string center of mass operator and its effect on brst cohomology we consider the theory of bosonic closed strings on the flat background 25 1 we show how the brst complex can be extended to a complex where the string center of mass operator x 0 is well defined we investigate the cohomology of the extended complex we demonstrate that this cohomology has a number of interesting features unlike in the standard brst cohomology there is no doubling of physical states in the extended complex the cohomology of the extended complex is more physical in a number of aspects related to the zero momentum states in particular we show that the ghost number one zero momentum cohomology states are in one to one correspondence with the generators of the global symmetries of the backgroundi e the poincare algebra

positive energy representations of the loop groups of non simply connected lie groups we classify and construct all irreducible positive energy representations of the loop group of a compact connectedand simple lie group and show that they admit an intertwining action of diff s 1

a less conservative robust stability test for linear uncertain time delay systems this note concerns with the robust stability of linear uncertain systems with state delay the uncertainty is assumed to be of polytopic type a less conservative delay dependent linear matrix inequality lmi method is presented based on a new lyapunov krasovskii functional the present method incorporates a relaxed parameter dependent technique combined with a recently proposed idea of introducing free weighting matrices when confined to delay free case the present result is also less conservative than existing stability tests using parameter dependent methods numerical examples are given to show the less conservativeness of the results

a natural construction of borcherds fake baby monster lie algebra we use a z 2 orbifold of the vertex operator algebra associated to the niemeier lattice with root lattice a 8 3 and the no ghost theorem of string theory to construct a generalized kac moody algebra borcherds theory of automorphic products allows us to determine the simple roots and identify the algebra with the fake baby monster lie algebra

the cohomology algebra of the semi infinite weil complex in 1993 lian zuckerman constructed two cohomology operations on the brst complex of a conformal vertex algebra with central charge 26 they gave explicit generators and relations for the cohomology algebra equipped with these operations in the case of the c 1 model in this paper we describe another such example namely the semi infinite weil complex of the virasoro algebra the semi infinite weil complex of a tame mathbb z graded lie algebra was defined in 1991 by feigin frenkel and they computed the linear structure of its cohomology in the case of the virasoro algebra we build on this result by giving an explicit generator for each non zero cohomology class and describing all algebraic relations in the sense of lian zuckerman among these generators

the kazhdan lusztig conjecture for w algebras the main result in this paper is the character formula for arbitrary irreducible highest weight modules of w algebras the key ingredient is the functor provided by quantum hamiltonian reduction which constructs the w algebras from affine kac moody km algebras and in a similar fashion w modules from km modules assuming certain properties of this functor the w characters are subsequently derived from the kazhdan lusztig conjecture for km algebras the result can be formulated in terms of a double coset of the weyl group of the km algebra the hasse diagrams give the embedding diagrams of the verma modules and the kazhdan lusztig polynomials give the multiplicities in the characters

quantization of hamiltonian loop group spaces we prove a fredholm property for spin c dirac operators mathsf d on non compact manifolds satisfying a certain condition with respect to the action of a semi direct product group k ltimes gamma with k compact and gamma discrete we apply this result to an example coming from the theory of hamiltonian loop group spaces in this context we prove that a certain index pairing mathcal x cap mathsf d yields an element of the formal completion r infty t of the representation ring of a maximal torus t subset h the resulting element has an additional antisymmetry property under the action of the affine weyl group indicating mathcal x cap mathsf d corresponds to an element of the ring of projective positive energy representations of the loop group

brst cohomology of the super virasoro algebras we study the superextension of the semi infinite cohomology theory of the virasoro algebra in particular we examine the brst complex with coefficients in the fock space of the rns superstring we prove a theorem of vanishing cohomology and establish the unitary equivalence between a positive definite transversal space a physical subspace and the zeroth cohomology group the cohomology of a subcomplex is identified as the covariant equivalent of the well known gso subspace an exceptional case to the vanishing theorem is discussed

