the oscillation and asymptotically monotone solutions of second order quasilinear differential equations abstract we offer sufficient conditions for the oscillation of all solutions of the perturbed quasilinear differential equation a t y 1 y q t y p t y y as well as for the existence of a positive monotone solution of the damped differential equation a t y 1 y b t y 1 y h t y 0 where 0 examples that dwell upon the importance of our results are also included

fast summation at nonequispaced knots by nfft we develop a new algorithm for the fast computation of discrete sums f y j sum k 1 n alpha k k y j x k j 1 m based on the recently developed fast fourier transform fft at nonequispaced knots our algorithm in particular our regularization procedure is simply structured and can be easily adapted to different kernels k our method utilizes the widely known fft and can consequently incorporate advanced fft implementations in summary it requires cal o n log n m arithmetic operations we prove error estimates to obtain clues about the choice of the involved parameters and present numerical examples in one and two dimensions

new approach to information fusion steady state kalman filtering by the modern time series analysis method based on the autoregressive moving average arma innovation model a unified and general information fusion steady state kalman filtering approach is presented for the general multisensor systems with different local dynamic models and correlated noises it can handle the filtering smoothing and prediction fusion problems for state or signal the optimal fusion rule weighted by matrices is re derived as a weighted least squares wls fuser and is reviewed an optimal fusion rule weighted by diagonal matrices is presented which is equivalent to the optimal fusion rule weighted by scalars for components and it realizes a decoupled fusion the new algorithms of the steady state kalman estimator gains are presented in order to compute the optimal weights the formulas of computing the cross covariances among local estimation errors by lyapunov equations are presented the exponential convergence of the iterative solution of lyapunov equation is proved it is proved that the optimal fusion estimators under three weighted fusion rules are locally optimal but are globally suboptimal the proposed steady state kalman fusers can reduce the on line computational burden and are suitable for real time applications a simulation example for the 3 sensor steady state kalman tracking fusion estimators shows their effectiveness and correctness and gives the accuracy comparison of the fusion rules

half linear differential equations linearization technique and its application abstract oscillatory properties of the half linear second order differential equation r t x c t x 0 x x p 2 x p 1 are investigated where is viewed as a perturbation of an equation of the same form and these properties are compared with the oscillatory behavior of a certain associated linear second order differential equation as a corollary a conjecture posed by the first author in the paper o dosl perturbations of the half linear euler weber differential equations j math anal appl 323 2006 426 440 is proved and some new research problems are formulated

rectifiable oscillations of self adjoint and damped linear differential equations of second order abstract asymptotic and oscillatory behaviours near x 0 of all solutions y y x of self adjoint linear differential equation p p q p y q y 0 on 0 t will be studied where p p x and q q x satisfy the so called hartman wintner type condition we show that the oscillatory behaviour near x 0 of p p q is characterised by the nonintegrability of q p on 0 t moreover under this condition we show that the rectifiable resp unrectifiable oscillations near x 0 of p p q are characterised by the integrability resp nonintegrability of q p 3 4 on 0 t next some invariant properties of rectifiable oscillations in respect to the liouville transformation are proved also sturm s comparison type theorem for the rectifiable oscillations is stated furthermore previous results are used to establish such kind of oscillations for damped linear second order differential equation y g x y f x y 0 and especially the bessel type damped linear differential equations are considered finally some open questions are posed for the further study on this subject

integral conditions for nonoscillation of second order nonlinear differential equations an extension of the fubini theorem is presented and applied in studying the possible coexistence of nonoscillatory solutions for the differential equation r t x sgnx q t x sgnx some discrepancies among the cases and are illustrated and compared with the linear case in addition when an application to the integral characterization of principal solutions which answers an open problem stated in o dosl a elbert integral characterization of the principal solution of half linear second order differential equations studia sci math hungar 36 2000 455 469 is given

oscillation criteria for second order nonlinear delay dynamic equations on time scales by employing the generalized riccati transformation we establish some new oscillation criteria for second order delay dynamic equations on time scales the obtained results essentially improve the well know oscillation results for half linear dynamic equations such as kamenev type and philos type oscillation criteria some interesting examples are given to illustrate the versatility of our results

