a property of left linear rewrite systems preserving recognizability abstract let r be a left linear rewrite system over sign r and let g sign r where g 1 sign r and 0 sign r we show that r effectively preserves recognizability if and only if r effectively preserves recognizability

bottom up tree pushdown automata classification and connection with rewrite systems we define different types of bottom up tree pushdown automata and study their connections with rewrite systems along this line of research we complete and generalize the results of gallier book and salomaa we define the notion of a tail reduction free trf rewrite system using the decidability of ground reducibility we prove the decidability of the trf property monadic rewrite systems of book gallier and salomaa become a natural particular case of trf rewrite systems we associate a deterministic bottom up tree pushdown automaton with any left linear trf rewrite system finally we generalize monadic rewrite systems by introducing the notion of a semi monadic rewrite system and show that like a monadic rewrite system it preserves recognizability

congruential complements of ground term rewrite systems abstract let a and b be ground term rewrite systems over some ranked alphabet with a b we say that a ground term rewrite system c over is a congruential complement of a for b if a c b and a c is the identity relation over t we show that given ground term rewrite systems a b c over some ranked alphabet with a b one can effectively decide if c is a congruential complement of a for b

sum rules and perfect screening conditions for the one component plasma first we show from the bbgky hierarchy and under exponential clustering assumption that the three dimensional one component plasma obeys the compressibility sum rule which links the compressibility to the fourth moment of the two point correlation function then it is proved that the first equation of the hierarchy is equivalent to the known value of the correlation function of momentum current and density finally we are concerned with the energy density its definition and its correlation with the numerical density and with itself

sum rules for correlation functions of ionic mixtures in arbitrary dimension d 2 the correlations in classical multi component ionic mixtures with a spatial dimension d 2 are studied by using a restricted grand canonical ensemble and the associated hierarchy equations for the correlation functions sum rules for the first few moments of the two particle correlation function are derived and their dependence on d is established by varying d continuously near d 2 it is shown how the sum rules for the two dimensional mixture are related to those for mixtures at higher d

cohomological finite generation for finite supergroup schemes abstract in this paper we compute extension groups in the category of strict polynomial superfunctors and thereby exhibit certain universal extension classes for the general linear supergroup some of these classes restrict to the universal extension classes for the general linear group exhibited by friedlander and suslin while others arise from purely super phenomena we then use these extension classes to show that the cohomology ring of a finite supergroup scheme equivalently of a finite dimensional cocommutative hopf superalgebra over a field is a finitely generated algebra implications for the rational cohomology of the general linear supergroup are also discussed

deterministic bottom up tree transducers and ground term rewrite systems we show that it is decidable for any deterministic bottom up tree transducer a and ground term rewrite system r which one of the following conditions holds i t a r ii r t a iii t a r iv t a and r are incomparable here t a is the tree transformation induced by a and r is the congruence generated by r

howe duality and combinatorial character formula for orthosymplectic lie superalgebras we study the howe dualities involving the reductive dual pairs o d spo 2m 2n and sp d osp 2m 2n on the super symmetric tensor of cd cm n we obtain complete decompositions of this space with respect to their respective joint actions we also use these dualities to derive a character formula for these irreducible representations of spo 2m 2n and osp 2m 2n that appear in these decompositions

linear generalized semi monadic rewrite systems effectively preserve recognizability abstract we introduce the notion of the generalized semi monadic rewrite system which is a generalization of well known rewrite systems the ground rewrite system the monadic rewrite system and the semi monadic rewrite system we show that linear generalized semi monadic rewrite systems effectively preserve recognizability we show that a tree language l is recognizable if and only if there exists a rewrite system r such that r r 1 is a linear generalized semi monadic rewrite system and that l is the union of finitely many r classes we show several decidability and undecidability results on rewrite systems effectively preserving recognizability and on generalized semi monadic rewrite systems for example we show that for a rewrite system r effectively preserving recognizability it is decidable if r is locally confluent moreover we show that preserving recognizability and effectively preserving recognizability are modular properties of linear collapse free rewrite systems finally as a consequence of our results on trees we get that restricted right left overlapping string rewrite systems effectively preserve recognizability

