orthomodularity and quadratic transformations in probabilistic theories of physics a characterization of orthomodularity of a set of effects is given in terms of a triangle closedness of this set this leads to a simple probabilistic characterization of observables with a boolean range quadratic transformations on expectation functionals of observables are studied in order to investigate the derivability of the heisenberg inequality and the form of the lower bound of such an inequality for a pair of observables

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

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

geometric computation of curvature driven plane curve evolutions we present a new numerical scheme for planar curve evolution with a normal velocity equal to f kappa where kappa is the curvature and f is a nondecreasing function such that f 0 0 and either x mapsto f x 3 is lipschitz with lipschitz constant less than or equal to 1 or f x x gamma for gamma geq 1 3 the scheme is completely geometrical and avoids some drawbacks of finite difference schemes in particular no special parameterization is needed and the scheme is monotone that is if a curve initially surrounds another one then this remains true during their evolution which guarantees numerical stability we prove consistency and convergence of this scheme in a weak sense finally we display some numerical experiments on synthetic and real data

the hamiltonian structures of the super kp hierarchy associated with an even parity super lax operator the even parity super lax operator is considered for the supersymmetric kp hierarchy of the form l d2 i 0 ui 2d i 1 and two hamiltonian structures are obtained following the standard method of gel fand and dikii it is observed that the first hamiltonian structure is local and linear whereas the second hamiltonian structure is nonlocal and nonlinear among the superfields appearing in the lax operator their connections with the super w algebra are discussed briefly

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

the hamiltonian structures associated with a generalized lax operator it is shown that with every lax operator which is a pseudodifferential operator of nonzero leading order is associated a kp hierarchy for each such operator we construct the second gelfand dikii bracket associated with the lax equation and show that it defines a hamiltonian structure when the leading order is positive the corresponding compatible first hamiltonian structure which turns out in general to be different from the naive first gelfand dikii bracket is derived the corresponding hamiltonian structures for the constrained lax operator where the next to leading order term vanishes or has a constant coefficient is discussed

lower and upper probabilities in the distributive lattice of subsystems the set of subsystems of a finite quantum system with variables in together with logical connectives is a distributive lattice with regard to this lattice the where is the projector to obeys a supermodularity inequality and it is interpreted as a lower probability in the sense of the dempster shafer theory and not as a kolmogorov probability it is shown that the basic concepts of the dempster shafer theory lower and upper probabilities and the dempster multivaluedness are pertinent to the quantum formalism of finite systems

partial order of quantum effects the set of effects is not a lattice with respect to its natural order projection operators do have the greatest lower bounds and the least upper bounds in that set but there are also other incomparable effects which share this property however the coexistence the commutativity and the regularity of a pair of effects are not sufficient for the existence of their infima and suprema the structure of the range of an observable as a normalized pov measure can vary from that of a commutative boolean to a noncommutative non boolean subset of effects

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

on affine plane curve evolution abstract an affine invariant curve evolution process is presented in this work the evolution studied is the affine analogue of the euclidean curve shortening flow evolution equations for both affine and euclidean invariants are developed an affine version of the classical euclidean isoperimetric inequality is proved this inequality is used to show that in the case of affine evolution of convex plane curves the affine isoperimetric ratio is a non decreasing function of time convergence of this affine isoperimetric ratio to the ellipse s value 8 2 as well as convergence in the hausdorff metric of the evolving curve to an ellipse is also proved

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

area based medial axis of planar curves a new definition of affine invariant medial axis of planar closed curves is introduced a point belongs to the affine medial axis if and only if it is equidistant from at least two points of the curve with the distance being a minimum and given by the areas between the curve and its corresponding chords the medial axis is robust eliminating the need for curve denoising in a dynamical interpretation of this affine medial axis the medial axis points are the affine shock positions of the affine erosion of the curve we propose a simple method to compute the medial axis and give examples we also demonstrate how to use this method to detect affine skew symmetry in real images

