transformation groups for soliton equations iv a new hierarchy of soliton equations of kp type abstract a new approach to soliton equations based on functions or hirota s dependent variables vertex operators and the clifford algebra of free fermions is applied to study a new hierarchy of kadomtsev petviashvili type equations the bkp hierarchy the infinite dimensional orthogonal group acts on the space of bkp functions the sawada kotera equation is obtained as a reduction of bkp its infinitesimal transformations constitute the euclidean lie algebra a2 2

representations in l2 spaces on infinite dimensional symmetric cones abstract in this paper we study representations of the automorphism groups of classical infinite dimensional tube domains in particular we construct the l2 realization of all unitary highest weight representations including the vector valued case we also find a projective representation of the full identity component of the affine automorphism group of the hilbert schmidt version of the tube domain with trivial cocycle on the subgroup corresponding to the trace class version but non trivial on the large group finally we show that the operator valued measures corresponding to the vector valued highest weight representations have densities of a rather weak type with respect to wishart distributions which makes it possible to determine their supports

a grassmann calculus for infinite spin groups the correlation functions of the two dimensional ising model satisfy nonlinear equations both on the lattice discovered by mccoy and wu nucl phys b 180 89 1981 and perk phys lett a1 79 3 1980 and in a continuum limit discovered by wu mccoy tracy and barouch and generalized by sato miwa and jimbo publ rims 14 223 1978 in this paper results are presented for infinite spin groups that extend results of sato miwa and jimbo publ rims 14 223 1978 and lead to normal ordered product formulas for the difference of adjacent ising spin fields these product formulas are shown to lead directly to the lattice difference equations for the correlations and are also a key ingredient in the scaling limit analysis

the wightman axioms for the fermionic federbush model all wightman axioms including asymptotic completeness are proved for the federbush model with coupling constants in the range 1 2 1 2

on differentiable vectors for representations of infinite dimensional lie groups in this paper we develop two types of tools to deal with differentiability properties of vectors in continuous representations g gl v of an infinite dimensional lie group g on a locally convex space v the first class of results concerns the space v of smooth vectors if g is a banach lie group we define a topology on the space v of smooth vectors for which the action of g on this space is smooth if v is a banach space then v is a frechet space this applies in particular to c dynamical systems a g where g is a banach lie group for unitary representations we show that a vector v is smooth if the corresponding positive definite function g v v is smooth the second class of results concerns criteria for ck vectors in terms of operators of the derived representation for a banach lie group g acting on a banach space v in particular we provide for each k n examples of continuous unitary representations for which the space of ck 1 vectors is trivial and the space of ck vectors is dense

a bott borel weil theory for direct limits of algebraic groups we develop a bott borel weil theory for direct limits of algebraic groups some of our results apply to locally reductive ind groups g in general i e to arbitrary direct limits of connected reductive linear algebraic groups our most explicit results concern root reductive ind groups g the locally reductive ind groups whose lie algebras admit root decomposition given a parabolic subgroup p of g and a rational irreducible p module we consider the irreducible g sheaves inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i and their duals inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i these sheaves are locally free in general of infinite rank we prove a general analog of the bott borel weil theorem for inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 03i namely that inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 04i is nonzero for at most one index q q 0 and that inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 05i is isomorphic to the dual of a rational irreducible g module v for q 0 0 we show that in contrast to the finite dimensional case v need not admit an irreducible p submodule there however one has a larger parabolic subgroup w p p constructed from p and a weyl group element w of length q 0 such that v is generated by an irreducible w p submodule consequently certain g modules v can appear only for q 0 0 never for q 0 0 for inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 06i we show that there is no analog of bott s vanishing theorem more precisely that inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 07i can have arbitrarily many nonzero cohomology groups finally we give an explicit criterion for the projectivity of the ind variety g p showing that g p is in general not projective

scattering theory for the federbush massless thirring and continuum ising models the existence of the lsz limits of the positive energy quantum fields of the federbush thirring and ising models is proved the corresponding s matrices are obtained explicitly confirming previous formal results and are shown to result from a large class of dynamics the scattering theory for the federbush and thirring models on the classical and negative energy quantum levels is studied as well the wave and scattering operators are shown to exist and are obtained explicitly and they are proved to be shared by a large class of dynamics containing in particular the polynomial conserved charges

