surface diffusion coefficients for room acoustics free field measures a surface diffusion coefficient is needed in room acoustics to enable the quality of diffusing surfaces to be evaluated it may also facilitate more accurate geometric room acoustic models this paper concentrates on diffusion coefficients derived from free field polar responses an extensive set of two and three dimensional measurements and predictions was used to test the worth of different diffusion coefficient definitions the merits and problems associated with these types of coefficients are discussed and past parameters reviewed two new coefficients are described the new measure based on the autocorrelation function is forwarded as the best free field coefficient the strengths and weaknesses of the coefficient are defined

conformal covariantization of moyal lax operators a covariant approach to the conformal property associated with moyal lax operators is given by identifying the conformal covariance with the second gelfand dickey flow we covariantize moyal lax operators to construct the primary fields of one parameter deformation of classical w algebras

generalized drinfel d sokolov hierarchies a general approach is adopted to the construction of integrable hierarchies of partial differential equations a series of hierarchies associated to untwisted kac moody algebras and conjugacy classes of the weyl group of the underlying finite lie algebra is obtained the generalized kdv hierarchies of v g drinfel d and v v sokolov are obtained as the special case for the coxeter element various examples of the general formalism are treated in some detail including the fractional kdv hierarchies

a short proof of a kupershmidt wilson theorem this is a short elementary proof of a statement originally observed by adler then pursued by the author by kupershmidt and wilson and in a more general setting by drinfeld and sokolov

w gauge structures and their anomalies an algebraic approach starting from flat two dimensional gauge potentials we propose the notion of w gauge structure in terms of a nilpotent becchi rouet stora brs differential algebra the decomposition of the underlying lie algebra with respect to an sl 2 subalgebra is crucial for the discussion of conformal covariance in particular the appearance of a projective connection different sl 2 embeddings lead to different w gauge structures we present a general soldering procedure which allows one to express zero curvature conditions for the w currents in terms of conformally covariant differential operators acting on the w gauge fields and to obtain at the same time the complete nilpotent brs differential algebra generated by w currents gauge fields and the ghost fields corresponding to w diffeomorphisms as illustrations we treat the cases of sl 2 itself and the two different sl 2 embeddings in sl 3 viz the w 1 3 and w 2 3 gauge structures in some detail in these cases we determine algebraically w anomalie

picard fuchs ordinary differential systems in n 2 supersymmetric yang mills theories in general picard fuchs systems in n 2 supersymmetric yang mills theories are realized as a set of simultaneous partial differential equations however if the quantum chromodynamics qcd scale parameter is used as a unique independent variable instead of moduli the resulting picard fuchs systems are represented by a single ordinary differential equation ode whose order coincides with the total number of independent periods this paper discusses some properties of these picard fuchs odes in contrast with the usual picard fuchs systems written in terms of moduli derivatives there exists a wronskian for this ordinary differential system and this wronskian produces a new relation among periods moduli and qcd scale parameter which in the case of su 2 is reminiscent of the scaling relation of prepotential on the other hand in the case of the su 3 theory there are two kinds of ordinary differential equations one of which is the equation directly constructed from periods and the other is derived

a geometrical formulation of fermionic integrable systems a fermionic hamiltonian system is formulated on a supermanifold it is shown that if the system possesses a bi hamiltonian structure one can naturally define a lax equation associated with a 1 1 tensor on this supermanifold and this allows one to construct a set of conserved quantities furthermore if the corresponding nijenhuis tensor vanishes it is shown that all these conserved quantities would be in involution which is a sufficient condition for integrability of the system the fermionic extension of the kdv equation with a bi hamiltonian structure within this geometrical approach is studied

a fully supersymmetric akns theory we construct a fully supersymmetric bihamiltonian theory in four superfields admitting zero curvature and lax formulation this theory is an extension of the classical akns which can be recovered as a reduction other supersymmetric theories are obtained as reductions of the susy akns namely a nonlinear schrodinger a modified kdv and the manin radul kdv the susy nonlinear schrodinger hierarchy is related to the one of roelofs and kersten we determine its bihamiltonian and lax formulation finally we show that the susy kdv s mentioned before are related through a susy miura map

