the complex geometry of weak piecewise smooth solutions of integrable nonlinear pde s of shallow water and dym type an extension of the algebraic geometric method for nonlinear integrable pde s is shown to lead to new piecewise smooth weak solutions of a class of n component systems of nonlinear evolution equations this class includes among others equations from the dym and shallow water equation hierarchies the main goal of the paper is to give explicit theta functional expressions for piecewise smooth weak solutions of these nonlinear pde s which are associated to nonlinear subvarieties of hyperelliptic jacobians

sdiff s2 and the orbit method the group of area preserving diffeomorphisms of the two sphere sdiff s2 is one of the simplest examples of an infinite dimensional lie group it plays a key role in incompressible hydrodynamics and it recently appeared in general relativity as a subgroup of two closely related newly defined symmetry groups we investigate its representation theory using the method of coadjoint orbits we describe the casimir functions and the cartan algebra then we evaluate the trace of a simple sdiff s2 operator using the atiyah bott fixed point formula the trace is divergent but we show that it has well defined truncations related to the structure of sdiff s2 finally we relate our results back to the recent appearances of sdiff s2 in black hole physics the group of area preserving diffeomorphisms of the two sphere sdiff s2 is one of the simplest examples of an infinite dimensional lie group it plays a key role in incompressible hydrodynamics and it recently appeared in general relativity as a subgroup of two closely related newly defined symmetry groups we investigate its representation theory using the method of coadjoint orbits we describe the casimir functions and the cartan algebra then we evaluate the trace of a simple sdiff s2 operator using the atiyah bott fixed point formula the trace is divergent but we show that it has well defined truncations related to the structure of sdiff s2 finally we relate our results back to the recent appearances of sdiff s2 in black hole physics

local and global well posedness of the fractional order epdiff equation on r d abstract of concern is the study of fractional order sobolev type metrics on the group of h diffeomorphism of r d and on its sobolev completions d q r d it is shown that the h s sobolev metric induces a strong and smooth riemannian metric on the banach manifolds d s r d for s 1 d 2 as a consequence a global well posedness result of the corresponding geodesic equations both on the banach manifold d s r d and on the smooth regular frechet lie group of all h diffeomorphisms is obtained in addition a local existence result for the geodesic equation for metrics of order 1 2 s 1 d 2 is derived

the geometry of the universal teichmuller space and the euler weil petersson equation on the identity component of the universal teichmuller space endowed with the takhtajan teo topology the geodesics of the weil petersson metric are shown to exist for all time this component is naturally a subgroup of the quasisymmetric homeomorphisms of the circle viewed this way the regularity of its elements is shown to be h3 2 epsilon for all epsilon 0 the evolutionary pde associated to the spatial representation of the geodesics of the weil petersson metric is derived using multiplication and composition below the critical sobolev index 3 2 geodesic completeness is used to introduce special classes of solutions of this pde analogous to peakons our setting is used to prove that there exists a unique geodesic between each two shapes in the plane in the context of the application of the weil petersson metric in imaging c 2015 elsevier inc all rights reserved

the matching conditions of controlled lagrangians and ida passivity based control this paper discusses the matching conditions resulting from the controlled lagrangians method and the interconnection and damping assignment passivity based control ida pbc method both methods have been presented recently in the literature as means to stabilize a desired equilibrium point of an euler lagrange respectively hamiltonian system in the context of mechanical systems with symmetry the original controlled lagrangians method is reviewed and an interpretation of the matching assumptions in terms of the matching of kinetic and potential energy is given secondly both methods are applied to the general class of underactuated mechanical systems and it is shown that the controlled lagrangians method is contained in the ida pbc method the lambda method as described in recent papers for the controlled lagrangians method transforming the matching conditions a set of non linear pdes into a set of linear pdes is discussed the method is used to transform the matching conditions obtained in the ida pbc method into a set of quadratic and linear pdes finally the extra freedom obtained in the ida pbc method with respect to the controlled lagrangians method is used to discuss the integrability of the closed loop system explicit conditions are derived under which the closed loop hamiltonian system is integrable leading to the introduction of gyroscopic terms