the mechanics of running how does stiffness couple with speed a mathematical model for terrestrial running is presented based on a leg with the properties of a simple spring experimental force platform evidence is reviewed justifying the formulation of the model the governing differential equations are given in dimensionless form to make the results representative of animals of all body sizes the dimensionless input parameters are u a horizontal froude number based on forward speed and leg length v a vertical froude number based on vertical landing velocity and leg length and kleg a dimensionless stiffness for the leg spring results show that at high forward speed kleg is a nearly linear function of both u and v while the effective vertical stiffness is a quadratic function of u for each u v pair the simulation shows that the vertical force at mid step may be minimized by the choice of a particular step length a particularly useful specification of the theory occurs when both kleg and v are assumed fixed when kleg 15 and v 0 18 the model makes predictions of relative stride length s and initial leg angle theta o that are in good agreement with experimental data obtained from the literature

the brst cohomology of the nsr string vanishing and no ghost theorems we investigate the brst cohomology of the nsr string we prove vanishing theorems for the full and relative sub complexes generalizing the work of frenkel garland and zuckerman for the bosonic string using these results we give simple proofs of the no ghost theorems for both sectors

reducing conservatism of stability criteria for linear systems with time varying delay using an improved triple integral inequality abstract this paper focuses on stability analysis of linear systems with time varying delay where two cases of the time varying delay are discussed that is the time varying delay is either differentiable or just uniformly continuous first an improved triple integral inequality is proposed to estimate triple integrals tightly then by introducing two novel lyapunov krasovskii functionals catering for two cases of time varying delay two sufficient conditions on stability respectively for the system under two cases of time varying delay are derived using the improved triple integral inequality and a necessary and sufficient condition on quadratic matrix inequalities reported recently finally three numerical examples show that the obtained results outperform some existing ones

geometric quantization and multiplicities of group representations the heisenberg uncertainty principle says that it is impossible to determine simultaneously the position and momentum of a quantum mechanical particle this can be rephrased as follows the smallest subsets of classical phase space in which the presence of a quantum mechanical particle can be detected are its lagrangian submanifolds for this reason it makes sense to regard the lagrangian submanifolds of phase space as being its true points see weinstein 17 now let g be a compact lie group and g x x x a hamiltonian action of g on x see w for definitions it is well known that the fixed points of this action form a symplectic submanifold of x see for instance guillemin and sternberg 5 however what can one say about the fixed points of g we will show that they are also the points of a symplectic manifold xc this manifold is the marsden weinstein reduction of x with respect to the zero orbit in g and will be described in sect 2 it was introduced in a completely different context fl om ours by marsden and weinstein 12 problems in classical mechanics can often be reduced to the study of hamiltonian systems on symplectic manifolds and problems in quantum mechanics to the study of linear operators on hilbert space this fact has inspired a number of efforts to quantize symplectic geometry by devising schemes for associating hilbert space to symplectic manifolds the no go theorems of groenwald and van hove impose some embarrassing limitations on all such schemes however it seems to be a useful idea heuristically to think of every symplectic manifold x a ic 1 as being symbiotically associated with a hilbert space xq a t in such a way that the classical observables on the first space correspond to quantum observables on the second space the heuristics further suggests that if g is a group of symmetries of x la i j it should also be a group of symmetries of xq a tum in this heuristic spirit we will state the main conjecture of this paper

semi infinite cohomology and string theory abstract we develop the theory of semi infinite cohomology of graded lie algebras first introduced by feigin we show that the relative semi infinite cohomology has a structure analogous to that of the de rham cohomology in kahler geometry we prove a vanishing theorem for a special class of modules and we apply our results to the case of the virasoro algebra and the fock module in this case the zero cohomology is identified as the physical subspace of the fock module and the no ghost theorem follows we reveal the profound relation of semi infinite cohomology theory to the gauge invariant free string theory constructed by banks and peskin we then indicate the connection between gauge invariant interacting string theories and the geometric realizations of the infinite dimensional lie algebras

brst cohomologies for non critical strings the brst cohomologies of non critical massive string models are analysed in detail in the range of dimensions 1 d 26 the classical theorems on vanishing of dolbeaut type and relative cohomologies are proved the no ghost theorem is proved in the same range of dimensions it is also shown that the brst complex of the massive string model is a resolution of the non critical nambu goto string in all spacetime dimensions 1 d 25

