jacobi identity for vertex algebras in higher dimensions vertex algebras in higher dimensions introduced previously by nikolov provide an algebraic framework for investigating axiomatic quantum field theory with global conformal invariance we develop further the theory of such vertex algebras by introducing formal calculus techniques and investigating the notion of polylocal fields we derive a jacobi identity which together with the vacuum axiom can be taken as an equivalent definition of vertex algebra

the existence and uniqueness of solution to wavelet collocation the study of the numerical solutions of pdes with wavelet collocation has yielded a number of substantial results however the existence and uniqueness of solution has not been discussed yet in this paper the existence and uniqueness of solution to wavelet collocation for elliptic equations is established and discussed moreover wavelet collocation is applied to numerical example to examine its appropriateness according to numerical example and analysis it is seen that the existence and uniqueness of solution of this paper is feasible and the new theory is meaningful for developing wavelet collocation

infinite dimensional primitive linearly compact lie superalgebras we classify open maximal subalgebras of all infinite dimensional linearly compact simple lie superalgebras this is applied to the classification of infinite dimensional lie superalgebras of vector fields acting transitively and primitively in a formal neighborhood of a point of a finite dimensional supermanifold

finite growth representations of conformal lie algebras that contain a virasoro subalgebra in the present paper we classify all finite growth representations of all infinite rank conformal subalgebras of gcn that contain a virasoro subalgebra

bounds on universal sequences universal sequences for graphs a concept introduced by aleliunas m sc thesis university of toronto toronto ontario canada january 1978 and aleliunas et al proc 20th annual symposium on foundation of computer science 1979 pp 218 223 are studied by letting u d n denote the minimum length of a universal sequence for d regular undirected graphs with n nodes the latter paper has proved the upper bound u d n o d 2 n 3 log n using a probabilistic argument here a lower bound of u 2 n omega n log n is proved from which u d n omega n log n for all d is deduced also for complete graphs u n 1 n omega n log 2 n log log n an explicit construction of universal sequences for cycles d 2 of length n o log n is given

low dimensional cohomology of general conformal algebras gcn we compute the low dimensional cohomologies hq gcn c hq gcn c of the infinite rank general lie conformal algebras gcn with trivial coefficients for q 3 n 1 or q 2 n 2 we also prove that the cohomology of gcn with coefficients in its natural module is trivial i e h gcn c n 0 and thus partially solve an open problem of bakalov kac voronov commun math phys 200 561 598 1999

a space lower bound for st connectivity on node named jags abstract given a directed graph g and two of its nodes s and t the directed st connectivity problem stcon is to decide whether there is a directed path from s to t in g establishing a super logarithmic space lower bound for stcon on a general computation model such as turing machine or branching program has been a big challenge in complexity theory as an intermediate step cook and rackoff siam j comput 9 3 1980 636 652 introduce a structured model called jag jumping automaton for graphs and prove a space lower bound of log 2 n log log n on this model berman and simon proc 24th annual symp on foundations of computer science ieee press new york tucson az november 1983 show a similar lower bound for a probabilistic jag we take a step further by introducing a stronger model called nn jag node named jag and obtain the same space lower bound of log 2 n log log n on a probabilistic nnjag we show that s log 2 n log log n log log t where s is the space and t is the expected time used respectively this gives the best expected time lower bound on this model when the space s is o log 2 n log log n

a general sequential time space tradeoff for finding unique elements an optimal omega n 2 lower bound is shown for the time space product of any r branching program that determines those values which occur exactly once in a list of n integers in the range 1 r where r geqq n this omega n 2 tradeoff also applies to the sorting problem and thus improves the previous time space tradeoffs for sorting because the r way branching program is such a powerful model these time space product tradeoffs also apply to all models of sequential computation that have a fair measure of space such as off line multitape turing machines and off line log cost random access machines rams

two applications of inductive counting for complementation problems following the recent independent proofs of immerman siam j comput 17 1988 pp 935 938 and szelepcsenyi bull european assoc theoret comput sci 33 1987 pp 96 100 that nondeterministic space bounded complexity classes are closed under complementation two further applications of the inductive counting technique are developed first an errorless probabilistic algorithm for the undirected graph s t connectivity problem that runs in o log n space and polynomial expected time is given then it is shown that the class logcfl is closed under complementation the latter is a special case of a general result that shows closure under complementation of classes defined by semi unbounded fan in circuits or equivalently nondeterministic auxiliary pushdown automata or tree size bounded alternating turing machines as one consequence it is shown that small numbers of role switches in two person pebbling can be eliminated