an interpolating by pass to pareto optimality in intuitionistic fuzzy technique for a eoq model with time sensitive backlogging abstract this article fuzzyfies eoq crisp model with backlogged while demand of the customers varies with selling price and promotional effort the demand rate in stock out situation decreases with duration of the shortage period and it comes back to its initial rate since promotional effort continues the cost function consists of set up cost inventory cost shortage cost and cost for promotional effort the coefficient vectors of the concerned minimization cost function are considered as fuzzy numbers which are transformed into interval numbers then the interval objective function has been transformed into a classical multi objective eoq model using intuitionistic fuzzy technique a comparative study on pareto optimality and optimality under lagrange s interpolating polynomial function has been made illustrating numerical example

non abelian harmonic oscillators and chiral theories we show that a large class of physical theories which has been under intensive investigation recently share the same geometric features in their hamiltonian formulation these dynamical systems range from harmonic oscillations to wzw like models and to the kdv dynamics on diff0s1 to the same class belong also the hamiltonian systems on groups of maps the common feature of these models are the chiral equations of motion for so called chiral decomposition of the phase space

optimization of fuzzy production inventory models in this paper we introduce two fuzzy production inventory models with fuzzy parameters for crisp production quantity or for fuzzy production quantity the fuzzy total production inventory costs of these models under the fuzzy arithmetical operations of function principle are proposed the final purpose is to find optimal solutions of these models by using graded mean integration representation method for defuzzifing fuzzy total production inventory cost and by using extension of the lagrangean method for solving inequality constrain problem furthermore we find that the optimal solutions are all crisp real numbers in addition when the fuzzy parameters fuzzy inventory cost fuzzy demand fuzzy setup cost fuzzy demand rate and fuzzy production rate are all crisp real numbers the optimal solutions of our proposed models can be specified to meet classical production inventory models

stabilization of a class of underactuated mechanical systems via interconnection and damping assignment we consider the application of a formulation of passivity based control pbc known as interconnection and damping assignment ida to the problem of stabilization of underactuated mechanical systems which requires the modification of both the potential and the kinetic energies our main contribution is the characterization of a class of systems for which ida pbc yields a smooth asymptotically stabilizing controller with a guaranteed domain of attraction the class is given in terms of solvability of certain partial differential equations one important feature of ida pbc stemming from its hamiltonian formulation is that it provides new degrees of freedom for the solution of these equations using this additional freedom we are able to show that the method of controlled lagrangians in its original formulation may be viewed as a special case of our approach as illustrations we design asymptotically stabilizing ida pbcs for the classical ball and beam system and a novel inertia wheel pendulum

diffeomorphisms groups and pattern matching in image analysis in a previous paper it was proposed to see the deformations of a common pattern as the action of an infinite dimensional group we show in this paper that this approac h can be applied numerically for pattern matching in image analysis of digital images using lie group ideas we construct a distance between deformations defined through a metric given the cost of infinitesimal deformations then we propose a numerical scheme to solve a variational problem involving this distance and leading to a sub optimal gradient pattern matching its links with fluid models are established

backorder fuzzy inventory model under function principle in this paper the fuzzy inventory model is discussed especially in the case of permitting backorder under the fuzzy environment of fuzzy demand fuzzy order cost fuzzy inventory cost and fuzzy backorder cost we use the function principle instead of the extension principle to calculate the total fuzzy inventory cost we also apply the median rule to find the optimal economic order quantity eoq and shortage quantity

weil petersson teichmuller space revisited abstract in our previous paper 23 it was proved that a sense preserving homeomorphism g on the unit circle s 1 belongs to the weil petersson class wp s 1 namely g can be extended to a quasiconformal mapping to the unit disk whose beltrami coefficient is square integrable in the poincare metric if and only if g is absolutely continuous such that log g belongs to the sobolev class h 1 2 in this sequel to 23 we show that the smooth hilbert manifold structure on wp s 1 inherited from h 1 2 by the pullback g log g is compatible with the standard hilbert manifold structure introduced by takhtajan teo 27 this enables us to give a fast approach to some results in our previous papers 23 and 24

