finite resolutions of modules for reductive algebraic groups of a suitable g module m by modules which are required to be direct sums of tensor products of exterior powers of the natural representation in particular in z 31 for partitions 1 and p resolutions are constructed for the modules l f and l f the schur functor corresponding to 1 and the skew schur functor corresponding to a p evaluated at f where f is a free module over a field or the integers the purpose of this paper is to characterise the gl modules which admit such a resolution as those modules which have a filtration in which each successive quotient has the form l f for some partition p by contrast with 2 3 we do not produce resolutions explicitly our methods are independent of those of akin and buchsbaum we give a new proof of their result on the existence of a resolution for l f and are algebraic group theoretic in nature we have therefore cast our main result the theorem of section 1 as a statement about resolutions for reductive algebraic groups over an algebraically closed field one may frequently wish to work over a more general coefficient ring see l 3 and so we treat in some detail chevalley group schemes and general linear group schemes over a principal ideal domain 2 6 and 2 7 giving the appropriate versions of our main result and relating it to the work of akin buchsbaum and weyman

a numerical model for the boltzmann equation with applications to micro flows given an integer lattice email protected r d we define g as the orthogonal group leaving l invariant starting from a basic kinetic model on g we construct a collision operator on l which keeps all the essential features of the classical boltzmann collision operator for a particular 3d lattice we demonstrate the suitability of this discrete model for the numerical simulation of rarefied flows for several examples e g in the context of micro flows we find a good qualitative and quantitative agreement of our simulation results with test data

the maximum covering shortest path problem a multiobjective network design and routing formulation abstract in this paper the authors introduce the maximum covering shortest path problem and the maximum population shortest path problem a special case of the former model both models are formulated as two objective integer programs a summary of the results of a sample problem for the latter formulation is given possible modifications to and extensions and applications of both models are also presented with these formulations the authors extend the concept of coverage from facility location analysis to network design and routing analysis

an l2 quotient algorithm for finitely presented groups abstract the paper develops algorithmic methods to enumerate all normal subgroups of a finitely presented group such that the factor groups are either isomorphic to psl 2 p n or to pgl 2 p n the case of two generators is treated in detail a range of examples starting with the free group on two generators and ending with groups having only finitely many normal subgroups of this type is discussed

discriminants of brauer algebras in this paper we compute gram determinants associated to all cell modules of brauer algebras fancyscript b n partial theoretically we know when a cell module of fancyscript b n partial is equal to its simple head this gives a solution of this long standing problem

algorithms for a multi level network optimization problem in this paper we work on a multi level network optimization problem that integrates into the same model important aspects of i discrete facility location ii topological network design and iii network dimensioning potential applications for the model are discussed stressing its growing importance the multi level network optimization problem treated is defined and a mathematical programming formulation is presented we make use of a branch and bound algorithm based on lagrangean relaxation lower bounds to introduce some new powerful auxiliary algorithms to exactly solve the problem we conduct a set of computational experiments that indicate the quality of the proposed approach

skew modules for reductive groups skew modules for symmetric groups have been investigated by james and peel 13 farahat and peel 9 and clausen s more recently skew modules for general linear groups have been investigated by akin buchsbaum weyman 3 l 2 and kouwenhoven 161 our aim in this paper is to set up in a rather general context a theory of skew modules for reductive algebraic groups for a partition 1 of it james peel 13 obtain a filtration of the specht module sj viewed as a module for the young subgroup corresponding to a decomposition n a b of n the successive quotients in the filtration have the form s h sj p kronecker product where p runs over the partitions of a such that p is a skew partition and s denotes the skew specht module the analogue of this result is proved for general linear groups by akin buchsbaum and weyman 3 theorem 11 4 1 l and kouwenhoven 16 proposition ii 2 2a the analogue for reductive groups is more or less our definition of skew modules this filtration property is in fact a characterisation of skew modules see 1 3 4 and our definition for general linear groups therefore agrees with that of akin buchsbaum and weyman 3 and kouwenhoven 161 it becomes apparent rather quickly from our point of view that the skew modules have a particular kind of filtration see 2 1 1 which in the case of the general linear group is a filtration by schur modules this is a result of kouwenhoven 16 proposition 11 2 2b a for general linear groups kouwenhoven is able to give an explicit description of such a filtration one may then obtain as in kouwenhoven 16 proposition ii 2 2b b the result of james and peel 131 on the existence of specht series for skew modules for the symmetric groups by specializing to a certain weight space i e applying the schur functor as in ll chap 63 we are also able to prove see 2 3 3 the existence of a certain kind of resolution considered by akin and buchsbaum see 1 sects 83 for skew modules for general linear groups our main point of reference is the representation theory of reductive 465 0021 8693 88 3 00

