiple isolated solutions together with a hydrodynamic limit control based on asymptotic expansions together with a rest term

characterizing sequential isomorphisms on hilbert space effect algebras let be any sequential product on the hilbert space effect algebra with and be a bijective map we show that if satisfies ab a b for then there is either a unitary or an anti unitary operator u such that a uau for every let be a borel function satisfying g 0 0 g 1 1 and let us define a binary operation g on by a gb a1 2 g a bg a a1 2 where t denotes the conjugate of the operator t we also show that a bijective map satisfies a gb a g b for if and only if there is either a unitary or an anti unitary operator u such that a uau for every

global weak solutions of the boltzmann equation a new definition of the concept of weak solution of the nonlinear boltzmann equation is introduced it is proved that without any truncation on the collision kernel the boltzmann equation in the one dimensional case has a global weak solution in this sense global conservation of energy follows

automorphisms of hilbert space effect algebras let h be a hilbert space and e h the effect algebra on h a bijective map is called an ortho order automorphism of e h if for every we have and the classical theorem of ludwig states that every such is of the form for some unitary or antiunitary operator u it is also known that each bijective map on e h preserving order and coexistency in both directions is of the same form can we improve these two theorems by relaxing the bijectivity assumption and or replacing the above preserving properties by the weaker assumptions of preserving above relations in one direction only and still get the same conclusion for both characterizations of automorphisms of effect algebras we will prove the optimal versions and give counterexamples showing the optimality of the obtained results

brst quantization of quasisymplectic manifolds and beyond we consider a class of factorizable poisson brackets which includes almost all reasonable poisson structures a particular case of the factorizable brackets are those associated with symplectic lie algebroids the brst theory is applied to describe the geometry underlying these brackets as well as to develop a deformation quantization procedure in this particular case this can be viewed as an extension of the fedosov deformation quantization to a wide class of irregular poisson structures in a more general case the factorizable poisson brackets are shown to be closely connected with the notion of n algebroid a simple description is suggested for the geometry underlying the factorizable poisson brackets based on construction of an odd poisson algebra bundle equipped with an abelian connection it is shown that the zero curvature condition for this connection generates all the structure relations for the n algebroid as well as a generalization of the yang baxter equation for the symplectic structure

infima of hilbert space effects the quantum effects for a physical system are usually described by the set h of positive operators on a hilbert spaceh that are bounded above by the unit operator under a natural order h becomes a partially ordered set that is not a lattice unless dimh 1 a characterization of the pairsa b h such that the infimuma b exists is an open problem called the infimum problem methods of linear algebra are employed to solve the infimum problem when dimh these methods do not appear to generalize to infinite dimensions so the general problem remains open progress toward solution of the general problem is discussed

characterization of sum automorphisms and jordan triple automorphisms of quantum probabilistic maps in quantum mechanics it is often important for the representation of a quantum system to study the structure preserving bijective maps of the system such maps are also called isomorphisms or automorphisms in this paper using the uhlhorn type of wigner s theorem we show that both sum automorphisms and jordan triple automorphisms of the unit ball of density operators are implemented by either unitary or anti unitary operators of the underlying hilbert space

coexistence of quantum operations quantum operations are used to describe the observed probability distributions and conditional states of the measured system in this paper we address the problem of their joint mea surability coexistence we derive two equivalent coexistence cri teria the two most common classes of operations luders opera tions and conditional state preparators are analyzed it is shown that luders operations are coexistent only under very restrictive conditions when the associated effects are either proportional to each other or disjoint

preservers on hilbert space effects in this paper we study a new class of transformations on the set of all hilbert space effects this consists of the bijective maps which preserve the order and zero product in both directions the main result of the paper gives a complete description of the structure of those transformations as applications we obtain additional new results and some former ones as easy corollaries in particular we obtain the form of the ortho order automorphisms as well as that of the sequential automorphisms in the last paragraph of the paper we show that the automorphisms of these two kinds belong to our class of transformations even when their domain is the set of all effects in a general von neumann algebra