spin and wedge representations of infinite dimensional lie algebras and groups abstract we suggest a purely algebraic construction of the spin representation of an infinite dimensional orthogonal lie algebra sections 1 and 2 and a corresponding group section 4 from this we deduce a construction of all level one highest weight representations of orthogonal affine lie algebras in terms of creation and annihilation operators on an infinite dimensional grassmann algebra section 3 we also give a similar construction of the level one representations of the general linear affine lie algebra in an infinite dimensional wedge space along these lines we construct the corresponding representations of the universal central extension of the group sln k t t 1 in spaces of sections of line bundles over infinite dimensional homogeneous spaces section 5

unitary highest weight modules of inductive limit lie algebras and groups abstract representations of inductive limits of finite dimensional lie groups and algebras am our main objects of study such representations can be constructed by taking inductive limits of the representations of the finite dimensional groups or algebras for finite dimensional lie groups and algebras of hermitian symmetric type enright howe wallach classified those highest weight representations which are unitarizable in this paper we consider the limits of the algebras u p n so 2n and sp n r the limits of the corresponding maximal compact subgroup and the limits of the corresponding generalized verma modules we give necessary and sufficient conditions for the inductive limit representation to be unitarizable in all three cases we show that a necessary condition for unitarizability is that the highest weight is eventually constant we also give sufficient conditions depending on the constant which will ensure that the limit is unitarizable

constrained state formulation for the stochastic control of multireservoir systems a new formulation is presented for the analysis of multireservoir systems based on the development of first and second moment expressions for the stochastic storage state variables these expressions give explicit consideration to the maximum and minimum storage bounds in the reservoir system a feature not incorporated in some existing formulations based on traditional control theory using this analysis expected values of the storage states variances of storage release policies reliability levels and failure probabilities useful information in the context of reservoir operations and design can be obtained from a nonlinear programming solution the approach does not involve any discretization of the system variables the results for the means and standard deviations of the storage states for a multireservoir system compare favorably with those obtained from simulation

critical scaling for monodromy fields the large scale asymptotics of the correlations for a family of two dimensional lattice field theories is calculated at the critical temperature

the landau lifshitz equation elliptic curves and the ward transform the landau lifshitz ll equation is studied from a point of view that is close to that of segal and wilson s work on kdv the ll hierarchy is defined and shown to exist using a dressing transformation that involves parameters 1 2 3 that live on an elliptic curve the crucial role of the groupk 2 2 of translations by the half periods of and its non trivial central extension tilde k is brought out and an analogue of birkhoff factorisation for tilde k equivariant loops in is given this factorisation theorem is given two treatments one in terms of the geometry of an infinite dimensional grassmannian and the other in terms of the algebraic geometry of bundles over further a ward like transform between a class of holomorphic vector bundles on the total spacez of a line bundle over and solutions of ll is constructed an appendix is devoted to a careful definition of the grassmannian of the frechet spacec s 1

finitary simple lie algebras abstract an algebra is called finitary if it consists of finite rank transformations of a vector space we classify finitary simple lie algebras over a field of characteristic 0 we also describe finitary irreducible lie algebras

real time forecasting and daily operation of a multireservoir system during floods by linear quadratic gaussian control the problem of short term daily operation of a multireservoir system during floods is examined the problem is how to use all available real time information to solve the tactical problem of regulating reservoirs to minimize the expected value of flood damage during a relatively short operating horizon and to do so consistently with the long term operating strategy a state space mathematical model is presented for short term forecasting of river flows and description of the dynamics of a multireservoir system the model includes reduced order state space unit hydrographs to forecast storm runoff from effective rainfall and state space representations of linear flood routing the optimization problem is solved in the framework of discrete time linear quadratic gaussian lqg control lqg control is a computationally efficient and flexible method of solving the large dimensional optimization problems associated with the solution of the tactical problem of short term operation of reservoirs for application of the lqg control methodology the system must be represented in state space form with quadratic cost functions subject to linear equality constraints given by the state transition equations the scheme was found to be suitable for operation under moderate flood conditions when capacity constraints are not likely to become binding the methodology has been applied and tested in a real world case