characters of the bms group in three dimensions using the frobenius formula we evaluate characters associated with certain induced representations of the centrally extended bms3 group this computation involves a functional integral over a coadjoint orbit of the virasoro group a delta function localizes the integral to a single point allowing us to obtain an exact result the latter is independent of the specific form of the functional measure and holds for all values of the bms3 central charges and all values of the chosen mass and spin it can also be recovered as a flat limit of virasoro characters

weil petersson teichmuller space iii dependence of riemann mappings for weil petersson curves the classical riemann mapping theorem implies that there exists a so called riemann mapping which takes the upper half plane onto the left domain bounded by a jordan curve in the extended complex plane the primary purpose of the paper is to study the basic problem how does a riemann mapping depend on the corresponding jordan curve we are mainly concerned with those jordan curves in the weil petersson class namely the corresponding riemann mappings can be quasiconformally extended to the whole plane with beltrami coefficients being square integrable under the poincare metric after giving a geometric characterization of a weil petersson curve we endow the space of all normalized weil petersson curves with a new real hilbert manifold structure in a geometric manner and show that this new structure is topologically equivalent to the standard complex hilbert manifold structure which implies that an appropriately chosen riemann mapping depends continuously on a weil petersson curve and vice versa this can be considered as the first result about the continuous dependence of riemann mappings on non smooth jordan curves

integrable teichmuller space abstract this paper deals with the p integrable teichmuller space and gives an intrinsic characterization of a p integrable asymptotic affine homeomorphism for p 2 more precisely it is proved that a sense preserving homeomorphism h on the unit circle is p integrable asymptotic affine namely h can be extended to a quasiconformal mapping to the unit disk whose beltrami coefficient is p integrable in the poincare metric if and only if h is absolutely continuous such that log h belongs to the besov class b p s 1

algebraic quantization on a group and nonabelian constraints a generalization of a previous group manifold quantization formalism is proposed in the new version the differential structure is circumvented so that discrete transformations in the group are allowed and a nonabelian group replaces the ordinary central u 1 subgroup of the heisenberg weyl like quantum group as an example of the former we obtain the wave functions associated with the system of two identical particles and the latter modification is used to account for the virasoro constraints in string theory

virasoro model space the representations of a compact lie groupg can be studied via the construction of an associated model space this space has the property that when geometrically quantized its hilbert space contains every irreducible representation ofg just once we construct an analogous space for the group diffs1 it is naturally a complex manifold with a holomorphic free action of diffs1 preserving a family of pseudo kahler structures all of the good coadjoint orbits are obtained from our space by hamiltonian constraint reduction we briefly discuss the connection to the work of alekseev and shatashvili

control of a class of underactuated mechanical systems obviating matching conditions abstract the presently established techniques for control of underactuated mechanical systems are dependent on solving partial differential equations pdes arising out of matching conditions in this brief a novel controller design methodology for asymptotic stabilization of nonlinear systems is proposed that obviates the need of solving pdes to obtain the control laws the geometry based energy shaping methodology forms the fully constructive procedure for control of underactuated mechanical systems the control methodology is based on manipulating symmetric structure of the system such that the power flow is established between the controller and unactuated part of the system the modifications leads to identification of the two new passive outputs which are further utilized for kinetic and potential shaping and the desired controller is obtained using passivity based techniques the theory is illustrated with two benchmark examples

constructive immersion and invariance stabilization for a class of underactuated mechanical systems a constructive approach to stabilize a desired equilibrium for a class of underactuated mechanical systems which obviates the solution of partial differential equations is proposed the immersion invariance methodology is adopted with the main result formulated in the port hamiltonian framework for both model and target dynamics the procedure is applicable to mechanical systems with under actuation degree larger than one extending the results recently reported by some of the authors the approach is successfully applied to two benchmark examples and some basic connections with the interconnection and damping assignment passivity based control are revealed an additional contribution of this work is the identification of a class of mechanical systems whose mechanical structure remains invariant under partial feedback linearization

