a smooth transition model between kinetic and diffusion equations this paper presents a model which provides a smooth transition between a kinetic and a diffusion domain the idea is to use a buffer zone in which both diffusion and kinetic equations will be solved the solution of the original kinetic equation will be recovered as the sum of the solutions of these two equations we use an artificial connecting function which makes the equation on each domain degenerate at the end of the buffer zone thus no boundary condition is needed at the transition point this model avoids the delicate issue of finding the interface condition or iteration in a typical domain decomposition method that couples a kinetic equation with hydrodynamic equations a new asymptotic preserving method for this model is introduced and numerical examples are used to validate this new model and the new numerical method

finiteness and iteration conditions for semigroups abstract let s be a semigroup and m and n two integers such that m 0 and n 0 we say that s verifies the iteration property c n m if the following condition is verified for any sequence s1 s2 sm of m elements of s there exist i j such that 1 i j m and s1 sm s1 si 1 si sj nsj 1 sm the main result of the paper is that if a finitely generated semigroup s satisfies c 2 m or c 3 m for a suitable m 0 then s is finite an application to the theory of regular languages is given there exists a positive uniform block pumping property which assures the regularity of a language this result gives a partial answer to a question raised in ehrenfeucht 1981

a relaxation procedure for domain decomposition methods using finite elements we present the convergence analysis of a new domain decomposition technique for finite element approximations this technique was introduced in 11 and is based on an iterative procedure among subdomains in which transmission conditions at interfaces are taken into account partly in one subdomain and partly in its adjacent no global preconditioner is needed in the practice but simply single domain finite element solvers are required an optimal strategy for an automatic selection of a relaxation parameter to be used at interface subdomains is indicated applications are given to both elliptic equations and incompressible stokes equations

adaptive mesh and algorithm refinement using direct simulation monte carlo adaptive mesh and algorithm refinement amar embeds a particle method within a continuum method at the finest level of an adaptive mesh refinement amr hierarchy the coupling between the particle region and the overlaying continuum grid is algorithmically equivalent to that between the fine and coarse levels of amr direct simulation monte carlo dsmc is used as the particle algorithm embedded within a godunov type compressible navier stokes solver several examples are presented and compared with purely continuum calculations

rational languages and the burnside problem abstract the problem of finding regularity conditions for languages is via the syntactic monoid closely related to the classical burnside problem this survey paper presents several results and conjectures in this direction as well as on related subjects including bounded languages pumping square free words commutativity and rational power series

a multiscale fast semi lagrangian method for rarefied gas dynamics in this paper we consider the extension of the method developed in dimarco and loubere 2013 22 23 with the aim of facing the numerical resolution of multi scale problems arising in rarefied gas dynamics the scope of this work is to consider situations in which the whole domain does not demand the use of a kinetic model everywhere this is the case of many realistic applications some regions of the computational domain require a microscopic description given by a kinetic model while the rest of the domain can be described by a coarser model of fluid type our aim is to show how the kinetic scheme developed in the pre cited articles is perfectly suited for building domain decomposition strategies which make the method more attractive with respect to classical numerical techniques for kinetic equations and multi scale realistic problems several numerical evidences are provided in this work in the two dimensional and three dimensional settings to assess the efficiency of the domain decomposition scheme

second order boltzmann schemes for compressible euler equations in one and two space dimensions a class of second order numerical schemes for the compressible euler equations is described and their l 1 stability i e rho geqq 0 t geqq 0 is proved following van leer s approach the solution rho u sqrt t here is represented as piecewise linear functions the necessity of a slope limitation appears naturally in the derivation of the schemes but it can be less strict than the slope reconstructions usually used these schemes are written in terms of explicit flux splitting formula and are naturally multidimensional in space the upwinding is obtained through a very generalized notion of characteristics the kinetic one

definability in the lattice of equational theories of commutative semigroups in this paper we study first order definability in the lattice of equational theories of commutative semigroups in a series of papers j jezek solving problems posed by a tarski and r mckenzie has proved in particular that each equational theory is first order definable in the lattice of equational theories of a given type up to automorphism and that such lattices have no automorphisms besides the obvious syntactically defined ones with exceptions for special unary types he has proved also that the most important classes of theories of a given type are so definable in a later paper jezek and mckenzie have almost proved the same facts for the lattice of equational theories of semigroups there were good reasons to believe that the same can be proved for the lattice of equational theories of commutative semigroups in this paper however we show that the case of commutative semigroups is different