the quasi complementarity problem abstract variational inequality techniques are used to suggest a unified and general iterative algorithm for computing the approximate solution of a new class of complementarity problems the convergence properties of this algorithm are also discussed

nonlinear functionals of multi d discrete velocity boltzmann equations in this paper we study nonlinear functionals measuring potential interactions and l1 distance between two mild solutions for the multi dimensional discrete velocity boltzmann equations when the initial data are a small perturbation of a vacuum we employ bony s dispersion estimates to show that these functionals satisfy lyapunov type estimates which are useful for the study of time asymptotics and l1 stability of mild solutions

automorphisms of hilbert space effect algebras abstract we consider bijections of the hilbert space effect algebra that preserve the algebraic structures in one direction and have some other properties it is shown that if e h e h is conditionally multiplicative and conditionally additive then is implemented by a unitary or antiunitary operator on h we also show that 2 local ortho order automorphisms on e h are of the same form if dim h 3

hua s fundamental theorem of geometry of rectangular matrices over eas division rings abstract the fundamental theorem of geometry of rectangular matrices describes the general form of bijective maps on the space of all m n matrices over a division ring d which preserve adjacency in both directions this result proved by hua in the nineteen forties has been recently improved in several directions one can study such maps without the bijectivity assumption or one can try to get the same conclusion under the weaker assumption that adjacency is preserved in one direction only and the last possibility is to study maps acting between matrix spaces of different sizes the optimal result would describe maps preserving adjacency in one direction only acting between spaces of rectangular matrices of different sizes in the absence of any regularity condition injectivity or surjectivity a division ring is said to be eas if it is not isomorphic to any proper subring it has been known before that it is possible to construct adjacency preserving maps with wild behavior on matrices over division rings that are not eas for matrices over eas division rings it has been recently proved that adjacency preserving maps acting between matrix spaces of different sizes satisfying a certain weak surjectivity condition are either degenerate or of the expected simple standard form we will remove this weak surjectivity assumption thus solving completely the long standing open problem of the optimal version of hua s theorem

measure solutions of the steady boltzmann equation in a slab it is shown that the steady boltzmann equation in a slab 0 a has solutionsx x such that the ingoing boundary measures 0 0 and 0 can be prescribed a priori the collision kernel is truncated such that particles with smallx component of the velocity have a reduced collision rate

characterizations of the automorphisms of hilbert space effect algebras in this paper we characterize the automorphisms of hilbert space effect algebras by means of their preserving properties which concern certain relations and quantities appearing in quantum measurement theory

linear maps on the space of all bounded observables preserving maximal deviation abstract in this paper we determine all the bijective linear maps on the space of bounded observables which preserve a fixed moment or the variance nonlinear versions of the corresponding results are also presented

measure valued solutions and the phenomenon of blow down in logarithmic diffusion abstract the existence of solutions of elliptic and parabolic equations with data a measure has always been quite important for the general theory a prominent example being the fundamental solutions of the linear theory in nonlinear equations the existence of such solutions may find special obstacles that can be either essential or otherwise they may lead to more general concepts of solution we give a particular review of results in the field of nonlinear diffusion as a new contribution we study in detail the case of logarithmic diffusion associated with ricci flow in the plane where we can prove existence of measure valued solutions the surprising thing is that these solutions become classical after a finite time in that general setting the standard concept of weak solution is not adequate but we can solve the initial value problem for the logarithmic diffusion equation in the plane with bounded nonnegative measures as initial data in a suitable class of measure solutions we prove that the problem is well posed the phenomenon of blow down in finite time is precisely described initial point masses diffuse into the medium and eventually disappear after a finite time t i m i 4