symplectic manifolds coherent states and semiclassical approximation the symplectic structure and hamiltonian dynamics for a class of grassmannian manifolds are described here using the two dimensional sphere s2 and disc d2 as illustrative cases we write their path integral representations using coherent state techniques these path integrals can be evaluated exactly by semiclassical methods thus providing examples of the localization formula along the way we also give a local coordinate description for a class of grassmannians

a single period inventory model with imperfect production and stochastic demand under chance and imprecise constraints abstract this paper develops a mathematical model for a single period multi product manufacturing system of stochastically imperfect items with continuous stochastic demand under budget and shortage constraints after calculating expected profit in general form in terms of density functions of the demand and percentage of imperfectness particular expressions for those density functions are considered here the constraints are of three types i both are stochastic ii one stochastic and other one imprecise fuzzy and iii both imprecise the stochastic constraints have been represented by chance constraints and fuzzy constraints in the form of possibility necessity constraints stochastic and fuzzy constraints are transformed to equivalent deterministic ones using here and now approach and fuzzy relations respectively the deterministic problems are solved using a non linear optimization technique generalized reduced gradient method the model is illustrated through numerical examples sensitivity analyses on profit functions due to different permitted aspiration and confidence levels are presented

field models from two cocycles on infinite dimensional lie groups and symplectic structures 2d gravity and chern simons theory in this paper the connection between field models and infinite dimensional lie groups is widely analysed on the bases of a new group quantization approach we also relate the poincare cartan form of variational calculus to the symplectic current structure of the covariant phase space formulation of higher derivative field theory the virasoro and kac moody groups are considered in the first case the action functional of the 2d induced gravity in the light cone formulation is derived the hidden sl 2 r simply appears as generated by the kernel of the lie algebra two cocycle and plays the role of a gauge type symmetry nevertheless it is shown that a proper space like formulation is out of reach of the virasoro group the corresponding symplectic structure of the nonlocal action functional is determined showing that it is related to the symplectic structure associated with the sl 2 r kac moody group this unravels the proper geometrical meaning of the hidden symmetry and differs from the analysis in related works based on the coadjoint orbit approach the relation between the kac moody groups and the chern simons gauge theory on a disc in the presence of a source is considered using the new approach

shaping the energy of mechanical systems without solving partial differential equations control of underactuated mechanical systems via energy shaping is a well established robust design technique unfortunately its application is often stymied by the need to solve partial differential equations pdes in this technical note a new fully constructive procedure to shape the energy for a class of mechanical systems that obviates the solution of pdes is proposed the control law consists of a first stage of partial feedback linearization followed by a simple proportional plus integral controller acting on two new passive outputs the class of systems for which the procedure is applicable is identified imposing some directly verifiable conditions on the systems inertia matrix and its potential energy function it is shown that these conditions are satisfied by three benchmark examples

fuzzy production inventory for fuzzy product quantity with triangular fuzzy number abstract in this paper we consider the fundamental production inventory problem such that the product quantity is a triangular fuzzy number q q 1 q 0 g 2 where q1 q0 1 q2 q0 2 suppose q denotes the crisp economic product quantity in the classical production inventory model and we assume 0 1 0 2 or 0 1 0 2 according to two relations of q and q1 q0 q2 q1 f q y of the fuzzy cost function f q and their centroid then obtain the economic product quantity q in the fuzzy sense

diff s 1 and the teichmuller spaces precisely two of the homogeneous spaces that appear as coadjoint orbits of the group of string reparametrizations widehat diff s 1 1 carry in a natural way the structure of infinite dimensional holomorphically homogeneous complex analytic kahler manifolds these aren diff s1 rot s1 andm diff s1 mob s1 note thatn is a holomorphic disc fiber space overm now m can be naturally considered as embedded in the classical universal teichmuller spacet 1 simply by noting that a diffeomorphism ofs1 is a quasisymmetric homeomorphism t 1 is itself a homomorphically homogeneous complex banach manifold we prove in the first part of the paper that the inclusion ofm int 1 iscomplex analytic