wavelets and multigrid this note explores the suggestive similarities between wavelet multiresolution and multigrid approaches to general operator equations after presenting the essentials of wavelet and multigrid methods it can be shown that classical multigrid methods use near orthogonal basis functions to provide the same orthogonal decomposition of the fine grid space bf omega h that multiresolution methods generate for the maximum resolution space v 0

automorphisms of the lattice of equational theories of commutative semigroups in this paper we complete the study of the first order definability in the lattice of equational theories of commutative semigroups started by a kisielewicz in trans amer math soc 356 2004 3483 3504 we describe the group of automorphisms of this lattice and characterize first order definable theories thus solving the problems posed by r mckenzie and a kisielewicz

control of modeling errors in the coupling of linear transport and diffusion models we consider in this paper the initial boundary value problem for the 1d neutron transport equation with isotropic scattering set in some bounded interval with inflow boundary conditions the usual parabolic scaling yields the diffusive limit a surrogate model coupling transport and diffusion equations is then introduced in order to accurately assess the value of specific quantities of interest the control of the quality of the computation with respect to such a quantity of interest is performed by means of an approach for modeling error estimation combined with an adaptive strategy to control the surrogate model if necessary

hybrid continuum molecular simulations of transient gas flows with rarefaction an adaptively coupled continuum molecular approach for compressible viscous flows in transient calculations is presented the continuum domain is described by the unsteady compressible navier stokes equations and the molecular domain is solved by direct simulation monte carlo a strategy is described to extend the overlapped schwarz method with dirichlet dirichlet boundary condition coupling procedure to transient simulations the method has been successfully validated against full direct simulation monte carlo results for transient simulations of a one dimensional shock tube and a two dimensional pressure driven slit flow a sensitivity analysis showed that the used overlapped schwarz coupling method with dirichlet dirichlet boundary conditions is only weakly sensitive to various parameters e g the exact position of the continuum molecular interface the size of the overlap region and the scatter in the molecular solution which is a clear advantage over the more commonly used flux based coupling technique another advantage of the chosen coupling method is that the continuum and molecular time steps can be decoupled and that in general a coupling time step can be used that is much larger than the molecular time step the study performed also highlighted a limit of the method it was found to be necessary to keep the courant number based on the coupling time step the cell size in the continuum region and the molecular most probable velocity below 1 to avoid instabilities

irreducible varieties of commutative semigroups abstract in this paper we describe the varieties of commutative semigroups that are meet and join irreducible in the lattice of the varieties of commutative semigroups we apply the method of a kisielewicz trans amer math soc 342 1994 275 305 this leads to investigation of the covering relation in the lattices of remainders and the algebraic structure of the remainders involving permutation groups acting on the sequences of positive integers in particular along the way we prove a theorem about existence of unique minimal generators for remainders and provide algorithms to determine all the covers and dual covers of a given variety of commutative semigroups

a new wavelet multigrid method the standard multigrid procedure performs poorly or may break down when used to solve certain problems such as elliptic problems with discontinuous or highly oscillatory coefficients the method discussed in this paper solves this problem by using a wavelet transform and schur complements to obtain the necessary coarse grid interpolation and restriction operators a factorized sparse approximate inverse is used to improve the efficiency of the resulting method numerical examples are presented to demonstrate the versatility of the method

a multiscale kinetic fluid solver with dynamic localization of kinetic effects this paper collects the efforts done in our previous works 7 9 10 to build a robust multiscale kinetic fluid solver our scope is to efficiently solve fluid dynamic problems which present non equilibrium localized regions that can move merge appear or disappear in time the main ingredients of the present work are the followings ones a fluid model is solved in the whole domain together with a localized kinetic upscaling term that corrects the fluid model wherever it is necessary this multiscale description of the flow is obtained by using a micro macro decomposition of the distribution function 9 the dynamic transition between fluid and kinetic descriptions is obtained by using a time and space dependent transition function to efficiently define the breakdown conditions of fluid models we propose a new criterion based on the distribution function itself several numerical examples are presented to validate the method and measure its computational efficiency

