high frequency green s function for planar periodic phased arrays with skewed grid and polygonal contour the derivation of an uniform high frequency asymptotic representation of the array green s function agf for finite planar periodic phased arrays with arbitrary polygonal contour and skewed grid is presented this result generalizes those obtained in a series of recent papers in the case of rectangular phased arrays with rectangular grid for the treatment of the high frequency phenomena the actual finite array is rigorously decomposed in terms of canonical constituents i e infinite semi infinite and sectoral arrays the final result is a representation of the agf in terms of spatially truncated floquet waves fws and fw induced diffracted fields arising from the edges and vertices of the polygonal rim of the array consequently the number of field contributions necessary to reconstruct the total field is independent of the number of elements of the array leading to a very efficient algorithm a series of numerical results is provided to demonstrate the effectiveness of the high frequency representation

existence of positive solutions for a class of second order ordinary differential systems abstract in this paper we present some new concepts of superlinearity and sublinearity for nonlinear terms of second order ordinary differential systems and then consider the existence of positive solutions for systems with such superlinear and sublinear nonlinear terms especially proving the existence of positive solutions for systems in which one nonlinear term is superlinear and the other is sublinear

multiple positive solutions of singularly perturbed differential systems with different orders in this paper we consider the multiplicity of positive solutions for a class of singular higher order perturbed differential systems with different orders by employing a well known fixed point theorem some new existence results are given under the case where nonlinearity can be sign changing

existence and multiplicity of positive solutions for multi parameter three point differential equations system abstract in this paper we study the existence and multiplicity of positive solutions for the differential equations system x a 1 t f 1 x t y t 0 0 t 1 y a 2 t f 2 x t y t 0 0 t 1 x 0 0 x 1 1 x 1 y 0 0 y 1 2 y 2 where 0 are parameters 0 2 1 1 1 2 0 1 a 1 c 0 1 0 and f 2 c 0 0 0 the system is a semi positone problem since the nonlinear term f 1 is allowed to take negative values and a 2 t may change sign on 0 1 the results are established via fixed point index theory

a multiplicative seasonal component in commodity derivative pricing abstract in this paper we focus on a seasonal jump diffusion model to price commodity derivatives we propose a novel approach to estimate the functions of the risk neutral processes directly from data in the market even when a closed form solution for the model is not known then this new approach is applied to price some natural gas derivative contracts traded at new york mercantile exchange nymex moreover we use nonparametric estimation techniques in order to avoid arbitrary restrictions on the model after applying this approach we find that a jump diffusion model allowing for seasonality outperforms a standard jump diffusion model to price natural gas futures furthermore we also show that there are considerable differences in the option prices and the risk premium when we consider seasonality or not these results have important implications for practitioners in the market

an efficient computation scheme for the free space green s function of a two dimensional semiinfinite phased array a simple scheme is developed to compute the green s function of a periodic semiinfinite array in free space it is based on the spectral representation of the fields radiated by an infinite linear array of dipoles results related to successive linear arrays are added in the space domain this summation can be accelerated tremendously by using an elementary extrapolation technique the resulting formulation converges everywhere in the plane containing the array and the number of terms required to achieve a given precision increases slowly away from this plane

singular nonlinear boundary value problems for second order ordinary differential equations abstract the boundary value problem y f x y 0 y 0 y 0 0 y 1 y 1 0 is studied under conditions which are modeled on the problem y a x y p 0y 0 y 1 0 or y 0 y 1 0 which occurs in a number of applications the technical arguments involve properties of solutions i e concavity and the use of iterative techniques a new fixed point theorem for cones for decreasing mappings is proved and used it is of interest in its own right since most such theorems are for monotone increasing mappings

existence results for the positive solutions of nonlinear elliptic systems in this paper we discuss the existence of solutions for nonlinear elliptic systems the positive weak solution is sought by the leray schauder degree

algorithm for the computation of the generalized fresnel integral the generalized fresnel integral appears as a canonical function in the uniform ray field representation of several high frequency diffraction mechanisms such as double wedge or vertex diffraction here we propose an algorithm for its calculation which is valid both for real and imaginary arguments as required for treating the general case in the uniform geometrical theory of diffraction framework