on the classification of the coadjoint orbits of the sobolev bott virasoro group the purpose of this paper is to give the classification of the bott virasoro coadjoint orbits with nonzero central charge in the functional analytic setting of smooth hilbert manifolds the central object of the paper is thus the completion of the bott virasoro group with respect to a sobolev topology giving rise to a smooth hilbert manifold and topological group called the sobolev bott virasoro group as a consequence of this approach analytic and geometric properties of the coadjoint orbits are studied c 2008 elsevier inc all rights reserved

weil petersson teichmuller space ii smoothness of flow curves of h32 vector fields abstract given a continuous vector field t of sobolev class h 3 2 on the unit circle s 1 the flow maps g t of the differential equation d d t t 0 are known to be quasisymmetric homeomorphisms very recently gay balmaz ratiu 15 conjectured that the flow curve g t is in the weil petersson class wp s 1 and is continuously differentiable with respect to the hilbert manifold structure of wp s 1 introduced by takhtajan teo 40 the first assertion had already been demonstrated in our previous paper 36 in this sequel to 36 we will continue to deal with the weil petersson class wp s 1 and completely solve this conjecture in the affirmative

coadjoint orbits of the virasoro group the coadjoint orbits of the virasoro group which have been investigated by lazutkin and pankratova and by segal should according to the kirillov kostant theory be related to the unitary representations of the virasoro group in this paper the classification of orbits is reconsidered with an explicit description of the possible centralizers of coadjoint orbits the possible orbits are diff s1 itself diff s1 s1 and diff s1 sl n 2 r withsl n 2 r a certain discrete series of embeddings ofsl 2 r in diff s1 and diffs1 t wheret may be any of certain rather special one parameter subgroups of diffs1 an attempt is made to clarify the relation between orbits and representations it appears that quantization of diffs1 s1 is related to unitary representations with nondegenerate kac determinant unitary verma modules while quantization of diffs1 sl n 2 r is seemingly related to unitary representations with null vectors in leveln a better understanding of how to quantize the relevant orbits might lead to a better geometrical understanding of virasoro representation theory in the process of investigating virasoro coadjoint orbits we observe the existence of left invariant symplectic structures on the virasoro group manifold as is described in an appendix these give rise to lie bialgebra structures with the virasoro algebra as the underlying lie algebra

infinite conformal symmetry of critical fluctuations in two dimensions we study the massless quantum field theories describing the critical points in two dimensional statistical systems these theories are invariant with respect to the infinite dimensional group of conformal analytic transformations it is shown that the local fields forming the operator algebra can be classified according to the irreducible representations of the virasoro algebra exactly solvable theories associated with degenerate representations are analized in these theories the anomalous dimensions are known exactly and the correlation functions satisfy the system of linear differential equations

a constructive procedure for energy shaping of port hamiltonian systems equilibrium stabilization of nonlinear systems via energy shaping is a well established robust passivity based controller design technique unfortunately its application is often stymied by the need to solve partial differential equations which is usually a difficult task in this paper a new fully constructive procedure to shape the energy for a class of port hamiltonian systems that obviates the solution of partial differential equations is proposed proceeding from the well known passive power shaping output we propose a nonlinear static state feedback that preserves passivity of this output but with a new storage function a suitable selection of a controller gain makes this function positive definite hence it is a suitable lyapunov function for the closed loop the resulting controller may be interpreted as a classical pi connections with other standard passivity based controllers are also identified

short distance expansion from the dual representation of infinite dimensional lie algebras we develop a method for computing the short distance expansion of fields or operators that live in the coadjoint representation of an infinite dimensional lie algebra by using only properties of the adjoint representation and its dual we explicitly implement this method by computing the short distance expansion for the duals of the virasoro algebra affine lie algebras and the geometrically realized n extended supersymmetric virasoro algebra this method can also be used to compute short distance expansions between fields that transform in the adjoint and those that transform in the coadjoint representations