solvability of second order nonlinear three point boundary value problems abstract we are interested in the existence of nontrivial solutions to the three point boundary value problem bvp u t f t u t 0 0 t 1 u 0 0 u 1 u u where 0 1 f t u c 0 1 r r and are real constants fixed point theorems and degree theory are frequently used to study such problems recently the authors demonstrated that in many situations the shooting method proves to be an effective approach often leading to better results with shorter proofs here we present another such example assume that f t 0 0 and that there exist nonnegative functions k h l 1 0 1 such that f t w k t w h t for all t w 0 1 r sun and liu 13 for the special case 0 and sun 14 for the special case 0 showed that if the l 1 norm k 1 is sufficiently small then there exists a nontrivial solution to the bvp in this paper their results are improved using the shooting method

sequential covariance intersection fusion kalman filter for multisensor system with unknown cross covariances among local estimation errors the batch covariance intersection bci fusion estimation algorithm requires the optimization of a multi dimensional nonlinear cost function which yields a larger computational burden and computational complexity a fast sequential covariance intersection sci kalman filtering algorithm is presented in this paper which only requires to solve the optimization problem of several one dimensional nonlinear cost functions it is equivalent to several two sensor covariance intersection ci kalman fusers and is a recursive two sensor ci kalman fuser its accuracy depends on the orders of sensors it is proved that the sci fuser is consistent and its accuracy is higher than that of each local estimator and is lower than that of the optimal kalman fuser with known cross covariances the geometric interpretation of accuracy relations based on the covariance ellipses is given and the properties of the covariance ellipses are rigorously proved two monte carlo simulation examples show the effectiveness of the proposed results show that the accuracies of the sci fusers are not very sensitive with respect to the orders of sensors and show that its actual accuracy is close to that of the optimal kalman fuser in general cases and its robust accuracy is close to that of the bci fuser so it has good performances

minimizing euclidian state estimation error for linear uncertain dynamic systems based on multisensor and multi algorithm fusion in this paper a multisensor linear dynamic system with model uncertainty and bounded noises is considered based on previously developed set valued estimation methods in terms of convex optimization we propose several efficient algorithms of centralized sensor fusion distributed sensor fusion and multi algorithm fusion to minimize the euclidian estimation error of the state vector obviously an ellipsoid box with a larger size cannot be in general guaranteed to contain another ellipsoid box with a smaller size since centers and shapes of the two ellipsoids boxes may be different from each other this fact and the complementary advantages of multiple sensors and multiple algorithms motivate us to construct multiple estimation ellipsoids boxes squashed along each entry of the state vector as much as possible respectively by using the technique of multiple differently weighted objectives then intersection fusion of these estimation ellipsoids boxes yields a final euclidian error minimized state estimate numerical examples show that the new method with multi algorithm at both the sensors and the fusion center can significantly reduce the euclidian estimation error of the state

sturmian comparison theorem for half linear second order differential equations let be defined by s s p 2 s with p 1 a fixed number we extend sturm comparison theorem of the linear differential equation to the nonlinear differential equation by using the wirtinger inequality a lyapunov inequality and some oscillation criteria of e are also given

half linear equations and characteristic properties of the principal solution abstract the characteristic properties of the principal solution for half linear differential equation a t x b t x 0 where the functions a b are positive and continuous for t 0 and u u p 2u p 1 are investigated in the linear case it is well known that the principal solution is the smallest one in a neighbourhood of infinity we show that this property continues to hold in the half linear case in addition it is proved that the principal solutions can be fully characterized by means of two different integral criteria which reduce to that one well known in the linear case

perturbations of the half linear euler weber type differential equation abstract we investigate oscillatory properties of the half linear second order differential equation r t x c t x 0 x x p 2 x p 1 viewed as a perturbation of another half linear differential equation of the same form r t x c t x 0 the obtained oscillation and nonoscillation criteria are formulated in terms of the integral c t c t h p t d t where h is a function which is close to the principal solution of in a certain sense a typical model of in applications is the half linear euler weber differential equation with the critical coefficients x p t p p t p log 2 t x 0 p p 1 p p p 1 2 p 1 p p 1 we establish oscillation and nonoscillation criteria for perturbations of this equation some open problems and perspectives of the further research along this line are also formulated

optimal linear estimation fusion i unified fusion rules this paper deals with data or information fusion for the purpose of estimation three estimation fusion architectures are considered centralized distributed and hybrid a unified linear model and a general framework for these three architectures are established optimal fusion rules based on the best linear unbiased estimation blue the weighted least squares wls and their generalized versions are presented for cases with complete incomplete or no prior information these rules are more general and flexible and have wider applicability than previous results for example they are in a unified form that is optimal for all of the three fusion architectures with arbitrary correlation of local estimates or observation errors across sensors or across time they are also in explicit forms convenient for implementation the optimal fusion rules presented are not limited to linear data models illustrative numerical results are provided to verify the fusion rules and demonstrate how these fusion rules can be used in cases with complete incomplete or no prior information