quantum line operators from lax pairs motivated by the realization of the yang baxter equation of 2d integrable models in the 4d gauge theory of costello witten yamazaki cwy we study the embedding of integrable 2d toda field models inside this construction this is done by using the lax formulation of 2d integrable systems and by thinking of the standard lax pair l in terms of components of cwy gauge connection propagating along particular directions in the gauge bundle we also use the results of the cwy theory to build quantum line operators for 2d toda models and compute the one loop contribution of two intersecting lines exchanging one gluon other features such as local symmetries and comments on extension of our method to other 2d integrable models are also discussed we also comment on some basic points that still need a refinement before discussing about a fully consistent embedding of lax pairs into cwy theory

on the nature of the gardner transformation it is shown that every higher korteveg de vries equation can be included in a one parameter family of integrable equations

classical r matrices and compatible poisson structures for lax equations on poisson algebras given a classical r matrix on a poisson algebra we show how to construct a natural family of compatible poisson structures for the hamiltonian formulation of lax equations examples for which our formalism applies include the benny hierarchy the dispersionless toda lattice hierarchy the dispersionless kp and modified kp hierarchies the dispersionless dym hierarchy etc

a supersymmetric extension of the kadomtsev petviashvili hierarchy an extension of the kadomtsev petviashvili hierarchy by odd variables is given conservation laws and formal integrability are proved

refining the shifted topological vertex we study aspects of the refining and shifting properties of the 3d macmahon function c3 q used in topological string theory and bkp hierarchy we derive the explicit expressions of the shifted topological vertex s q and its refined version t q t these vertices complete results in literature

the integrable hierarchy constructed from a pair of kdv type hierarchies and its associated w algebra for any two arbitrary positive integers n and m using them th kdv hierarchy and the n m th kdv hierarchy as building blocks we are able to construct another integrable hierarchy referred to as the n m th kdv hierarchy thew algebra associated to the second hamiltonian structure of the n m th kdv hierarchy calledw n m algebra is isomorphic via a miura map to the direct sum of aw m algebra aw n m algebra and an additionalu 1 current algebra in turn from the latter we can always construct a representation of aw algebra

nonstandard drinfeld sokolov reduction subject to some conditions the input data for the drinfeld sokolov construction of kdv type hierarchies is a quadruplet where the are gradations of a loop algebra and is a semisimple element of the nonzero grade a new sufficient condition on the quadruplet under which the construction works is proposed and examples are presented the proposal relies on splitting the grade zero part of into a vector space direct sum of two subalgebras this permits one to interpret certain gelfand dickey type systems associated with a nonstandard splitting of the algebra of pseudodifferential operators in the drinfeld sokolov framework

a boundary integral formulation for the prediction of acoustic scattering from periodic structures the scattering of sound by reflecting surfaces is an important feature in room acoustics the boundary element method has been shown in the past to be an accurate method to calculate the scattering pattern of complex surfaces however this numerical method is expensive to use on large surfaces where a large number of elements is required this paper proposes a method of reducing the number of boundary elements required to model large but periodic structures the method is based on a consideration of the relationship between the field variables at two points exactly one period apart the problem is reduced to the modeling of just one period of the structure in cases of plane wave incidence the prediction using this method agrees very well with the prediction obtained by modeling the complete structure with the point source in the near field of the surface the incidence field is no longer periodic and the assumption of a constant periodic factor does not hold in this case it is shown that the metho

on diff s1 covariantization of pseudodifferential operator a study of diff s1 covariant properties of a pseudodifferential operator of integer degree is presented first it is shown that the action of diff s1 defines a hamiltonian flow defined by the second gelfand dickey bracket if and only if the pseudodifferential operator transforms covariantly second the covariant form of a pseudodifferential operator of degree n 0 1 is constructed by exploiting the inverse of the covariant derivative this in particular implies the existence of a primary basis for wkp n n 0 1