total energy shaping control of mechanical systems simplifying the matching equations via coordinate changes total energy shaping is a controller design methodology that achieves asymptotic stabilization of mechanical systems endowing the closed loop system with a lagrangian or hamiltonian structure with a desired energy function that qualifies as lyapunov function for the desired equilibrium the success of the method relies on the possibility of solving two pdes which identify the kinetic and potential energy functions that can be assigned to the closed loop particularly troublesome is the partial differential equation pde associated to the kinetic energy which is nonlinear and inhomogeneous and the solution that defines the desired inertia matrix must be positive definite in this note we prove that we can eliminate or simplify the forcing term in this pde by modifying the target dynamics and introducing a change of coordinates in the original system furthermore it is shown that in the particular case of transformation to the lagrangian coordinates the possibility of simplifying the pdes is determined by the interaction between the coriolis and centrifugal forces and the actuation structure the examples of pendulum on a cart and furuta s pendulum are used to illustrate the results

continuous review inventory model in mixed fuzzy and stochastic environment in this paper we consider a continuous review inventory system where fuzziness and randomness appear simultaneously into an optimization setting since demand plays an important role in such type of inventory systems we develop a model in a mixed environment by incorporating fuzzy random variable as customer demand after fuzzifying the random lead time demand we consider the annual average demand as a fuzzy random variable we provide an elegant methodology to determine the optimal order quantity and reorder point such that the total expected annual cost in the fuzzy sense has a minimum value since the expected value of a fuzzy random variable is a fuzzy quantity a method of ranking fuzzy numbers using their possibilistic mean values is adopted to achieve the optimal solution a numerical example is presented to illustrate the proposed model

geometric investigations of a vorticity model equation abstract this article consists of a detailed geometric study of the one dimensional vorticity model equation t u x 2 u x 0 h u x t r x s 1 which is a particular case of the generalized constantin lax majda equation wunsch showed that this equation is the euler arnold equation on diff s 1 when the latter is endowed with the right invariant homogeneous h 1 2 metric in this article we prove that the exponential map of this riemannian metric is not fredholm and that the sectional curvature is locally unbounded furthermore we prove a beale kato majda type blow up criterion which we then use to demonstrate a link to our non fredholmness result finally we extend a blow up result of castro cordoba to the periodic case and to a much wider class of initial conditions using a new generalization of an inequality for hilbert transforms due to cordoba cordoba

on the lambda equations for matching control laws we discuss matching control laws for underactuated systems we previously showed that this class of matching control laws is completely characterized by a linear system of first order partial differential equations for one set of variables lambda followed by a linear system of first order partial differential equations for the second set of variables widehat g widehat v here we derive a new first order system of partial differential equations that encodes all compatibility conditions for the lambda equations we give four examples illustrating different features of matching control laws the last example is a system with two unactuated degrees of freedom that admits only basic solutions to the matching equations there are systems with many matching control laws where only basic solutions are potentially useful we introduce a rank condition indicating when this is likely to be the case

aspects of infinite dimensional l super galilean conformal algebra in this work we construct an infinite dimensional l super galilean conformal algebra which is a generalization of the l 1 algebra found in the literature we give a classification of central extensions the vector field representation the coadjoint representation and the operator product expansion of the infinite dimensional l super galilean conformal algebra keeping possible applications in physics and mathematics in mind

on flows of h 3 2 vector fields on the circle in this paper we study the regularity of flow maps of h 3 2 vector fields on the circle in terms of fractional sobolev spaces this problem is motivated by the understanding of the geometry of bers s universal teichmuller space

some notes on quasisymmetric flows of zygmund vector fields abstract in an important paper 24 reimann showed that the flow mappings of a continuous vector field of zygmund class are quasisymmetric homeomorphisms in this paper we will discuss the flow mappings when the vector field belongs to the smooth zygmund class or the sobolev class h 3 2

controlled lagrangians and the stabilization of mechanical systems i the first matching theorem we develop a method for the stabilization of mechanical systems with symmetry based on the technique of controlled lagrangians the procedure involves making structured modifications to the lagrangian for the uncontrolled system thereby constructing the controlled lagrangian the euler lagrange equations derived from the controlled lagrangian describe the closed loop system where new terms in these equations are identified with control forces since the controlled system is lagrangian by construction energy methods can be used to find control gains that yield closed loop stability we use kinetic shaping to preserve symmetry and only stabilize systems module the symmetry group the procedure is demonstrated for several underactuated balance problems including the stabilization of an inverted planar pendulum on a cart moving on a line and an inverted spherical pendulum on a cart moving in the plane