trading space for time in undirected s t connectivity aleliunas et al 20th annual symposium on foundations of computer science ieee computer society press los alamitos ca 1979 pp 218 223 posed the following question the reachability problem for undirected graphs can be solved in log space and o mn time m is the number of edges and n is the number of vertices by a probabilistic algorithm that simulates a random walk or in linear time and space by a conventional deterministic graph traversal algorithm is there a spectrum of time space trade offs between these extremes this question is answered in the affirmative for sparse graphs by presentation of an algorithm that is faster than the random walk by a factor essentially proportional to the size of its workspace for denser graphs this algorithm is faster than the random walk but the speed up factor is smaller

time space lower bounds for directed st connectivity on graph automata models directed st connectivity is the problem of detecting whether there is a path from a distinguished vertex s to a distinguished vertex t in a directed graph we prove time space lower bounds of st omega n 2 log n over log n log n s and s 1 over 2 t omega m n log n 1 over 2 for directed st connectivity on cook and rackoff s jumping automaton for graphs jag model siam j comput 9 1980 pp 636 652 where n is the number of vertices and m the number of edges in the input graph s is the space and t the time used by the jag these lower bounds are simple and elegant they approach the known upper bound of t o m when s approaches theta n log n and they are the first time space tradeoffs for jags with an unrestricted number of jumping pebbles

on n ary hom lie h pseudoalgebras the aim of this paper is to study n ary hom lie h pseudoalgebras generalizing both n ary hom nambu lie algebras and n lie h pseudoalgebras we list examples of the new structure and present some properties and the construction theorem furthermore we provide a way to construct an n ary hom nambu lie algebra from an n ary hom lie h pseudoalgebra the equivalent definition of n ary hom lie h pseudoalgebra is also described finally we discuss the prospects of n ary hom lie h pseudoalgebras in physics

tight lower bounds for st connectivity on the nnjag model directed st connectivity is the problem of deciding whether or not there exists a path from a distinguished node s to a distinguished node t in a directed graph we prove a time space lower bound on the probabilistic nnjag model of poon proc 34th annual symposium on foundations of computer science palo alto ca 1993 pp 218 227 let n be the number of nodes in the input graph and s and t be the space and time used by the nnjag respectively we show that for any delta 0 if an nnjag uses space s in o n 1 delta then t in 2 omega log 2 n s otherwise t in 2 omega log 2 n log n over s log log n times ns log n 1 2 in a preliminary version of this paper by edmonds and poon proc 27th annual acm symposium on theory of computing las vegas nv 1995 pp 147 156 a lower bound of t in 2 omega log 2 n log n over s log log n times ns log n 1 2 was proved our result greatly improves the previous lower bound of st in omega n 2 log n on the jag model by barnes and edmonds proc 34th annual symposium on foundations of computer science palo alto ca 1993 pp 228 237 and that of s 1 3 t in omega n 4 3 on the nnjag model by edmonds time space lower bounds for undirected and directed st connectivity on jag models ph d thesis university of toronto toronto on canada 1993 our lower bound is tight for s in o n 1 delta for any delta 0 matching the upper bound of barnes etal proc 7th annual ieee conference on structure in complexity theory boston ma 1992 pp 27 33 as a corollary of this improved lower bound we obtain the first tight space lower bound of omega log 2 n on the nnjag model no tight space lower bound was previously known even for the more restricted jag model

on the classification of subalgebras of cendn and gcn the problem of classification of infinite subalgebras of cendn and of gcn that acts irreducibly on c n is discussed in this paper

theory structure of n lie h pseudoalgebras in this paper we introduce a new algebraic structure n lie h pseudoalgebras which generalize both lie h pseudoalgebras and filippov algebras furthermore we discuss the structure of n lie h pseudoalgebras and display an analogue of engel s classical theorem for lie algebras finally we explain the good prospects of the n lie h pseudoalgebras theory in physics

nondeterministic space is closed under complementation in this paper we show that nondeterministic space s n is closed under complementation for s n greater than or equal to log n it immediately follows that the context sensitive languages are closed under complementation thus settling a question raised by kuroda inform and control 7 1964 pp 207 233

