optimal waveform selection for tracking systems investigates adaptive waveform selection schemes where selection is based on overall target tracking system performance optimal receiver assumptions allow the inclusion of transmitted waveform specification parameters in the tracking subsystem defining equations the authors give explicit expressions for two one step ahead optimization problems for a single target in white gaussian noise when the tracker is a conventional kalman filter these problems may be solved to yield the most improvement possible in tracking performance for each new transmitted pulse in cases where target motion is restricted to one dimension closed form solutions to the local one step ahead waveform optimization problem have been obtained the optimal waveform selection algorithms in the paper may be included with conventional kalman filtering equations to form an enhanced kalman tracker simulation examples are presented to illustrate the potential of the waveform selection schemes for the optimal utilization of the capabilities of modern digital waveform generators including multiple waveform classes the extension of the basic waveform optimization scheme to more complex tracking scenarios is also discussed

existence and concentration of positive solutions for a system of coupled saturable schrodinger equations abstract it is considered a saturable system of coupled schrodinger equations with asymptotically linear nonlinearities the bound states solutions with finite energy are proved to exist and have a concentration behavior under hypotheses involving the coupling and saturation parameters the proof is based on variational methods

theory and simulation of time fractional fluid diffusion in porous media we simulate a fluid flow in inhomogeneous anisotropic porous media using a time fractional diffusion equation and the staggered fourier pseudospectral method to compute the spatial derivatives a fractional derivative of the order of 0 2 replaces the first order time derivative in the classical diffusion equation it implies a time dependent permeability tensor having a power law time dependence which describes memory effects and accounts for anomalous diffusion we provide a complete analysis of the physics based on plane waves the concepts of phase group and energy velocities are analyzed to describe the location of the diffusion front and the attenuation and quality factors are obtained to quantify the amplitude decay we also obtain the frequencydomain green function the time derivative is computed with the gr unwald letnikov summation which is a finite difference generalization of the standard finite difference operator to derivatives of fractional order the results match the analytical solution obtained from the green function an example of the pressure field generated by a fluid injection in a heterogeneous sandstone illustrates the performance of the algorithm for different values of t he calculation requires storing the whole pressure field in the computer memory since anomalous diffusion recalls the past

generalized langevin equation with a three parameter mittag leffler noise abstract the relaxation functions for a given generalized langevin equation in the presence of a three parameter mittag leffler noise are studied analytically the results are represented by three parameter mittag leffler functions exact results for the velocity and displacement correlation functions of a diffusing particle are obtained by using the laplace transform method the asymptotic behavior of the particle in the short and long time limits are found by using the tauberian theorems it is shown that for large times the particle motion is subdiffusive for 1 and superdiffusive for many previously obtained results are recovered due to the many parameters contained in the noise term the model considered in this work may be used to improve the description of data and to model anomalous diffusive processes in complex media

thermal wave model of bioheat transfer with modified riemann liouville fractional derivative in this paper a new fractional thermal wave model of the bioheat transfer ftwmbt caused by spatial heating is built using taylor s series expansion of modified riemann liouville fractional derivatives a one dimensional analytical solution of the ftwmbt in a finite medium is obtained the ftwmbt in the case 1 interpolates the standard thermal wave model of bioheat transfer and the well known pennes bioheat equation 0 finally numerical results are presented graphically for various values of different parameters this study demonstrates that fractional models can provide a unified approach to examine the heat transfer in biological tissue

abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity critical point theorems and applications to some nonlinear problems with strong resonance at infinity p bartolo and v benci istituto di matematica applicata via re david x0 bari ital and istituto di analisi matematica palazzo ateneo l ia scolai 2 bari italy received in revised form 20 december 1952

multiple solutions for a semilinear problem with combined terms and nonlinear boundary conditions abstract we consider the problem u u f x u in u h x u q 2 u on where r n is a smooth bounded domain n 3 1 q 2 and h belongs to an appropriated lebesgue space in our main results we suppose that f is an asymptotically linear function and we obtain multiplicity of solutions when the norm of h is small we also present a multiplicity result in the case that f is nonquadratic at infinity