projective representations of symmetric groups via sergeev duality in this article we determine the irreducible projective representations of the symmetric group sd and the alternating group ad over an algebraically closed field of characteristic p 6 2 these matters are well understood in the case p 0 thanks to the fundamental work of schur 24 in 1911 as well as the much more recent work of nazarov 19 20 sergeev 25 26 and others so the focus here is primarily on the case of positive characteristic where surprisingly little is known as yet in particular we obtain a natural combinatorial labelling of the irreducibles in terms of a certain set rpp d of restricted p strict partitions of d such partitions arose recently in work of kashiwara miwa peterson and yung 11 and leclerc and thibon 14 on the q deformed fock space of the affine kac moody algebra of type a p 1 leclerc and thibon proposed that rpp d should label the irreducible projective representations in some natural way and we show here how this can be done note that for p 3 5 the labelling problem was solved in 1 3 while if p 2 all projective representations of sd and ad are linear so do not need to be considered further here to be more precise recall that is a partition of d if 1 2 is a non increasing sequence of non negative integers summing to d call p strict if in addition

equational tree transformations we define an equational relation as the union of some components of the least solution of a system of equations of tree transformations in a pair of algebras we focus on equational tree transformations which are equational relations obtained by considering the least solutions of such systems in pairs of term algebras we characterize equational tree transformations in terms of tree transformations defined by different bimorphisms to demonstrate the robustness of equational tree transformations we give equational definitions of some well known tree transformation classes for which bimorphism characterizations also exist these are the class of alphabetic tree transformations the class of linear and nondeleting extended top down tree transformations and the class of bottom up tree transformations and its linear and linear and nondeleting subclasses finally we prove that a relation is equational if and only if it is the morphic image of an equational tree transformation

sum rules and perfect screening conditions for the 2d one component plasma first we show from the bbgky hierarchy and under exponential clustering assumption that the three dimensional one component plasma obeys the compressibility sum rule which links the compressibility to the fourth moment of the two point correlation function then it is proved that the first equation of the hierarchy is equivalent to the known value of the correlation function of momentum current and density finally we are concerned with the energy density its definition and its correlation with the numerical density and with itself

levels of undecidability in rewriting undecidability of various properties of first order term rewriting systems is well known an undecidable property can be classified by the complexity of the formula defining it this classification gives rise to a hierarchy of distinct levels of undecidability starting from the arithmetical hierarchy classifying properties using first order arithmetical formulas and continuing into the analytic hierarchy where quantification over function variables is allowed in this paper we give an overview of how the main properties of first order term rewriting systems are classified in these hierarchies we consider properties related to normalization strong normalization weak normalization and dependency problems and properties related to confluence confluence local confluence and the unique normal form property for all of these we distinguish between the single term version and the uniform version where appropriate we also distinguish between ground and open terms most uniform properties are p 2 0 complete the particular problem of local confluence turns out to be p 2 0 complete for ground terms but only p 2 0 complete and thereby recursively enumerable for open terms the most surprising result concerns dependency pair problems without minimality flag we prove this problem to be p 1 1 complete hence not in the arithmetical hierarchy but properly in the analytic hierarchy some of our results are new or have appeared in our earlier publications others are based on folklore constructions and are included for completeness as their precise classifications have hardly been noticed previously

debye huckel theory for charge symmetric coulomb systems it is proven that the pressure density and correlation functions of a classical charge symmetric coulomb system are asymptotic as the plasma parameter e tends to zero to the approximations predicted by the debye huckel theory these approximations consist of the ideal gas term plus a term of one lower order in e the sine gordon transformation and some new correlation inequalities for the associated functional integrals are used

