canonical forms for time delay systems polynomial transformations are considered for linear systems with time delays a technique for state reduction is given as well as schemes for obtaining other useful canonical forms the results are achieved using a combination of module theoretic ideas polynomial ring and functional analysis

equivalence of linear time delay systems the question of characterizing those time delay systems which are equivalent up to bicausal transformations to a delay free system is a natural and fundamental problem which has been raised since the early 1980s surprisingly this problem remains largely open despite that some partial answers have been provided this technical note tackles this problem for linear systems with constant time delays and gives necessary and sufficient conditions to eliminate whenever is possible or to reduce the number of time delays and a constructive way to get the corresponding bicausal change of coordinates

convergence rates of moving mesh methods for moving boundary partial integro differential equations from regime switching jump diffusion asian option pricing abstract this paper studies the convergence rates of moving mesh methods for a system of moving boundary partial integro differential equations pides which arise in the asian option pricing under the state dependent regime switching jump diffusion models the value function of the asian option under the model is governed by a system of two dimensional pides in this paper the two dimensional pides are recast into a one dimensional moving boundary problem of the pides a moving finite difference method fdm is proposed to solve the one dimensional moving boundary problem and the convergence rates are proved numerical examples are provided to confirm the theoretical results

decoupling of multivariable control systems over unique factorization domains necessary and sufficient conditions are established for the existence of a state variable feedback decoupling of an m input m output time invariant linear control system over a unique factorization domain an explicit computation is provided for the feedback and the feedforward gain matrix also necessary and sufficient conditions for the existence of a stability preserving state feedback decoupling are given the results are illustrated by some examples

local well posedness for membranes in the light cone gauge in this paper we consider the classical initial value problem for the bosonic membrane in light cone gauge a hamiltonian reduction gives a system with one constraint the area preserving constraint the hamiltonian evolution equations corresponding to this system however fail to be hyperbolic making use of the area preserving constraint an equivalent system of evolution equations is found which is hyperbolic and has a well posed initial value problem we are thus able to solve the initial value problem for the hamiltonian evolution equations by means of this equivalent system we furthermore obtain a blowup criterion for the membrane evolution equations and show making use of the constraint that one may achieve improved regularity estimates

area preserving diffeomorphisms and supermembrane lorentz invariance the lie algebra of area preserving diffeomorphisms on closed membranes of arbitrary topology is investigated on the basis of a harmonic decomposition we define the structure constants as well as two other tensors which appear in the supermembrane lorentz generators we derive certain identities between these tensors and analyze their validity when the areapreserving diffeomorphisms are approximated bysu n one of the additional tensors can then be identified with the invariant symmetric three index tensor ofsu n while the second has no obvious analog we prove that the lorentz generators are classically conserved in the light cone gauge for arbitrary membrane topology as a consequence of these tensor identities this formulation allows a systematic study of the violations of lorentz invariance in thesu n approximation

a natural basis of states for the noncommutative sphere and its moyal bracket an infinite dimensional algebra which is a nondecomposable reducible representation of su 2 is given this algebra is defined with respect to two real parameters if one of these parameters is zero the algebra is the commutative algebra of functions on the sphere otherwise it is a noncommutative analog this is an extension of the algebra normally referred to as the berezin quantum sphere or fuzzy sphere a natural indefinite inner product and a basis of the algebra orthogonal with respect to it are given the basis elements are homogeneous polynomials eigenvectors of a laplacian and related to the hahn polynomials it is shown that these elements tend to the spherical harmonics for the sphere a moyal bracket is constructed and shown to be the standard moyal bracket for the sphere

on non commutative g2 structure using an algebraic orbifold method we present non commutative aspects of g2 structure of seven dimensional real manifolds we first develop and solve the non commutativity parameter constraint equations defining g2 manifold algebras we show that there are eight possible solutions for this extended structure one of which corresponds to the commutative case then we obtain a matrix representation solving such algebras using combinatorial arguments an application to matrix model of m theory is discussed

gl and geometric quantization an axiomatic approach to the approximation of infinite dimensional algebras is presented examples illustrating the need for a rigorous treatment of this subject geometric quantization is employed to construct systematicallysu n approximations of diffeomorphism algebras which first appeared in the theory of relativistic membranes

singular perturbation methods for a class of initial and boundary value problems in discrete systems a class of singularly perturbed initial and boundary value problems occurring in discrete systems is formulated singular perturbation methods are developed separately for initial value problems and boundary value problems the methods essentially consist of seeking an approximate solution in terms of an outer series based on the degenerate problem and a correction series to recover the auxiliary conditions sacrificed in the process of degeneration some interesting features are explored and the asymptotic correctness of the formal series expansions is clearly established illustrative examples are provided in support of the proposed methods