the hierarchical network design problem with multiple primary paths abstract in this paper we develop a suboptimal solution for the hierarchical network design problem hndp with multiple primary paths in practice some networks may require solutions to the hndp with more than one origin destination pair to be connected by primary paths this paper develops a dynamic programming solution to find a suboptimal solution to the problem

a computational strategy for the regularized 13 moment equations with enhanced wall boundary conditions the challenge of modeling low speed rarefied gas flow in the transition regime is well known in this paper we propose a numerical solution procedure for the regularized 13 moment equations within a finite volume framework the stress and heat flux equations arising in the method of moments are transformed into the governing equations for the stress and heat flux deviators based on their first order approximation to model confined flows a complete set of wall boundary conditions for the 13 moment equations are derived based on the maxwell wall boundary model this has been achieved by expanding the molecular distribution function to fourth order accuracy in hermite polynomials empirical correction factors are introduced into the boundary conditions and calibrated against direct simulation monte carlo data the numerical predictions obtained from the regularized 13 moment equations and the navier stokes fourier equations are compared with data generated using the direct simulation monte carlo method for planar couette flow for a range of wall velocities and knudsen numbers 0 012 1 0 the results indicate that the regularized 13 moment equations are in good qualitative agreement with the direct simulation monte carlo data the results also highlight limitations that are caused by the use of a first order expansion of the third moment

an invariant of regular isotopy this paper studies a two variable laurent polynomial invariant of regular isotopy for classical unoriented knots and links this invariant is denoted lk for a link k and it satisfies the axioms 1 regularly isotopic links receive the same polynomial 2 lo0 1 3 l al l a l 4 l small diagrams indicate otherwise identical parts of larger diagrams regular isotopy is the equivalence relation generated by the reidemeister moves of type ii and type iii invariants of ambient isotopy are obtained from l by writhe normalization

enhanced formulations and branch and cut for the two level network design problem with transition facilities abstract we consider a new combinatorial optimization problem that combines network design and facility location aspects given a graph with two types of customers and two technologies that can be installed on the edges the objective is to find a minimum cost subtree connecting all customers while the primary customers are served by a primary subtree that is embedded into the secondary subtree in addition besides fixed link installation costs facility opening costs associated to each node where primary and secondary subtree connect have to be paid the problem is called the two level network design problem with transition facilities tlndf we first model the problem on an extended graph where an additional set of arcs corresponds to the installation of node facilities and propose a cut set based model for the tlndf that is defined on this extended graph we present several theoretical results relating families of cut set inequalities on the extended graph with subfamilies of cut set inequalities on the original graph we then show how a standard multi commodity flow model defined on the original graph can be strengthened using disaggregation by technology we prove that the disaggregated compact formulation on the original graph provides the same lower bound as the cut set formulation on the extended graph we develop a branch and cut algorithm for solving the tlndf the performance of this algorithm is improved by separating subfamilies of cut set inequalities on the original graph our computational study confirms the efficiency and applicability of the new approach