oka s principle for holomorphic submersions with sprays the oka principle is a fundamental principle of complex analysis which says that on stein manifolds closed complex submanifolds of affine spaces analytic problems of cohomological or even homotopical nature have only topological obstructions the story began in 1939 when k oka proved that on a domain of holomorphy a secondcousin problem is solvable by holomorphic functions if it is solvable by continuous functions oka oka s result has the following equivalent formulation ife x is a holomorphicc bundle over adomainof holomorphy then every continuous section of e is homotopic to a holomorphic section in 1957 h grauert gra extended oka s result to sections of holomorphic fiber bundles with complex homogeneous fibers over stein manifolds see also the papers car fr hl in 1989 m gromov gr1 announced a major generalization of grauert s theorem replacing complex lie groups and homogeneous spaces by a larger class of complex manifolds with a spray a spray on a complex manifold y is a holomorphic vector bundle p e y with a holomorphic map s e y the spray map which is the identity on the zero section and whose restriction to each fibre of e is a submersion at zero such sprays exist on complex homogeneous spaces on complements of affine algebraic subvarieties of codimension at least two and more generally on manifolds whose holomorphic tangent bundle is spanned by finitely many c complete holomorphic vector fields the notion of spray extends in a natural way to submersions the following is theorem 4 5 in gr1 if h z x is a holomorphic submersion onto a stein manifold x such that every point x x has an open neighborhood u x such that z u h 1 u u admits a fiber dominating spray then the inclusion of the

a quantum group structure in integrable conformal field theories we discuss a quantization prescription of the conformal algebras of a class ofd 2 conformal field theories which are integrable we first give a geometrical construction of certain extensions of the classical virasoro algebra known as classicalw algebras in which these algebras arise as the lie algebra of the second hamiltonian structure of a generalized korteweg de vries hierarchy this fact implies that thew algebras obtained as a reduction with respect to the nilpotent subalgebras of the kac moody algebra describe the integrability of a toda field theory subsequently we determine the coadjoint operators of thew algebras and relate these to classical yang baxter matrices the quantization of these algebras can be carried out using the concept of a so called quantum group we derive the condition under which the representations of these quantum groups admit a hilbert space completion by exploring the relation with the braid group then we consider a modification of the miura transformation which we use to define a quantumw algebra this leads to an alternative interpretation of the coset construction for kac moody algebras in terms of nonlinear integrable hierarchies subsequently we use the connection between the induced braid group representations and the representations of the mapping class group of riemann surfaces to identify an action of thew algebras on the moduli space of stable curves and we give the invariants of this action this provides a generalization of the situation for the virasoro algebra where such as invariant is given by the so called mumford form which describes the partition function of the bosonic string

zero curvature conditions and conformal covariance two dimensional zero curvature conditions with special emphasis on conformal properties are investigated in detail and the appearance of covariant higher order differential operators constructed in terms of a projective connection is elucidated the analysis is based on the kostant decomposition of simple lie algebras in terms of representations with respect to their principal sl 2 subalgebra

large chiral diffeomorphisms on riemann surfaces and w algebras the diffeomorphism action lifted on truncated chiral taylor expansion of a complex scalar field over a riemann surface is presented in the paper under the name of large diffeomorphisms after an heuristic approach we show how a linear truncation in the taylor expansion can generate an algebra of symmetry characterized by some structure functions such a linear truncation is explicitly realized by introducing the notion of forsyth frame over the riemann surface with the help of a conformally covariant algebraic differential equation the large chiral diffeomorphism action is then implemented through a becchi rouet stora brs formulation for a given order of truncation leading to a more algebraic setup in this context the ghost fields behave as holomorphically covariant jets subsequently the link with the so called w algebras is made explicit once the ghost parameters are turned from jets into tensorial ghost ones we give a general solution with the help of the structure functions pertaining to al