partition identities and labels for some modular characters in this paper we prove two conjectures on partitions with certain conditions a motivation for this is given by a problem in the modular representation theory of the covering groups sn of the finite symmetric groups s n in characteristic 5 one of the conjectures conjecture b below has been open since 1974 when it was stated by the first author in his memoir a3 recently the second and third author jointly with a 0 morris arrived at essentially the same conjecture from a completely different direction their paper bmo was concerned with decomposition matrices of sn in characteristic 3 a basic difficulty for obtaining similar results in characteristic 5 or larger was the lack of a class of partitions which would be natural character labels for the modular characters of these groups in this connection two conjectures were stated conjectures a and b below whose solutions would be helpful in the characteristic 5 case one of them conjecture b is equivalent to the old conjecture b mentioned above conjecture a is concerned with a possible inductive definition of the set of partitions which should serve as the required labels in 1 we give a brief description of the groups sn and their representations leading up to conjectures a and b as they were formulated in bmo that section also presents the background for conjecture b as stated in a3 and the equivalence of conjectures b and b is explained sections 2 and 3 are devoted to the proof of conjecture b and 4 to the proof of conjecture a 1 the conjectures and their background for facts concerning the general representation theory of finite groups needed in the following the reader is referred to f nt in 191 1 schur s1 proved that the finite symmetric groups s have covering groups s of order 2is i 2 n this means that there is an exact sequence

support varieties and representation types for basic classical lie superalgebras abstract let be an algebraically closed field of characteristic p 3 and g a restricted lie superalgebra over we introduce the definition of restricted cohomology for g and show its cohomology ring is finitely generated provided g is a basic classical lie superalgebra as a consequence we show that the restricted enveloping algebra of a basic classical lie superalgebra g is always wild except g sl 2 or g osp 1 2 or g c 2

some undecidability results concerning the property of preserving regularity a finite string rewriting system r preserves regularity if and only if it preserves regularity where is the alphabet containing exactly those letters that have occurrences in the rules of r this proves a conjecture of gyenizse and vagvolgyi 1997 in addition some undecidability results are presented that generalize results of gilleron and tison 1995 from term rewriting systems to string rewriting systems it follows that the property of being regularity preserving is undecidable for term rewriting systems thus answering another question of gyenizse and vagvolgyi 1997 finally it is shown that it is undecidable in general whether a finite lengthreducing and confluent string rewriting system yields a regular set of normal forms for each regular language

restricted representations of the witt superalgebras abstract let k be an algebraically closed field of characteristic p 3 and w n the superversion of the witt algebra over k i e the lie superalgebra of superderivations of the grassmann algebra of rank n over k the simple modules and projective indecomposable modules in the restricted supermodule category for w n are studied the character formulas for such simple modules are given and the cartan invariants for this category are presented

yang baxter bases of 0 hecke algebras and representation theory of 0 ariki koike shoji algebras after reformulating the representation theory of 0 hecke algebras in an appropriate family of yang baxter bases we investigate certain specializations of the ariki koike algebras obtained by setting q 0 in a suitably normalized version of shoji s presentation we classify the simple and projective modules and describe restrictions induction products cartan invariants and decomposition matrices this allows us to identify the grothendieck rings of the towers of algebras in terms of certain graded hopf algebras known as the mantaci reutenauer descent algebras and poirier quasi symmetric functions we also describe the ext quivers and conclude with numerical tables

representation theory of 0 hecke clifford algebras abstract the representation theory of 0 hecke clifford algebras as a degenerate case is not semisimple and also with rich combinatorial meaning bergeron hivert and thibon have proved that the grothendieck ring of the category of finitely generated supermodules of 0 hecke clifford algebras is isomorphic to the algebra of peak quasisymmetric functions defined by stembridge in this paper we further study the category of finitely generated projective supermodules and clarify the correspondence between it and the peak algebra of symmetric groups in particular two kinds of restriction rules for induced projective supermodules are obtained after that we consider the corresponding heisenberg double and its fock representation to prove that the ring of peak quasisymmetric functions is free over its subring of symmetric functions spanned by schur s q functions