homogeneous averaging operators on simple finite conformal lie algebras we describe all homogeneous averaging operators on finite simple conformal lie algebras in the case of current algebras these operators are closely related to rational solutions of the classical yang baxter equation

representations of a symplectic type subalgebra of w n in this paper we classify the irreducible quasifinite highest weight modules over the symplectic type lie subalgebra of the lie algebra of all regular differential operators on circle that kill constants we also realize them in terms of the representations theory of the complex lie algebra gl m of infinite matrices with a finite number of non zero diagonals with entries in the algebra of truncated polynomials and the corresponding subalgebras of type c

a time space tradeoff for element distinctness in a time space tradeoff for sorting on non oblivious machines borodin et al b 81 proved that to sort n elements requires ts n2 where t time and s space on a comparison based branching problem although element distinctness and sorting are equivalent problems on a computation tree the stated tradeoff result does not immediately follow for element distinctness or indeed for any decision problem in this paper we are able to show that ts n3 2 for deciding element distinctness or the sign of a permutation

simple associative conformal algebras of linear growth abstract we describe simple finitely generated associative conformal algebras of gel fand kirillov dimension one

wavelet optimized finite difference mesh for mhd flow in a circular duct abstract there is a large class of important problems in scientific and engineering applications where the solution shows very little variation in the core region but very rapid changes close to the boundary of the domain of interest magnetohydrodynamic flow problems belong to this category treatment of such problems numerically therefore requires a non uniform mesh which is very fine near the boundary the determination of the size of the grid in different parts of the domain is therefore a challenging problem some recent studies suggest that wavelet methods can be effectively applied to create an optimized mesh the method has mostly been used for one dimensional problems the present paper investigates the problem for fully developed mhd duct flow problems which are basically two dimensional the boundary layer character is more pronounced in one direction as compared to the other the governing equations comprise a coupled system of two partial differential equations with dirichlet boundary conditions wavelet based adaptive mesh is first created and then the system is discretized over this mesh computations have been carried out at different precision levels for various hartmann numbers for a pipe of circular section contours are also drawn to depict the core and the boundary layer region

irreducible modules over finite simple lie pseudoalgebras ii primitive pseudoalgebras of type k abstract one of the algebraic structures that has emerged recently in the study of the operator product expansions of chiral fields in conformal field theory is that of a lie conformal algebra a lie pseudoalgebra is a generalization of the notion of a lie conformal algebra for which c is replaced by the universal enveloping algebra h of a finite dimensional lie algebra the finite i e finitely generated over h simple lie pseudoalgebras were classified in our previous work bakalov et al 2001 2 the present paper is the second in our series on representation theory of simple lie pseudoalgebras in the first paper we showed that any finite irreducible module over a simple lie pseudoalgebra of type w or s is either an irreducible tensor module or the kernel of the differential in a member of the pseudo de rham complex in the present paper we establish a similar result for lie pseudoalgebras of type k with the pseudo de rham complex replaced by a certain reduction called the contact pseudo de rham complex this reduction in the context of contact geometry was discovered by rumin

two dynamic programming algorithms for which interpreted pebbling helps we consider extensions of one person and two person pebble games that take into account the types of the gates of the circuits on which the games are played a simple relationship is established between the extended games and the corresponding original games this is useful in showing that the extended games allow more efficient pebbling than the original games on certain natural circuits for problems such as context free language recognition and transitive closure of directed graphs

unital associative pseudoalgebras and their representations abstract pseudoalgebras introduced in b bakalov a d andrea v g kac adv math 162 2001 1 140 are multi dimensional analogues of conformal algebras which provide an axiomatic description of the singular part of the operator product expansion our main interest in this paper is the pseudoalgebra cendn which is the analogue of an algebra of endomorphisms of a finite module we study its algebraic properties in particular we introduce the class of unital pseudoalgebras and describe their structure and representations also we classify pseudoalgebras algebraically similar to cendn

on conformal bialgebras abstract we study conformal algebras from the point of view of conformal dual of classical lie coalgebra structures we define the notions of lie conformal coalgebra and bialgebra we obtain a conformal analog of the cybe the manin triples and drinfeld s double with the definition of vertex duals we obtain a natural description of the lie algebra associated to a conformal algebra as a convolution algebra clarifying the classical constructions in the theory of conformal algebras and vertex algebras