the fractional finite hankel transform and its applications in fractal space in the present work a generalized finite hankel transform is derived which is useful in solving equations in fractal dimension df and involving a fractal diffusion coefficient d0r the corresponding inversion formula is established and some properties are given then the transform is successfully used to solve a class of time fractional diffusion equations in fractional spatial dimension with an absorbent term and schrodinger equation in fractional dimensional space green s functions and exact wave function of the above problems are found

new linking theorem and elliptic systems with nonlinear boundary condition in this paper we establish a new linking theorem without ps type assumption the new theorem produces bounded ps sequences the abstract result will be used to study the existence of nontrivial positive solutions to the elliptic system u u v v in with nonlinear boundary condition u gv u gu on where is a bounded domain of rn with smooth boundary is the outer normal derivative we consider weak superlinear and asymptotically linear cases

perturbations from symmetric elliptic boundary value problems abstract we study the multiplicity of solutions for the elliptic problem u f x u eg x u in and u 0 on where e is a parameter is a smooth bounded domain in r n f c r f x t is odd with respect to t and g c r under suitable conditions only on f we prove that for any j n there exists ej 0 such that if e ej then the above problem possesses at least j distinct solutions

the palais smale condition versus coercivity possesses a convergent subsequence and cp is said to satisfy ps if ir satisfies ps for every c e ir recently among other results in critical point theory shujie i i showed that if a c functional p x k is bounded from below and satisfies the condition ps then p is coercive shujie s proof uses a gradient flow approach through the so called deformation theorem cf 3 io and for that he needs the notion of a pseudo gradient vector field tjassociated with the functional cp whose existence is guaranteed for c functionals by palais 8 in this paper we present some new results which relate the palais smale condition and the notion of coercivity and are based on the well known variational principle due to ekeland 5 61 in particular a new proof of the above mentioned result of shujie is given it should be pointed out that throughout the paper the given functional p could be assumed to be only gateaux differentiable rather than c and in addition to being conceptually simpler this approach could be used in more general situations where the functional is not even differentiable cf 4 the strong form of ekeland s variational principle to be repeatedly used is given in the following theorem

multiplicity of nontrivial solutions for quasilinear elliptic equation two nontrivial solutions are obtained by the reduction method for the nonautonomous semilinear elliptic dirichlet boundary value problem some well known multiplicity results are generalized

nonresonance below the first eigenvalue for a semilinear elliptic problem let be a bounded open subset in hbox i r n with smooth boundary and let f x s be a real valued caratheodory function on upomega times hbox i r we consider the semilinear dirichlet problem

nonlinear degenerate elliptic equation with hardy potential and critical parameter abstract some embedding inequalities in hardy sobolev spaces with general weight functions were proved and a positive answer to an open problem raised by brezis vazquez was given in the weighted hardy sobolev spaces the existence of nontrivial many solutions to the corresponding nonlinear degenerated elliptic equations with hardy potential and critical parameter under conditions weaker than ambrosetti rabinowitz condition was obtained

nontrivial solutions for neumann problems with an indefinite linear part abstract in this paper we consider a semilinear neumann problem with an indefinite linear part and a caratheodory nonlinearity which is superlinear near infinity and near zero but does not satisfy the ambrosetti rabinowitz condition using an abstract existence theorem for c 1 functions having a local linking at the origin we establish the existence of at least one nontrivial smooth solution

the time fractional heat conduction equation in the general orthogonal curvilinear coordinate and the cylindrical coordinate systems abstract in this paper a time fractional fourier law is obtained from fractional calculus according to the fractional fourier law a fractional heat conduction equation with a time fractional derivative in the general orthogonal curvilinear coordinate system is built the fractional heat conduction equations in other orthogonal coordinate systems are readily obtainable as special cases in addition we obtain the solution of the fractional heat conduction equation in the cylindrical coordinate system in terms of the generalized h function using integral transformation methods the fractional heat conduction equation in the case 0 1 interpolates the standard heat conduction equation 1 and the localized heat conduction equation 0 finally numerical results are presented graphically for various values of order of fractional derivative

resonance problems for p q laplacian systems abstract some existence results of weak solutions are established for p q laplacian systems which are resonant at an arbitrary eigenvalue by the minimax methods in critical point theory