exact state variable reconstruction of delay systems the problem of state variable reconstruction for a class of single input single output siso linear time delay system is considered a method for the exact reconstruction of state variables from the input and observed output of the system is presented

numerical solution of 2d singularly perturbed reaction diffusion system with multiple scales abstract in this article a robust numerical method is studied to approximate singularly perturbed system of reaction diffusion problems with multiple scales the analytical properties of the exact solution have been studied the numerical method consists of the classical central difference scheme on a shishkin mesh for spatial semidiscretization processes and the implicit euler scheme on a uniform time stepping for temporal derivative the error estimate is deduced which exhibits that the numerical approximation is uniformly convergent of almost second order in spatial variable and first order in temporal variable numerical experiments are given which reveals the effectiveness of the proposed scheme

a parameter robust higher order numerical method for singularly perturbed two parameter problems with non smooth data a singularly perturbed second order ordinary differential equation having two parameters with a discontinuous source term is presented for numerical analysis theoretical bounds on the derivatives regular and singular components of the solution are derived a hybrid monotone difference scheme with the method of averaging at the discontinuous point is constructed on shishkin mesh parameter uniform error bounds for the numerical approximation are established numerical results are presented which support the theoretical results

comparison of a higher order method and the simple upwind and non monotone methods for singularly perturbed boundary value problems in this paper we will present a new scheme for discretization of singularly perturbed boundary value problems based on finite difference methods this method is a combination of simple upwind scheme and central difference method on a special non uniform mesh shishkin mesh for the space discretization numerical results show that the convergence of method is uniform with respect to singular perturbation parameter and has a higher order of convergence

numerical solution of a singularly perturbed two point boundary value problem using equidistribution analysis of convergence abstract adaptive grid methods are becoming established as valuable computational techniques for the numerical solution of differential equations with near singular solutions adaptive methods are equally effective in approximating solutions of problems with boundary layers or interior layers see for example mulholland et al siam j sci comput 19 4 1998 1261 1289 much is now being done in developing error analyes for methods that are based on adaptivity in this paper we present a rigorous error analysis for the solution of a singularly perturbed two point boundary value problem on a grid that is constructed adaptively from a knowledge of the exact solution the discrete solutions are generated by an upwind finite difference scheme and the grid is formed by equidistributing a monitor function based on arc length an error analysis shows that the discrete solutions are uniformly convergent with respect to the perturbation parameter epsilon the epsilon uniform convergence is confirmed by numerical computations

decoupling and arbitrary coefficient assignment in time delay systems this paper considers decoupling control of time delay systems we assume a new decoupling condition which is stronger than the one obtained until now and r controllability then a dynamic compensator to achieve decoupling and arbitrary coefficient assignment is presented

linear systems with commensurate time delays stability and stabilization independent of delay notions of exponential stability independent of delay and stabilizability independent of delay are developed for the class of delay differential systems of the retarded type with commensurate time delays various criteria for exponential stability independent of delay with a given order are specified in terms of matrices whose entries are functions of a single real parameter and polynomials in one variable whose coefficients are functions of a single real parameter sufficient conditions and a necessary condition based on local stabilizability are given for stabilizability independent of delay using state feedback with commensurate time delays constructive methods for determining a stabilizing feedback are also presented the last part of the paper deals with a standard type of observer and regulator with the requirement that the closed loop system be stable independent of delay

unknown input observer for linear time delay systems this paper investigates an unknown input observer design for a large class of linear systems with unknown inputs and commensurate delays a luenberger like observer is proposed by involving only the past and actual values of the system output the required conditions for the proposed observer are considerably relaxed in the sense that they coincide with the necessary and sufficient conditions for the unknown input observer design of linear systems without delays

on noncommutative orbifolds of k3 surfaces using the algebraic geometry method of berenstein and leigh for the construction of the toroidal orbifold t2 t2 t2 z2 z2 with discrete torsion and considering local k3 surfaces we present noncommutative aspects of the orbifolds of product of k3 surfaces in this way the ordinary complex deformation of k3 can be identified with the resolution of stringy singularities by noncommutative algebras using crossed products we give representations and make some comments regarding the fractionation of branes illustrating examples are presented

central extensions of sphere groups closed forms for the central extensions of the infinite dimensional lie algebras of smooth maps from two and three spheres to compact lie groups are given