affine kac moody algebras and semi infinite flag manifolds we study representations of affine kac moody algebras from a geometric point of view it is shown that wakimoto modules introduced in 18 which are important in conformal field theory correspond to certain sheaves on a semi infinite flag manifold with support on its schhubert cells this manifold is equipped with a remarkable semi infinite structure which is discussed in particular the semi infinite homology of this manifold is computed the cousin grothendieck resolution of an invertible sheaf on a semi infinite flag manifold gives a two sided resolution of an irreducible representation of an affine algebras consisting of wakimoto modules this is just the brst complex as a byproduct we compute the homology of an algebra of currents on the real line with values in a nilpotent lie algebra

the construction of the sh lie algebra of closed bosonic strings we present a construction of the closed string algebra in terms of gaussian processes and crossed products also we give a purely functional analytical prove of the sh lie structure

the operator quantization of the open bosonic string field algebra our aim in this paper is to make explicit the operator theory of the heuristic open bosonic string and to abstract a suitable field algebra for the string this is done on a fock krein space and we examine integrability and j unitary implementability of all the defining transformations of the string i e time translations gauge transformations and poincare transformations the results obtained agree partially with those of bowick and rajeev i e the gauge transformations do not leave the fock krein complex structure invariant once we obtained integrated transformation groups on a suitable symplectic space for the infinitesimal transformations of the string and proved implementability of these for the fock krein representation we are then free to define an abstract c algebra carrying all the algebraic information of the string and to examine different representations

a generalized kac moody algebra of rank 14 abstract we construct a vertex algebra of central charge 26 from a lattice orbifold vertex operator algebra of central charge 12 the brst cohomology group of this vertex algebra is a new generalized kac moody algebra of rank 14 we determine its root space multiplicities and a set of simple roots

technical communique improved delay range dependent stability criteria for linear systems with time varying delays this paper is concerned with the stability analysis of linear systems with time varying delays in a given range a new type of augmented lyapunov functional is proposed which contains some triple integral terms in the proposed lyapunov functional the information on the lower bound of the delay is fully exploited some new stability criteria are derived in terms of linear matrix inequalities without introducing any free weighting matrices numerical examples are given to illustrate the effectiveness of the proposed method

string localized quantum fields and modular localization we study free covariant quantum bose fields that are associated with irreducible representations of the poincare group and localized in semi infinite strings extending to spacelike infinity among these are fields that generate the irreducible representations of mass zero and infinite spin that are known to be incompatible with point like localized fields for the massive representations and the massless representations of finite helicity all string localized free fields can be written as an integral along the string of point localized tensor or spinor fields as a special case we discuss the string localized vector fields associated with the point like electromagnetic field and their relation to the axial gauge condition in the usual setting

automorphic forms fake monster algebras and hyperbolic reflection groups abstract we construct two families of automorphic forms related to twisted fake monster algebras and calculate their fourier expansions this gives a new proof of their denominator identities and shows that they define automorphic forms of singular weight we also obtain new infinite product identities which are the denominator identities of generalized kac moody superalgebras finally we describe the reflection groups of the root lattices of these algebras

effects of independently altering body weight and mass on the energetic cost of a human running model the mechanisms underlying the metabolic cost of running and legged locomotion in general remain to be well understood prior experimental studies show that the metabolic cost of human running correlates well with the vertical force generated to support body weight the mechanical work done and changes in the effective leg stiffness further previous work shows that the metabolic cost of running decreases with decreasing body weight increases with increasing body weight and mass and does not significantly change with changing body mass alone in the present study we seek to uncover the basic mechanism underlying this existing experimental data we find that an actuated spring mass mechanism representing the effective mechanics of human running provides a mechanistic explanation for the previously reported changes in the metabolic cost of human running if the dimensionless relative leg stiffness effective stiffness normalized by body weight and leg length is regulated to be constant the model presented in this paper provides a mechanical explanation for the changes in metabolic cost due to changing body weight and mass which have been previously measured experimentally and highlights the importance of active leg stiffness regulation during human running