representations of lie pseudoalgebras with coefficients abstract we introduce a natural generalization of the concept of lie pseudoalgebra representation and show that it can be used to study discrete irreducible modules of the linearly compact cartan lie algebra of poisson type

associative conformal algebras with finite faithful representation abstract the classification of irreducible subalgebras of the associative conformal algebra cend n is presented in this paper the structure theory of associative conformal algebras with finite faithful representation is developed

on associative conformal algebras of linear growth ii abstract we classify unital associative conformal algebras of linear growth and provide new examples of such

leibniz h pseudoalgebras abstract we define a leibniz h pseudoalgebra over a cocommutative hopf algebra h and a tensor product of leibniz h pseudoalgebras and prove that every leibniz h pseudoalgebra of free rank one over h is a lie h pseudoalgebra to characterize simple leibniz h pseudoalgebras we define the leibniz cohomology of leibniz h pseudoalgebras and determine some simple leibniz h pseudoalgebras by calculating leibniz cohomological groups of finite simple lie h pseudoalgebras defined in 2

on finite representations of conformal algebras abstract we prove that a finite torsion free associative conformal algebra has a finite faithful conformal representation as a corollary it is shown that one may join a conformal identity to such an algebra some examples are stated to demonstrate that a conformal identity cannot be joined to any torsion free associative conformal algebra in particular there exist associative conformal algebras of linear growth and even locally finite ones that have no finite faithful representation we also consider the problem of existence of a finite faithful representation for a torsion free finite lie conformal algebra the analogue of ado s theorem it turns out that the conformal analogue of the poincare birkhoff witt theorem would imply the ado theorem for finite lie conformal algebras we also prove that every torsion free finite solvable lie conformal algebra has a finite faithful representation

γ conformal algebras conformal algebra is an axiomatic description of the operator product expansion of chiral fields with simple poles at finitely many points we classify these algebras and their representations in terms of lie algebras and their representations with an action of the group to every conformal algebra and a character of we associate a lie algebra generated by fields with the ope with simple poles examples include twisted affine kac moody algebras the sin algebra which is a conformal analogue of the general linear algebra and its analogues the algebra of pseudodifferential operators on the circle etc

finite growth representations of infinite lie conformal algebras we classify all finite growth representations of all infinite rank subalgebras of the lie conformal algebra gc1 that contain a virasoro subalgebra

infinite rank schrodinger virasoro type lie conformal algebras motivated by the structure of certain modules over the loop virasoro lie conformal algebra and the lie structures of schrodinger virasoro algebras we construct a class of infinite rank lie conformal algebras csv a b where a b are complex numbers the conformal derivations of csv a b are uniformly determined the rank one conformal modules and graded free intermediate series modules over csv a b are classified corresponding results of the conformal subalgebra chv a b of csv a b are also presented

cohomology of conformal algebras the notion of a conformal algebra encodes an axiomatic description of the operator product expansion of chiral fields in conformal field theory on the other hand it is an adequate tool for the study of infinite dimensional lie algebras satisfying the locality property the main examples of such lie algebras are those based on the punctured complex plane such as the virasoro algebra and loop lie algebras in the present paper we develop a cohomology theory of conformal algebras with coefficients in an arbitrary module it possesses standards properties of cohomology theories for example it describes extensions and deformations we offer explicit computations for the most important examples

lower bounds on universal traversal sequences for cycles and other low degree graphs universal traversal sequences for cycles require length omega n 1 29 improving the previous bound of omega n log n for d geq 3 universal traversal sequences for d regular graphs require length omega d 0 71 n 2 29 for constant d the best previous bound was omega n 2 log n

higher dimensional generalizations of affine kac moody and virasoro conformal lie algebras we discuss the generalizations of the notion of conformal algebra and local distribution lie algebras for multi dimensional bases we replace the algebra of laurent polynomials on open image in new window by an infinite dimensional representation with some additional structures of a simple finite dimensional lie algebra open image in new window in the space of regular functions on the corresponding grassmann variety open image in new window that can be described as a right higher dimensional generalization of open image in new window from the point of view of a corresponding group action for open image in new window it gives us the usual vertex algebra notion we construct the higher dimensional generalizations of the virasoro and the affine kac moody conformal lie algebras explicitly and in terms of the operator product expansion