domain decomposition for compressible navier stokes equations with different discretizations and formulations the purpose of this work is to couple different numerical models and approximations for the calculation of high speed external flows governed by the compressible navier stokes equations the proposed coupling is achieved by the boundary conditions which impose viscous fluxes and friction forces on the body for the calculation of the global external flow and which impose dirichlet type boundary conditions on the interface for the local model

coupling boltzmann and navier stokes equations by friction the aim of this paper is to introduce and validate a coupled navier stokes boltzman approach for the calculation of hypersonic rarefied flows around manoeuvering vehicles the proposed strategy uses locally a kinetic model in the boundary layer coupled through wall friction forces to a global navier stokes solver dif ferent numerical experiments illustrate the potentialities of the method

unification in commutative idempotent monoids abstract embedding sets as a datastructure into resolution based deduction requires a unification algorithm respecting associativity commutativity and idempotence of the constructor function union we shall present such an algorithm and prove its correctness and termination although this algorithm is very simple the enormous proliferation of unifiers restricts its value to theoretical considerations for practical purposes the more special unitary theory of boolean expressions seem to be better suited

convergence analysis of a transmission algorithm for convection diffusion problems we prove the convergence of the transmission time marching algorithm for the beta monoscale multimodel methods for hydrodynamics type problems our analysis is based on the author s transmission multiplier method we introduced in c r acad sci paris ser i math 328 1999 pp 637 642 and the local global and trace estimates we developed in j math anal appl 229 1999 pp 137 157 abstr appl anal 3 2001 pp 131 150

infinite words with linear subword complexity abstract in section 1 we study the relations among some combinatorial properties of infinite words especially in the case of infinite words with linear subword complexity the main result of section 1 concerns a permutation property of infinite words with linear complexity in section 2 we investigate the special case of the sturmian infinite words the main result is that a sturmian infinite word associated to a real number contains no k th powers iff has a continued fraction expansion with bounded partial quotients in section 3 it is shown that some of the results of sections 1 and 2 are optimal

coupling of viscous and inviscid stokes equations via a domain decomposition method for finite elements a generalized stokes problem is addressed in the framework of a domain decomposition method in which the physical computational domain is partitioned into two subdomains 1 and 2 three different situations are covered in the former the viscous terms are kept in both subdomains then we consider the case in which viscosity is dropped out everywhere in finally a hybrid situation in which viscosity is dropped out only in 1 is addressed the latter is motivated by physical applications in all cases correct transmission conditions across the interface between 1 and 2 are devised and an iterative procedure involving the successive resolution of two subproblems is proposed the numerical discretization is based upon appropriate finite elements and stability and convergence analysis is carried out we also prove that the iteration by subdomain algorithms which are associated with the various domain decomposition approaches converge with a rate independent of the finite element mesh size

a fast wavelet multigrid method to solve elliptic partial differential equations abstract in this paper we present a wavelet based multigrid approach to solve elliptic boundary value problems encountered in mathematical physics the system of equations arising from finite difference discretization is represented in wavelet basis these equations are solved using multiresolution properties of wavelets characterized by sparse matrices having condition number o 1 together with a multigrid strategy for accelerating convergence the filter coefficients of d 2 k k 2 3 4 from daubechies family of wavelets are used to demonstrate the effectiveness and efficiency of the method the distinguishing feature of the method is it works as both solver and preconditioner as a consequence it avoids instability minimizes error and speeds up convergence compared to the classical multigrid method this approach requires substantially shorter computation time at the same time meeting accuracy requirements it is found that just one cycle is enough for the convergence of wavelet multigrid scheme whereas normally 7 8 cycles are required in classical multigrid schemes to meet the same accuracy numerical examples show that the scheme offers a fast and robust technique for elliptic pde s

rigorous derivation and analysis of coupling of kinetic equations and their hydrodynamic limits for a simplified boltzmann model in this paper we derive rigorously the coupling of kinetic equations and their hydrodynamic limits for a simplified kinetic model we prove the global convergence of the chapman enskog expansion for this model we then study the existence theory and asymptotic behaviour of the coupled systems to solve the coupled problems we propose to use the transmission time marching algorithm we then develop a convergence theory for the resulting algorithms