analysis on groups of diffeomorphisms of manifolds with boundary and the averaged motion of a fluid we establish the existence of three new subgroups of the group of volumepreserving diffeomorphisms of a compact n dimensional n 2 riemannian manifold which are associated with the dirichlet neumann and mixed type boundary conditions that arise in second order elliptic pdes we prove that when endowed with the hs hilbert class topologies for s n 2 1 these subgroups are c differential manifolds we consider these new diffeomorphism groups with an h1 equivalent right invariant metric and prove the existence of unique smooth geodesics t of this metric as well as existence and uniqueness of the jacobi equations associated to this metric geodesics on these subgroups are in fact the flows of a timedependent velocity vector field u t x so that t t u t t with 0 x x and remarkably the vector field u t x solves the so called lagrangian averaged euler lae equations on m these equations and their viscous counterparts the lagrangian averaged navier stokes lans equations model the motion of a fluid at scales larger than an a priori fixed parameter 0 while averaging or filtering out the small scale motion and this is achieved without the use of artificial viscosity we prove that for divergence free initial data satisfying u 0 on m the lae equations are well posed globally when n 2 we also find the boundary conditions that make the lans equations well posed globally when n 3 and prove that solutions of the lans equations converge when n 2 3 for almost all t in some fixed time interval 0 t in hs s n 2 1 3 to solutions of the lae equations thus confirming the scaling arguments of barenblatt chorin received april 26 2000 1991 mathematics subject classification 35q35 35q53 58b20 58d05

multi objective decision making model under fuzzy random environment and its application to inventory problems in this paper we concentrate on developing a fuzzy random multi objective model about inventory problems by giving some definitions and discussing some properties of fuzzy random variable we design a method of solving solution sets of fuzzy random multi objective programming problems these are applied to numerical inventory problems in which all inventory costs purchasing and selling prices in the objectives and constraints are assumed to be fuzzy random variables in nature and then the impreciseness of fuzzy random variables in the above objectives and constraints are transformed into fuzzy variables which are similar trapezoidal fuzzy numbers the exact parameters of fuzzy membership function and probability density function can be obtained through fuzzy random simulating the past dates by comparing the results with those from the fuzzy multi objective models we believe that the proposed fuzzy random multi objective model and hybrid intelligent algorithm provide significant solutions to construct other inventory models with fuzzy random variables in real life

canonical transformation and stabilization of generalized hamiltonian systems abstract this paper introduces generalized canonical transformations for generalized hamiltonian systems which convert a generalized hamiltonian system into another one and preserve the generalized hamiltonian structure of the original as in classical mechanics it is expected that canonical transformations will provide new insights and fundamental tools for both analysis and synthesis of those systems firstly the class of generalized canonical transformations and some of their properties are indicated secondly it is shown how to stabilize the generalized hamiltonian systems using canonical transformations in addition some examples illustrate how such transformations are utilized for control systems design

fuzzy periodic review system with fuzzy random variable demand in this paper a periodic review inventory system has been analyzed in a mixed imprecise and uncertain environment where fuzziness and randomness appear simultaneously a model has been developed with customer demand assumed to be a fuzzy random variable the lead time has been assumed to be a constant the lead time demand and the lead time plus one period s demand have also been assumed to be fuzzy random variables a methodology has been developed to determine the optimal inventory level and the optimal period of review such that the total expected annual cost in the fuzzy sense is minimized a numerical example has been presented to illustrate the model