positive solution of singular dirichlet boundary value problems for second order differential equation system this paper investigates the existence of positive solutions of singular dirichlet boundary value problems for second order differential system a necessary and sufficient condition for the existence of c 0 1 c 0 1 positive solutions as well as c1 0 1 c1 0 1 positive solutions is given by means of the method of lower and upper solutions and the fixed point theorems our nonlinearity fi t x1 x2 may be singular at x1 0 x2 0 t 0 and or t 1 i 1 2

estimation of risk neutral processes in single factor jump diffusion interest rate models the estimation of the market price of risk is an open question in the jump diffusion term structure literature when a closed form solution is not known furthermore the estimation of the physical drift has a high risk of misspecification in this paper we obtain some results that relate the risk neutral drift and the risk neutral jump intensity of interest rates with the prices and yields of zero coupon bonds these results open a way to estimate the drift and jump intensity of the risk neutral interest rates directly from data in the markets these two functions are unobservable but their estimations provide an original procedure for solving the pricing problem moreover this new approach avoids the estimation of the physical drift as well as the market prices of risk an application to us treasury bill data is illustrated

the risk neutral stochastic volatility in interest rate models with jump diffusion processes abstract in this paper we consider a two factor interest rate model with stochastic volatility and we propose that the interest rate follows a jump diffusion process the estimation of the market price of risk is an open question in two factor jump diffusion term structure models when a closed form solution is not known we prove some results that relate the slope of the yield curves interest rates and volatility with the functions of the processes under the risk neutral measure these relations allow us to estimate all the functions with the bond prices observed in the markets moreover the market prices of risk which are unobservable can be easily obtained then we can solve the pricing problem an application to us treasury bill data is illustrated and a comparison with a one factor model is shown finally the effect of the change of measure on the jump intensity and jump distribution is analysed

positive solutions for singular second order neumann boundary value problems via a cone fixed point theorem in this paper we consider the existence of positive solutions for the singular second order neumann boundary value problem x k 2x f t g t x 0

positive solutions of two point boundary value problems for systems of nonlinear second order singular and impulsive differential equations abstract this paper is devoted to the study of multiple and single positive solutions of two point boundary value problems for nonlinear second order singular and impulsive differential systems by constructing a cone k 1 k 2 which is the cartesian product of two cones in the space c 0 1 and computing the fixed point index in the k 1 k 2 we establish the conditions for the existence of at least one or at least two positive solutions to two point boundary value problems for systems of nonlinear second order singular and impulsive differential equations

positive solutions for 2p order and 2q order nonlinear ordinary differential systems abstract in this paper by using krasnosel skii fixed point theorem and under suitable conditions we present the existence of single and multiple positive solutions to the following systems 1 p u 2 p a t f u t v t t 0 1 1 q v 2 q b t g u t v t t 0 1 u 2 i 0 u 2 i 1 0 0 i p 1 v 2 j 0 v 2 j 1 0 0 j q 1 where 0 0 p q n we derive two explicit intervals of and such that for any and in the two intervals respectively the existence of at least one solution to the systems is guaranteed and the existence of at least two solutions for and in appropriate intervals is also discussed

a new technique to estimate the risk neutral processes in jump diffusion commodity futures models in order to price commodity derivatives it is necessary to estimate the market prices of risk as well as the functions of the stochastic processes of the factors in the model however the estimation of the market prices of risk is an open question in the jump diffusion derivative literature when a closed form solution is not known in this paper we propose a novel approach for estimating the functions of the risk neutral processes directly from market data moreover this new approach avoids the estimation of the physical drift as well as the market prices of risk in order to price commodity futures more precisely we obtain some results that relate the risk neutral drifts volatilities and parameters of the jump amplitude distributions with market data finally we examine the accuracy of the proposed method with nymex new york mercantile exchange data and we show the benefits of using jump processes for modelling the commodity price dynamics in commodity futures models