admissible delay upper bounds for global asymptotic stability of neural networks with time varying delays this paper is concerned with global asymptotic stability of a neural network with a time varying delay where the delay function is differentiable uniformly bounded with delay derivative bounded from above first a general reciprocally convex inequality is presented by introducing some slack vectors with flexible dimensions this inequality provides a tighter bound in the form of a convex combination than some existing ones second by constructing proper lyapunov krasovskii functional global asymptotic stability of the neural network is analyzed for two types of the time varying delays depending on whether or not the lower bound of the delay derivative is known third noticing that sufficient conditions on stability from estimation on the derivative of some lyapunov krasovskii functional are affine both on the delay function and its derivative allowable delay sets can be refined to produce less conservative stability criteria for the neural network under study finally two numerical examples are given to substantiate the effectiveness of the proposed method

the monster lie algebra abstract we calculate the multiplicities of all the roots of the monster lie algebra this gives an example of a lie algebra all of whose simple roots and root multiplicities are known and which is not finite dimensional or an affine kac moody algebra there seem to be several similar infinite dimensional lie algebras which to a sympathetic eye appear to correspond to some of the sporadic simple groups

β γ systems and the deformations of the brst operator we describe the relation between simple logarithmic cfts associated with closed and open strings and their infinite metric limits corresponding to the systems this relation is studied on the level of the brst complex we show that the consideration of metric as a perturbation leads to a certain deformation of the algebraic operations of the lian zuckerman type on the vertex algebra associated with the systems the maurer cartan equations corresponding to this deformed structure in the quasi classical approximation lead to the nonlinear field equations as an explicit example we demonstrate that using this construction yang mills equations can be derived this gives rise to a nontrivial relation between the courant dorfman algebroid and homotopy algebras emerging from the gauge theory we also discuss a possible algebraic approach to the study of beta functions in sigma models

the ricci curvature of diff s1 sl 2 r previous calculations of the ricci curvature for the manifold diff diff s1 s1 are extended to diff s1 sl 2r these manifolds are distinguished by being coadjoint orbits of diff s1 which admit compatible symphectic and complex structures making them kahler manifolds

wirtinger based integral inequality application to time delay systems in the last decade the jensen inequality has been intensively used in the context of time delay or sampled data systems since it is an appropriate tool to derive tractable stability conditions expressed in terms of linear matrix inequalities lmis however it is also well known that this inequality introduces an undesirable conservatism in the stability conditions and looking at the literature reducing this gap is a relevant issue and always an open problem in this paper we propose an alternative inequality based on the fourier theory more precisely on the wirtinger inequalities it is shown that this resulting inequality encompasses the jensen one and also leads to tractable lmi conditions in order to illustrate the potential gain of employing this new inequality with respect to the jensen one two applications on time delay and sampled data stability analysis are provided

quasiclassical lian zuckerman homotopy algebras courant algebroids and gauge theory we define a quasiclassical limit of the lian zuckerman homotopy bv algebra quasiclassical lz algebra on the subcomplex corresponding to light modes i e the elements of zero conformal weight of the semi infinite brst cohomology complex of the virasoro algebra associated with vertex operator algebra voa with a formal parameter we also construct a certain deformation of the brst differential parametrized by a constant two component tensor such that it leads to the deformation of the a subalgebra of the quasiclassical lz algebra altogether this gives a functor the category of voa with a formal parameter to the category of a algebras the associated generalized maurer cartan equation gives the analogue of the yang mills equation for a wide class of voas applying this construction to an example of voa generated by systems we find a remarkable relation between the courant algebroid and the homotopy algebra of the yang mills theory

free matrix based integral inequality for stability analysis of systems with time varying delay the free weighting matrix and integral inequality methods are widely used to derive delay dependent criteria for the stability analysis of time varying delay systems because they avoid both the use of a model transformation and the technique of bounding cross terms this technical note presents a new integral inequality called a free matrix based integral inequality that further reduces the conservativeness in those methods it includes well known integral inequalities as special cases using it to investigate the stability of systems with time varying delays yields less conservative delay dependent stability criteria which are given in terms of linear matrix inequalities two numerical examples demonstrate the effectiveness and superiority of the method

novel inequality with application to improve the stability criterion for dynamical systems with two additive time varying delays abstract in this paper the stability of the system with two additive time varying delay components is studied and improved stability condition is obtained it firstly establishes two novel integral inequalities which are better than the same type inequalities found in the literature secondly a new constructed lyapunov functional is constructed based on the additive time varying delays property following two steps to handle the lyapunov functional the delay dependent stability condition is obtained which in terms of linear matrix inequalities finally two numerical examples are given to verify the effectiveness of the proposed method and the superiority of the results