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

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

adjunctions in pyramids curve evolution and scale spaces we have been witnessing lately a convergence among mathematical morphology and other nonlinear fields such as curve evolution pde based geometrical image processing and scale spaces an obvious benefit of such a convergence is a cross fertilization of concepts and techniques among these fields the concept of adjunction however so fundamental in mathematical morphology is not yet shared by other disciplines the aim of this paper is to show that other areas in image processing can possibly benefit from the use of adjunctions in particular a strong relationship between pyramids and adjunctions is presented we show how this relationship may help in analyzing existing pyramids and construct new pyramids moreover it will be explained that adjunctions based on a curve evolution scheme can provide idempotent shape filters this idea is illustrated in this paper by means of a simple affine invariant polygonal flow finally the use of adjunctions in scale space theory is also addressed

poisson and hamiltonian superpairs over polarized associative algebras a poisson superpair is a pair of poisson superalgebra structures on a supercommutative associative algebra whose any linear combination is also a poisson superalgebra structure in this paper we first construct certain linear and quadratic poisson superpairs over a semi finitely filtered polarized 2 graded associative algebra then we give a construction of certain hamiltonian superpairs in the formal variational calculus over any finite dimensional 2 graded associative algebra with a supersymmetric nondegenerate associative bilinear form our constructions are based on the adler mapping in a general sense our results in this paper can be viewed as noncommutative generalizations of the adler gel fand dikii hamiltonian pair

the limit shape of convex hull peeling we prove that the convex peeling of a random point set in dimension d approximates motion by the 1 d 1 power of gaussian curvature we use viscosity solution theory to interpret the limiting partial differential equation pde we use the martingale method to solve the cell problem associated to convex peeling our proof follows the program of armstrong and cardaliaguet for homogenization of geometric motions but with completely different ingredients

affine plane curve evolution a fully consistent scheme we present an accurate numerical scheme for the affine plane curve evolution and its morphological extension to grey level images this scheme is based on the iteration of a nonlocal fully affine invariant and numerically stable operator which can be exactly computed on polygons the properties of this operator ensure that a few iterations are sufficient to achieve a very good accuracy unlike classical finite difference schemes that generally require a lot of iterations convergence results are provided as well as theoretical examples and experiments

constraining active contour evolution via lie groups of transformation we present a novel approach to constraining the evolution of active contours used in image analysis the proposed approach constrains the final curve obtained at convergence of curve evolution to be related to the initial curve from which evolution begins through an element of a desired lie group of plane transformations constraining curve evolution in such a way is important in numerous tracking applications where the contour being tracked in a certain frame is known to be related to the contour in the previous frame through a geometric transformation such as translation rotation or affine transformation for example it is also of importance in segmentation applications where the region to be segmented is known up to a geometric transformation our approach is based on suitably modifying the euler lagrange descent equations by using the correspondence between lie groups of plane actions and their lie algebras of infinitesimal generators and thereby ensures that curve evolution takes place on an orbit of the chosen transformation group while remaining a descent equation of the original functional the main advantage of our approach is that it does not necessitate any knowledge of nor any modification to the original curve functional and is extremely straightforward to implement our approach therefore stands in sharp contrast to other approaches where the curve functional is modified by the addition of geometric penalty terms we illustrate our algorithm on numerous real and synthetic examples

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

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

quantum probabilities as dempster shafer probabilities in the lattice of subspaces the orthocomplemented modular lattice of subspaces l h d of a quantum system with d dimensional hilbert space h d is considered a generalized additivity relation which holds for kolmogorov probabilities is violated by quantum probabilities in the full lattice l h d it is only valid within the boolean subalgebras of l h d this suggests the use of more general than kolmogorov probability theories and here the dempster shafer probability theory is adopted an operator d h1 h2 which quantifies deviations from kolmogorov probability theory is introduced and it is shown to be intimately related to the commutator of the projectors p h1 p h2 to the subspaces h1 h2 as an application it is shown that the proof of the inequalities of clauser horne shimony and holt for a system of two spin 1 2 particles is valid for kolmogorov probabilities but it is not valid for dempster shafer probabilities the violation of these inequalities in experiments supports the interpretation of quantum proba

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

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

d 2 n 2 superconformally covariant operators and super w algebras we construct and classify superconformally covariant differential operators defined on n 2 super riemann surfaces by contrast to the n 1 theory these operators give rise to partial rather than ordinary differential equations which leads to novel features for their matrix representation the latter is applied to the derivation of n 2 super w algebras in terms of n 2 superfields

the heat equation shrinks embedded plane curves to round points soit c 0 s 1 r 2 une courbe lisse plongee dans le plan alors c s 1 0 t r 2 existe en satisfaisant c t k n ou k est la courbure de c et n est son vecteur unite normal entrant c t est lisse pour tout t il converge vers un point quand t t et sa forme limite quand t t est un cercle rond avec convergence dans norme c

a simple proof of convergence for an approximation scheme for computing motions by mean curvature we prove the convergence of an approximation scheme recently proposed by bence merriman and osher for computing motions of hypersurfaces by mean curvature our proof is based on viscosity solutions methods