frequency domain green s function for a planar periodic semi infinite phased array i truncated floquet wave formulation this two part sequence deals with the derivation and physical interpretation of a uniform high frequency solution for the field radiated at finite distance by a planar semi infinite phased array of parallel elementary electric dipoles the field obtained by direct summation over the contributions from the individual radiators is restructured into a double series of wavenumber spectral integrals whose asymptotic reduction yields a series encompassing propagating and evanescent floquet waves fws together with corresponding diffracted rays which arise from scattering of the fw at the edge of the array the formal aspects of the solution are treated in the present paper they involve a sequence of manipulations in the complex spectral wavenumber planes that prepare the integrands for subsequent efficient and physically incisive asymptotics based on the method of steepest descent different species of spectral poles define the various species of propagating and evanescent fw their interception by the steepest descent path sdp determines the variety of shadow boundaries for the edge truncated fw the uniform asymptotic reduction of the sdp integrals performed by the van der waerden 1951 procedure and yielding a variety of edge diffracted fields completes the formal treatment

a truncated floquet wave diffraction method for the full wave analysis of large phased arrays ii generalization to 3 d cases for pt i see ibid vol 48 no 3 p 594 600 2000 this paper deals with the generalization to three dimensional 3 d arrays of the truncated floquet wave tfw diffraction method for the full wave analysis of large arrays this generalization potentially includes arrays consisting of microstrip excited slots cavity backed apertures and patches the formulation is carried out first by deriving an appropriate fringe integral equation ie and next by defining entire domain basis functions in terms of global array functions shaped as tfw diffracted rays whose analytical expression is derived on the basis of prototype canonical problems the efficiency and the accuracy of this method is demonstrated by comparison with the results of an element by element full wave approach for a rectangular slot array

positive solutions of second order two delay differential systems with twin parameter abstract the paper is concerned with the existence of positive solutions for a second order two delay differential systems with twin parameter firstly we present some sufficient conditions with the twin parameter belonging to an open rectangular region eigenvalue region to ensure the existence of positive solutions for the differential systems with singularity secondly we deal with the superlinear semipositone problem of the differential systems and establish the existence of positive solutions for the systems the proofs are based on a fixed point theorem in cones

existence of positive solutions for a second order ordinary differential system abstract in this paper we consider the existence of positive solutions for a second order ordinary differential system where the nonlinear term is superlinear in one equation and sublinear in the other equation by constructing a cone k 1 k 2 which is the cartesian product of two cones in space c 0 1 and computing the fixed point index in k 1 k 2 we establish the existence of positive solutions for the system we remark that differently from the literature we deal with our problem on the cartesian product of two cones in which the feature of two equations can be exploited better

positive solutions of n order and m order multi point singular boundary value system in this paper we study the existence of positive solutions for the nonlinear n order and m order multi point singular boundary value system by using the fixed point index theory the existence of positive solution and many positive solutions for nonlinear singular boundary value system are obtained

asymptotic high frequency green s function for a large rectangular planar periodic phased array of dipoles with weakly tapered excitation in two dimensions this paper deals with the derivation and physical interpretation of a uniform high frequency representation of the green s function for a large planar rectangular phased array of dipoles with weakly varying excitation thereby our earlier published results valid for equiamplitude excitation and those for tapered illumination in one dimension are extended to tapering along both dimensions including dipole amplitudes tending to zero at the edges as previously the field obtained by direct summation over the contributions from the individual radiators is restructured into a double spectral integral whose high frequency asymptotic reduction yields a series of propagating and evanescent floquet waves fws together with corresponding fw modulated diffracted fields which arise from fw scattering at the array edges and vertexes to accommodate the weak amplitude tapering new generalized periodicity modulated edge and vertex slope transition functions are introduced accompanied by a systematic procedure for their numerical evaluation special attention is given to the analysis and physical interpretation of the complex vertex diffracted ray fields a sample calculation is included to demonstrate the accuracy of the asymptotic algorithm the resulting array green s function forms the basic building block for the full wave analysis of planar weakly amplitude tapered phased array antennas and for the description of electromagnetic radiation and scattering from weakly amplitude tapered rectangular periodic structures