solutions to semilinear elliptic problems with combined nonlinearities abstract we are concerned with the following nonlinear dirichlet problem u h x u q f x u 0 u h 0 1 0 where is a bounded smooth domain in rn n 1 and h x l f x s is asymptotically linear with respect to s at infinity by a variant version of mountain pass theorem we prove that there exist at least two nonnegative solutions under suitable assumptions on f x s our methods also work for the cases where f x s is superlinear or linear in s

modified riemann liouville derivative and fractional taylor series of nondifferentiable functions further results the paper gives some results and improves the derivation of the fractional taylor s series of nondifferentiable functions obtained recently in the form f g h e a h ad g a f g 0 a 1 where e a is the mittag leffier function here one defines fractional derivative as the limit of fractional difference and by this way one can circumvent the problem which arises with the definition of the fractional derivative of constant using riemann liouville definition as a result a modified riemann liouville definition is proposed which is fully consistent with the fractional difference definition and avoids any reference to the derivative of order greater than the considered one s in order to support this f taylor series one shows how its first term can be obtained directly in the form of a mean value formula the fractional derivative of the dirac delta function is obtained together with the fractional taylor s series of multivariate functions the relation with irreversibility of time and symmetry breaking is exhibited and to some extent this f taylor s series generalizes the fractional mean value formula obtained a few years ago by kolwantar

frequency tracking using hidden markov models with amplitude and phase information it is demonstrated how the hidden markov model hmm frequency tracker can be extended by the addition of amplitude and phase information the hmm tracker as originally formulated uses a gate of spectral bins from fast fourier transform fft processing and associates each cell with a state of the hidden markov chain a measurement sequence based on the output of a simple threshold detector forms the input to the hmm tracker two extensions to the original tracker are proposed the first the hmm a tracker incorporates the fft amplitudes in the cells of the measurement sequence the second the hmm ap tracker does not use a measurement sequence but uses instead the fft amplitude and phase values in all cells within the gate a comparison of the results obtained in using the three hmm based trackers with simulated data reveals that the extended trackers outperform the original an analysis of the effect of parameter mismatch for the three trackers is presented their use as detectors is also discussed

multiple solutions for resonant elliptic equations via local linking theory and morse theory abstract we consider two classes of elliptic resonant problems first by local linking theory we study the double double resonant case and obtain three solutions second we introduce some new conditions and compute the critical groups both at zero and at infinity precisely combining morse theory we get three solutions for the completely resonant case

superlinear problems without ambrosetti and rabinowitz growth condition superlinear elliptic boundary value problems without ambrosetti and rabinowitz growth condition are considered existence of nontrivial solution result is established by combining some arguments used by struwe and tarantello and schechter and zou also by wang and wei firstly by using the mountain pass theorem due to ambrosetti and rabinowitz is constructed a solution for almost every parameter by varying the parameter then it is considered the continuation of the solutions

multiplicity of solutions for resonant elliptic systems we establish the existence and multiplicity of solutions for some resonant elliptic systems the results are proved by applying minimax arguments and morse theory

analytical solutions of multi term time fractional differential equations and application to unsteady flows of generalized viscoelastic fluid this paper derives analytical solutions for a class of new multi term fractional order partial differential equations which include the terms for spatial diffusion time fractional diffusion multi term and reaction these models can be used to describe the nonlinear relationship between the shear stress and shear rate of generalized viscoelastic oldroyd b fluid and burgers fluid by using a modified separation of variables method the governing fractional order partial differential equations are transformed into a set of fractional order ordinary differential equations mikusiski type operational calculus is then employed to obtain the exact solutions of the linear fractional ordinary differential equations with constant coefficients the solutions are expressed in terms of multivariate mittag leffler functions different situations for the unsteady flows of generalized oldroyd b fluid and burgers fluid due to a moving plate are considered via examples integral representations of the solutions are presented it is shown that the presented results reduce to the corresponding results for classical navierstokes oldroyd b maxwell and second grade fluids as special cases

multiple solutions for a class of semilinear elliptic equations with general potentials abstract in this paper we study the existence of infinitely many nontrivial solutions for a class of semilinear elliptic equations u a x u g x u in a bounded smooth domain of r n n 3 with the dirichlet boundary value where the primitive of the nonlinearity g is of superquadratic growth near infinity in u and the potential a is allowed to be sign changing recent results in the literature are generalized and significantly improved