restricted ground tree transducers we consider restricted versions of ground tree transducers total deterministic and symmetric subclasses and all other subclasses created by applying any combination of these restrictions we present the inclusion diagram of the tree transformation classes induced by these restricted ground tree transducers we show that the following four classes of term relations are the same i tree transformations induced by symmetric deterministic ground tree transducers ii congruence relations on term algebras induced by reduced ground term rewriting systems iii congruence relations on term algebras induced by convergent ground term rewriting systems and iv finitely generated congruence relations on term algebras as a by product of our results we obtain a new ground completion algorithm moreover we show that the following three classes of term relations on term algebras with at least one non nullary function symbol are also the same i tree transformations induced by total symmetric deterministic ground tree transducers ii congruence relations on term algebras of finite index iii finitely generated congruence relations on term algebras of which the trunk is the whole set of terms

equilibrium properties of a multi component ionic mixture i sum rules for correlation functions abstract equilibrium statistical methods are used to derive sum rules for two and three particle correlation functions of a multi component ionic mixture some of these rules are general consequences of the electrostatic character of the interaction whereas others depend on specific thermodynamic properties of the system the first group of rules follows from the bbgky hierarchy and a clustering hypothesis for ursell functions the sum rules of the second group are obtained by describing the system with the help of a restricted grand canonical ensemble in which the particle numbers of the various components in the mixture fluctuate under the condition that the total charge in the system remains constant

a generalization of the stillinger lovett sum rules for the two dimensional jellium in the equilibrium statistical mechanics of classical coulomb fluids the long range tail of the coulomb potential gives rise to the stillinger lovett sum rules for the charge correlation functions for the jellium model of mobile particles of charge q immersed in a neutralizing background the stillinger lovett sum rules give the charge and second moment of the screening cloud around a particle of the jellium in this paper we generalize these sum rules to the screening cloud induced around a pointlike guest charge zq immersed in the bulk interior of the 2d jellium with the coupling constant q2 is the inverse temperature in the whole region of the thermodynamic stability of the guest charge amplitude z 2 the derivation is based on a mapping technique of the 2d jellium at the coupling even positive integer onto a discrete 1d anticommuting field theory we assume that the final results remain valid for all real values of corresponding to the fluid regime the generalized sum rules reproduce for arbitrary coupling the standard z 1 and the trivial z 0 results they are also checked in the debye huckel limit 0 and at the free fermion point 2 the generalized second moment sum rule provides some exact information about possible sign oscillations of the induced charge density in space

invariant theory for matrices over the grassmann algebra we prove that the algebra of polynomial maps mn e e invariant under simultaneous conjugation is generated by the queer trace polynomials

decidability of the confluence of finite ground term rewrite systems and of other related term rewrite systems abstract the aim of this paper is to propose an algorithm to decide the confluence of finite ground term rewrite systems actually a more general class of possibly infinite ground term rewrite systems is studied it is well known that the confluence is not decidable for general term rewrite systems but this paper proves it is for ground term rewrite systems following a conjecture made by huet and oppen in their survey the result is also applied to the confluence of left linear and right ground term rewrite systems we also sketch an algorithm for checking this property this algorithm is based on tree automata and tree transducers here we regard them as rewrite systems and specialists in automata theory would translate that easily in their language

james regularization theorem for double covers of symmetric groups abstract this paper is concerned with the modular representation theory of schur s double covers of symmetric groups we establish an analogue of james regularization theorem which describes leading terms for branching multiplicities and decomposition numbers with respect to the usual dominance ordering

an invariant structure of the multi particle correlations of the two dimensional one component plasma the model under consideration is that of a two dimensional one component plasma confined to the surface of a sphere in the canonical format the system is mapped onto a discrete one dimensional anticommuting field theory a unitary transformation of anticommuting variables is revealed to generate a correlation hierarchy truncated rigorously at each hierarchical level in the thermodynamic limit of the fluid regime this truncation provides a specific invariant structure of multi particle densities of the plasma formulated on an infinite plane

term rewriting restricted to ground terms we study rewriting of ground terms for an arbitrary term rewrite system r over a ranked alphabet we restrict the rewriting relation r to ground terms we introduce the relation r g r t t we show that r g r t t we show that for a given term rewrite system r and a given ground term rewrite system s over a ranked alphabet it is decidable if r g s we show that for a given left linear right ground term rewrite system r over a ranked alphabet it is decidable if there is a ground term rewrite system s over such that r g s

the church rosser property for ground term rewriting systems is decidable abstract a term rewriting system is said to be a ground system if no variable occurs in any of its rewrite rules this paper shows that the church rosser property i e confluence problem for ground term rewriting systems is decidable this is an affirmative solution to this problem posed by huet and oppen 1980