truncated floquet wave full wave analysis of large phased arrays of open ended waveguides with a nonuniform amplitude excitation recently an efficient hybrid asymptotic method of moments mom approach has been proposed for the analysis of large periodic planar arrays of elements excited with equal amplitude and linear phase the aforementioned method which is based on a floquet wave diffraction representation of the array green s function agf is here extended to treat arrays with tapered amplitude excitation to this end the asymptotic agf is refined by introducing additional slope diffraction contributions an appropriate fringe integral equation solved via a mom scheme provides the effects of array truncation in addition to the infinite array solution the dimension of the corresponding linear algebraic system is independent of the number of elements of the array numerical results are provided to prove the accuracy and the efficiency of this method with respect to an ordinary element by element mom

a hybrid spectral spatial method to evaluate the active green s function of large planar rectangular arrays a combined asymptotic numerical algorithm the article illustrates a formulation to evaluate the array green s function agf of large finite planar phased array for observation points on the array plane possibly close to the array contour the procedure is based on the agf representation in terms of a double spectral integral whose integration paths are properly deformed to have an exponential attenuation of the integrand the diffraction integral is evaluated numerically for point close to the array edges while an asymptotic treatment is proposed far from the edges this latter comprises higher order contributions thanks to the convergence properties the final algorithm is numerically accurate stable and more efficient with respect to the individual element summation for large arrays it also constitutes the basic step for the efficient evaluation of the agf of a multilayer environment

existence results for some nonlinear elliptic systems abstract the paper is concerned with some nonlinear elliptic systems by using variational methods we obtain the existence of weak solutions for the semilinear elliptic system and the quasilinear elliptic system

a truncated floquet wave diffraction method for the full wave analysis of large phased arrays i basic principles and 2 d cases this two part sequence deals with the formulation of an efficient method for the full wave analysis of large phased array antennas this is based on the method of moments mom solution of a fringe integral equation ie in which the unknown function is the difference between the exact solution of the finite array and that of the associated infinite array the unknown currents can be interpreted as produced by the field diffracted at the array edge which is excited by the floquet waves fws pertinent to the infinite configuration following this physical interpretation the unknown in the ie is efficiently represented by a very small number of basis functions with domain on the entire array aperture in order to illustrate the basic concepts the first part of this sequence deals with the two dimensional example of a linearly phased slit array it is shown that the dominant phenomenon fur describing the current perturbation with respect to the infinite array is accurately represented in most cases by only three diffracted ray shaped unknown functions this also permits a simple interpretation of the element by element current oscillation which was described by other authors

uniqueness of positive solutions for a class of elliptic systems abstract in this article we consider uniqueness of positive radial solutions to the elliptic system u a x f u v 0 v b x g u v 0 subject to the dirichlet boundary condition on the open unit ball in r n n 2 our uniqueness results applies to for instance f u v u q v p g u v u p v q p q 0 p q 1 or more general cases

multiple positive solutions to second order neumann boundary value problems in this paper the existence of multiple positive solutions to the second order neumann bvps u mu f t u u 0 u 1 0andu mu f t u u 0 u 1 0are proved by a fixed point theorem in cone due to krasnoselskii

truncated floquet wave full wave t fw sup 2 analysis of large periodic arrays of rectangular waveguides a new hybrid technique has been recently proposed for the analysis of large periodic arrays this method is based on a high frequency representation of the active green s function of a finite array involving a floquet wave fw expansion with the relevant edge and vertex diffracted ray fields originating at the array border using this representation the unknown current of an appropriate fringe integral equation is expanded in terms of a few basis functions shaped as fw induced diffracted rays this representation drastically reduces the numerical effort and provides a physical insight into the mechanism of the array truncation in this paper this method is applied to the analysis of large arrays of rectangular waveguides opened on an infinite ground plane numerical results are shown to demonstrate the effectiveness and the numerical efficiency of the method

positive solutions and eigenvalue regions of two delay singular systems with a twin parameter abstract the paper is concerned with a two delay singular differential system with a twin parameter applying fixed point index theory we show the relationship between the asymptotic behaviors of nonlinearities at zero and infinity and the open regions eigenvalue regions of parameters which are correlated with delays such that the system has zero one and two positive solution s

positive solutions for 2p order and 2q order systems of singular boundary value problems with integral boundary conditions abstract in this paper we study the existence multiplicity and nonexistence of positive solutions for 2p order and 2q order systems of singular boundary value problems with integral boundary conditions the results are based upon the fixed point theorem of cone expansion and compression type due to krasnosel skill moreover it generalizes and includes some known results