stochastic control of reservoir systems using indicator functions new enhancements 1 in our previous works deterministic release policies were considered for the development of approximations of the two lower moments of the storage volume defined by the dynamic equation of the reservoir in discrete time but in continuous state space important innovation in that work was the incorporation of the lower and upper bounds of reservoir systems into the dynamic equation for the storage volume using indicator functions the current work which also does not use discretization looks at an extension of previous developments that incorporates standard operating policies and also a new randomized release policy both of which make the moments calculations exact under the assumptions that 1 the sum of current random inflow and the previous storage volume can be described by just the two lower moments and 2 only the means and variances of the inflows are known first and second moment expressions are derived for the stochastic storage state variable and include terms for the failure probabilities probabilities of spills or deficits expected values of the storage state variances of storage release policies and failure probabilities are obtained by solving the optimal reservoir operations problem using nonlinear programming the various statistics thus obtained from this optimization compare extremely well with those obtained from simulation for the single reservoir monthly operations problem studied the exact characterization of the mean and variance of the storage state variable is derived which is a difficulty in existing formulations based on linear quadratic gaussian methods for example the latter methods have been unable to estimate these moments reasonably accurately especially for long term operations whereas the traditional storage theory based on discretization brings on the curse of dimensionality the presentation herein is directed to both traditional reservoir storage theorists who are interested in the design of a reservoir where estimating the probabilities of spills and deficits is important and modern reservoir analysts who are interested in multiperiod optimal release decisions in the operations of reservoirs

the classification of locally finite split simple lie algebras one of the great early achievements in lie theory is the classification of the finite dimensional simple complex lie algebras by w killing and e cartan more than 50 years later new aspects were added to this classification by the theory of coxeter groups and the visualization of the classification in terms of dynkin diagrams furthermore serre s description of the simple lie algebras by generators and relations provided a direct way to construct the lie algebras from the cartan matrix corresponding to the choice of a root base i e a system of simple roots

measures on infinite dimensional grassmann manifolds abstract a 1 parameter family of quasi invariant measures is presented these measures are cylinder measures in graph coordinates their characteristic functions are represented as integrals relative to an infinite product measure this is applied to the problem of determining the support properties of the measures one of the measures can be used to define the unitary structure for the basic representation of the affine extension of the restricted unitary group

improved bounds for some nonstandard problems in generalized heat conduction abstract we consider the maxwell cattaneo system of equations for generalized heat conduction where the temperature and heat flux satisfy a nonstandard auxiliary condition which prescribes a combination of their values initially and at a later time we obtain l 2 bounds for the temperature and heat flux by means of lagrange identities these bounds extend the range of validity for the parameter in the nonstandard condition under a constraint on the coefficients in the differential equations

ising field theory quadratic difference equations for the n point green s functions on the lattice for the two dimensional ising model at arbitrary temperature a system of quadratic difference equations is presented involving the correlations of n order variables and that of n ensuremath 2 order and two disorder variables with suitable boundary conditions these equations specify the correlations

on quasifree representations of infinite dimensional symplectic group abstract we consider an infinite dimensional generalization of metaplectic representations weil representations for the double covering of symplectic group given quasifree states of an infinite dimensional ccr algebra projective unitary representations of the infinite dimensional symplectic group are constructed via unitary implementors of bogoliubov automorphisms complete classification of these representations up to quasi equivalence is obtained

infinite dimensional groups and riemann surface field theories we show how to obtain positive energy representations of the groupg of smooth maps from a union of circles tou n from geometric data associated with a riemann surface having these circles as boundary using covering spaces we can reduce to the case wheren 1 then our main result shows that mackey induction may be applied and yields representations of the connected component of the identity ofg which have the form of a fock representation of an infinite dimensional heisenberg group tensored with a finite dimensional representation of a subgroup isomorphic to the first cohomology group of the surface obtained by capping the boundary circles with discs we give geometric sufficient conditions for the correlation functions to be positive definite and derive explicit formulae for them and for the vacuum or cyclic vector this gives a geometric construction of correlation functions which had been obtained earlier using tau functions by choosing particular functions ing with non zero winding numbers on the boundary we obtain analogues of vertex operators described by segal in the genus zero case these special elements ofg which have a simple interpretation in terms of function theory on theriemann surface approximate fermion or clifford algebra operators they enable a rigorous derivation of a form of boson fermion correspondence in the sense that we construct generators of a clifford algebra from the unitaries representing these elements ofg

hilbert schmidt groups as infinite dimensional lie groups and their riemannian geometry abstract we describe the exponential map from an infinite dimensional lie algebra to an infinite dimensional group of operators on a hilbert space notions of differential geometry are introduced for these groups in particular the ricci curvature which is understood as the limit of the ricci curvature of finite dimensional groups is calculated we show that for some of these groups the ricci curvature is

riemann surfaces clifford algebras and infinite dimensional groups we introduce a class of riemann surfaces which possess a fixed point free involution and line bundles over these surfaces with which we can associate an infinite dimensional clifford algebra acting by automorphisms of this algebra is a gauge group of meromorphic functions on the riemann surface there is a natural fock representation of the clifford algebra and an associated projective representation of this group of meromorphic functions in close analogy with the construction of the basic representation of kac moody algebras via a fock representation of the fermion algebra in the genus one case we find a form of vertex operator construction which allows us to prove a version of the boson fermion correspondence these results are motivated by the analysis of soliton solutions of the landau lifshitz equation and are rather distinct from recent developments in quantum field theory on riemann surfaces