nonoscillatory half linear differential equations and generalized karamata functions abstract we introduce a natural generalization of the concept of regularly varying functions in the sense of karamata and show that the class of generalized karamata functions is a well suited framework for the study of the asymptotic behavior of nonoscillatory solutions of the half linear differential equation of the type a p t y 1 y q t y 1 y 0

growth conditions for uniform asymptotic stability of damped oscillators abstract the present paper is devoted to an investigation on the uniform asymptotic stability for the linear differential equation with a damping term x h t x 2 x 0 and its generalization p x h t p x p p x 0 where 0 and p z z p 2 z with p 1 sufficient conditions are obtained for the equilibrium x x 0 0 to be uniformly asymptotically stable under the assumption that the damping coefficient h t is integrally positive the obtained condition for the damped linear differential equation is given by the form of a certain uniform growth condition on h t another representation which is equivalent to this uniform growth condition is also given our results assert that the equilibrium can be uniformly asymptotically stable even if h t is unbounded an example is attached to show this fact in addition easy to use conditions are given to guarantee that the uniform growth condition is satisfied moreover a sufficient condition expressed by an infinite series is presented the relation between the representation of an infinite series and the uniform growth condition is also clarified finally our results are extended to be able to apply to the above mentioned nonlinear differential equation

on the track to track correlation problem the testing of the hypothesis whether two tracks represent the same target is considered previous works in the literature assumed that the estimates of the same target s state from two track files are uncorrelated a test that includes their correlation is presented

on the oscillation of hill s equations under periodic forcing abstract we use the floquet theory of the hill s equation to prove the conjecture that all solutions of the second order forced linear differential equation y c sin t y cos t are oscillatory on 0 for all c 0

nonoscillation of mathieu equations with two frequencies abstract as is well known mathieu s equation is a representative of mathematical models describing parametric excitation phenomena this paper deals with the oscillation problem for mathieu s equation with two frequencies the ratio of these two frequencies is not necessarily a rational number when the ratio is an irrational number the coefficient of mathieu s equation is quasi periodic but not periodic for this reason the basic knowledge for linear periodic systems such as floquet theory is not useful whether all solutions of mathieu s equation oscillate or not is determined by parameters and frequencies our results provide parametric conditions to guarantee that all solutions are nonoscillatory the advantage of the obtained parametric conditions is that it can be easily checked parametric nonoscillation region is drawn to understand these results easily finally several simulations are carried out to clarify the remaining problems

nonoscillation and oscillation of second order half linear differential equations abstract we study the oscillation problems for the second order half linear differential equation p t x q t x 0 where u u r 1 u with r 0 1 p and q are locally integrable on r p 0 q 0 a e on r and 0 p 1 r t d t we establish new criteria for this equation to be nonoscillatory and oscillatory respectively when p 1 our results are complete extensions of work by huang c huang oscillation and nonoscillation for second order linear differential equations j math anal appl 210 1997 712 723 and by wong j s w wong remarks on a paper of c huang j math anal appl 291 2004 180 188 on linear equations to the half linear case for all r 0 these results provide corrections to the wrongly established results in j jiang oscillation and nonoscillation for second order quasilinear differential equations math sci res hot line 4 6 2000 39 47 on nonoscillation when 0 r 1 and on oscillation when r 1 the approach in this paper can also be used to fully extend elbert s criteria on linear equations to half linear equations which will cover and improve a partial extension by yang x yang oscillation nonoscillation criteria for quasilinear differential equations j math anal appl 298 2004 363 373

integral inequalities and second order linear oscillation on the interval 0 a u 0 below by a solution we mean a non trivial solution a solution is oscillatory if it has an infinite number of zeros numerous oscillation criteria are known and diversified approaches have proved fruitful among these is the use of the associated riccati equation although the theory of differential and integral inequalities has been used by some investigators see e g hartman 4 71 the authors believe that it has not been fully exploited the non oscillation of 1 1 is equivalent to the existence of a solution of the associated riccati equation on a half line thus one technique of proving oscillation is to show that any solution of the riccati equation diverges to i co at a finite point the theory of differential and integral inequalities comes in handy in the estimation of the growth of such a solution below we describe some known results that are relevant to results established in this paper although these are stated here for the case i co in the rest of the paper we consider both cases a 0 and a 00 it is well known that if q is large in the mean then 1 1 is oscillatory a typical example of such a criterion is due to fite leighton and wintner if