a generalized free matrix based integral inequality for stability analysis of time varying delay systems abstract this paper focuses on the delay dependent stability problem of time varying delay systems a generalized free matrix based integral inequality gfmbii is presented this inequality is able to deal with time varying delay systems without using the reciprocal convexity lemma it overcomes the drawback that the bessel legendre inequality is inconvenient to cope with a time varying delay system as the resultant bound contains a reciprocal convexity through the use of the derived inequality and by constructing a suitable lyapunov krasovskii function lkf improved stability criteria are presented in the form of linear matrix inequalities lmis two numerical examples are carried out to demonstrate that the results outperform the state of the art in the literature

monstrous moonshine and monstrous lie superalgebras we prove conway and norton s moonshine conjectures for the infinite dimensional representation of the monster simple group constructed by frenkel lepowsky and meurman to do this we use the no ghost theorem from string theory to construct a family of generalized kac moody superalgebras of rank 2 which are closely related to the monster and several of the other sporadic simple groups the denominator formulas of these superalgebras imply relations between the thompson functions of elements of the monster i e the traces of elements of the monster on frenkel lepowsky and meurman s representation which are the replication formulas conjectured by conway and norton these replication formulas are strong enough to verify that the thompson functions have most of the moonshine properties conjectured by conway and norton and in particular they are modular functions of genus 0 we also construct a second family of kac moody superalgebras related to elements of conway s sporadic simple group col these superalgebras have even rank between 2 and 26 for example two of the lie algebras we get have ranks 26 and 18 and one of the superalgebras has rank 10 the denominator formulas of these algebras give some new infinite product identities in the same way that the denominator formulas of the a n n e kac moody algebras give the macdonald identities

stability analysis of systems with time varying delay via novel augmented lyapunov krasovskii functionals and an improved integral inequality abstract delay dependent stability analysis of linear systems with a time varying delay is investigated in this paper firstly instead of developing a lyapunov krasovskii functional lkf including augmented non integral quadratic terms as usual this paper proposes two augmented integral function based lkfs which can reflect closer relationships among system states secondly to bound the derivative of lkf more accurately a new integral inequality with several free matrices is developed compared with the free matrix based integral inequality this inequality can provide additional freedom due to the free matrices introduced then by employing those lkfs and the improved integral inequality several delay dependent stability criteria are established for two types of delays finally two numerical examples are given to demonstrate the superiority of the proposed method

locality in free string field theory free string field operators are constructed for the open bosonic string in the light cone gauge in any dimension these are naturally localized by the center of mass coordinate relative to this localization they are shown to have a causal commutator provided there are no tachyons for the critical string in d 26 the result still holds if the tachyon is suppressed we also show a causal commutator relative to the string light cone

borel weil bott theory on the moduli stack of g bundles over a curve let g be a semi simple group and m the moduli stack of g bundles over a smooth complex projective curve using representation theoretic methods i prove the pure dimensionality of sheaf cohomology for certain evaluation vector bundles over m twisted by powers of the fundamental line bundle this result is used to prove a borel weil bott theorem conjectured by g segal for certain generalized flag varieties of loop groups along the way the homotopy type of the group of algebraic maps from an affine curve to g and the homotopy type the hodge theory and the picard group of m are described one auxiliary result in appendix a is the alexander cohomology theorem conjectured in gro2 a self contained account of the uniformization theorem of ls for the stack m is given including a proof of a key result of drinfeld and simpson in characteristic 0 a basic survey of the simplicial theory of stacks is outlined in appendix b

semi infinite weil complex and the virasoro algebra we define a semi infinite analogue of the weil algebra associated an infinite dimensional lie algebra it can be used for the definition of semi infinite characteristic classes by analogy with the chern weil construction the second term of a spectral sequence of this weil complex consists of the semi infinite cohomology of the lie algebra with coefficients in its adjoint semi infinite symmetric powers we compute this cohomology for the virasoro algebra this is just the brst cohomology of the bosonic system with central charge 26 we give a complete description of the fock representations of this bosonic system as modules over the virasoro algebra using friedan martinec shenker bosonization we derive a combinatorial identity from this result

