nontrivial solutions for impulsive fractional differential equations via morse theory abstract in this paper we study the existence of nontrivial solutions for an impulsive fractional differential equation with dirichlet boundary conditions by using morse theory coupled with local linking arguments we obtain some new criteria to guarantee that the impulsive fractional differential equations have at least one nontrivial solution

multiplicity of solutions for integral boundary value problems of fractional differential equations with upper and lower solutions abstract in this paper we study the existence of multiple solutions for the integral boundary value problems of fractional differential equations by the method of upper and lower solutions and leray schauder degree theory the sufficient conditions about the existence of at least three solutions are obtained moreover it is proved that the integral boundary value problem has at least three positive solutions under the conditions of m 0 and f is nonnegative by given two upper and lower solutions which can be easily obtained through our methods we can present the existence theorem of at least three solutions two examples are also included to illustrate the effectiveness of the proposed results

an algorithm for moment matching scenario generation with application to financial portfolio optimisation abstract we present an algorithm for moment matching scenario generation this method produces scenarios and corresponding probability weights that match exactly the given mean the covariance matrix the average of the marginal skewness and the average of the marginal kurtosis of each individual component of a random vector optimisation is not employed in the scenario generation process and thus the method is computationally more advantageous than previous approaches the algorithm is used for generating scenarios in a mean cvar portfolio optimisation model for the chosen optimisation example it is shown that desirable properties for a scenario generator are satisfied including in sample and out of sample stability it is also shown that optimal solutions vary only marginally with increasing number of scenarios in this example thus good solutions can apparently be obtained with a relatively small number of scenarios the proposed method can be used either on its own as a computationally inexpensive scenario generator or as a starting point for non convex optimisation based scenario generators which aim to match all the third and the fourth order marginal moments rather than average marginal moments

reflection positivity and monotonicity we prove general reflection positivity results on riemannian manifolds for both scalar fields and dirac fields and comment on applications to quantum field theory as another application we prove the inequality cd cn between dirichlet and neumann covariance operators on a manifold with a reflection

different approaches for state filtering in nonlinear systems with uncertain observations this paper addresses the least squares filtering problem for nonlinear systems with uncertain observations when random interruptions in the observation process are modelled by a sequence of independent bernoulli random variables we propose four filtering algorithms which are based on different approximations of the first and second order statistics of a nonlinear transformation of random vectors perturbed by additive and multiplicative noises these algorithms generalize the extended and unscented kalman filters to the case in which there is a positive probability that the observation in each time consists of noise alone and hence does not contain the signal to be estimated the accuracy of the different approximations is also analyzed and the performance of the proposed algorithms is compared in a numerical simulation example

gaussian filters for nonlinear filtering problems we develop and analyze real time and accurate filters for nonlinear filtering problems based on the gaussian distributions we present the systematic formulation of gaussian filters and develop efficient and accurate numerical integration of the optimal filter we also discuss the mixed gaussian filters in which the conditional probability density is approximated by the sum of gaussian distributions a new update rule of weights for gaussian sum filters is proposed our numerical tests demonstrate that new filters significantly improve the extended kalman filter with no additional cost and the new gaussian sum filter has a nearly optimal performance

a new algorithm for latent state estimation in non linear time series models we consider the problem of optimal state estimation for a wide class of non linear time series models a modified sigma point filter is proposed which uses a new procedure for generating sigma points unlike the existing sigma point generation methodologies in engineering where negative probability weights may occur we develop an algorithm capable of generating sample points that always form a valid probability distribution while still allowing the user to sample using a random number generator the effectiveness of the new filtering procedure is assessed through simulation examples

construction of a unique self adjoint generator for a symmetric local semigroup abstract a definition is given of a symmetric local semigroup of unbounded operators p t 0 t t for some t 0 on a hilbert space h such that p t is eventually densely defined as t 0 it is shown that there exists a unique unbounded below self adjoint operator h on h such that p t is a restriction of e th as an application it is proven that h0 v is essentially self adjoint where e th0 is an lp contractive semigroup and v is multiplication by a real measurable function such that v l2 e and e v l1 for some e 0

random fields on riemannian manifolds a constructive approach we extend to euclidean fields on a wide class of riemannian manifolds two results which have proven to be crucial in the construction of interacting quantum fields in the flat case namely local regularity properties of the free covariance in two dimensions and osterwalder schrader positivity