optimal distributed kalman filtering fusion with singular covariances of filtering errors and measurement noises in this paper we present the globally optimal distributed kalman filtering fusion with singular covariances of filtering errors and measurement noises the following facts motivate us to consider the problem first the invertibility of estimation error covariance matrices is a necessary condition for most of the existing distributed fusion algorithms however it can not be guaranteed to exist in practice for example when state estimation for a given dynamic system is subject to state equality constraints the estimation error covariance matrices must be singular second the proposed fused state estimate is still exactly the same as the centralized kalman filtering using all sensor raw measurements moreover the existing performance analysis results on the distributed kalman filtering fusion for the multisensor system with feedback are also extended to the singular covariance matrices of filtering error the final numerical examples support the theoretical results and show an advantage of less computational burden

note on forced oscillation of nth order sublinear differential equations in the case of oscillatory potentials we establish an oscillation theorem for the forced sublinear differential equation x n q t x sgnx e t t t0 no restriction is imposed on the forcing term e t to be the nth derivative of an oscillatory function in particular we show that all solutions of the equation x t sint x sgnx mt cost t 0 0 2 1 this provides an analogue of a result of nasr proc amer math soc 126 1998 123 for the forced superlinear equation and answers a question raised in an earlier paper j s w wong siam j math anal 19 1988 673

growth conditions for oscillation of nonlinear differential equations with p laplacian abstract in this paper oscillation criteria are established for all solutions of second order nonlinear differential equations of the form p x 1 t p g x 0 t 0 here p y is the one dimensional p laplacian operator and g x satisfies the signum condition x g x 0 if x 0 but is not assumed to be monotone the equation naturally includes the famous euler differential equation and half linear differential equations the main purpose is to examine the influence of certain growth conditions of the nonlinear term g x on the oscillation of solutions the conditions are shown to be sharp some of differential inequalities play important roles to prove our results a simple example is included to illustrate the main result a conjecture on the inverse problem is also given finally elliptic equations with p laplacian operator are discussed as an application to our results

asymptotic properties of kneser solutions to nonlinear second order odes with regularly varying coefficients in this work we investigate properties of a class of solutions to the second order ode p t u t q t f u t 0 on the interval a a 0 where p and q are functions regularly varying at infinity and f satisfies f l 0 f 0 f l 0 with l0 0

power comparison theorems in half linear oscillation theory we compare oscillatory behavior of two half linear differential equations with different powers by the homogeneous functions appearing in these equations our results generalize and extend several previously proved power comparison theorems

group decision making models for sequential tasks the sequential probability ratio test sprt and related drift diffusion model ddm are optimal for choosing between two hypotheses using the minimal average number of samples and relevant for modeling the decision making process in human observers this work extends these models to group decision making previous works have focused almost exclusively on group accuracy here we explicitly address group decision time first we derive explicit solutions for the error rate and probability distribution function of decision times for a group of independent possibly nonidentical decision makers using one of three simple rules race majority total and majority first we illustrate our solutions with a group of n i i d decision makers who each make an individual decision using the sprt based ddm then compare the performance of each group rule under different constraints we then generalize these group rules to the eta total and eta first schemes to demonstrate the flexibility and power of our approach in characterizing the performance of a group given the performance of its individual members

an efficient higher order fast multipole boundary element solution for poisson boltzmann based molecular electrostatics in order to compute polarization energy of biomolecules we describe a boundary element approach to solving the linearized poisson boltzmann equation our approach combines several important features including the derivative boundary formulation of the problem and a smooth approximation of the molecular surface based on the algebraic spline molecular surface state of the art software for numerical linear algebra and the kernel independent fast multipole method is used for both simplicity and efficiency of our implementation we perform a variety of computational experiments testing our method on a number of actual proteins involved in molecular docking and demonstrating the effectiveness of our solver for computing molecular polarization energy

interval oscillation theorems for asecond order linear differential equation interval oscillation criteria are given for the forced second order linear differential equation ly t p t y q t y t email protected 0 where p q are locally integrable functions and p t 0 for t 0 no restriction is imposed on t to be the second derivative of an oscillatory function as assumed by kartsatos 1 our results also allow both q and f to change sign in the neighborhood at infinity in particular we show that all solutions of y c sin t y t b cos t with b 0 are oscillatory for c 1 3448 this improves an estimate given by nasr 2 for the linear equation