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

decidable call by need computations in term rewriting the theorem of huet and levy stating that for orthogonal rewrite systems i every reducible term contains a needed redex and ii repeated contraction of needed redexes results in a normal form if the term under consideration has a normal form forms the basis of all results on optimal normalizing strategies for orthogonal rewrite systems however needed redexes are not computable in general in the paper we show how the use of approximations and elementary tree automata techniques allows one to obtain decidable conditions in a simple and elegant way surprisingly by avoiding complicated concepts like index and sequentiality we are able to cover much larger classes of rewrite systems we also study modularity aspects of the classes in our hierarchy it turns out that none of the classes is preserved under signature extension by imposing various conditions we recover the preservation under signature extension by imposing some more conditions we are able to strengthen the signature extension results to modularity for disjoint and constructor sharing combinations

complete axiomatizations of some quotient term algebras we show that t f e can be completely axiomatized when e is a quasi free theory quasi free theories are a wider class of theories than permutative theories of mal71 for which mal cev gave decision results as an example of application we show that the first order theory of t f e is decidable when e is a set of ground equations besides we prove that the 1 fragment of the theory of t f e is decidable when e is acompact set of axioms in particular the existential fragment of the theory of associative commutative function symbols is decidable

on endotrivial modules for lie superalgebras abstract let g g 0 g 1 be a lie superalgebra over an algebraically closed field k of characteristic 0 an endotrivial g module m is a g supermodule such that hom k m m k ev p as g supermodules where k ev is the trivial module concentrated in degree 0 and p is a projective g supermodule in the stable module category these modules form a group under the operation of the tensor product we show that for an endotrivial module m the syzygies n m are also endotrivial and for certain lie superalgebras of particular interest we show that 1 k ev and the parity change functor actually generate the group of endotrivials additionally for a broader class of lie superalgebras for a fixed n we show that there are finitely many endotrivial modules of dimension n

derivation trees of ground term rewriting systems a notion of derivation tree is introduced for ground term rewriting systems using standard tree language theory new proofs are given for some old results

euclidean invariance in statistical mechanics of classical continuous system it is shown that equilibrium states of classical particles with short range interactions are euclidean invariant whenever their correlation functions have a clustering which is integrable the relation between invariance and clustering is analysed for spatial rotations and internal rotational degrees of freedom the analysis is then extended to the case of long range interactions including the coulomb force and jellium systems

a fast algorithm for constructing a tree automaton recognizing a congruential tree language abstract it is well known that congruential tree languages are the same as recognizable tree languages in this paper we construct in o n log n time for a given ground term equation system e and given ground trees p 1 p k a deterministic tree automaton a recognizing the congruential tree language p1 e pk e where n is the number of occurrences of symbols in e and p 1 p k

unitary highest weight representations of quantum general linear superalgebra fock space realisations of unitary highest weight representations of compact and noncompact real forms of the quantum general linear superalgebra uq glm n are constructed we decompose all tensor powers of the fock spaces into direct sums of irreducible unitary submodules for compact or noncompact real forms of the quantum superalgebra obtaining multiplicities of the irreducibles and also explicit formulae for their highest weight vectors a generalised howe duality of type uq glm n uq glk is also established which is used in the study of unitary representations and should also be of independent interest

generalized nonlinear fluctuation dissipation relation for the one component plasma we present a novel procedure leading to compact and tractable cubic p 3 and quartic p 4 scalar fluctuation dissipation relations for the classical one component plasma subjected to a weak external coulombic perturbation there is no external magnetic field the ultimate goal here is to establish a generalized nonlinear fluctuation dissipation relation in which a single p 1 point dynamical structure function is expressed as a linear combination of pth order external density response functions when cast in this form such an architecture by definition is invariant with respect to rotation on the p 1 sided polygon formed by the wave vector frequency arguments of the dynamical structure function the application of this rotation symmetry to suppress unphysical isolated singularities is a basic ingredient of the derivation