pid passivity based control of port hamiltonian systems in this note we address the problem of stabilization of port hamiltonian systems via the ubiquitous proportional integral derivative pid controller the design is based on passivity theory hence the first step is to identify all passive outputs of the system which is the first contribution of the paper adding a pid around this signal ensures that the closed loop system is mathcal l 2 stable for all positive pid gains global stability and or global attractivity of a desired constant equilibrium is also guaranteed for a new class of systems for which a lyapunov function can be constructed a second contribution is to prove that this class that is identified via some easily verifiable integrability conditions is strictly larger than the ones previously reported in the literature comparisons of the proposed pid controller with control by interconnection passivity based control are also discussed

construction of local one parameter subgroups generated by the virasoro operators via feynman path integrals abstract it is well known that the virasoro algebra acts on the representations of an infinite dimensional heisenberg algebra called the fock models we calculate feynman path integrals on an coadjoint orbit of the infinite dimensional heisenberg group to give explicit formulae of actions of local one parameters subgroups generated by the virasoro operators

traffic assignment model with fuzzy level of travel demand an efficient algorithm based on quasi logit formulas abstract the place of fuzzy concepts in traffic assignment ta models has been studied in recent literature keeping fuzzy level of travel demand in mind we propose a new ta model in which the travel costs of links are depended on their congestion from the results of such fuzzy ta model network planners are able to estimate the number of travelers on network links by using zero one variables the proposed model is transformed into a crisp mixed integer problem with respect to path flow variables in order to produce the logit flows from this problem damberg et al algorithm is modified then the level of certainty is maximized and perceived travel delays are minimized for a fixed certainty degree the obtained solution which is named the fuzzy equilibrium flow satisfies a quasi logit formula similar to ordinary expression of the logit route choice model eventually we examine the quality of different path enumeration techniques in the proposed model

higher order polarizations on the virasoro group and anomalies in a previous paper the authors showed that the space of first order polarized functions on the virasoro group is not in general irreducible the full reduction was explicitly achieved by taking the orbit of the enveloping algebra through the vacuum this additional step provided the proper quantization in the strong coupling domain 0 c 1 in this paper we introduce the concept of higher order polarization as a generalization of that of polarization we prove that the imposing of the additional higher order polarization conditions is equivalent to the taking of the above mentioned orbit this demonstrates that the generalized higher order polarization conditions suffice to obtain the irreducible hilbert spaces we also discuss the need for higher order polarizations in terms of anomalies

the weil petersson curvature operator on the universal teichmuller space the universal teichmuller space is an infinitely dimensional generalization of the classical teichmuller space of riemann surfaces it carries a natural hilbert structure on which one can define a natural riemannian metric the weil petersson metric in this paper we investigate the weil petersson riemannian curvature operator tilde q of the universal teichmuller space with the hilbert structure and prove the following i tilde q is non positive definite ii tilde q is a bounded operator iii tilde q is not compact the set of the spectra of tilde q is not discrete as an application we show that neither the quaternionic hyperbolic space nor the cayley plane can be totally geodesically immersed in the universal teichmuller space endowed with the weil petersson metric

energy shaping of mechanical systems via pid control and extension to constant speed tracking in a recent contribution it was shown that a class of mechanical systems which contains many practical examples can be stabilized via energy shaping without solving partial differential equations the proposed controller consists of two terms a partial linearizing state feedback and a linear pid loop around two new passive outputs in this brief note we prove that the first admittedly non robust step can be obviated leaving only the linear pid a second contribution of the note is to propose a slight modification to the controller to go beyond regulation tasks being able to follow ramp references in the actuated coordinates

a multi objective decision making model with fuzzy rough coefficients and its application to the inventory problem in this paper we concentrate on developing a fuzzy rough multi objective decision making model according to uncertainty theory we present some equivalent models and a traditional algorithm based on an interactive fuzzy satisfying method which is similar to the interactive fuzzy rough satisfying method in order to obtain a satisfying solution for the decision maker in addition the technique of fuzzy rough simulation is applied to deal with general fuzzy rough objective functions and fuzzy rough constraints which are usually difficult to convert into their equivalents furthermore combined with the techniques of fuzzy rough simulation a genetic algorithm using the compromise approach is designed for solving a fuzzy rough multi objective programming problem finally a model is applied to an inventory problem to illustrate the usefulness of the proposed model and algorithm and then a sensitivity analysis is made