quantum weyl reciprocity and tilting modules quantum weyl reciprocity relates the representation theory of hecke algebras of type a with that of q schur algebras this paper establishes that weyl reciprocity holds integrally i e over the ring q q 1 of laurent polynomials and that it behaves well under base change a key ingredient in our approach involves the theory of tilting modules for q schur algebras new results obtained in that direction include an explicit determination of the ringel dual algebra of a q schur algebra in all cases in particular in the most interesting situation the ringel dual identifies with a natural quotient algebra of the hecke algebra

on schur algebras and related algebras vi some remarks on rational and classical schur algebras abstract in a recent paper dipper and doty 4 introduced certain finite dimensional algebras associated with the natural module of the general linear group and its dual which they call rational schur algebras we give a proof via tilting modules that these algebras are in fact generalised schur algebras using the same technique we show that certain finite dimensional algebras associated with classical groups introduced by doty 20 are quasi hereditary algebras a generalised schur algebras may be viewed as a quotient of the algebra of distributions of a reductive group by a certain ideal we give generators for this ideal

scale induced closure for approximations of kinetic equations the order of magnitude method proposed by struchtrup phys fluids 16 11 3921 3934 2004 is a new closure procedure for the infinite moment hierarchy in kinetic theory of gases taking into account the scaling of the moments the scaling parameter is the knudsen number kn which is the mean free path of a particle divided by the system size

cellular bases for the brauer and birman murakami wenzl algebras abstract an explicit combinatorial construction is given for cellular bases in the sense of graham and lehrer for the birman murakami wenzl and brauer algebra we provide cell modules for the birman murakami wenzl and brauer algebras with bases index by certain bitableaux generalising the murphy basis for the specht modules of the iwahori hecke algebra of the symmetric group the bases for the cell modules given here are constructed non diagrammatically and hence are relatively amenable to computation

reducing the hierarchical network design problem abstract the hierarchical network design problem hndp can be seen as a minimum spanning tree problem involving two weight functions it is shown that the hndp is a special case of the directed steiner tree problem theorems are given to obtain optimal arcs that are used in a lagrangean relaxation of the linear programming model reduction tests reducing the size of the problem graph and or eliminating variables from this program are specialized and developed for the hndp the presented techniques are illustrated on example problems from the literature and computational results for the reduction tests are given

schur weyl duality for orthogonal groups we prove schur weyl duality between the brauer algebra bn m and the orthogonal group om k over an arbitrary infinite field k of odd characteristic if m is even we show that each connected component of the orthogonal monoid is a normal variety this implies that the orthogonal schur algebra associated to the identity component is a generalized schur algebra as an application of the main result an explicit and characteristic free description of the annihilator of n tensor space v n in the brauer algebra bn m is also given

heuristics lps and trees on trees network design analyses we study a class of models known as overlay optimization problems composed of base and overlay subproblems linked by the requirement that the overlay solution be contained in the base solution in some telecommunication settings a feasible base solution is a spanning tree and the overlay solution is an embedded steiner tree or path for the general overlay optimization problem we describe a composite heuristic solution procedure that selects the better of two feasible solutions obtained by independently solving the base and the overlay subproblems and establish worst case performance guarantees as a function of the worst case bounds for the subproblems for the composite heuristic as well as an lp relaxation of the model for certain special cases both the heuristic and the lp relaxation have a worst case bound of 4 3 we extend this analysis to multiple overlays on the same base solution producing the first known worst case bounds approximately proportional to the square root of the number of commodities for the uncapacitated multicommodity network design problem in a companion paper we develop heuristic performance guarantees for various new multi tier survivable network design models that incorporate both multiple facility types and differential node connectivity levels

a dual based algorithm for multi level network design given an undirected network with l possible facility types for each edge and a partition of the nodes into l levels or grades the multi level network design mlnd problem seeks a fixed cost minimizing design that spans all the nodes and connects the nodes at each level by facilities of the corresponding or higher grade this problem generalizes the well known steiner network problem and the hierarchical network design problem and has applications in telecommunication transportation and electric power distribution network design in a companion paper we studied alternative model formulations for a two level version of this problem and analyzed the worst case performance of several heuristics based on steiner network and spanning tree solutions this paper develops a dual based algorithm for the mlnd problem the method first performs problem preprocessing to fix certain design variables and then applies a dual ascent procedure to generate upper and lower bounds on the optimal value we report extensive computational results on large random two level test problems containing up to 500 nodes and 5 000 edges with varying cost structures the integer programming formulation of the largest of these problems has 20 000 integer variables and over 5 million constraints our tests indicate that the dual based algorithm is very effective producing solutions that are within 0 9 of optimality