a new n 6 superconformal algebra in this paper we construct a newn 6 superconformal algebra which extends the virasoro algebra by theso 6 current algebra by 6 odd primary fields of conformal weight 3 2 and by 10 odd primary fields of conformal weight 1 2 the commutation relations of this algebra which we will refer to asck 6 are represented by short distance operator product expansions ope we constructck 6 as a subalgebra of theso 6 superconformal algebra k6 thus giving it a natural representation as first order differential operators on the circle withn 6 extended symmetry we show thatck 6 has no nontrivial central extensions

a remark on simplicity of vertex algebras and lie conformal algebras abstract i give a short proof of the following algebraic statement in a simple vertex algebra the underlying lie conformal algebra is either abelian or it is an irreducible central extension of a simple lie conformal algebra this provides many examples of non finite simple lie conformal algebras and should prove useful for classification purposes

supersymmetric vertex algebras we define and study the structure of susy lie conformal and vertex algebras this leads to effective rules for computations with superfields

bounds on monotone switching networks for directed connectivity we separate monotone analogues of l and nl by proving that any monotone switching network solving directed connectivity on n vertices must have size at least n lg n

a time space tradeoff for undirected graph traversal by walking automata we prove a time space tradeoff for traversing undirected graphs using a structured model that is a nonjumping variant of cook and rackoff s jumping automata for graphs

numerical solution of fredholm integral equations of the first kind by using linear legendre multi wavelets in this paper we suggest an efficient method for solving fredholm integral equations of the first kind the continuous legendre multi wavelets constructed on 0 1 are utilized as a basis in galerkin method to reduce the solution of linear integral equations to a system of algebraic equations illustrative examples are included to demonstrate the efficiency and the application of the technique

two familiar transitive closure algorithms which admit no polynomial time sublinear space implementations any boolean straight line program which computes the transitive closure of an n times n boolean matrix by successive squaring requires time exceeding any polynomial in n if the space used is o n this is the first demonstration of a natural algorithm which 1 has a polynomial time implementation and 2 has a small e g o log 2 n space implementation but 3 has no implementation running in polynomial time and small space simultaneously it is also shown that any implementation of warshall s transitive closure algorithm requires omega n space and that many familiar sorting algorithms exhibit similar behavior

wavelet moment method for solving fredholm integral equations of the first kind in this paper we suggest an efficient method for solving fredholm integral equations of the first kind using wavelets as basis functions in the moment method and reducing the order of the linear equation rather than making the matrix sparse in the end we give some numerical examples

lie algebra structures on cohomology complexes of some h pseudoalgebras abstract suppose h is a cocommutative hopf algebra and p is the operad a ss or l ie for any left h module v we construct a graded lie algebra l p v n z l p n v and prove that l p 1 satisfies 0 if and only if it determines a pseudoalgebra structure on v over the operad p and l p v is a differential graded lie algebra with a differentiation determined by the structure map of the h pseudoalgebra v moreover we construct a lie algebra by using symmetric schouten product for any pseudoalgebra v over the operad l ie

on the cohomology of leibniz conformal algebras we construct a new cohomology complex of leibniz conformal algebras with coefficients in a representation instead of a module the low dimensional cohomology groups of this complex are computed meanwhile we construct a leibniz algebra from a leibniz conformal algebra and prove that the category of leibniz conformal algebras is equivalent to the category of equivalence classes of formal distribution leibniz algebras

an efficient data structure for lattice operations in this paper we consider the representation and management of an element set on which a lattice partial order relation is defined in particular let n be the element set size we present an nradn space implicit data structure for performing the following set of basic operations 1 test the presence of an order relation between two given elements in constant time 2 find a path between two elements whenever one exists in o l steps where l is the path length 3 compute the successors and or predecessors set of a given element in o h steps where h is the size of the returned set 4 given two elements find all elements between them in time o k log d where k is the size of the returned set and d is the maximum in degree or out degree in the transitive reduction of the order relation 5 given two elements find the least common ancestor and or the greatest common successor in o sqrt n time 6 given k elements find the least common ancestor and or the greatest common successor in o sqrt n k log n time unless stated otherwise all logarithms are to the base 2 the preprocessing time is o n2 focusing on the first operation representing the building box for all the others we derive an overall nradn space times time bound which beats the order n2 bottleneck representing the present complexity for this problem moreover we will show that the complexity bounds for the first three operations are optimal with respect to the worst case additionally a stronger result can be derived in particular it is possible to represent a lattice in space o n sqrt t where t is the minimum number of disjoint chains which partition the element set