a homotopy theorem for oka theory we prove a homotopy theorem for sheaves its application shortens and simplifies the proof of many oka principles such as gromov s oka principle for elliptic submersions

integrability of the frobenius algebra valued kadomtsev petviashvili hierarchy we introduce a frobenius algebra valued kadomtsev petviashvili kp hierarchy and show the existence of frobenius algebra valued function for this hierarchy in addition we construct its hamiltonian structures by using the adler dickey gelfand method as a byproduct of these constructions we show that the coupled kp hierarchy defined by casati and ortenzi j geom phys 56 418 449 2006 has at least n basic different local bi hamiltonian structures finally via the construction of the second hamiltonian structures we obtain some local matrix or frobenius algebra valued generalizations of classical w algebras

riemann liouville integrals of fractional order and extended kp hierarchy an attempt to formulate the extensions of the kp hierarchy by introducing fractional order pseudo differential operators is given in the case of the extension with the half order pseudo differential operators a system analogous to the supersymmetric extensions of the kp hierarchy is obtained unlike the supersymmetric extensions no grassmannian variable appears in the hierarchy considered here more general hierarchies constructed by the 1 nth order pseudo differential operators their integrability and the reduction procedure are also investigated in addition to finding the new extensions of the kp hierarchy a brief introduction to the riemann liouville integral is provided to yield a candidate for the fractional order pseudo differential operators

fermionic covariant prolongation structure theory for multidimensional super nonlinear evolution equation the fermionic covariant prolongation structure theory is investigated we extend the fermionic covariant prolongation structure technique to the multidimensional super nonlinear evolution equation and present the fermionic covariant fundamental equations determining the prolongation structure furthermore we investigate a 2 1 dimensional super nonlinear schrodinger equation and analyze its integrability by means of this prolongation structure technique we derive its lax representation and backlund transformation moreover we present a solution of this multidimensional super integrable equation

homotopy principles for equivariant isomorphisms let g be a reductive complex lie group acting holomorphically on stein manifolds x and y let px x qx and py y qy be the quotient mappings when is there an equivariant biholomorphism of x and y a necessary condition is that the categorical quotients qx and qy are biholomorphic and that the biholomorphism sends the luna strata of qx isomorphically onto the corresponding luna strata of qy fix we demonstrate two homotopy principles in this situation the first result says that if there is a g diffeomorphism x y inducing which is g biholomorphic on the reduced fibres of the quotient mappings then is homotopic through g diffeomorphisms satisfying the same conditions to a g equivariant biholomorphism from x to y the second result roughly says that if we have a g homeomorphism x y which induces a continuous family of gequivariant biholomorphisms of the fibres px 1 q and py 1 q for q qx and if x satisfies an auxiliary property which holds for most x then is homotopic through g homeomorphisms satisfying the same conditions to a g equivariant biholomorphism from x to y our results improve upon those of our earlier paper j reine angew math 706 2015 193 214 and use new ideas and techniques

classical a n w geometry by analyzing theextrinsic geometry of two dimensional surfaces chirally embedded incp n thecp n w surface 1 we give exact treatments in various aspects of the classical w geometry in the conformal gauge first the basis of tangent and normal vectors are defined at regular points of the surface such that their infinitesimal displacements are given by connections which coincide with the vector potentials of the conformal a n toda lax pair since the latter is known to be intrinsically related with the w symmetries this gives the geometrical meaning of thea n w algebra second w surfaces are put in one to one correspondence with solutions of the conformally reduced wznw model which is such that the toda fields give the cartan part in the gauss decomposition of its solutions third the additional variables of the toda hierarchy are used as coordinates ofcp n this allows us to show that w transformations may be extended as particular diffeomorphisms of this target space higher dimensional generalizations of the wznw equations are derived and related with the zakharov shabat equations of the toda hierarchy fourth singular points are studied from a global viewpoint using our earlier observation 1 that w surfaces may be regarded as instantons the global indices of the w geometry which are written in terms of the toda fields are shown to be the instanton numbers for associated mappings of w surfaces into the grassmannians the relation with the singularities of w surface is derived by combining the toda equations with the gauss bonnet theorem