fast analytical methods for macroscopic electrostatic models in biomolecular simulations we review recent developments of fast analytical methods for macroscopic electrostatic calculations in biological applications including the poisson boltzmann pb and the generalized born models for electrostatic solvation energy the focus is on analytical approaches for hybrid solvation models especially the image charge method for a spherical cavity and also the generalized born theory as an approximation to the pb model this review places much emphasis on the mathematical details behind these methods

asymptotics of instability zones of the hill operator with a two term potential let n denote the length of the nth zone of instability of the hill operator ly y 4t cos2x 2 2cos4x y where 0 and either both t are real or both are pure imaginary numbers for even n we prove if t n are fixed then for 0 n 8 n2n n 1 2 k 1n 2 t2 2k 1 2 1 o and if t are fixed then for n n 8 2 n 2 4 n 2 2 cos 2t 1 o lognn the asymptotics for 0 for n 2m imply the following identities for squares of integers s 1k m2 is2 1 j1 jk m s 1k 2js 1 2 where 1 k m and the left sum is over all indices i1 ik such that m i1 ik m is ir 2if s r similar formulae see theorems 7 9 hold for odd n

an order insensitive sequential fast covariance intersection fusion algorithm the proposed sfci fusion algorithm can handle the problem of unknown cross correlation in local estimation errors the fusion accuracy of the proposed algorithm is not relevant to the fusion orders i e all fusion nodes can acquire identical result the fusion coefficients are straightforward to calculate owing to not require optimizing nonlinear cost function the proposed algorithm is computationally efficient and is therefore applicable for use in real time fusion systems in this article data cross correlation in distributed sensor system is investigated via an order insensitive sequential fast covariance intersection fusion algorithm among the existing approaches the common drawbacks are that the fusion results are sensitive to fusion orders and the computational burden is tremendous due to the optimization of multi dimensional nonlinear cost function in order to overcome these drawbacks a sequential fast covariance intersection sfci algorithm is presented the new fusion coefficients can be calculated straightforward by taking the reciprocal of the trace of the inverse variances as local fusion coefficients and using an iterative process for fusion step to revise the coefficient weight note that the proposed fusion algorithm is consistent and its accuracy is unrelated to the fusion order of the distributed system finally real radar data and simulation examples are provided to verify the effectiveness of the proposed algorithm

linearization of second order nonlinear oscillation theorems the problem of oscillation of super and sublinear emden fowler equations is studied established are a number of oscillation theorems involving comparison with related linear equations recent results on linear oscillation can thus be used to obtain interesting oscillation criteria for nonlinear equations 25 references

high degree efficient symmetrical gaussian quadrature rules for the triangle gaussian quadrature is required for the computation of matrices based on the isoparametric formulztion of the finite element method a brief review of existing quadrature rules for the triangle is given and the method for the determination of high degree efficient symmetrical rules for the triangle is discussed new quadrature rules of degree 12 20 are presented and a short fortran program is included

sensors optimal dimensionality compression matrix in estimation fusion when there exists the limitation of communication bandwidth between sensors and a fusion center one needs to optimally pre compress sensor outputs sensor observations or estimates before sensors transmission to obtain a constrained optimal estimation at the fusion center in terms of the linear minimum error variance criterion this paper will give an analytic solution of the optimal linear dimensionality compression matrix for the single sensor case and analyze the existence of the optimal linear dimensionality compression matrix for the multisensor case as well as how to implement a gauss seidel algorithm to search for an optimal solution to linear dimensionality compression matrix

global existence and nonexistence of solutions for second order nonlinear differential equations abstract this paper deals with the global existence and nonexistence of solutions of the second order nonlinear differential equation x x 0 satisfying x 0 x 0 and x 0 x 1 where is a positive parameter and with 0 and 0 is strictly increasing odd bijective and continuous on necessary and sufficient conditions are obtained for the initial value problem to have a unique global solution which is oscillatory and periodic examples are given to illustrate our main result finally a nonexistence result for the equation with a damping term is discussed as an application to our result

asymptotic formulae for solutions of half linear differential equations we establish asymptotic formulae for regularly varying solutions of the half linear differential equation r t y 1 sgn y p t y 1 sgn y where r p are positive continuous functions on a and 1 the results can be understood in several ways some open problems posed in the literature are solved results for linear differential equations are generalized some of the observations are new even in the linear case a refinement on information about behavior of solutions in standard asymptotic classes is provided a precise description of regularly varying solutions which are known to exist is given regular variation of all positive solutions is proved