on restrictions of modular spin representations of symmetric and alternating groups let f be an algebraically closed field of characteristic p and h be an almost simple group or a central extension of an almost simple group an important problem in representation theory is to classify the subgroups g of h and fh modules v such that the restriction v g is irreducible for example this problem is a natural part of the program of describing maximal subgroups in finite classical groups in this paper we investigate the case of the problem where h is the schur s double cover n or s n

on proving uniform termination and restricted termination of rewriting systems in mechanical theorem proving particularly in proving properties of algebraically specified data types we frequently need a decision procedure for the theory of a given finite set of equations axioms a general approach to this problem is to try to derive from the axioms a set of rewrite rules that are canonical i e they rewrite to a canonical form all terms that are equal according the axioms and the equivalence and substitution properties of equality rewrite rules are canonical if and only if they determine a relation that is both confluent and uniformly terminating the difficulty of proving uniform termination has been the major drawback of the rewrite rule approach to deciding equations a new method of proving uniform termination is proposed assuming that the rewriting relation is globally finite for any term there are only finitely many terms to which it can be rewritten nontermination can occur only if there are cycles uniform termination is proved by showing that no cycles can occ

modular representations of the supergroup q n i the representation theory of the algebraic supergroup q n has been studied quite intensively over the complex numbers in recent years especially by penkov and serganova 18 19 20 culminating in their solution 21 22 of the problem of computing the characters of all irreducible finite dimensional representations ofq n the characters of one important family of irreducible representations the so called polynomial representations had been determined earlier by sergeev 24 exploiting an analogue of schur weyl duality connecting polynomial representations of q n to the representation theory of the double covers n of the symmetric groups in 2 we used sergeev s ideas to classify for the first time the irreducible representations of n over fields of positive characteristic p 2 in the present article and its sequel we begin a systematic study of the representation theory of q n in positive characteristic motivated by its close relationship to n let us briefly summarize the main facts proved in this article by purely algebraic techniques let g q n defined over an algebraically closed field k of characteristic p 6 2 see 2 3 for the precise definition in 4 we construct the superalgebra dist g of distributions on g by reduction modulo p from a kostant z form for the enveloping superalgebra of the lie superalgebra q n c this provides one of the main tools in the remainder of the paper there is an explicit equivalence between the category of representations of g and the category of integrable dist g supermodules see corollary 5 7 in 6 we classify the irreducible representations of g by highest weight theory they turn out to be parametrized by the set x p n 1 n z 1 n with i i 1 only if p i for x p n the corresponding irreducible representation is denoted l and is constructed naturally as the simple socle of an induced representation h indbu where b is a borel subgroup of g and u is a certain irreducible representation of b of dimension a power of 2 the main difficulty here is to show that h0 6 0 for x p n which we prove by exploiting the main result of 2 classifying the irreducible polynomial representations of g so ultimately the proof that h0 6 0 depends on a counting argument involving p regular conjugacy classes in n

an algorithm for finding canonical sets of ground rewrite rules in polynomial time in this paper it is shown that there is an algorithm that given by finite set e of ground equations produces a reduced canonical rewriting system r equivalent to e in polynomial time this algorithm based on congruence closure performs simplification steps guided by a total simplification ordering on ground terms and it runs in time o n 3

quasifinite representations of classical lie subalgebras of w1 we show that there are precisely two up to conjugation anti involutions of the algebra of differential operators on the circle preserving the principal gradation we classify the irreducible quasifinite highest weight representations of the central extension d of the lie subalgebra of this algebra fixed by and find the unitary ones we realize them in terms of highest weight representations of the central extension of the lie algebra of infinite matrices with finitely many non zero diagonals over the algebra c u um 1 and its classical lie subalgebras ofb canddtypes character formulas forpositive primitiverepresentations of d including all the unitary ones are obtained we also realize a class of primitive representations of d in terms of free fields and establish a number of duality results between these primitive representations and finite dimensional irreducible representations of finite dimensional lie groups and supergroups we show that the vacuum modulevcof d carries a vertex algebra structure and establish a relationship betweenvcforc 12z and w algebras