a particle particle hybrid method for kinetic and continuum equations we present a coupling procedure for two different types of particle methods for the boltzmann and the navier stokes equations a variant of the dsmc method is applied to simulate the boltzmann equation whereas a meshfree lagrangian particle method similar to the sph method is used for simulations of the navier stokes equations an automatic domain decomposition approach is used with the help of a continuum breakdown criterion we apply adaptive spatial and time meshes the classical sod s 1d shock tube problem is solved for a large range of knudsen numbers results from boltzmann navier stokes and hybrid solvers are compared the cpu time for the hybrid solver is 3 4 times faster than for the boltzmann solver

algorithm refinement for stochastic partial differential equations i linear diffusion a hybrid particle continuum algorithm is formulated for fickian diffusion in the fluctuating hydrodynamic limit the particles are taken as independent random walkers the fluctuating diffusion equation is solved by finite differences with deterministic and white noise fluxes at the interface between the particle and continuum computations the coupling is by flux matching giving exact mass conservation this methodology is an extension of adaptive mesh and algorithm refinement to stochastic partial differential equations results from a variety of numerical experiments are presented for both steady and time dependent scenarios in all cases the mean and variance of density are captured correctly by the stochastic hybrid algorithm for a nonstochastic version i e using only deterministic continuum fluxes the mean density is correct but the variance is reduced except in particle regions away from the interface extensions of the methodology to fluid mechanics applications are discussed

nonlinear multigrid method for solving the llt model our goal in this paper is to study a nonlinear multigrid method for solving the llt model in order to improve the convergence rate of the proposed multigrid method an improved dual iteration is proposed as its smoother furthermore we give the local fourier analysis lfas of the chambolle s dual iterations and a modified smoother for solving the llt model respectively numerical results illustrate the efficiency of the proposed method and indicate that such a multigrid method is more suitable to deal with large sized images

application of maximum principles to the analysis of a coupling time marching algorithm abstract in this paper we study the convergence properties of a coupling time marching algorithm solving convection diffusion problems on two domains using incompatible approximations convergence properties are obtained using local and global estimates of the solutions of convection diffusion problems

a hybrid method for hydrodynamic kinetic flow part i a particle grid method for reducing stochastic noise in kinetic regimes in this work we present a hybrid particle grid monte carlo method for the boltzmann equation which is characterized by a significant reduction of the stochastic noise in the kinetic regime the hybrid method is based on a first order splitting in time to separate the transport from the relaxation step the transport step is solved by a deterministic scheme while a hybrid dsmc based method is used to solve the collision step such a hybrid scheme is based on splitting the solution in a collisional and a non collisional part at the beginning of the collision step and the dsmc method is used to solve the relaxation step for the collisional part of the solution only this is accomplished by sampling only the fraction of particles candidate for collisions from the collisional part of the solution performing collisions as in a standard dsmc method and then projecting the particles back onto a velocity grid to compute a piecewise constant reconstruction for the collisional part of the solution the latter is added to a piecewise constant reconstruction of the non collisional part of the solution which in fact remains unchanged during the relaxation step numerical results show that the stochastic noise is significantly reduced at large knudsen numbers with respect to the standard dsmc method indeed in this algorithm the particle scheme is applied only on the collisional part of the solution so only this fraction of the solution is affected by stochastic fluctuations but since the collisional part of the solution reduces as the knudsen number increases stochastic noise reduces as well at large knudsen numbers

complexity of makanin s algorithm the exponent of periodicity is an important factor in estimates of complexity of word unification algorithms we prove that the exponent of periodicity of a minimal solution of a word equation is of order 2 1 07d where d is the length of the equation we also give a lower bound 2 0 29d so our upper bound is almost optimal and exponentially better than the original bound 6d 22d4 2 consequently our result implies an exponential improvement of known upper bounds on complexity of word unification algorithms

covering relation for equational theories of commutative semigroups abstract in this paper we describe the covering relation in the lattice of the equational theories of commutative semigroups we use the description and the methods worked out in an earlier paper by the second author 1994 trans amer math soc 342 275 306