existence and multiplicity of solutions for a class of elliptic boundary value problems abstract in this paper we investigate the existence and multiplicity of solutions for the following elliptic boundary value problems u a x u g x u in u 0 on where g x u k u x u w u x u by using the symmetric mountain pass theorem we obtain two results about infinitely many solutions when g x u is odd in u k satisfies the pinching condition and w has a super quadratic growth moreover when the condition g x u is odd is not assumed by using the mountain pass theorem we also obtain two existence results of one nontrivial weak solution one of these results generalizes a recent result in mao zhu and luan 2012 10

a stochastic model for thermal transport of nanofluid in porous media derivation and applications abstract in this paper a stochastic thermal transport model is developed for nanofluid flowing through porous media this model incorporates the influences of nanoparticle migration on convective heat transfer of the colloidal solution we show that levy flight movement patterns of nanoparticles result in the derived model using fractional derivative for the diffusion term the new thermal transport model is then applied to the mixed convective problem which is solved using finite difference method numerical results show that the smaller values of levy index lead to larger nusselt numbers thus the occurrence of long jumps for nanoparticles increases the heat transport of nanofluids the effects of other involved physical parameters are also presented and discussed

on a class of asymptotically linear elliptic problems in rn under these conditions p is an asymptotically linear problem when this equation is considered in a bounded domain 0 r with say the dirichlet boundary condition there is a large literature on existence and multiplicity results of particular interest is then the case of resonance where s and s is the asymptotic linearization of the problem in other words s d s l 0 l 0 is the operator given by

a variational approach to subquadratic perturbations of elliptic systems abstract we consider subquadratic perturbations of semilinear elliptic systems which are in variational form a unified approach to both the cooperative and noncooperative problems is presented and a condition of nonquadraticity at infinity is introduced to treat the resonant cases through minimax techniques

variational elliptic problems which are nonquadratic at infinity p co if n 1 2 then it is well known that the weak solutions u e h 2 of p are the critical points of the c functional j u ulvul dx jcf x u dx where f x s jif x t dt in this variational setting the literature usually distinguishes between two situations for prob lem p the subquadratic situation where the potential f satisfies lim suplsl f x s s2 i c m and the superquadratic situation where f satisfies limlsl m f x s s2 00 the main goal of this paper is to present a unified approach to both situations by means of a condition of nonquadraticity at infinity on f more precisely our hypotheses are as follows

void probabilities and cauchy schwarz divergence for generalized labeled multi bernoulli models the generalized labeled multi bernoulli glmb is a family of tractable models that alleviates the limitations of the poisson family in dynamic bayesian inference of point processes in this paper we derive closed form expressions for the void probability functional and the cauchy schwarz divergence for glmbs the proposed analytic void probability functional is a necessary and sufficient statistic that uniquely characterizes a glmb while the proposed analytic cauchy schwarz divergence provides a tractable measure of similarity between glmbs we demonstrate the use of both results on a partially observed markov decision process for glmbs with cauchy schwarz divergence based reward and void probability constraint

numerical algorithms to estimate relaxation parameters and caputo fractional derivative for a fractional thermal wave model in spherical composite medium in this paper we formulate a fractional thermal wave model for a bi layered spherical tissue implicit finite difference method is employed to obtain the solution of the direct problem the inverse analysis for simultaneously estimating the caputo fractional derivative and the relaxation time parameters is implemented by means of the levenberg marquardt method compared with the experimental data we can obviously find out that the estimated temperature increase values are excellently consistent with the measured temperature increase values in the experiment we have also discussed the effect of the fractional derivative the relaxation time parameters the initial guess as well as the sensitivity problem all the results show that the proposed fractional thermal wave model is efficient and accurate in modeling the heat transfer in the hyperthermia experiment and the proposed numerical method for simultaneously estimating multiple parameters for the fractional thermal wave model in a spherical composite medium is effective