the riemann hilbert problem approach to a representation of the virasoro group ii the development of a riemann hilbert rh problem approach to the representation of the virasoro group introduced in our earlier paper w li and b y hou j math phys 30 1198 1989 is continued the rouche theorem is employed to prove that there exists a set of scalar functions in the complex plane in terms of which the structure of the virasoro group can be decided the general form of the rh problem will also be presented and the uniqueness of its solution will be proven for future use a standard form of a matrix fredholm equation equivalent to our rh problem will be deduced this may help to establish in a future paper the existence of a solution of the rh problem

new perspectives on the brst algebraic structure of string theory motivated by the descent equation in string theory we give a new interpretation for the action of the symmetry charges on the brst cohomology in terms of what we callthe gerstenhaber bracket this bracket is compatible with the graded commutative product in cohomology and hence gives rise to a new class of examples of what mathematicians call agerstenhaber algebra the latter structure was first discussed in the context of hochschild cohomology theory 11 off shell in the chiral brst complex all the identities of a gerstenhaber algebra hold up to homotopy applying our theory to thec 1 model we give a precise conceptual description of the brst gerstenhaber algebra of this model we are led to a direct connection between the bracket structure here and the anti bracket formalism in bv theory 29 we then discuss the bracket in string backgrounds with both the left and the right movers we suggest that the homotopy lie algebra arising from our gerstenhaber bracket is closely related to the hla recently constructed by witten zwiebach finally we show that our constructions generalize to any topological conformal field theory

quantum group as semi infinite cohomology we obtain the quantum group slq 2 as semi infinite cohomology of the virasoro algebra with values in a tensor product of two braided vertex operator algebras with complementary central charges c bar c 26 each braided voa is constructed from the free fock space realization of the virasoro algebra with an additional q deformed harmonic oscillator degree of freedom the braided voa structure arises from the theory of local systems over configuration spaces and it yields an associative algebra structure on the cohomology we explicitly provide the four cohomology classes that serve as the generators of slq 2 and verify their relations we also discuss the possible extensions of our construction and its connection to the liouville model and minimal string theory

the c algebra of bosonic strings we give a rigorous definition of witten sc string algebra to this end we present a new construction ofc algebras associated to special geometric situations kahler foliations and generalize this later construction to the string case through this we get a natural geometrical interpretation of the string of semi infinite forms as well as the fermionic algebra structure using the non commutative geometric concepts for investigating the string algebra we get a natural fredholm module representation of dimension 26

string quantization on group manifolds and the holomorphic geometry of diffs1 s1 the recent results by bowick and rajeev on the relation of the geometry of diffs1 s1 and string quantization in d are extended to a string moving on a group manifold a new derivation of the curvature formula 26 12m3 1 6m n m for the canonical holomorphic line bundle over diffs1 s1 is given which clarifies the relation of that bundle with the complex line bundles over infinite dimensional grassmannians studied by pressley and segal

quantum dynamics on super groups constraints and the brst supergroup the smallest supergroup b k containing among its generators those of a constraint group k the brst charge and the corresponding ghost and antighost operators is constructed the supergroup b k can be enlarged to include the ordinary dynamical variables of the unconstrained physical system in a group approach to quantization b k generalizes the ordinary u 1 phase invariance of wave functions in particular this mechanism reproduces the essential features of the brst quantization when k is diff s1 the critical values of string theory are those for which the space of polarized functions on the enlarged brst supergroup is not irreducible

semi infinite homology and 2d gravity i in 33 we studied the constraint problem for two dimensional quantum gravity in the conformal gauge in this gauge we proposed an ansatz for the gravitational sector using this ansatz we established a striking connection between the matrix models and continuum 2d gravity we also announced several results on semi infinite homology of the virasoro algebra with coefficients in a suitable class of positive energy modules in this article we will provide details of the proof of the announced results

construction of lyapunov krasovskii functionals for networks of iiss retarded systems in small gain formulation this paper tackles a problem of verifying stability of retarded dynamical networks in a dissipative formulation subsystems are assumed to be integral input to state stable iiss time delays are allowed to reside in both subsystems and interconnection channels and may be both discrete and distributed no assumption is made on the interconnection topology a small gain methodology is developed for constructing a lyapunov krasovskii functional to establish iiss of such a network