a unified gas kinetic scheme for continuum and rarefied flows iv fluid dynamic equations are valid in their respective modeling scales such as the particle mean free path scale of the boltzmann equation and the hydrodynamic scale of the navier stokes ns equations with a variation of the modeling scales theoretically there should have a continuous spectrum of fluid dynamic equations even though the boltzmann equation is claimed to be valid in all scales many boltzmann solvers including direct simulation monte carlo method require the cell resolution to the order of particle mean free path scale therefore they are still single scale methods in order to study multiscale flow evolution efficiently the dynamics in the computational fluid has to be changed with the scales a direct modeling of flow physics with a changeable scale may become an appropriate approach the unified gas kinetic scheme ugks is a direct modeling method in the mesh size scale and its underlying flow physics depends on the resolution of the cell size relative to the particle mean free path the cell size of ugks is not limited by the particle mean free path with the variation of the ratio between the numerical cell size and local particle mean free path the ugks recovers the flow dynamics from the particle transport and collision in the kinetic scale to the wave propagation in the hydrodynamic scale the previous ugks is mostly constructed from the evolution solution of kinetic model equations even though the ugks is very accurate and effective in the low transition and continuum flow regimes with the time step being much larger than the particle mean free time it still has space to develop more accurate flow solver in the region where the time step is comparable with the local particle mean free time in such a scale there is dynamic difference from the full boltzmann collision term and the model equations this work is about the further development of the ugks with the implementation of the full boltzmann collision term in the region where it is needed the central ingredient of the ugks is the coupled treatment of particle transport and collision in the flux evaluation across a cell interface where a continuous flow dynamics from kinetic to hydrodynamic scales is modeled the newly developed ugks has the asymptotic preserving ap property of recovering the ns solutions in the continuum flow regime and the full boltzmann solution in the rarefied regime in the mostly unexplored transition regime the ugks itself provides a valuable tool for the non equilibrium flow study the mathematical properties of the scheme such as stability accuracy and the asymptotic preserving will be analyzed in this paper as well

permutability class of a semigroup given a permutation sn a semigroup s is called permutable if x1x2 xn x 1 x 2 x n for all n tuples x1 x2 xn s various permutability conditions were considered for special classes of permutations we define the permutability class of a semigroup s to be the infinite sequence g2 g3 g4 of the invariance groups gn gn s of the operation x1x2 xn on s the aim of this paper is to give a description of such sequences which generalizes a number of old results on permutability conditions in semigroups

coupling of the boltzmann and euler equations with automatic domain decomposition a criterion for automatic domain decomposition has been introduced for the coupling of the boltzmann and euler equations this criterion is obtained by using the grad s 13 moments expansion method the boltzmann and euler equations have been solved by the particle method this criterion has been further tested for the spatial homogeneous relaxation case and the coupling of the boltzmann and euler equations in two dimensional physical space some numerical results obtained from the particle code of the full boltzmann equation are compared with those of coupling of the boltzmann and euler equations

an iteration by subdomain overlapping dirichlet robin domain decomposition method for advection diffusion problems we present a new overlapping dirichlet robin domain decomposition method the method uses dirichlet and robin transmission conditions on the interfaces of an overlapping partitioning of the computational domain we derive interface equations to study the convergence of the method and show its properties through four numerical examples the mathematical framework is general and can be applied to derive overlapping versions of all the classical nonoverlapping methods

some combinatorial properties of the thue morse sequence and a problem in semigroups abstract some combinatorial properties of the special factors of the thue morse sequence in a two letter alphabet are considered an application of this analysis to a problem in semigroups is given

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

unification in primal algebras their powers and their varieties this paper examines the unification problem in the class of primal algebras and the varieties they generate an algebra is called primal if every function on its carrier can be expressed just in terms of the basic operations of the algebra the two element boolean algebra is the simplest nontrivial example every truth function can be realized in terms of the basic connectives for example negation and conjunction it is shown that unification in primal algebras is unitary that is if an equation has a solution it has a single most general one two unification algorithms based on equation solving techniques for boolean algebras due to boole and lo wenheim are studied in detail applications include certain finite post algebras and matrix rings over finite fields the former are algebraic models for many valued logics the latter cover in particular modular arithmetic then unification is extended from primal algebras to their direct powers which leads to unitary unification algorithms covering finite post algebras finite semisimple artinian rings and finite semisimple nonabelian groups finally the fact that the variety generated by a primal algebra coincides with the class of its subdirect powers is used this yields unitary unification algorithms for the equational theories of post algebras and p rings