filtered lie conformal algebras whose associated graded algebras are isomorphic to that of general conformal algebra gc1 abstract let g be a filtered lie conformal algebra whose associated graded conformal algebra is isomorphic to that of general conformal algebra g c 1 in this paper we prove that g g c 1 or gr g c 1 the associated graded conformal algebra of g c 1 by making use of some results on the second cohomology groups of the conformal algebra g with coefficients in its module m b 0 of rank 1 where g vir m a 0 is the semi direct sum of the virasoro conformal algebra vir with its module m a 0 furthermore we prove that gr g c 1 does not have a nontrivial representation on a finite c module this provides an example of a finitely freely generated simple lie conformal algebra of linear growth that cannot be embedded into the general conformal algebra g c n for any n

fast wavelet transforms and numerical algorithms i a class of algorithms is introduced for the rapid numerical application of a class of linear operators to arbitrary vectors previously published schemes of this type utilize detailed analytical information about the operators being applied and are specific to extremely narrow classes of matrices in contrast the methods presented here are based on the recently developed theory of wavelets and are applicable to all calderon zygmund and pseudo differential operators the algorithms of this paper require order o n or o n log n operations to apply an n n matrix to a vector depending on the particular operator and the version of the algorithm being used and our numerical experiments indicate that many previously intractable problems become manageable with the techniques presented here

cohomology of vertex algebras abstract let v be a vertex algebra and m a v module we define the first and second cohomology of v with coefficients in m and we show that the second cohomology h 2 v m corresponds bijectively to the set of equivalence classes of square zero extensions of v by m in the case that m v we show that the second cohomology h 2 v v corresponds bijectively to the set of equivalence classes of first order deformations of v

on the hochschild cohomologies of associative conformal algebras with a finite faithful representation associative conformal algebras of conformal endomorphisms are of essential importance for the study of finite representations of conformal lie algebras lie vertex algebras we describe all semisimple algebras of conformal endomorphisms which have the trivial second hochschild cohomology group with coefficients in every conformal bimodule as a consequence we state a complete solution of the radical splitting problem in the class of associative conformal algebras with a finite faithful representation

calculus structure on the lie conformal algebra complex and the variational complex we construct a calculus structure on the lie conformal algebra cochain complex by restricting to degree one chains we recover the structure of a g complex introduced in a de sole and v g kac

zeta values and differential operators on the circle abstract the fock representation of the virasoro lie algebra is extended to a larger graded lie subalgebra of the algebra of differential operators on the circle the central cocycle is related to values of the riemann zeta function at odd negative integers the corresponding generating function is related to eisenstein series for sl 2 z an analogous result is obtained for values of l series associated to even dirichlet characters using differential operators of infinite order

classification of finite irreducible conformal modules over some lie conformal algebras related to the virasoro conformal algebra in this paper we classify all finite irreducible conformal modules over a class of lie conformal algebras w b with b related to the virasoro conformal algebra explicitly any finite irreducible conformal module over w b is proved to be isomorphic to m with 0 or 0 if b 0 or m with 0 if b 0 as a byproduct all finite irreducible conformal modules over the heisenberg virasoro conformal algebra and the w 2 2 lie conformal algebra are classified finally the same thing is done for the schrodinger virasoro conformal algebra

numerical expansion methods for solving integral equations by interpolation and gauss quadrature rules in this paper we introduce a numerical method for solving linear integral equations the main idea based on interpolation for unknown function where is interpolated in the zeros of the chebyshev s polynomials next we use gauss quadrature rules as gauss chebyshev or clenshaw curtis the technique is very effective and simple specially for integral equations of first kind as fredholm s and volterra s types in the end for showing efficiency of this method we use numerical examples

composition diamond lemma for associative conformal algebras abstract we prove the composition diamond lemma for associative conformal algebras as some corollaries we prove that the word problem for some homogeneous associative conformal algebras is solvable while it is unsolvable in general

a sublinear space polynomial time algorithm for directed s t connectivity directed s t connectivity is the problem of detecting whether there is a path from vertex s to vertex t in a directed graph we present the first known deterministic sublinear space polynomial time algorithm for directed s t connectivity for n vertex graphs our algorithm can use as little as n 2 theta sqrt log n space while still running in polynomial time