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

waveform design for radar stap in signal dependent interference waveform design is a pivotal component of the fully adaptive radar construct in this paper we consider waveform design for radar space time adaptive processing stap accounting for the waveform dependence of the clutter correlation matrix due to this dependence in general the joint problem of receiver filter optimization and radar waveform design becomes an intractable nonconvex optimization problem nevertheless it is however shown to be individually convex either in the filter or in the waveform variables we derive constrained versions of a the alternating minimization algorithm b proximal alternating minimization and c the constant modulus alternating minimization which at each step iteratively optimizes either the stap filter or the waveform independently a fast and slow time model permits waveform design in radar stap but the primary bottleneck is the computational complexity of the algorithms

saddle point techniques from the beginning of the calculus of variations over 300 years ago scientists were interested in finding extrema of expressions now called functionals involving unknown functions it was discovered that functions producing extrema are solutions of differential equations called euler equations in one dimentional problems these were ordinary differential equations and the easiest procedure was to solve the corresponding euler equation and then check if the solution produces the desired maximum or minimum however as researchers began to study higher dimensional problems it became obvious that it was more difficult to solve the euler equations than obtain an extremum of the functional moreover many partial differential equations and systems that were being studied by various scientists happened to be the euler equations of functionals in this case any critical point of the corresponding functional will provide a solution of the given equation this led to the search for critical points of functionals in this paper we describe several methods of finding critical points we present applications

on fractional regularity methods for a class of nonlocal problems abstract in the past years the phenomenon of fractional regularity has been addressed for a large class of linear and or quasilinear differential operators mostly in terms of certain besov spaces as it turned out for equations governed by the p laplacian in general the regularity of solutions appears in terms of functional spaces with nonlinear order of smoothness moreover despite its own interest fractional regularity methods may be used as a tool for the investigation of some partial differential equations which are not usually addressed in this manner thus the purpose of the present paper is to exploit such methods in order to provide some results regarding existence and regularity of solutions to a class nonlocal elliptic equations which are linked to the p laplacian this is done by means of explicit a priori estimates regarding lebesgue and nikolskii spaces which are part of the present contribution as a consequence this approach allows a relaxation on some of the standard conditions employed in this class of problems

detection thresholds for tracking in clutter a connection between estimation and signal processing in the kalman bucy filter and other trackers the dependence of tracking performance upon the quality of the measurement data is well understood in terms of the measurement noise covariance matrix which specifies the uncertainty in the values of the measurement inputs the measurement noise and process noise covariances determine via the riccati equation the state estimation error covariance when the origin of the measurements is also uncertain one has the widely studied problem of data association or data correlation and tracking performance depends critically on signal processing parameters primarily the probabilities of detection and false alarm in this paper we derive a modified riccati equation that quantifies approximately the dependence of the state error covariance on these parameters we also show how to use a receiver operating characteristic roc curve in conjunction with the above relationship to determine the detection threshold in the signal processing system that provides measurements to the tracker so as to minimize tracking errors the approach presented in this paper provides a feedback mechanism from the information processing tracking subsystem to the signal processing subsystem so as to optimize the overall performance in clutter

existence result for fractional neutral stochastic integro differential equations with infinite delay this paper is concerned with the existence of mild solutions for a class of fractional neutral stochastic integro differential equations with infinite delay in hilbert spaces a sufficient condition for the existence is obtained under non lipschitz conditions by means of sadovskii s fixed point theorem an example is given to illustrate the theory

solutions for resonant elliptic systems with nonodd or odd nonlinearities we consider by minimax techniques a class of cooperative elliptic systems at resonance if the nonlinear term is nonodd we establish some new existence theorems about nontrivial solutions if the nonlinearity is odd we obtain existence of infinitely many solutions a topic about which very little is known

a boundary value problem with a periodic nonlinearity soit g r r une fonction continue et periodique de periode t 0 et soit h l 1 0 on considere le probleme d existence pour le probleme aux limites de picard u u g u h u 0 0 u