integrable fermionic extensions of the garnier system and the anharmonic oscillator we first derive a fermionic extension of the garnier system by applying the method of binary nonlinearization of spectral problem to the supersymmetric kdv equation of kupershmidt and then a fermionic extension of the anharmonic oscillator by a simple reduction the integrable properties of resulting systems such as lax representations corresponding r matrices and conversed integrals of motion are established

non local matrix generalizations of w algebras there is a standard way to define two symplectic hamiltonian structures the first and second gelfand dikii brackets on the space of ordinarymth order linear differential opeatorsl d m u1dm 1 u2dm 2 u m in this paper i consider in detail the case where theu k aren n matrix valued functions with particular emphasis on the more interesting second gelfand dikii bracket of particular interest is the reduction to the symplectic submanifoldu1 0 this reduction gives rise to matrix generalizations of the classical version of thenon linear w m algebras calledv n m algebras the non commutativity of the matrices leads tonon local terms in thesev n m algebra s i show that these algebras contain a conformal virasoro subalgebra and that combinationsw k of theu k can be formed that aren n matrices of conformally primary fields of spink in analogy with the scalar casen 1 in general however thev m n algebras have a much richer structure than thew m algebras as can be seen on the examples of thenon linear andnon local poisson brackets u2 ab u2 cd u2 ab w3 cd and w3 ab w3 cd which i work out explicitly for allm andn a matrix miura transformations is derived mapping these complicated second gelfand dikii brackets of theu k to a set of much simpler poisson brackets providing the analogoue of the free field representation of thew m algebras

on the completeness of the set of classical w algebras obtained from ds reductions we clarify the notion of the ds generalized drinfeld sokolov reduction approach to classical cal w algebras we first strengthen an earlier theorem which showed that an sl 2 embedding cal s subset cal g can be associated to every ds reduction we then use the fact that a cal w algebra must have a quasi primary basis to derive severe restrictions on the possible reductions corresponding to a given sl 2 embedding in the known ds reductions found to date for which the cal w algebras are denoted by cal w s g algebras and are called canonical the quasi primary basis corresponds to the highest weights of the sl 2 here we find some examples of noncanonical ds reductions leading to cal w algebras which are direct products of cal w s g algebras and lq lq free field algebras with conformal weights delta in 0 1 over 2 1 we also show that if the conformal weights of the generators of a cal w algebra obtained from ds reduction are nonnegative delta geq 0 which is the case for all ds reductions known to date then the delta geq 3 over 2 subsectors of the weights are necessarily the same as in the corresponding cal w s g algebra these results are consistent with an earlier result by bowcock and watts on the spectra of cal w algebras derived by different means we are led to the conjecture that up to free fields the set of cal w algebras with nonnegative spectra delta geq 0 that may be obtained from ds reduction is exhausted by the canonical ones

on the huge lie superalgebra of pseudo superdifferential operators and super kp hierarchies lie superalgebraic methods are used to establish a connection between the huge lie superalgebra of super pseudo differential operators and various super kp hierarchies we show in particular that splits into 5 2 2 1 graded algebras expected to correspond to five classes of super kp hierarchies generalizing the well known manin radul and figueroa mas ramos supersymmetric kp hierarchies

supersymmetric extension of the korteweg de vries equation it is shown that among a one parameter family of supersymmetric extensions of the korteweg de vries equation there is a special system that has an infinite number of conservation laws which can be formulated in the second hamiltonian structure and which has a nontrivial lax representation its modified version is also discussed

a supertrace identity and its applications to superintegrable systems a supertrace identity on lie superalgebras is established it provides a tool for constructing super hamiltonian structures of zero curvature equations associated with lie superalgebras applications in the case of the lie superalgebra b 0 1 present super hamiltonian structures of a super akns soliton hierarchy and a super dirac soliton hierarchy