cascade control of systems over integral domains necessary and sufficient conditions for the existence of cascade compensators and dynamic equivalence of linear systems over integral domains arc derived the considerations lead to constructive procedures for dynamic compensation

mirror manifolds in higher dimension we describe mirror manifolds in dimensions different from the familiar case of complex threefolds we isolate certain simplifying features present only in dimension three and supply alternative methods that do not rely on these special characteristics and hence can be generalized to other dimensions although the moduli spaces for calabi yaud folds are not special kahler manifolds whend 3 they still have a restricted geometry and we indicate the new geometrical structures which arise we formulate and apply procedures which allow for the construction of mirror maps and the calculation of order by order instanton corrections to yukawa couplings mathematically these corrections are expected to correspond to calculating chern classes of various parameter spaces hilbert schemes for rational curves on calabi yau manifolds our mirror aided calculations agree with those chern class calculations in the limited number of cases for which the latter can be carried out with current mathematical tools finally we make explicit some striking relations between instanton corrections for various yukawa couplings derived from the associativity of the operator product algebra

representations of some quantum tori lie subalgebras in this paper we define the q analog virasoro like lie subalgebras in x a b c d the embedding formulas into x are introduced irreducible highest weight representations of aq bq and cq series of the q analog virasoro like lie algebras in terms of vertex operators are constructed we also construct the polynomial representations of the aq bq cq and dq series of the q analog virasoro like lie algebras

surviving extrema for the action on the twisted su one point lattice we give a simplified construction of twist eating configurations based on a theorem due to frobenius these configurations are defined through the equation u u u u exp 2 in n withu su n 1 tod andn an antisymmetric matrix with integer entries in the twisted eguchi kawai model they yield extrema some of which survive forn comparison is made with the monte carlo data of the internal energy in the small coupling region

smith forms over r z_ 1 z_ 2 relationships between a polynomial matrix and its smith forms are explored it is shown for example that a matrix over r z 1 z 2 is equivalent to its smith form over r z 1 z 2 if and only if a certain system of linear polynomial equations has a solution

optimal error estimate using mesh equidistribution technique for singularly perturbed system of reaction diffusion boundary value problems in this article we study the problem of determining an appropriate grading of meshes for a system of coupled singularly perturbed reaction diffusion problems having diffusion parameters with different magnitudes the central difference scheme is used to discretize the problem on adaptively generated mesh where the mesh equation is derived using an equidistribution principle an a priori monitor function is obtained from the error estimate a suitable a posteriori analogue of this monitor function is also derived for the mesh construction which will lead to an optimal second order parameter uniform convergence we present the results of numerical experiments for linear and semilinear reaction diffusion systems to support the effectiveness of our preferred monitor function obtained from theoretical analysis

a robust adaptive method for a quasi linear one dimensional convection diffusion problem a quasi linear conservative convection diffusion two point boundary value problem is considered to solve it numerically an upwind finite difference scheme is applied the mesh used has a fixed number n 1 of nodes and is initially uniform but its nodes are moved adaptively using a simple algorithm of de boor based on equidistribution of the arc length of the current computed piecewise linear solution it is proved for the first time that a mesh exists that equidistributes the arc length along the polygonal solution curve and that the corresponding computed solution is first order accurate uniformly in varepsilon where varepsilon is the diffusion coefficient in the case when the boundary value problem is linear if n is sufficiently large independently of varepsilon it is shown that after o rm ln 1 varepsilon rm ln n iterations of the algorithm the piecewise linear interpolant of the computed solution achieves first order accuracy in the l infty 0 1 norm uniformly in varepsilon numerical experiments are presented that support our theoretical results

some twisted self dual solutions for the yang mills equations on a hypertorus thesu n yang mills equations are considered in a four dimensional euclidean box with periodic boundary conditions hypertorus gauge invariant twists can be introduced in these boundary conditions to be labeled with integersn n defined modulon the pontryagin number in this space is often fractional whenever this number is zero there are solutions to the equationsg 0 hereg is the covariant curl when this number is not zero we find a set of solutions to the equations g mu nu tilde g mu nu provided that the periodsa of the box satisfy certain relations

a numerical method for a system of singularly perturbed reaction diffusion equations a dirichlet problem for a system of two coupled singularly perturbed reaction diffusion ordinary differential equations is examined a numerical method whose solutions converge pointwise at all points of the domain independently of the singular perturbation parameters is constructed and analysed numerical results are presented which illustrate the theoretical results