stability analysis of systems with time varying delays via the second order bessel legendre inequality this paper is concerned with the delay dependent stability of systems with time varying delays the novelty relies on the use of the second order bessel legendre integral inequality which is less conservative than the jensen and wirtinger based inequalities unlike similar contributions the features of this inequality are fully integrated into the construction of augmented lyapunov krasovskii functionals leading to novel stability criteria expressed in terms of linear matrix inequalities the stability condition is tested on some classical numerical examples illustrating the efficiency of the proposed method

further refinements in stability conditions for time varying delay systems abstract this paper addresses the problem of assessing the stability of linear time invariant lti systems with time varying delay the first contribution is a new stability criterion specified as a negativity condition for a quadratic function parameterized by the delay this result mainly follows from an augmented affine parameter dependent lyapunov krasovskii functional which in turn takes advantages of convexity properties then as a second contribution we invoke a result from robust control literature to show how the proposed stability condition can be checked exactly in terms of linear matrix inequality lmi conditions the improvements obtained by the proposed refinements are illustrated via numerical examples drawn from the literature

suspending loads decreases load stability but may slightly improve body stability here we seek to determine how compliantly suspended loads could affect the dynamic stability of legged locomotion we theoretically model the dynamic stability of a human carrying a load using a coupled spring mass damper model and an actuated spring loaded inverted pendulum model as these models have demonstrated the ability to correctly predict other aspects of locomotion with a load in prior work such as body forces and energetic cost we report that minimizing the load suspension natural frequency and damping ratio significantly reduces the stability of the load mass but may slightly improve the body stability of locomotion when compared to a rigidly attached load these results imply that a highly compliant load suspension could help stabilize body motion during human animal or robot load carriage but at the cost of a more awkward less stable load

generalized classical brst cohomology and reduction of poisson manifolds in this paper we formulate a generalization of the classical brst construction which applies to the case of the reduction of a poisson manifold by a submanifold in the case of symplectic reduction our procedure generalizes the usual classical brst construction which only applies to symplectic reduction of a symplectic manifold by a coisotropic submanifold i e the case of reducible first class constraints in particular our procedure yields a method to deal with second class constraints we construct the brst complex and compute its cohomology brst cohomology vanishes for negative dimension and is isomorphic as a poisson algebra to the algebra of smooth functions on the reduced poisson manifold in zero dimension we then show that in the general case of reduction of poisson manifolds brst cohomology cannot be identified with the cohomology of vertical differential forms

semi infinite induction and wakimoto modules the purpose of this paper is to suggest the construction and study properties of semi infinite induction which relates to semi infinite cohomology the same way induction relates to homology and coinduction to cohomology we prove a version of the shapiro lemma showing that the semi infinite cohomology of a module is isomorphic to that of the semi infinitely induced module a practical outcome of our construction is a simple construction of the wakimoto modules highest weight modules used in double sided bgg resolutions of irreducible modules

multiplets of representations and kostant s dirac operator for equal rank loop groups let g be a semisimple lie algebra and leth be a reductive subalgebra of maximal rank ing given any irreducible representation ofg consider its tensor product with the spin representation associated to the orthogonal complement ofh in g recently b gross b kostant p ramond and s sternberg 2 proved a generalization of the weyl character formula which decomposes the signed character of this product representation in terms of the characters of a set of irreducible representations of h called a multiplet kostant 7 then constructed a formalh equivariant dirac operator on such product representations whose kernel is precisely the multiplet of h representations corresponding to the given representation ofg we reproduce these results in the kac moody setting for the extended loop algebras lg and lh we prove a homogeneous generalization of the weyl kac character formula which now yields a multiplet of irreducible positive energy representations of lh associated to any irreducible positive energy representation of lg we construct an lh equivariant operator analogous to kostant s dirac operator on the tensor product of a representation of lg with the spin representation associated to the complement of lh in lg we then prove that the kernel of this operator gives the lh multiplet corresponding to the original representation of lg

geometric realization of conformal field theory on riemann surfaces conformal field theory on a family of riemann surfaces is formulated we derive equations of motion of vacua which are parametrized by moduli of riemann surfaces and show that these vacua are characterized uniquely by these equations our theory has a deep connection with sato s theory of kp equations