classical w algebras we reconsider the relation between classicalw algebras and deformations of differential operators emphasizing the consistency with diffeomorphisms generators of thew algebra that arek differentials are constructed by a systematic procedure the method extends following drinfeld and sokolov tow algebras based on arbitrary simple lie algebras

prediction and evaluation of the scattering from quadratic residue diffusers the scattering from quadratic residue diffusers has been predicted using methods based on the helmholtz kirchhoff integral equation the methods consisted of two boundary integral methods and two more approximate solutions utilizing kirchhoff s boundary conditions the predictions were compared to measurements made in both the near and far fields an accurate boundary integral method which works below and above the well cutoff frequency has been found the limitations of the more approximate methods have been defined the approximations behind the quadratic residue diffuser s design have been tested the important assumption of a phase change local reacting admittance over each well face was found to be good over a wide range of frequencies the frequency limit of this approximation has also been defined

the constrained modified kp hierarchy and the generalized miura transformations in this letter we consider the second hamiltonian structure of the constrained modified kp hierarchy after mapping the lax operator to a pure differential operator the second structure becomes the sum of the second and the third gelfand dickey brackets defined by this differential operator we simplify this hamiltonian structure by factorizing the lax operator into linear terms

higher spin fields and the gelfand dickey algebra we show that in 2 dimensional field theory higher spin algebras are contained in the algebra of formal pseudodifferential operators introduced by gelfand and dickey to describe integrable nonlinear differential equations in lax form the spin 2 and 3 algebras are discussed in detail and the generalization to all higher spins is outlined this provides a conformal field theory approach to the representation theory of gelfand dickey algebras

on the gelfand dickey algebra gd sln and the wn symmetry i the bosonic case the algebra of nonlinear local and nonlocal differential operators acting on the ring of analytic functions is studied it is shown in particular that this space splits into 3 2 special subalgebras jr j 0 1 r 1 each subalgebra is completely specified by quantum numbers s and p q describing the conformal spin and the lowest and the highest degrees respectively the algebra and its dual of local pure nonlocal differential operators is used to calculate the general expression of the gelfand dickey bracket and the wn symmetry poisson one in terms of a set of spin j canonical fields uj 2 j n and a nonlinear u cubic dependent differential operator d n i j z u the explicit form of this operator is worked out other remarkable features are also discussed

classical extended conformal algebras associated with constrained kp hierarchy the conformal property of the second hamiltonian structure of constrained kp hierarchy derived by oevel and strampp is examined it is found that it naturally gives a family of nonlocal extended conformal algebras two examples of such algebras are given and it is found that they are similar to bilal s v algebra by taking a gauge transformation one can map the constrained kp hierarchy to kupershmidt s nonstandard lax hierarchy the second hamiltonian structure in this representation is considered it is shown that after mapping the lax operator to a pure differential operator the second structure becomes the sum of the second and the third gelfand dickey brackets defined by this differential operator the corresponding conformally covariant form of this differential operator is also given

oka s principle for holomorphic sections of elliptic bundles 2 the h principle for locally trivial fibrations 2 1 the h principle over small subsets 2 2 the h principle over totally real submanifolds 2 3 local extension of the h principle 2 4 localizable extensions 2 5 the h principle for cm bundles 2 6 manifolds with totally real souls 2 7 totally real extensions 2 8 nicely localizable extensions 2 9 the basic h principle for z x 2 10 homomorphisms and holomorphic maps of rank r

bihamiltonian hierarchies in 2d topological field theory at one loop approximation we compute the genus one correction to the integrable hierarchy describing coupling to gravity of a 2d topological field theory the bihamiltonian structure of the hierarchy is given by a classical w algebra we compute the central charge of this algebra we also express the generating function of elliptic gromov witten invariants via tau function of the isomonodromy deformation problem arising in the theory of wdvv equations of associativity