a geometric approach to dynamic feedback cyclization over commutative rings a different geometric point of view is introduced in the study of dynamic feedback cyclization over rings this considerably simplifies the theory in the free case in the sense that the main results can now be obtained by simple proofs the non free case remains to be examined

smith mcmillan factorizations at infinity of rational matrix functions and their control interpretation in this paper the smith mcmillan factorizations at infinity of a transfer function are studied the non uniqueness of these factorizations is characterized via a multiplicative group of bicausal isomorphisms control interpretations are given in terms of system equivalence under some groups of transformations a characterization of the stabilizer of morse group at a b c is given for irreducible systems

decoupling and coefficient assignment for a b c d time delay systems using v as the time delay operator a linear invariant time delay system is expressed by a quadruple a b c v d v with the matrices over a polynomial ring in v this paper studies the decoupling and coefficient assignment of such a system for a class of time delay systems non controllable over the polynomial ring in v but controllable over the field of rational functions in v we present sufficient conditions under which the system characteristic polynomial may be determined arbitrarily by feasible control laws two examples are investigated to illustrate the theory

an almost third order finite difference scheme for singularly perturbed reaction diffusion systems this paper addresses the numerical approximation of solutions to coupled systems of singularly perturbed reaction diffusion problems in particular a hybrid finite difference scheme of hodie type is constructed on a piecewise uniform shishkin mesh it is proved that the numerical scheme satisfies a discrete maximum principle and also that it is third order except for a logarithmic factor uniformly convergent even for the case in which the diffusion parameter associated with each equation of the system has a different order of magnitude numerical examples supporting the theory are given

percolation beyond ℤd the contributions of oded schramm oded schramm 1961 2008 influenced greatly the development of percolation theory beyond the usual d setting in particular the case of nonamenable lattices here we review some of his work in this field

observer design for linear singular time delay systems this paper investigates the problem of observer design for a general class of linear singular time delay systems in which the time delays are involved in the state and its derivatives the output and the known input if there exists the involvement of the delay could be multiple which however is rarely studied in the literature sufficient conditions are proposed which guarantees the existence of a luenberger like observer for the general system

on a uniformly accurate finite difference approximation of a singulary peturbed reaction diffusion problem using grid equidistribution we examine the convergence properties of a finite difference approximation of a singularly perturbed reaction diffusion boundary value problem using a nonuniform grid the grid is based on the equidistribution of a positive monitor function that is a linear combination of a constant floor and a power of the second derivative of the solution analysis shows how the monitor function can be chosen to ensure that the accuracy of the numerical approximation is insensitive to the size of the singular perturbation parameter the use of equidistribution principles appears in many practical grid adaption schemes and our analysis provides insight into the convergence behaviour on such grids numerical results are given that confirm the uniform convergence rates

a robust computational method for singularly perturbed coupled system of reaction diffusion boundary value problems abstract in this paper we devise a robust computational method for singularly perturbed system of reaction diffusion boundary value problems bvps we use cubic spline on nonuniform mesh to obtain the difference scheme and apply it to the system of bvps on a piecewise uniform shishkin mesh on the whole domain we observed that the cubic spline scheme is not stable in the regular outer region where the mesh is coarse to overcome this difficulty we use the classical central difference scheme only for that portion and the cubic spline scheme elsewhere this newly proposed scheme is uniformly stable throughout the domain and provides second order uniform convergence results we derive the uniform error estimate for this scheme and apply it to a test problem to verify the efficiency and accuracy of the method

a booster method for singular perturbation problems arising in chemical reactor theory a numerical method for singularly perturbed two point boundary value problems bvps for second order ordinary differential equations odes arising in chemical reactor theory is proposed in this method an asymptotic approximation is incorporated into a suitable finite difference scheme to improve the numerical solution uniform error estimates are derived when implemented in known difference schemes numerical results are presented in support of this claim

area preserving diffeomorphisms of the tetrahedron expressions for the curvature and structure constants of the area preserving diffeomorphism group of the tetrahedron are derived finite dimensional algebras are identified that yield the diffeomorphism lie algebra in an infinite limit

f theory duals of m theory on g2 manifolds from mirror symmetry using mirror pairs m3 w3 in type ii superstring compactifications on calabi yau threefolds we study geometrically f theory duals of m theory on seven manifolds with g2 holonomy we first develop a way of obtaining landau ginzburg lg calabi yau threefolds w3 embedded in four complex dimensional toric varieties mirror to the sigma model on toric calabi yau threefolds m3 this method gives directly the right dimension without introducing non dynamical variables then using toric geometry tools we discuss the duality between m theory on s1 m3 z2 with g2 holonomy and f theory on elliptically fibred calabi yau fourfolds with su 4 holonomy containing w3 mirror manifolds illustrative examples are presented