a time space tradeoff for sorting on a general sequential model of computation in a general sequential model of computation no restrictions are placed on the way in which the computation may proceed except that parallel operations are not allowed we show that in such an unrestricted environment text time cdot text space omega n 2 log n in order to sort n integers each in the range 1 n 2

classification of finite irreducible conformal modules over a class of lie conformal algebras of block type abstract we classify finite irreducible conformal modules over a class of infinite lie conformal algebras b p of block type where p is a nonzero complex number in particular we obtain that a finite irreducible conformal module over b p may be a nontrivial extension of a finite conformal module over vir if p 1 where vir is a virasoro conformal subalgebra of b p as a byproduct we also obtain the classification of finite irreducible conformal modules over a series of finite lie conformal algebras b n for n 1

deformations and generalized derivations of lie conformal superalgebras in this paper we study deformations and generalized derivations of lie conformal superalgebras first we study conformal derivations of the semidirect product of a lie conformal superalgebra and its conformal module second we extend the cohomology theory of lie conformal algebras to the super case and discuss some applications to deformations of lie conformal superalgebras finally we introduce generalized derivations of lie conformal superalgebras and study their properties

lower bounds on universal traversal sequences based on chains of length five universal traversal sequences for cycles require length n1 43 improving the previous bound of n1 33 for d 3 universal traversal sequences for d regular graphs require length d0 57n2 43 for constant d the best previous bound was n2 33

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

symmetric space bounded computation abstract a symmetric turing machine is one such that the yields relation between configurations is symmetric the space complexity classes for such machines are found to be intermediate between the corresponding deterministic and nondeterministic space complexity classes certain natural problems are shown to be complete for symmetric space complexity classes and the relationship of symmetry to determinism and nondeterminism is investigated

on pseudo bialgebras abstract we study pseudoalgebras from the point of view of pseudo dual of classical lie coalgebra structures we define the notions of lie h coalgebra and lie pseudo bialgebra we obtain the analog of the cybe the manin triples and drinfeld s double for lie pseudo bialgebras we also get a natural description of the annihilation algebra associated to a pseudoalgebra as a convolution algebra clarifying this construction in the theory of pseudoalgebras

lie conformal algebra cohomology and the variational complex we find an interpretation of the complex of variational calculus in terms of the lie conformal algebra cohomology theory this leads to a better understanding of both theories in particular we give an explicit construction of the lie conformal algebra cohomology complex and endow it with a structure of a mathfrak g complex on the other hand we give an explicit construction of the complex of variational calculus in terms of skew symmetric poly differential operators

gelfand dorfman algebras derived identities and the manin product of operads abstract gelfand dorfman bialgebras gd algebras are nonassociative systems with two bilinear operations satisfying a series of identities that express hamiltonian property of an operator in the formal calculus of variations the paper is devoted to the study of gd algebras related with differential poisson algebras as a byproduct we obtain a general description of identities that hold for operations a b d a b and a b a d b on a non associative differential algebra with a derivation d

quasifinite highest weight modules over the lie algebra of differential operators on the circle we classify positive energy representations with finite degeneracies of the lie algebraw 1 and construct them in terms of representation theory of the lie algebra hat gl infty r m of infinites matrices with finite number of non zero diagonals over the algebrar m t t m 1 the unitary ones are classified as well similar results are obtained for the sin algebras

generalization of h pseudoalgebraic structures the goal of this paper is to study hom h pseudoalgebraic structures generalizing h pseudoalgebras of associative and lie type we provide examples of the new structures and present some properties and construction theorems similar to the case of h pseudoalgebras the annihilator algebras are also discussed we also describe the equivalent definitions of hom h pseudoalgebra finally we consider the cohomology theory of hom h pseudoalgebra with coefficients in an arbitrary module furthermore the connection between the cohomology of hom lie h pseudoalgebra and its corresponding annihilator algebra is depicted

representations of simple finite lie conformal superalgebras of type w and s we construct all finite irreducible modules over lie conformal superalgebras of type w and s

schrodinger virasoro lie conformal algebra we first construct two new nonsimple conformal algebras associated with the schrodinger virasoro lie algebra and the extended schrodinger virasoro lie algebra respectively then we study conformal derivations and free nontrivial rank one conformal modules of these two conformal algebras also we provide a computation of their universal central extensions