global bifurcation of positive radial solutions for an elliptic system in reactor dynamics in this paper we are concerned with the existence of positive radial solutions of the elliptic system email protected email protected f x u r 1 0 is a constant m 0 is a parameter and 0 0 is continuous and f t s 0 for all t s r 1 r 2 x 0 under some appropriate conditions on the nonlinearity f we show that the above system possesses at least one positive radial solution for any email protected 0 the proof of our main results is based upon bifurcation techniques

on the functional estimation of jump diffusion models abstract we provide a general asymptotic theory for the fully functional estimates of the infinitesimal moments of continuous time models with discontinuous sample paths of the jump diffusion type minimal requirements are placed on the dynamic properties of the underlying jump diffusion process i e stationarity is not required our theoretical framework justifies consistent in a statistical sense nonparametric extraction of the parameters and functions that drive the dynamic evolution of the process of interest i e the potentially nonaffine and level dependent intensity of the jump arrival being an example from the estimated infinitesimal conditional moments as suggested in johannes 2003 the statistical and economic role of jumps in continuous time interest rate models journal of finance forthcoming

positive solutions for a nonlinear second order semipositone boundary value system abstract in this paper by using the fixed point theorem in cones the existence of positive solutions for systems of nonlinear second order semipositone boundary value system x t f 1 t x t y t g 1 t x t y t 0 y t f 2 t x t y t g 2 t x t y t 0 x 0 x 1 y 0 y 1 0 0 t 1 which nonlinearity f i and g i i 1 2 are both semipositone is obtained under the condition that f i i 1 2 and g i i 1 2 are suplinear or sublinear the results obtained in this paper essentially improve and generalize many well known results

point processes and queues martingale dynamics i martingales 1 histories and stopping times 2 martingales 3 predictability 4 square integrable martingales references solutions to exercises chapter i ii point processes queues and intensities 1 counting processes and queues 2 watanabe s characterization 3 stochastic intensity general case 4 predictable intensities 5 representation of queues 6 random changes of time 7 cryptographic point processes references solutions to exercises chapter ii iii integral representation of point process martingales 1 the structure of internal histories 2 regenerative form of the intensity 3 the representation theorem 4 hilbert space theory of poissonian martingales 5 useful extensions references solutions to exercises chapter iii iv filtering 1 the theory of innovations 2 state estimates for queues and markov chains 3 continuous states and nontrivial prehistory references solutions to exercises chapter iv v flows in markovian networks of queues 1 single station the historical results and the filtering method 2 jackson s networks 3 burke s output theorem for networks 4 cascades and loops in jackson s networks 5 independence and poissonian flows in markov chains references solutions to exercises chapter v vi likelihood ratios 1 radon nikodym derivatives and tests of hypotheses 2 changes of intensities a la girsanov 3 filtering by the method of the probability of reference 4 applications 5 the capacity of a point process channel 6 detection formula187 references189 solutions to exercises chapter vi vii optimal control 1 modeling intensity controls 2 dynamic programming for intensity controls complete observation case 3 input regulation a case study in impulsive control 4 attraction controls 5 existence via likelihood ratio references solutions to exercises chapter vii viii marked point processes 1 counting measure and intensity kernels 2 martingale representation and filtering 3 radon nikodym derivatives 4 towards a general theory of intensity references solutions to exercises chapter viii a1 background in probability and stochastic processes 1 introduction 2 monotone class theorem 3 random variables 4 expectations 5 conditioning and independence 6 convergence 7 stochastic processes 8 markov processes references a2 stopping times and point process histories 1 stopping times 2 changes of time and meyer dellacherie s integration formula 3 point process histories references a3 wiener driven dynamical systems 1 ito s stochastic integral 2 square integrable brownian martingales 3 girsanov s theorem references a4 stieltjes lebesgue calculus 1 the stieltjes lebesgue integral 2 the product and exponential formulas references general bibliography

multiple solutions of singular boundary value problems for differential systems by constructing a special cone and using fixed point index theory in cone this paper investigates the existence of multiple solutions of singular boundary value problems for differential systems