continuous jordan triple endomorphisms of p2 abstract we describe the structure of all continuous jordan triple endomorphisms of the set p 2 of all positive definite 2 2 matrices thus completing a recent result of ours we also mention an application concerning sorts of surjective generalized isometries on p 2 and as second application we complete another former result of ours on the structure of sequential endomorphisms of finite dimensional effect algebras

order automorphisms of hilbert space effect algebras the two dimensional case it is well known that the order automorphisms of the effect algebra of a hilbert space of dimension not less than three are implemented by unitary or antiunitary operators the aim of this paper is to show that the same assertion also holds true in the two dimensional case

fedosov quantization of lagrange finsler and hamilton cartan spaces and einstein gravity lifts on co tangent bundles we provide a method of converting lagrange and finsler spaces and their legendre transforms to hamilton and cartan spaces into almost kahler structures on tangent and cotangent bundles in particular cases the hamilton spaces contain nonholonomic lifts of pseudo riemannian einstein metrics on effective phase spaces this allows us to define the corresponding fedosov operators and develop deformation quantization schemes for nonlinear mechanical and gravity models on lagrange and hamilton fedosov manifolds

global weak solutions and uniform lp stability of the boltzmann enskog equation abstract we present the regularity theory of renormalized solutions and uniform l p stability estimates of the boltzmann enskog model we use a multi dimensional bony type functional to control the time phase space integral of a truncated collision operator we employ cercignani s arguments and a bony type functional to show that the renormalized solutions to the boltzmann enskog model are weak solutions in usual distributional sense for the uniform l p stability estimate we use lu s trick together with the holder inequality

a geometric characterization of invertible quantum measurement maps a geometric characterization is given for invertible quantum measurement maps denote by s h the convex set of all states i e trace 1 positive operators on hilbert space h with dimh and 1 2 the line segment joining two elements 1 2 in s h it is shown that a bijective map s h s h satisfies 1 2 1 2 for any 1 2 s if and only if has one of the following forms m m tr m m or m tm tr m tm where m is an invertible bounded linear operator and t is the transpose of with respect to an arbitrarily fixed orthonormal basis

a boundary value problem for the two dimensional broadwell model it is shown that a certain boundary value problem for the steady two dimensional broadwell model on a rectangle has a solution the boundary conditions specify the ingoing particle densities on each side of the rectangle

transformations of the unitary group on a hilbert space abstract let h be an infinite dimensional separable complex hilbert space and u be the group of all unitary operators on h motivated by the algebraic properties of surjective isometries of u that have recently been revealed and also by some classical results related to automorphisms of the unitary groups of operator algebras we determine the structures of bijective transformations of u that respect certain algebraic operations these are among others the usual product of operators the jordan triple product the inverted jordan triple product and the multiplicative commutator our basic approach to obtain these results is the use of commutativity preserving transformations on the unitary group

the mackey gleason problem let a be a von neumann algebra with no direct summand of type i 2 and let p a be its lattice of projections let x be a banach space let m p a x be a bounded function such that m p q m p m q whenever p and q are orthogonal projections the main theorem states that m has a unique extension to a bounded linear operator from a to x in particular each bounded complex valued finitely additive quantum measure on p a has a unique extension to a bounded linear functional on a

on the cauchy problem for boltzmann equations global existence and weak stability we study the large data cauchy problem for boltzmann equations with general collision kernels we prove that sequences of solutions which satisfy only the physically natural a priori bounds converge weakly in l to a solution from this stability result we deduce global existence of a solution to the cauchy problem our method relies upon recent compactness results for velocity averages a new formulation of the boltzmann equation which involves nonlinear normalization and an analysis of subsolutions and supersolutions it allows us to overcome the lack of strong a priori estimates and define a meaningful collision operator for general configurations

order preserving bijections of c x i abstract let x be a compact hausdorff space which satisfies the first axiom of countability i 0 1 and c x i the set of all continuous functions from x to i in the paper we will give a description of bijective maps on c x i which preserve the order in both directions