instabilities in the chapman enskog expansion and hyperbolic burnett equations it is well known that the classical chapman enskog procedure does not work at the level of burnett equations the next step after the navier stokes equations roughly speaking the reason is that the solutions of higher equations of hydrodynamics burnett s etc become unstable with respect to short wave perturbations this problem was recently attacked by several authors who proposed different ways to deal with it we present in this paper one of possible alternatives first we deduce a criterion for hyperbolicity of burnett equations for the general molecular model and show that this criterion is not fulfilled in most typical cases then we discuss in more detail the problem of truncation of the chapman enskog expansion and show that the way of truncation is not unique the general idea of changes of coordinates based on analogy with the theory of dynamical systems leads finally to nonlinear hyperbolic burnett equations hbes without using any information beyond the classical burnett equations it is proved that hbes satisfy the linearized h theorem the linear version of the problem is studied in more detail the complete chapman enskog expansion is given for the linear case a simplified proof of the slemrod identity for burnett coefficients is also given

asymptotic codimensions of mk e abstract we show that the codimension sequence of the algebra of k k matrices over the grassmann algebra c n m k e is asymptotic to n 1 k 2 2 2 k 2 n where is an undetermined constant

an addendum to the hierarchical network design problem abstract the hierarchical network design problem is the problem to find a spanning tree of minimum total weight when the edges of the path between two given nodes are weighted by an other cost function than the tree edges not on this path we point out that a dynamic programming oriented heuristic can already be found in literature further we report on possible extensions and improvements

on tensor spaces for birman murakami wenzl algebras abstract let l n n let sp 2 l be the symplectic lie algebra over the complex number field c let v be the natural representation of the quantized enveloping algebra u q sp 2 l and b n q the specialized birman murakami wenzl algebra with parameters q 2 l 1 q in this paper we construct a certain element in the annihilator of v n in b n q which comes from some one dimensional two sided ideal of birman murakami wenzl algebra and is explicitly characterized modulo the determination of some constants we prove that the two sided ideal generated by this element is indeed the whole annihilator of v n in b n q and conjecture that the same is true over arbitrary ground fields and for any specialization of the parameter q the conjecture is verified in the case when q is specialized to 1 i e the brauer algebra case and the case when n l 1

on schur algebras and related algebras ii this paper is a continuation of 7 the purpose of 7 was to set up in the context of reductive algebraic groups a theory of generalized schur algebras a special case of our construction gives the schur algebras s n r studied extensively in lo we concentrate here on the schur algebras themselves and show that our construction yields new results in their representation theory by means of the schur functor see 10 chap 6 we obtain new results in the representation theory of the symmetric groups the main results are as follows the schur algebras s n r defined over a principal ideal domain r have finite global dimension see also 1 i over a field or complete valuation ring r every finitely generated projective s n r module has a weyl module filtration we prove the irreducibility of the socle of certain weyl modules see also 15 we describe a connection between weights of projective indecomposable modules for the schur algebras in terms of the involution on irreducible representations of symmetric groups given by tensoring with the sign representation we show that over a complete valuation ring or a field every young module for a symmetric group has a specht series in particular the projective indecomposables have specht series finally we show that for r n and a complete valuation ring or field r the blocks of the schur algebra s n r are given by the rule embodied in nakayama s conjecture the notations and conventions are as in the first part of this work 7