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

curvature and the evolution of fronts the evolution of a front propagating along its normal vector field with speedf dependent on curvaturek is considered the change in total variation of the propagating front is shown to depend only ondf dk only wherek changes sign analysis of the casef k 1 ek where e is a constant shows that curvature plays a role similar to that of viscosity in burgers equation for e 0 and non convex initial data the curvature blows up corners develop and an entropy condition can be formulated to provide an explicit construction for a weak solution beyond the singularity we then numerically show that the solution as e goes to zero converges to the constructed weak solution numerical methods based on finite difference schemes for marker particles along the front are shown to be unstable in regions where the curvature builds as a remedy we show that front tracking based on volume of fluid techniques can be used together with the entropy condition to provide transition from the classical to weak solution

the heat equation shrinking convex plane curves soient m et m des varietes de riemann et f m m une application reguliere si m est une courbe convexe plongee dans le plan r 2 l equation de la chaleur contracte m a un point

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

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

evolution of plane curves driven by a nonlinear function of curvature and anisotropy in this paper we study evolution of plane curves satisfying a geometric equation v beta k nu where v is the normal velocity and k and nu are the curvature and tangential angle of a plane curve gamma we follow the direct approach and we analyze the so called intrinsic heat equation governing the motion of plane curves obeying such a geometric equation the intrinsic heat equation is modified to include an appropriate nontrivial tangential velocity functional alpha we show how the presence of a nontrivial tangential velocity can prevent numerical solutions from forming various instabilities from an analytical point of view we present some new results on short time existence of a regular family of evolving curves in the degenerate case when beta k nu gamma nu k m 0 m le 2 and the governing system of equations includes a nontrivial tangential velocity functional

on a characterization of classical and nonclassical probabilities in this paper a comparison of various approaches to the problem of characterization of probabilities is presented the notion of multidimensional probability or s probability is introduced and it is shown that this notion can be profitably used for characterization of probability systems the main results are given in theorems 3 and 4 in theorem 3 the conditions are considered under which a system of s probabilities admits a model on a generalized event space while in theorem 4 the conditions under which the system admits a classical model are considered an interpretation for s probabilities is discussed and it is shown that theorems 3 and 4 allow one to derive the logical structure of events from the observed probabilities

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

a one parameter family of hamiltonian structures for the kp hierarchy and a continuous deformation of the nonlinear wkp algebra the kp hierarchy is hamiltonian relative to a one parameter family of poisson structures obtained from a generalized adler map in the space of formal pseudodifferential symbols with noninteger powers the resulting w algebra is a one parameter deformation of wkp admitting a central extension for generic values of the parameter reducing naturally to w n for special values of the parameter and contracting to the centrally extended w1 w and further truncations in the classical limit all algebras in the one parameter family are equivalent and isomorphic towkp the reduction induced by setting the spin one field to zero yields a one parameter deformation of hat w infty which contracts to a new nonlinear algebra of the w type

heisenberg inequality and the complex field in quantum mechanics observables a and b satisfy the heisenberg inequality if the product of their variances has a positive lower bound independent of the state of the system in the hilbert space formulation of quantum mechanics it is a consequence of the schwarz inequality that the heisenberg type inequality var a var b 1 4 a b b a 2 holds for any pair of observables a and b represented as self adjoint operators and for any vector state represented as a unit vector if inf a b b a dom a dom b 0 then a and b satisfy the heisenberg inequality in the present paper the derivability of the heisenberg type inequality is analyzed within the general theoretical frame of a sum logic it is shown that any real valued non negative function a f a of observables a and of states which has a symmetry property f a b f a b 2f a 2f b with respect to observables satisfies the heisenberg type inequality f a f b 1 4 f a b f a f b 2 for all observables a and

on the bi hamiltonian structures of the skdv the first and the second hamiltonian structures of the supersymmetric kdv equation are derived following the conventional approach of gel fand and dickey in particular it is shown that the nonlocal nature of the first bracket is a direct consequence of the constrained nature of the lax operator

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

an a contrario decision method for shape element recognition shape recognition is the field of computer vision which addresses the problem of finding out whether a query shape lies or not in a shape database up to a certain invariance most shape recognition methods simply sort shapes from the database along some dis similarity measure to the query shape their main weakness is the decision stage which should aim at giving a clear cut answer to the question do these two shapes look alike in this article the proposed solution consists in bounding the number of false correspondences of the query shape among the database shapes ensuring that the obtained matches are not likely to occur by chance as an application one can decide with a parameterless method whether any two digital images share some shapes or not

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