convergence analysis of domain decomposition algorithms with full overlapping for the advection diffusion problems the aim of this paper is to study the convergence properties of a time marching algorithm solving advection diffusion problems on two domains using incompatible discretizations the basic algorithm is first presented and theoretical or numerical results illustrate its convergence properties this study is based on spectral theory a priori estimates and a di giorgi nash maximum principle

unified solver for rarefied and continuum flows with adaptive mesh and algorithm refinement this paper describes a unified flow solver ufs for rarefied and continuum gas flows the ufs separates the rarefied and continuum flow domains and selects appropriate solvers to combine the efficiency of continuum models with the accuracy of kinetic models the direct numerical solution of the boltzmann transport equation is used in rarefied regions while kinetic schemes of continuum fluid dynamics are used elsewhere using similar computational techniques for the kinetic and continuum solvers and employing intelligent domain decomposition algorithms attain the efficiency and numerical stability of the ufs solutions of test problems are presented to illustrate the capabilities of the ufs for high and low speed flows it is shown that the ufs can dynamically adapt the computational mesh and automatically introduce and remove kinetic patches to provide significant savings by limiting molecular scale solutions only to the regions where they are needed

a coupled ordinates method for solution acceleration of rarefied gas dynamics simulations non equilibrium rarefied flows are frequently encountered in a wide range of applications including atmospheric re entry vehicles vacuum technology and microscale devices rarefied flows at the microscale can be effectively modeled using the ellipsoidal statistical bhatnagar gross krook esbgk form of the boltzmann kinetic equation numerical solutions of these equations are often based on the finite volume method fvm in physical space and the discrete ordinates method in velocity space however existing solvers use a sequential solution procedure wherein the velocity distribution functions are implicitly coupled in physical space but are solved sequentially in velocity space this leads to explicit coupling of the distribution function values in velocity space and slows down convergence in systems with low knudsen numbers furthermore this also makes it difficult to solve multiscale problems or problems in which there is a large range of knudsen numbers in this paper we extend the coupled ordinates method comet previously developed to study participating radiative heat transfer to solve the esbgk equations in this method at each cell in the physical domain distribution function values for all velocity ordinates are solved simultaneously this coupled solution is used as a relaxation sweep in a geometric multigrid method in the spatial domain enhancements to comet to account for the non linearity of the esbgk equations as well as the coupled implementation of boundary conditions are presented the methodology works well with arbitrary convex polyhedral meshes and is shown to give significantly faster solutions than the conventional sequential solution procedure acceleration factors of 5 9 are obtained for low to moderate knudsen numbers on single processor platforms

local and global estimates for the solutions of convection diffusion problems abstract in this paper we develop and study local and global estimates for the solutions of convection diffusion problems respectively with dirichlet neumann and dirichlet boundary conditions this study is based on a combination of aleksandrov bakelman and pucci theory with more standard traces estimates

a wavelet based algebraic multigrid preconditioner for sparse linear systems this work considers the use of discrete wavelet transform dwt based in filters in the construction of the hierarchy of matrices in the algebraic multigrid method amg the two dimensional dwt is applied to produce an approximation of the matrix in each level of the wavelets multiresolution decomposition process in this procedure an operator is created formed only by lowpass filters that is applied to the rows and columns of the matrix capturing this approximation this same operator is used as an intergrid transfer in the amg wavelet based algebraic multigrid method wamg was implemented with daubechies wavelets of orders 6 4 and 2 and used as a preconditioner for the generalized minimal residual method gmres numerical results are presented comparing this new approach with the standard algebraic multigrid as preconditioner for sparse linear systems

a smooth transition model between kinetic and hydrodynamic equations this paper presents a model which provides a smooth transition between a kinetic and a hydrodynamic domain the idea is to use a buffer zone in which both hydrodynamics and kinetic equations will be solved the solution of the original kinetic equation will be recovered as the sum of the solutions of these two equations we use an artificial connecting function which makes the equation on each domain degenerate at the end of the buffer zone thus no boundary condition is needed at the transition point consequently this model avoids the delicate issue of finding the interface condition in a typical domain decomposition method that couples a kinetic equation with hydrodynamic equations a simple kinetic scheme is developed to discretize our model and numerical examples are used to validate the method