on orthogonal invariants in characteristic 2 abstract working over an algebraically closed base field k of characteristic 2 the ring of invariants r g is studied where g is the orthogonal group o n or the special orthogonal group so n acting naturally on the coordinate ring r of the m fold direct sum k n k n of the standard vector representation it is proved for o 2 o 3 so 3 so 4 and o 4 that there exists an m linear invariant with m arbitrarily large which is not expressible as a polynomial of invariants of lower degree this is in sharp contrast with the uniform description of the ring of invariants valid in all other characteristics and supports the conjecture that the same phenomena occur for all n for general even n new o n invariants are constructed which are not expressible as polynomials of the quadratic invariants in contrast with these results it is shown that rational invariants have a uniform description valid in all characteristics similarly if m n then r o n is generated by the obvious invariants for all n the algebra r g is a finitely generated module over the subalgebra generated by the quadratic invariants and for odd n the square of any so n invariant is a polynomial of the quadratic invariants finally we mention that for even n an n linear so n invariant is given which distinguishes between so n and o n just like the determinant in all characteristics different from 2

a branch and cut algorithm for the hierarchical network design problem the hierarchical network design problem consists of locating a minimum cost bi level network on a graph the higher level sub network is a path visiting two or more nodes the lower level sub network is a forest connecting the remaining nodes to the path we optimally solve the problem using an ad hoc branch and cut procedure relaxed versions of a base model are solved using an optimization package and if binary variables have fractional values or if some of the relaxed constraints are violated in the solution cutting planes are added once no more cuts can be added branch and bound is used the method for finding valid cutting planes is presented finally we use different available test instances to compare the procedure with the best known published optimal procedure with good results in none of the instances we needed to apply branch and bound but only the cutting planes

the second fundamental theorem of invariant theory for the orthogonal group let v c n be endowed with an orthogonal form and g o v be the corresponding orthogonal group brauer showed in 1937 that there is a surjective homomorphism br n endg v r where br n is the r string brauer algebra with parameter n however the kernel of has remained elusive in this paper we show that in analogy with the case of gl v for r n 1 has a kernel which is generated by a single idempotent element e and we give a simple explicit formula for e using the theory of cellular algebras we show how e may be used to determine the multiplicities of the irreducible representations of o v in v r we also show how our results extend to the case where c is replaced by an appropriate eld of positive characteristic and we comment on quantum analogues of our results

separating invariants of three nilpotent 3 3 matrices abstract the algebra o n n d g l n of g l n invariants of d tuple of n n nilpotent matrices with respect to the action by simultaneous conjugation is generated by the traces of products of nilpotent generic matrices in the case of an algebraically closed field of characteristic zero we describe a minimal separating set for this algebra in case n d 3

theory and methodology abstract the hierarchial network design problem with transshipment facilites was first formulated in current j 1988 the design of a hierarchical transportation network with transshipment facilities transportation science 22 270 277 the objective of the fc hndp is to identify a least cost two level network the network must include a primary path from a prespecified origin node to a prespecified terminus node all nodes not on the primary path must be connected to that path via secondary arcs in addition transshipment facilities are required at the intersections of the two network levels in this paper we present two efficient heuristics for solving the fc hndp these heuristics were based upon a lagrangian relaxation of the problem to facilitate this relaxation we have reformulated the original problem results for 240 randomly generated problems are summarized the heuristics yielded the optimal solution in 72 of these problems the mean gap between the lagrangian lower bound and the feasible solution value was 0 38 and the maximum gap was 4 33 of the lower bound

moment closure hierarchies for kinetic theories this paper presents a systematicnonperturbative derivation of a hierarchy of closed systems of moment equations corresponding to any classical kinetic theory the first member of the hierarchy is the euler system which is based on maxwellian velocity distributions while the second member is based on nonisotropic gaussian velocity distributions the closure proceeds in two steps the first ensures that every member of the hierarchy is hyperbolic has an entropy and formally recovers the euler limit the second involves modifying the collisional terms so that members of the hierarchy beyound the second also recover the correct navier stokes behavior this is achieved through the introduction of a generalization of the bgk collision operator the simplest such system in three spatial dimensions is a 14 moment closure which also recovers the behavior of the grad 13 moment system when the velocity distributions lie near local maxwellians the closure procedure can be applied to a general class of kinetic theories