string theory and loop space index theorems we study index theorems for the dirac ramond operator on a compact riemannian manifold the existence of a group action on the loop space makes possible the definition of a character valued index which we calculate by using a two dimensional sigma model withn 1 2 supersymmetry we compute the euler characteristic the hirzebruch signature and the dirac ramond genus of loop space we compare our results to the calculations made by using the atiyah singer character valued index theorem

chiral equivariant cohomology iii this is the third of a series of papers on a new equivariant cohomology that takes values in a vertex algebra and contains and generalizes the classical equivariant cohomology of a manifold with a lie group action a la h cartan in this paper we compute this cohomology for spheres and show that for any simple connected group g there is a sphere with infinitely many actions of g which have distinct chiral equivariant cohomology but identical classical equivariant cohomology unlike the classical case the description of the chiral equivariant cohomology of spheres requires a substantial amount of new structural theory which we fully develop in this paper this includes a quasi conformal structure equivariant homotopy invariance and the values of this cohomology on homogeneous spaces these results rely on crucial features of the underlying vertex algebra valued complex that have no classical analogues

note on stability of linear systems with time varying delay this note considers the stability of linear systems with a time varying delay we are interested in a simple lyapunov krasovskii functional lkf approach without delay decomposition in this category all recent tractable results had a fixed bound on the allowable maximum size of the delay for years we propose a new simple lkf including the cross terms of variables and quadratic terms multiplied by a higher degree scalar function and present a new result expressed in the form of lmis we show by two well known examples that our result overcomes the previous allowable maximum size of delay and it is less conservative than the previous results having a relatively small upper bound in the derivative of time delay

twisted strong macdonald theorems and adjoint orbits the strong macdonald theorems state that for l reductive and s an odd variable the cohomology algebras h l z z n and h l z s are freely generated and describe the cohomological s and z degrees of the generators the resulting identity for the z weighted euler characteristic is equivalent to macdonald s constant term identity for a finite root system we calculate h mathfrak p z n mathfrak p and h mathfrak p s for mathfrak p a standard parahoric in a twisted loop algebra giving strong macdonald theorems that take into account both a parabolic component and a possible diagram automorphism twist in particular we show that h mathfrak p z n mathfrak p contains a parabolic subalgebra of the coinvariant algebra of the fixed point subgroup of the weyl group of l and thus is no longer free we also prove a strong macdonald theorem for h mathfrak b s mathfrak n and h mathfrak b z n mathfrak n when mathfrak b and mathfrak n are iwahori and nilpotent subalgebras respectively of a twisted loop algebra for each strong macdonald theorem proved taking z weighted euler characteristics gives an identity equivalent to macdonald s constant term identity for the corresponding affine root system as part of the proof we study the regular adjoint orbits for the adjoint action of the twisted arc group associated to l proving an analogue of the kostant slice theorem

an improved reciprocally convex inequality and an augmented lyapunov krasovskii functional for stability of linear systems with time varying delay this paper is concerned with stability of a linear system with a time varying delay first an optimal reciprocally convex inequality is proposed compared with the extended reciprocally convex inequality recently reported the optimal reciprocally convex inequality not only provides an optimal bound for the reciprocally convex combination but also introduces less slack matrix variables second a new lyapunov krasovskii functional is tailored for the use of auxiliary function based integral inequality third based on the optimal reciprocally convex inequality and the new lyapunov krasovskii functional a stability criterion is derived for the system under study finally two well studied numerical examples are given to show that the obtained stability criterion can produce a larger upper bound of the time varying delay than some existing methods

the fake monster superalgebra abstract we show that the physical states of a 10 dimensional superstring moving on a torus form a generalized kac moody superalgebra this gives the first explicit realizations of these algebras for a special torus the denominator function of this algebra is an automorphic form so that we can determine the simple roots we call this algebra the fake monster superalgebra

brst cohomology and highest weight vectors i we initiate a program to study certain recent problems in non compact coset cft by the brst approach we derive a reduction formula for the brst cohomology by making use of a twisting by highest weight modules as illustrations we apply the formula to the bosonic string model and a rank one non compact coset model dpl our formula provides a completely new approach to non compact coset construction