a matrix integral solution to two dimensional w p gravity thep th gel fand dickey equation and the string equation l p 1 have a common solution expressible in terms of an integral overn n hermitean matrices for largen the integrand being a perturbation of a gaussian generalizing kontsevich s integral beyond the kdv case it is equivalent to showing that is a vacuum vector for aw generated from the coefficients of the vertex operator this connection is established via a quadratic identity involving the wave function and the vertex operator which is a disguised differential version of the fay identity the latter is also the key to the spectral theory for the two compatible symplectic structures of kdv in terms of the stress energy tensor associated with the virasoro algebra given a differential operator l d p q 2 t d p 2 cdots q p t with d frac partial dx t t 1 t 2 t 3 x equiv t 1 consider the deformation equations1 0 1 begin gathered frac partial l partial t n l n p l n 1 2 n 0 mod p hfill p reduced kp equation hfill end gathered ofl for which there exists a differential operatorp possibly of infinite order such that 0 2 l p 1 string equation in this note we give a complete solution to this problem in section 1 we give a brief survey of useful facts about thei function t the wave function t z solution of t n l n p x andl 1 p z and the corresponding infinitedimensional planev 0 of formal power series inz for largez v 0 span psi t z for all t in mathbb c infty in sato s grassmannian the three theorems below form the core of the paper their proof will be given in subseuqent sections each of which lives on its own right

classical n 2 w superalgebras from superpseudodifferential operators we study the supersymmetric gelfand dickey algebras associated with the superpseudodifferential operators of positive as well as negative leading order we show that upon the usual constraint these algebras contain the n 2 super virasoro algebra as a subalgebra when the leading order is odd the decompositions of the coefficient functions into n 1 primary fields are then obtained by covariantizing the superpseudodifferential operators we discuss the problem of identifying n 2 supermultiplets and work out a couple of supermultiplets by explicit computations

poisson algebras associated with constrained dispersionless modified kadomtsev petviashvili hierarchies we investigate the bi hamiltonian structures associated with constrained dispersionless modified kadomtsev petviashvili kp hierarchies which are constructed from truncations of the lax operator of the dmkp hierarchy after transforming their second hamiltonian structures to those of the gelfand dickey type we obtain the poisson algebras of the coefficient functions of the truncated lax operators then we study the conformal property and free field realizations of these poisson algebras some examples are worked out explicitly to illustrate the obtained results

superconformal covariantization of superdifferential operator on 1 1 superspace and classical n 2 w superalgebras a study of the superconformal covariantization of superdifferential operators defined on 1 1 superspace is presented it is shown that a superdifferential operator with a particular type of constraint can be covariantized only when it is of odd order in such a case the action of superconformal transformation on the superdifferential operator is nothing but a hamiltonian flow defined by the corresponding supersymmetric second gelfand dickey bracket the covariant form of a superdifferential operator of odd order is given

supersymmetric extension of the scalar born infeld equation in this paper a supersymmetric extension of the scalar born infeld equation is constructed through a superspace formalism which involves the addition of one independent fermionic grassmann variable to the existing bosonic spacetime coordinates the bosonic scalar field is replaced by a fermionic superfield which is composed of two component fields one bosonic and one fermionic the resulting equation is invariant under a space supersymmetric transformation and in its most general form involves four arbitrary parameters for a certain specific case the lie superalgebra of symmetries was identified and the one dimensional subalgebras were systematically classified into splitting and non splitting conjugate classes a number of group invariant solutions were obtained including polynomial solutions solutions by radicals and solitary waves including bumps kinks and doubly periodic solutions

w algebras for generalized toda theories the generalized toda theories obtained in a previous paper by the conformal reduction of wznw theories possess a new class of w algebras namely the algebras of gauge invariant polynomials of the reduced theories an algorithm for the construction of base elements for the w algebras of all such generalized toda theories is found and the w algebras for the maximal sl n r generalized toda theories are constructed explicitly the primary field basis being identified 1992 springer verlag