brauer algebras symplectic schur algebras and schur weyl duality in this paper we prove the schur weyl duality between the symplectic group and the brauer algebra over an arbitrary infinite field k we show that the natural homomorphism from the brauer algebra b n 2m to the endomorphism algebra of the tensor space k 2m n as a module over the symplectic similitude group gsp 2m k or equivalently as a module over the symplectic group sp 2m k is always surjective another surjectivity that of the natural homomorphism from the group algebra for gsp 2m k to the endomorphism algebra of k 2m n as a module over b n 2m is derived as an easy consequence of s oehms s results s oehms j algebra 1 244 2001 19 44

the hierarchical network design problem abstract in this paper the authors introduce the hierarchical network design problem hndp the object of the hndp is to identify the least cost two level hierarchical network the network must include a primary path from a predetermined starting node to a predetermined terminus node in addition each node not on the primary path must be connected to some node on that path by means of a secondary path the problem is initially formulated as an integer linear program an heuristic is then presented which employs a k shortest path algorithm and a minimum spanning tree algorithm heuristic results of two sample problems are presented and compared to the results obtained by solving the integer lp formulation potential applications of the formulation are also discussed

on the classification of finite dimensional irreducible modules for affine bmw algebras in this paper we classify the finite dimensional irreducible modules for affine bmw algebra over an algebraically closed field with arbitrary characteristic

comparison of analysis techniques for the lattice boltzmann method we show that the chapman enskog expansion can be viewed as a special instance of a general expansion procedure which also encompasses other methods like the regular error expansion and multi scale techniques and that any two expansions which properly describe the lattice boltzmann solution necessarily coincide up to higher order terms for a model problem both the regular error expansion and the chapman enskog expansion are carried out it turns out that the classical chapman enskog method leads to an unstable equation at super burnett order in a parameter regime for which the underlying lattice boltzmann algorithm is stable however our approach naturally allows us to consider variants of the super burnett equation which do not suffer from instabilities the article concludes with a detailed comparison of the chapman enskog and the regular error expansion

moment closure approximations of the boltzmann equation based on varphi divergences this paper is concerned with approximations of the boltzmann equation based on the method of moments we propose a generalization of the setting of the moment closure problem from relative entropy to varphi divergences and a corresponding closure procedure based on minimization of varphi divergences the proposed description encapsulates as special cases grad s classical closure based on expansion in hermite polynomials and levermore s entropy based closure we establish that the generalization to divergence based closures enables the construction of extended thermodynamic theories that avoid essential limitations of the standard moment closure formulations such as inadmissibility of the approximate phase space distribution potential loss of hyperbolicity and singularity of flux functions at local equilibrium the divergence based closure leads to a hierarchy of tractable symmetric hyperbolic systems that retain the fundamental structural properties of the boltzmann equation

cellularity of wreath product algebras and a brauer algebras abstract a cellular algebra is called cyclic cellular if all cell modules are cyclic most important examples of cellular algebras appearing in representation theory are in fact cyclic cellular we prove that if a is a cyclic cellular algebra then the wreath product algebras a s n are also cyclic cellular we also introduce a brauer algebras for algebras a with an involution and trace this class of algebras includes in particular g brauer algebras for non abelian groups g we prove that if a is cyclic cellular then the a brauer algebras d n a are also cyclic cellular

on the quasi heredity of birman wenzl algebras abstract in this paper we consider the birman wenzl algebras over an arbitrary field and prove that they are cellular in the sense of graham and lehrer furthermore we determine for which parameters the birman wenzl algebras are quasi hereditary so the general theory of cellular algebras and quasi hereditary algebras applies to birman wenzl algebras as a consequence we can determine all irreducible representations of the birman wenzl algebras by linear algebra methods we prove also that the new hecke algebras induced from birman wenzl algebras are frobenius over a field but not always cellular