optimal dimensionality reduction of sensor data in multisensor estimation fusion when there exists the limitation of communication bandwidth between sensors and a fusion center one needs to optimally precompress sensor outputs sensor observations or estimates before the sensors transmission in order to obtain a constrained optimal estimation at the fusion center in terms of the linear minimum error variance criterion or when an allowed performance loss constraint exists one needs to design the minimum dimension of sensor data this paper will answer the above questions by using the matrix decomposition pseudo inverse and eigenvalue techniques

estimates for the hill operator ii consider the hill operator ty y q t y in l2 r where the real potential q is 1 periodic and q q l2 0 1 the spectrum of t consists of spectral bands separated by gaps n n 1 with length n 0 we obtain two sided estimates of the gap lengths n2 n 2 in terms of 01q t 2dt moreover we obtain the similar two sided estimates for spectral data the height of the corresponding slit on the quasimomentum domain action variables for the kdv equation and so on in order prove this result we use the analysis of a conformal mapping corresponding to quasimomentum of the hill operator that makes it possible to reformulate the problems for the differential operator as the problems of the conformal mapping theory then the proof is based on the analysis of the conformal mapping the embedding theorems and the identities furthermore we obtain the similar two sided estimates for potentials which have p 2 derivatives

networked fusion estimation with bounded noises most of time varying systems in fusion estimation are generally modeled without bounded noises in this paper we study the distributed fusion estimation problem for networked time varying systems with bounded noises where the resource constraints i e bandwidth or energy and quantization effect are described by a unified model a new local estimator with time varying gain is designed by solving a class of convex optimization problems such that the square error of the estimator is bounded when each local estimate is transmitted to the fusion center over communication networks the selection probability criterion is derived such that the mean square error of the each compensating state estimate is bounded then a convex optimization problem on the design of an optimal weighting fusion criterion is established in terms of linear matrix inequalities which can be solved by standard software packages target tracking system with time varying sampling period is given to show the effectiveness of the proposed method

selection of a convolution function for fourier inversion using gridding computerised tomography application in the technique known as gridding the data samples are weighted for sampling density and convolved with a finite kernel then resampled on a grid preparatory to a fast fourier transform the authors compare the artifact introduced into the image for various convolving functions of different sizes including the kaiser bessel window and the zero order prolate spheroidal wave function pswf they also show a convolving function that improves upon the pswf in some circumstances

note on wong s paper using the method of interval integral average we establish some new oscillation criteria which improve the oscillation criteria due to james s w wong

oscillation and nonoscillation of hill s equation with periodic damping we prove new results on the oscillation and nonoscillation of the hill s equation with periodic damping y p t y q t y 0 t 0 where p t and q t are continuous and periodic the results show that the equation y sint y cost y 0 is nonoscillatory whilst the equation y cost y sint y 0 is oscillatory

asymptotic formulas for non oscillatory solutions of perturbed half linear euler equation abstract we establish asymptotic formulas for non oscillatory solutions of the half linear second order differential equation x t p x c t x 0 where this equation is viewed as a perturbation of the half linear euler equation

oscillation criterion for half linear differential equations with periodic coefficients abstract in this paper we present an oscillation criterion for second order half linear differential equations with periodic coefficients the method is based on the nonexistence of a proper solution of the related modified riccati equation our result can be regarded as an oscillatory counterpart to the nonoscillation criterion by sugie and matsumura 2008 these two theorems provide a complete half linear extension of the oscillation criterion of kwong and wong 2003 dealing with the hill s equation

modified prufer angle and conditional oscillation of perturbed linear and half linear differential equations abstract the research and results described in this paper belong to the qualitative theory of differential equations more precisely the partial differential equations with the one dimensional p laplacian using a method whose core is formed by the prufer technique we identify a borderline case between oscillatory and non oscillatory equations moreover we are able to decide whether the studied equations are oscillatory or not even in the so called critical i e the borderline case the advantage of our approach is the fact that we obtain new and strong results for linear and half linear equations i e the equations with the one dimensional p laplacian at the same time in addition we are able to work with equations whose coefficients are non constant and non periodic the novelty of our results is documented by examples and corollaries

optimal interval estimation fusion based on sensor interval estimates with confidence degrees the interval estimation fusion method based on sensor interval estimates and their confidence degrees is developed when sensor estimates are independent of each other a combination rule to merge sensor estimates and their confidence degrees is proposed moreover two optimization criteria minimizing interval length with an allowable minimum confidence degree or maximizing confidence degree with an allowable maximum interval length are suggested in terms of the two criteria an optimal interval estimation fusion can be obtained based on the combined intervals and their confidence degrees then we can extend the results on the combined interval outputs and their confidence degrees to obtain a conditional combination rule and the corresponding optimal fault tolerant interval estimation fusion in terms of the two criteria it is easy to see that marzullo s fault tolerant interval estimation fusion marzullo 1990 tolerating failures of continuous valued sensors acm transactions on computer system 8 4 284 304 is a special case of our method