a finiteness condition for semigroups generalizing a theorem of hotzel in 1979 hotzel proved 1 l the following interesting finiteness condition for semigroups let s be a finitely generated semigroup if s verifies the minimal condition on principal left ideals resp right ideals and all subgroups of s have finite orders then s is finite this theorem solved a question posed by coudrain and schiitzenberger 3 who proved a similar result with the only difference that s satisfies the minimal condition on principal bi ideals instead of left ideals moreover two finiteness conditions for semigroups due respectively to simon 16 and to de luca and restivo 4 are based on hotzel s theorem in this paper we prove the following generalization of hotzel s theorem in which one supposes that only finitely generated subgroups are finite

a fast solver for navier stokes equations in the lamina regime using mortar finite element and boundary element methods a multistep method is used to solve the navier stokes equations formulated with vorticity and stream function each time step is decomposed into three stages a convection step using the character

unification in commutative semigroups abstract unification is one of the basic concepts of automated theorem proving it concerns such questions as finding solutions of finite sets of equations determining if every solution comes from a most general solution and if so determining how many most general solutions are needed to generate all solutions these solutions given in terms of substitutions are called more formally unifiers the unification type of a variery equational class of algebras is defined according to the cardinality or existence of minimal complete sets of most general unifiers of particular interest from a computational point of view are varieties of groups and semigroups so far the problem has been considered mainly for particular varieties in this paper we determine unification types for all varieties of commutative semigroups in particular we prove that for commutative semigroups the unification problem is solvable in the very strong sense that there is an algorithm which for any two finite sets 1and 2of semigroup equations produces the minimal complete set of the most general unifiers of 1over the variety of commutative semigroups generated by 2 it seems that this is the first so general decidability result in the area

discrete velocity models and numerical schemes for the boltzmann bgk equation in plane and axisymmetric geometries we present new numerical models for computing transitional or rarefied gas flows as described by the boltzmann bgk and bgk es equations we first propose a new discrete velocity model based on the entropy minimization principle this model satisfies the conservation laws and the entropy dissipation moreover the problem of conservation and entropy for axisymmetric flows is investigated we find algebraic relations that must be satisfied by the discretization of the velocity derivative appearing in the transport operator then we propose some models that satisfy these constraints owing to these properties we obtain numerical schemes that are economic in terms of discretization and robust in particular we develop a linearized implicit scheme for computing stationary solutions of the discrete velocity bgk and bgk es models this scheme is the basis of a code which can compute high altitude hypersonic flows in 2d plane and axisymmetric geometries our results are analyzed and compared to other methods

assessment of bhatnagar gross krook approaches for near continuum regime nozzle flows accurate and numerically efficient modeling of low to moderate reynolds number nozzle flow expansions to vacuum can be difficult due to the presence of multiple flow length scales such simulations are important for the prediction of propulsive thrust as well as spacecraft contamination both of which can be difficult to measure in ground based facilities to that end conical nozzle flows were studied for reynolds numbers of 1230 and 12 300 using the direct simulation monte carlo method navier stokes with velocity slip and temperature jump boundary conditions and statistical and deterministic approaches to the solution of the bhatnagar gross krook and ellipsoidal statistical bhatnagar gross krook equations the deterministic and statistical solutions of the bhatnagar gross krook equation were found to be in good agreement with the benchmark direct simulation monte carlo results statistical bhatnagar gross krook and ellipsoidal statistical bhatnagar gross krook methods were also found to be more efficient methods than direct simulation monte carlo in the continuum and near continuum regime and more accurate than the navier stokes equations in the portions of the flow with rarefaction such as the boundary layer and the flow around the nozzle lip

the complexity of the word problems for commutative semigroups and polynomial ideals abstract any decision procedure for the word problems for commutative semigroups and polynomial deals inherently requires computational storage space growing exponentially with the size of the problem instance to which the procedure is applied this bound is achieved by a simple procedure for the semigroup problem