intersection of finitely generated congruences over term algebra we show that it is decidable for any given ground term rewrite systems r and s if there is a ground term rewrite system u such that u r s if the answer is yes then we can effectively construct such a ground term rewrite system u in other words for any given finitely generated congruences and over the term algebra it is decidable if is a finitely generated congruence if the answer is yes then we can effectively construct a ground term rewrite system u such that u

reductions in tree replacement systems abstract certain kinds of church rosser tree replacement systems reduction systems are studied most results presented here generalize results proved for string rewriting systems by book 1982 the concept of a tree rewriting system with a norm is introduced and studied a new tree reducing machine which reduces every input tree to an irreducible tree is defined as a consequence when the norm under consideration is the size of the tree the number of nodes the word problem for finite church rosser reduction systems is decidable in linear time in the size of the input tree church rosser monadic reduction systems generalizing the monadic thue systems of book 1982 and book et al 1982 are also studied it is shown that every congruence class and every finite union of congruence classes defined by such a system is accepted by a deterministic bottom up tree pushdown automation this new form of a tree automation is briefly studied

a new proof of the stillinger lovett complete shielding condition it is shown that any equilibrium state of classical charged particles with correlation having a spatial decay faster than 1 x v 2 in dimensionv 2 3 obeys the stillinger lovett second moment condition under the same clustering hypothesis arbitrary localized external charge distributions are completely shielded

howe duality for quantum queer superalgebras abstract we establish a new howe duality between a pair of quantum queer superalgebras u q 1 q n u q q m the key ingredient is the construction of a non commutative analogue a q q n q m of the symmetric superalgebra s c m n m n with the use of quantum coordinate queer superalgebra it turns out that this superalgebra is equipped with a u q 1 q n u q q m supermodule structure that admits a multiplicity free decomposition we also show that the u q 1 q n u q q m howe duality implies the sergeev olshanski duality

termination for direct sums of left linear complete term rewriting systems a term rewriting system is called complete if it is confluent and terminating we prove that completeness of trss is a modular property meaning that it stays preserved under direct sums provided the constituent trss are left linear here the direct sum r 0 r is the union of trss r 0 r 1 with disjoint signature the proof hinges crucially upon the non deterministic collapsing behavior of terms from the sum trs

a quantum analogue of the first fundamental theorem of classical invariant theory we establish a noncommutative analogue of the first fundamental theorem of classical invariant theory for each quantum group associated with a classical lie algebra we construct a noncommutative associative algebra whose underlying vector space forms a module for the quantum group and whose algebraic structure is preserved by the quantum group action the subspace of invariants is shown to form a subalgebra which is finitely generated we determine generators of this subalgebra of invariants and determine their commutation relations in each case considered the noncommutative modules we construct are flat deformations of their classical commutative analogues our results are therefore noncommutative generalisations of the first fundamental theorem of classical invariant theory which follows from our results by taking the limit as q 1 our method similarly leads to a definition of quantum spheres which is a noncommutative generalisation of the classical case with orthogonal quantum group symmetry

on ground tree transformations and congruences induced by tree automata for a tree automaton a over a ranked alphabet we study the ground tree transformation a induced by a and the restriction a of the congruence a to terms over we define a congruence relation a a on a called the determiner of a and the quotient tree automaton a we show the following results it is decidable if a a if a is deterministic then a a the determiner of a can be effectively constructed a is deterministic and a a for a connected tree automaton a a a if and only if a b for some deterministic tree automaton b if and only if a a

shifted tableaux and the projective representations of symmetric groups les groupes de representation de s n classes de conjugaison algebres de clifford et la representation spin de base produits induits pour des representations spin une application caracteristique pour des caracteres de spin tableaux decales et q fonctions de schur les caracteres de spin irreductibles de s n et a n une analogue decalee de la regle lr produits tensoriels interieurs