fractional diffusion equation with a generalized riemann liouville time fractional derivative in this paper the solution of a fractional diffusion equation with a hilfer generalized riemann liouville time fractional derivative is obtained in terms of mittag leffler type functions and fox s h function the considered equation represents a quite general extension of the classical diffusion heat conduction equation the methods of separation of variables laplace transform and analysis of the sturm liouville problem are used to solve the fractional diffusion equation defined in a bounded domain by using the fourier laplace transform method it is shown that the fundamental solution of the fractional diffusion equation with a generalized riemann liouville time fractional derivative defined in the infinite domain can be expressed via fox s h function it is shown that the corresponding solutions of the diffusion equations with time fractional derivative in the caputo and riemann liouville sense are special cases of those diffusion equations with the hilfer generalized riemann liouville time fractional derivative the asymptotic behaviour of the solutions are found for large values of the spatial variable the fractional moments of the fundamental solution of the fractional diffusion equation are obtained the obtained results are relevant in the context of glass relaxation and aquifer problems

simulation based optimal sensor scheduling with application to observer trajectory planning the sensor scheduling problem can be formulated as a controlled hidden markov model and this paper solves the problem when the state observation and action spaces are continuous this general case is important as it is the natural framework for many applications the aim is to minimise the variance of the estimation error of the hidden state w r t the action sequence we present a novel simulation based method that uses a stochastic gradient algorithm to find optimal actions

on quasilinear elliptic problems without the ambrosetti rabinowitz condition abstract using variational arguments we establish the existence of multiple solutions for quasilinear elliptic problems driven by the laplacian operator a major point is that we ensure compactness without the well known ambrosetti rabinowitz superlinearity condition

existence of solutions for a class of noncooperative elliptic systems we establish the existence of a nontrivial solution for a class of noncooperative elliptic systems with nonlinearities of superlinear growth moreover if there is resonance we also find at least a solution all results are obtained by the minimax methods in critical point theory

remarks on existence and multiplicity of solutions for a class of semilinear elliptic equations the existence and multiplicity results are obtained for solutions of a class of the dirichlet problem for semilinear elliptic equations by the least action principle and the minimax methods respectively

periodic and subharmonic solutions of a class of subquadratic second order hamiltonian systems some solvability conditions of periodic and subharmonic solutions are obtained for a class of subquadratic nonautonomous second order hamiltonian systems by the minimax methods in critical point theory

the restaurant at the end of the random walk recent developments in the description of anomalous transport by fractional dynamics fractional dynamics has experienced a firm upswing during the past few years having been forged into a mature framework in the theory of stochastic processes a large number of research papers developing fractional dynamics further or applying it to various systems have appeared since our first review article on the fractional fokker planck equation metzler r and klafter j 2000a phys rep 339 1 77 it therefore appears timely to put these new works in a cohesive perspective in this review we cover both the theoretical modelling of sub and superdiffusive processes placing emphasis on superdiffusion and the discussion of applications such as the correct formulation of boundary value problems to obtain the first passage time density function we also discuss extensively the occurrence of anomalous dynamics in various fields ranging from nanoscale over biological to geophysical and environmental systems

existence of a periodic solution for subquadratic second order discrete hamiltonian system some solvability conditions of periodic solutions are obtained for a class of nonautonomous subquadratic second order discrete hamiltonian system by minimax methods in critical point theory

existence of solutions for elliptic equations with discontinuous nonlinearities strong resonance at infinity abstract in the present paper our main purposes are to study nonlinear elliptic equations with strong resonance at infinity some existence theorems for nontrivial solutions are obtained by using some nonsmooth critical point theorems in n c kourogenis n s papageorgiou nonsmooth critical point theory and nonlinear elliptic equations at resonance j austral math soc ser a 69 2000 245 271 the two of our theorems generalize theorems 0 1 and 5 2 in p bartolo v benci d fortunato abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity nonlinear anal tma 7 1983 981 1012 to nonsmooth cases another theorem is new even if for the smooth case

quasilinear elliptic problems under strong resonance conditions abstract in this paper we establish the existence and multiplicity of solutions for a quasilinear elliptic problem under strong resonance conditions at infinity in order to control the resonance we consider a new hypothesis on the nonlinear term in all results we use variational methods critical groups and the morse theory

existence of solutions to a class of semilinear elliptic equations involving general subcritical growth in this paper we consider the semilinear elliptic equation u f x u with the dirichlet boundary value and under suitable assumptions on the nonlinear term f with a more general growth condition some existence results of solutions are given for all 0 via the variational method and some analysis techniques