half linear oscillation criteria perturbation in term involving derivative abstract we consider the nonoscillatory half linear differential equation r t x c t x 0 x x p 2 x p 1 and we study oscillatory properties of its perturbation r t r t x c t c t x 0 we use the riccati technique and relationship between and a certain associated linear equation the results are applied to the perturbed euler type equation

global attractivity for half linear differential systems with periodic coefficients abstract the system to be considered in this paper is x y a t x y b t p x p y here a t is a 2 2 diagonal matrix and b t is a 2 2 anti diagonal matrix and q z z q 2 z with q 1 the coefficients of b t are assumed to be periodic but the coefficients of a t are not necessarily periodic the system is of half linear type sufficient conditions are given for the zero solution of the half linear system to be globally asymptotically stable the zero solution of the system x y b t p x p y is stable but is not attractive our concern is to clarify a positive effect of the diagonal part a t x y on the global asymptotic stability for the half linear system some simple examples are included to illustrate the main result

on intermediate solutions and the wronskian for half linear differential equations the asymptotic behavior of nonoscillatory solutions of the half linear differential equation is studied in particular two wronskian type functions which have some interesting properties similar to the one of the wronskian in the linear case are given using these properties and suitable integral inequalities the existence of the so called intermediate solutions is examined and an open problem is solved

a nonoscillation theorem for half linear differential equations with periodic coefficients abstract the half linear differential equation p x a t p x b t p x 0 is considered under the assumption that the coefficient a t and an indefinite integral b t of b t are periodic functions with period t 0 it is proved that p 1 p b t a t b t 0 0 t t is sufficient for all nontrivial solutions to be nonoscillatory here p 1 and q y y q 2 y for q p or q p p p 1 the proof is given by means of riccati technique the condition is shown to be sharp sufficient conditions are also presented for all nontrivial solutions are oscillatory in the linear case p 2 some examples and simulations are included to illustrate our results

positive solutions of fourth order emden fowler type differential equations in the framework of regular variation abstract the fourth order nonlinear differential equations a x 4 q t x sgn x 0 0 1 with regularly varying coefficient q t are studied in the framework of regular variation it is shown that thorough and complete information can be acquired about the existence of all possible regularly varying solutions of a and their accurate asymptotic behavior at infinity

simple conditions for parametrically excited oscillations of generalized mathieu equations abstract the following equation is considered in this paper x cos t x 0 where and are real parameters and 0 this equation is referred to as mathieu s equation when 2 the parameters determine whether all solutions of this equation are oscillatory or nonoscillatory our results provide parametric conditions for oscillation and nonoscillation there is a feature in which it is very easy to check whether these conditions are satisfied or not parametric oscillation and nonoscillation regions are drawn to help understand the obtained results

interval oscillation of a general class of second order nonlinear differential equations with nonlinear damping abstract the paper is concerned with the oscillation of a class of general type second order differential equations with nonlinear damping terms several new interval oscillation criteria are established for such a class of differential equations under quite general assumptions examples are also given to illustrate the results in particular it is shown that under some very mild conditions on k 1 k 2 and f the equation k 1 x x cos tk 2 x x x sin tf x 0 is oscillatory which extends the result obtained by kwong and wong j math anal appl 288 2003 15

conjugacy criteria for half linear ode in the theory of pde with generalized p laplacian and mixed powers abstract in this paper we use conjugacy criteria for a half linear ordinary differential equation to prove some nonexistence results for a partial differential equation with generalized p laplacian and mixed derivatives div a x y p 2 y b x y p 2 y c x y p 2 y i 1 m c i x y p i 2 y e x the results can be used also to study equations with strongly non radial potential c x since the usual dependence on the mean value of c x over a sphere can be replaced by a more general term

de haan type increasing solutions of half linear differential equations abstract we study asymptotic behavior of eventually positive increasing solutions to the half linear equation r t y 1 sgn y p t y 1 sgn y where r p are positive continuous functions and 1 we give conditions which guarantee that any such a solution is in the class in the de haan sense we also discuss regularly varying solutions and connections with a generalized regular variation and other related concepts the results can be viewed as a half linear extension of existing statements for linear equations but in some aspects they are new also in the linear case