equivariant maps and purely atomic spectrum abstract let g be a connected semisimple lie group with no compact factors and finite center and g an irreducible lattice if x1 1 and x2 2 are g spaces with finite invariant measures and the action of g has purely atomic spectrum and is essentially free or essentially transitive we prove that every measure preserving map x1 x2 is also a g map

linear estimation for discrete time systems in the presence of time correlated disturbances and uncertain observations this note considers optimum linear recursive estimation for linear discrete time systems with uncertain observations in cases where state and measurement noises are correlated the different kinds of estimation problems treated include one stage prediction and filtering

existence of solutions for a fractional boundary value problem via the mountain pass method and an iterative technique in this paper we consider the existence of solution to the following fractional boundary value problem ddx p 0d x b u x q xd 1 b u x f x u x 0 email protected 0 1 u 0 u 1 0 where the constants email protected 0 1 0d x b and xd 1 b denote left and right riemann liouville fractional integrals of order b respectively 0r is continuous due to the general assumption on the constants p and q the problem does not have a variational structure despite that here we study it performing variational methods combining with an iterative technique and give an existence criteria of solution for the problem under suitable assumptions the results extend the results in f jiao y zhou existence of solutions for a class of fractional boundary value problems via critical point theory comput math appl 62 2011 1181 1199

numerical and analytical solutions of new generalized fractional diffusion equation our current paper is devoted to studying the numerical and analytical solutions for a class of generalized fractional diffusion equations gfdes with new generalized time fractional derivative gtfd the gtfd we propose here is defined in the caputo sense we consider the gfdes on a bounded domain the numerical solutions are obtained by using the finite difference method fdm of full discretization the stability of fdm is discussed and the order of convergence is evaluated numerically numerical experiments are given which illustrate that the fdm is simple and effective for solving the gfdes with different coefficients and source functions an interesting phenomenon is that we can observe the period like solution in gfdes with a particular positive periodic weight function using the method of separation of variables we convert the homogeneous gfde into two ordinary differential equations and solve them via the help of solutions of the initial value problem with caputo derivative in the analytical solution we observe that the weight function in the denominator and scale function mapping the response domain differently since the derivative considered in this article is new many existing results of fdes are generalized

polynomial extended kalman filter this work presents a polynomial version of the well known extended kalman filter ekf for the state estimation of nonlinear discrete time stochastic systems the proposed filter denoted polynomial ekf pekf consists in the application of the optimal polynomial filter of a chosen degree spl mu to the carleman approximation of a nonlinear system when spl mu 1 the pekf algorithm coincides with the standard ekf for the filter implementation the moments of the state and output noises up to order 2 spl mu are required numerical simulations compare the performances of the pekf with those of some other existing filters showing significant improvements

doubly resonant semilinear elliptic problems via nonsmooth critical point theory abstract we consider the existence of weak solutions for classical doubly resonant semilinear elliptic problems we show how the main technical assumptions can be used to define appropriate metrics on the underlying function space so that extensions of the results already known in the literature can be obtained using only basic facts from critical point theory for continuous functionals on complete metric spaces

higher order sigma point filter a new heuristic for nonlinear time series filtering in this paper we present some new results related to the higher order sigma point filter hospof introduced in 1 for filtering nonlinear multivariate time series this paper makes two distinct contributions firstly we propose a new algorithm to generate a discrete statistical distribution to match exactly a specified mean vector a specified covariance matrix the average of specified marginal skewness and the average of specified marginal kurtosis both the sigma points and the probability weights are given in closed form and no numerical optimization is required combined with hospof this random sigma point generation algorithm provides a new method for generating proposal density which propagates the information about higher order moments a numerical example on nonlinear multivariate time series involving real financial market data demonstrates the utility of this new algorithm secondly we show that hospof achieves a higher order estimation accuracy as compared to ukf for smooth scalar nonlinearities we believe that this new filter provides a new and powerful alternative heuristic to existing filtering algorithms and is useful especially in econometrics and in engineering applications

a general variational principle and some of its applications abstract in this paper given a reflexive real banach space x and two sequentially weakly lower semicontinuous functionals on x with strongly continuous and coercive we are mainly interested in the existence of infinitely many local minima of the functional for each sufficiently large r