extended linear quadratic gaussian control further extensions the extended linear quadratic gaussian elqg control method georgakakos and marks 1987 is a stochastic control algorithm for the optimal operation of multiobjective reservoirs mathematically this method optimizes a general functional of a stochastic system in state space form with upper and lower release constraints and probabilistic storage bounds elqg is a sequential algorithm which accounts for stochastic effects by preserving the first two statistical moments of the system s inputs and storages in this paper the method is first extended to handle nongaussian features which frequently characterize reservoir inputs second elqg s efficiency with respect to reliability storage constraints is discussed and a new barrier function method is researched these modifications are tested in case studies with the savannah river system

iwasawa decompositions of some infinite dimensional lie groups we set up an abstract framework that allows the investigation of iwasawa decompositions for involutive infinite dimensional lie groups modeled on banach spaces this provides a method to construct iwasawa decompositions for classical real or complex banach lie groups associated with the schatten ideals o p h on a complex separable hilbert space h if 1 p

qualitative aspects in dual phase lag thermoelasticity we consider the system of dual phase lag thermoelasticity proposed by chandrasekharaiah and tzou first we prove that the solutions of the problem are generated by a semigroup of quasi contractions thus the problem of the third order in time is well posed then the exponential stability is investigated finally the spatial behavior of solutions is analyzed in a semi infinite cylinder and a result on the domain of influence is obtained

minimizing variance of reservoir systems operations benefits using soft computing tools soft computing based tools including fuzzy inference systems fis artificial neural networks ann and genetic algorithms ga are used here to tackle the minimization of variance of benefits from reservoir operation variance reduction is a very hard optimization problem and solvable only using implicit methods like simulation especially if the problem is nonlinear first a recently developed stochastic optimization method develops the optimal release policy which is simply the recommended release in each season of the system whose objective function maximizes the expected benefits the policy is then simulated for a long inflow series to provide the trajectories of optimal releases and storages of the reservoir these trajectories are then used as input output data to train an adaptive neuro fuzzy inference system anfis to obtain updated fuzzy operating rules the anfis based fuzzy rules are simulated and compared with policies developed using a multiple regression analysis a commonly used method in water resources optimization as the anfis performed better further a parameterized t norm operator is applied and its parameters numbering only two are optimized through ga but with the objective of variance reduction in the benefits achieved results compare the better performance of the anfis based policies with other methods such as stochastic dynamic programming and the original stochastic method to demonstrate the usefulness of ga optimized parameters of a t norm fuzzy operator for variance reduction

temperature states on loop groups theta functions and the luttinger model abstract we consider projective representations of the loop group of u n suggested by statistical mechanics these representations are defined by certain positive definite functions called temperature states on the universal central extension of the loop group we find that the boson fermion correspondence known to exist in a mathematically precise form at zero temperature persists at non zero temperature by expressing the temperature state for u 1 in two different ways we obtain identities between elliptic functions we apply these ideas to a simple model in statistical physics the luttinger model establishing the existence of a projective representation of the loop group of u 1 u 1 in the presence of interaction and at all temperatures a rigorous derivation of the correlation functions for this model is given using the boson fermion correspondence

on two classes of nonstandard parabolic problems abstract in this paper the authors continue an investigation of nonstandard parabolic problems this investigation was motivated by one of the suggested methods for stabilizing ill posed problems for evolution equations two different methods are employed methods which in a sense complement one another

unitary highest weight representations in hilbert spaces of holomorphic functions on infinite dimensional domains abstract automorphism groups of symmetric domains in hilbert spaces form a natural class of infinite dimensional lie algebras and corresponding banach lie groups we give a classification of the algebraic category of unitary highest weight modules for such lie algebras and show that infinite dimensional versions of the lie algebras s o 2 n have no unitary highest weight representations and thus do not meet the physical requirement of having positive energy highest weight modules correspond to unitary representations of global banach lie groups realized in hilbert spaces of vector valued holomorphic functions on the relevant domains in hilbert spaces the construction of such holomorphic representations of certain banach lie groups followed by the application of the general framework of harish chandra type groups in an appropriate banach setting leads to the integration of the lie algebra representation to a group representation the extension of this theory to infinite dimensional settings is explored