coefficient assignability for linear systems with delays using canonical forms for the linear delay systems with commensurate delays an approach to coefficient assignment of the characteristic polynomial under feedback control of polynomial delay type is given the results are achieved under quite weak requirements of controllability

shooting method for the solution of singularly perturbed two point boundary value problems having less severe boundary layer singularly perturbed two point boundary value problems bvps having less severe boundary layers are considered a method is presented in this paper to solve these problems numerically the domain of definition of the differential equation is divided into two subintervals in one subinterval inner region an initial value problem ivp obtained from the given bvp is solved by an exponentially fitted difference efd scheme whereas a classical upwind scheme is used to solve the bvp in the other subinterval outer region in order to obtain initial and boundary conditions an asymptotic approximation is used error estimates are derived for the numerical solution the implementation of the method on parallel architectures is discussed numerical results are also presented in support of the proposed method

stabilization of generalized linear systems via the algebraic riccati equation abstract this paper presents results from a study to examine the stabilization properties of linear time delay systems and systems depending on a parameter using techniques associated with the algebraic riccati equation are these classes of systems can be viewed as members of a broader class of systems called generalized linear systems gls techniques of spectral factorization for the gls play an essential role in the methods for performing this stabilization necessary and sufficient conditions for the existence of a polynomial solution to the generalized are are derived numerical examples are given in order to illustrate and clarify the results

mirror symmetry and landau ginzburg calabi yau superpotentials in f theory compactifications we study the landau ginzburg lg theory mirror to two dimensional 2d n 2 gauged linear sigma models on toric calabi yau manifolds we derive and solve new constraint equations for lg elliptic calabi yau superpotentials depending on the physical data of dual linear sigma models in the calabi yau threefold case we consider two examples first we give the mirror symmetry of the canonical line bundle over the hirzebruch surfaces fn second we find a special geometry with the affine so 8 lie algebra toric data extending the geometry of elliptically fibred k3 this geometry leads to a pure n 1 six dimensional so 8 gauge model from the f theory compactification for calabi yau fourfolds we give a new algebraic realization for ade hypersurfaces

quantum screening operators and canonical q de rham cocycles in this paper a close connection is established between certain cohomology spaces of representations of the quantum affine algebra and a twisted q de rham jackson aomoto cohomology of configuration spaces using the quantum screening operators

nc calabi yau orbifolds in toric varieties with discrete torsion using the algebraic geometric approach of berenstein et al hep th 005087 and hep th 009209 and methods of toric geometry we study non commutative nc orbifolds of calabi yau hypersurfaces in toric varieties with discrete torsion we first develop a new way of getting complex d mirror calabi yau hypersurfaces h d in toric manifolds m d 1 with a c r action and analyse the general group of the discrete isometries of h d then we build a general class of d complex dimensional nc mirror calabi yau orbifolds where the non commutativity parameters are solved in terms of discrete torsion and toric geometry data of m d 1 in which the original calabi yau hypersurfaces are embedded next we work out a generalization of the nc algebra for generic d dimensional nc calabi yau manifolds and give various representations depending on different choices of the calabi yau toric geometry data we also study fractional d branes at orbifold points we refine and extend the result for nc t 2 x t 2 x t 2 z 2 x z 2 to higher dimensional torii orbifolds in terms of clifford algebra

asymptotic behavior and positive solutions of a chemical reaction diffusion system abstract this paper is concerned with some qualitative analysis for a coupled system of three reaction diffusion equations which arises from certain chemical reactions first discovered by belousov and zhabotinskii the analysis includes the existence of a bounded global time dependent solutions the stability and instability of the zero solution and the existence and nonexistence of a positive steady state solution including a global attractor of the system the global existence and stability problem is determined by the method of upper and lower solutions and the existence of a positive steady state solution is based on the fixed point index and bifurcation theory this analysis leads to a necessary and sufficient condition for the existence and nonexistence of a positive steady state solution in relation to the various physical parameters of the system

on noncommutative multi solitons solitons in noncommutative scalar field theories possess many stringy features in particular multi solitons in these theories behave like multiple d branes a useful moduli space description for multi solitons exists which reproduces stringy features of d brane moduli spaces in a simple way via properties of special projection operators in particular they are equivalent to a hilbert scheme resolution of symmetric product spaces