on nonlinear stationary half space problems in discrete kinetic theory we show that every steady discrete velocity model of the boltzmann equation on the real line i d dx fi ci f which satisfies anh theorem and for which all i 0 has solutions on the half line 0 which take prescribed non negativefi o if i 0 and approach a certain manifold of maxwellians asx such solutions give the density distribution in a knudsen boundary layer in the discrete velocity case

boundary value problems for the steady boltzmann equation we discuss steady boundary value problems for the boltzmann equation with inflow and diffusive boundary conditions in one two and three dimensions with suitable truncations of the collision kernel general existence and uniqueness results are obtained if the domain is sufficiently small in one dimension the existence of solutions on general intervals is obtained by abstract fixed point theory

a classification of well posed kinetic layer problems in the first part of this paper we study the half space boundary value problem for the boltzmann equation with an incoming distribution obtained when considering the boundary layer arising in the kinetic theory of gases as the mean free path tends to zero we linearize it about a drifting maxwellian and prove that as conjectured by cercignani 4 the problem is well posed when the drift velocity u exceeds the sound speed c but that one respectively four five additional conditions must be imposed when 0 u c respectively c u 0 and u c in the second part we show that the well posedness and the asymptotic behavior results for kinetic layers equations with prescribed incoming flux can be extended to more general and realistic boundary conditions

a global existence theorem for the initial boundary value problem for the boltzmann equation when the boundaries are not isothermal we extend the existence theorem recently proved by hamdache for the initial boundary value problem for the nonlinear boltzmann equation in a vessel with isothermal boundaries to more general situations including the case when the boundaries are not isothermal in the latter case a cut off for large speeds is introduced in the collision term of the boltzmann equation

trend to equilibrium of weak solutions of the boltzmann equation in a slab with diffusive boundary conditions recently r illner and the author proved that under a physically realistic truncation on the collision kernel the boltzmann equation in the one dimensional slab 0 1 with general diffusive boundary conditions at 0 and 1 has a global weak solution in the traditional sense here it is proved that when the maxwellians associated with the boundary conditions atx 0 andx 1 are the same maxwellianmw then the solution is uniformly bounded and tends tomw fort

global weak solutions of the boltzmann equation in a slab with diffusive boundary conditions it is proved that under a physically realistic truncation of the collision kernel the boltzmann equation in the one dimensional slab 0 1 with general diffusive boundary conditions at 0 and 1 has a global weak solution in the traditional sense this solution satisfies the boundary conditions almost everywhere and has at worst exponentially growing total energy

multiplicative lie isomorphisms between factors abstract let m n be factors if m n is a multiplicative lie isomorphism then is of the form where is a linear isomorphism or a conjugate linear isomorphism or the negative of a linear anti isomorphism or the negative of a conjugate linear anti isomorphism of m onto n and is a mapping of m into c i i c which maps commutators into zero

a constructive approach to steady nonlinear kinetic equations abstract we study steady boundary value problems of nonlinear kinetic theory using a continuation argument based on the variation of the knudsen number we derive a method for the construction of steady solutions of discrete velocity models in a slab this method is readily transformed into a numerical code in a preliminary numerical test case the numerical scheme turns out to yield solutions even for knudsen numbers small enough to calculate with high precision the asymptotic flow field adjacent to a kinetic boundary layer thus we are able to numerically simulate in a simplified situation the transition from a mesoscopic kinetic boundary layer to the macroscopic far field

characterization of the sequential product on quantum effects we present a characterization of the standard sequential product of quantum effects the characterization is in terms of algebraic continuity and duality conditions that can be physically motivated

order automorphisms of the set of bounded observables let h be a complex hilbert space and denote by bs h the set of all self adjoint bounded linear operators on h in this article we describe the form of all bijective maps no linearity or continuity is assumed on bs h which preserve the order in both directions

a boundary value problem for discrete velocity models on considere deux problemes aux valeurs limites non lineaires concernant un ecoulement stationnaire a une dimension entre des plaques paralleles