a tutorial on particle filters for online nonlinear non gaussian bayesian tracking increasingly for many application areas it is becoming important to include elements of nonlinearity and non gaussianity in order to model accurately the underlying dynamics of a physical system moreover it is typically crucial to process data on line as it arrives both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics in this paper we review both optimal and suboptimal bayesian algorithms for nonlinear non gaussian tracking problems with a focus on particle filters particle filters are sequential monte carlo methods based on point mass or particle representations of probability densities which can be applied to any state space model and which generalize the traditional kalman filtering methods several variants of the particle filter such as sir asir and rpf are introduced within a generic framework of the sequential importance sampling sis algorithm these are discussed and compared with the standard ekf through an illustrative example

random orthogonal matrix simulation this paper introduces a method for simulating multivariate samples that have exact means covariances skewness and kurtosis we introduce a new class of rectangular orthogonal matrix which is fundamental to the methodology and we call these matrices l matrices they may be deterministic parametric or data specific in nature the target moments determine the l matrix then infinitely many random samples with the same exact moments may be generated by multiplying the l matrix by arbitrary random orthogonal matrices this methodology is thus termed rom simulation considering certain elementary types of random orthogonal matrices we demonstrate that they generate samples with different characteristics rom simulation has applications to many problems that are resolved using standard monte carlo methods but no parametric assumptions are required unless parametric l matrices are used so there is no sampling error caused by the discrete approximation of a continuous distribution which is a major source of error in standard monte carlo simulations for illustration we apply rom simulation to determine the value at risk of a stock portfolio

quantum field theory on curved backgrounds i the euclidean functional integral we give a mathematical construction of euclidean quantum field theory on certain curved backgrounds we focus on generalizing osterwalder schrader quantization as these methods have proved useful to establish estimates for interacting fields on flat space times in this picture a static killing vector generates translations in euclidean time and the role of physical positivity is played by positivity under reflection of euclidean time we discuss the quantization of flows which correspond to classical space time symmetries and give a general set of conditions which imply that broad classes of operators in the classical picture give rise to well defined operators on the quantum field hilbert space in particular killing fields on spatial sections give rise to unitary groups on the quantum field hilbert space and corresponding densely defined self adjoint generators we construct the schrodinger representation using a method which involves localizing certain integrals over the full manifold to integrals over a codimension one submanifold this method is called sharp time localization and implies reflection positivity

multiple solutions for a coupled system of nonlinear fractional differential equations via variational methods in this paper a coupled system of nonlinear fractional differential equations is considered the existence of at least three distinct weak solutions is obtained by means of the variational methods and the critical point theory due to bonanno and marano in addition an example is presented to illustrate the feasibility and effectiveness of the main results

reflection positivity and conformal symmetry abstract a reflection positive hilbert space is a triple e e where e is a hilbert space a unitary involution and e a closed subspace on which the hermitian form v w v w is positive semidefinite for a triple g s where g is a lie group an involutive automorphism of g and s a subsemigroup invariant under the involution s s s 1 a unitary representation of g on e e is called reflection positive if g g and s e e this is the first in a series of papers in which we develop a new and systematic approach to reflection positive representations based on reflection positive distributions and reflection positive distribution vectors this approach is most natural to obtain classification results in particular in the abelian case among the tools we develop is a generalization of the bochner schwartz theorem to positive definite distributions on open convex cones we further illustrate our techniques with a non abelian example by constructing reflection positive distribution vectors for complementary series representations of the conformal group o 1 n 1 r of the sphere s n

some critical point theorems and their applications to periodic solution for second order hamiltonian systems abstract some critical point theorems without the compactness assumptions are obtained by the reduction method the perturbation argument and the least action principle as applications some existence results of periodic solutions are obtained for nonautonomous second order hamiltonian systems which unify and generalize some recent corresponding results

reflection positivity in higher derivative scalar theories reflection positivity constitutes an integral prerequisite in the osterwalder schrader reconstruction theorem which relates quantum field theories defined on euclidean space to their lorentzian signature counterparts in this work we rigorously prove the violation of reflection positivity in a large class of free scalar fields with a rational propagator this covers in particular higher derivative theories where the propagator admits a partial fraction decomposition as well as degenerate cases including e g p4 type propagators