on the radical of brauer algebras the radical of the brauer algebra mathcal b f x is known to be non trivial when the parameter x is an integer subject to certain conditions with respect to f in these cases we display a wide family of elements in the radical which are explicitly described by means of the diagrams of the usual basis of mathcal b f x the proof is by direct approach for x 0 and via classical invariant theory in the other cases exploiting then the well known representation of brauer algebras as centralizer algebras of orthogonal or symplectic groups acting on tensor powers of their standard representation this also gives a great part of the radical of the generic indecomposable mathcal b f x modules we conjecture that this part is indeed the whole radical in the case of modules and it is the whole part in a suitable step of the standard filtration in the case of the algebra as an application we find some more precise results for the module of pointed chord diagrams and for the temperley lieb algebra realised inside mathcal b f 1 acting on it ahi quanto a dir che sia e cosa dura lo radical dell algebra di brauer pur se l pensier gia muove a congettura n barbecue scholia

model reduction of kinetic equations by operator projection by a further study of the mechanism of the hyperbolic regularization of the moment system for the boltzmann equation proposed in cai et al commun math sci 11 2 547 571 2013 we point out that the key point is treating the time and space derivative in the same way based on this understanding a uniform framework to derive globally hyperbolic moment systems from kinetic equations using an operator projection method is proposed the framework is so concise and clear that it can be treated as an algorithm with four inputs to derive hyperbolic moment systems by routine calculations almost all existing globally hyperbolic moment systems can be included in the framework as well as some new moment systems including globally hyperbolic regularized versions of grad s ordered moment systems and a multi dimensional extension of the quadrature based moment system

boundary conditions for regularized 13 moment equations for micro channel flows boundary conditions are the major obstacle in simulations based on advanced continuum models of rarefied and micro flows of gases in this paper we present a theory how to combine the regularized 13 moment equations derived from boltzmann s equation with boundary conditions obtained from maxwell s kinetic accommodation model while for the linear case these kinetic boundary conditions suffice we need additional conditions in the non linear case these are provided by the bulk solutions obtained after properly transforming the equations while keeping their asymptotic accuracy with respect to boltzmann s equation after finding a suitable set of boundary conditions and equations a numerical method for generic shear flow problems is formulated several test simulations demonstrate the stable and oscillation free performance of the new approach

characters of algebras containing a jones basic construction the temperley lieb okada brauer and birman wenzl algebras abstract we begin by determining in a general form the characters of irreducible representations of a jones basic construction and use this result to compute the characters of the temperley lieb algebras and the okada algebras in the case of the birman wenzl algebra some of the characters are determined by the general theorem and the others are computed by using the duality between the birman wenzl algebras and the drinfeld jimbo quantum groups of types b and c the computations involve certain characters of the quantum group these are polynomials invariant under the weyl group of type b we are able to decompose these weyl group symmetric functions and obtain a combinatorial rule for computing the irreducible characters of the birman wenzl algebras the combinatorial rules for computing the irreducible characters of the iwahori hecke algebras and the combinatorial rule for computing the irreducible characters of the brauer algebras are both special cases of our rule for the birman wenzl algebras

on block partial linearizations of the pfaffian abstract amitsur s formula which expresses det a b as a polynomial in coefficients of the characteristic polynomial of a matrix is generalized for partial linearizations of the pfaffian of block matrices as applications in upcoming papers we determine generators for the so n invariants of several matrices and relations for the o n invariants of several matrices over a field of arbitrary characteristic

a suboptimal solution to a hierarchial network design problem using dynamic programming abstract each arc of a network has two nonnegative costs the primary cost is larger than the secondary cost for each arc given a source node and a destination node it is required to connect these in a path p to which all other nodes are linked in one or more tree like structures the cost of the resulting tree is found from the primary costs of the arcs used in p and the secondary costs of all other arcs a dynamic programming formulation is presented which finds a suboptimal solution to the problem and the paper indicates the reasons for this formulation falling under certain circumstances