on the oscillation of differential equations with an oscillatory coefficient we derive lower bounds for the distance between consecutive zeros of solutions of y q t y 0 when q takes both positive and negative values we apply our results to the limit point limit circle classifications of

distributed fusion estimation with communication bandwidth constraints this technical note is concerned with the distributed kalman filtering problem for a class of networked multi sensor fusion systems nmfss with communication bandwidth constraints to satisfy finite communication bandwidth only partial components of the local vector estimation signals are transmitted to the fusion center fc at each time step where multiple binary variables are introduced to model this component transmitting process a novel compensation strategy is proposed to restructure the untransmitted components of each local estimate at the fc end and a recursive distributed fusion kalman filter dfkf is designed in the linear minimum variance sense moreover a simple suboptimal judgement criterion is proposed to determine a group of binary variables such that the mean square error of the designed dfkf is minimal at each time step an illustrative example is given to show the effectiveness of the proposed methods

technical communique distributed optimal component fusion weighted by scalars for fixed lag kalman smoother based on the optimal fusion criterion in the linear minimum variance sense a distributed optimal fusion fixed lag kalman smoother with a three layer fusion structure is given for the discrete time varying linear stochastic control systems with multiple sensors and correlated noises its components are estimated by scalar weighting fusion respectively it only requires in parallel a series of computations of the weighted scalars and avoids the computations of the weighted matrices so that the computational burden can obviously be reduced further the steady state fusion smoother is also given for the discrete time invariant linear stochastic control systems the scalar weights can be obtained by fusing once after all local estimations reach steady state it can reduce the online computational burden also the computation formulas of smoothing error cross covariance matrices are given two simulation examples show the performance

fast molecular solvation energetics and forces computation the total free energy of a molecule includes the classical molecular mechanical energy which is understood as the free energy in vacuum and the solvation energy which is caused by the change of the environment of the molecule solute from vacuum to solvent the solvation energy is important to the study of the intermolecular interactions in this paper we develop a fast surface based generalized born method to compute the electrostatic solvation energy along with the energy derivatives for the solvation forces the most time consuming computation is the evaluation of the surface integrals over an algebraic spline molecular surface asms and the fast computation is achieved by the use of the nonequispaced fast fourier transform nfft algorithm the main results of this paper involve a an efficient sampling of quadrature points over the molecular surface by using nonlinear patches b fast linear time estimation of energy and intermolecular forces c error analysis and d efficient implementation combining fast pairwise summation and the continuum integration using nonlinear patches

on certain riccati integral equations and second order linear oscillation are closely related is well known many important results in the oscillation theory of 1 1 are in fact established by studying either 1 2 or 1 3 recent studies suggest that a great deal can still be said about 1 2 and l 3 thus leading to new results on 1 1 see 7 91 particularly useful in these studies is the theory of differential and integral inequalities the present work further supports this view point in this paper we first give a comparison theorem section 2 theorem 1 for riccati integral equations of the form 1 3 involving monotonic rearrangements of the function q t ji q s ds as a corollary we establish an extension of the well known oscillation criteria of hille s 6 to more general potentials section 3 theorem 4 in section 4 we elaborate on a method of hartman to derive a comparison type result involving the square of the integral j h q s ds and then deduce a lyapunov type inequality for disfocality the preliminaries will be introduced in the appropriate sections 315 0022 247x 82 020315 16 02 00 o

oscillation problems for hill s equation with periodic damping abstract this paper deals with the second order linear differential equation x a t x b t x 0 where a and b are periodic coefficients the main purpose is to present new criteria which guarantee that all nontrivial solutions are nonoscillatory and that those are oscillatory our nonoscillation theorem and oscillation theorem are proved by using the riccati technique in our theorem the composite function of an indefinite integral of b and a suitable multiple valued continuously differentiable function are focused and the composite function of them plays an important role the results obtained here include a result by kwong and wong 15 and a result by sugie and matsumura 26 an application to a equation of whittaker hill type is given to show the usefulness of our results finally simulations are also attached to illustrate that our oscillation criterion is sharp

nonlinear weighted measurement fusion unscented kalman filter with asymptotic optimality for the general nonlinear systems a universal weighted measurement fusion wmf algorithm is presented via the taylor series expansion method based on the proposed fusion algorithm and the well known unscented kalman filter ukf the wmf ukf is presented it is proven that the proposed wmf ukf asymptotically approaches to the centralized measurement fusion ukf cmf ukf with the increase of the order of taylor series expansion so it has the asymptotical global optimality we find that wmf ukf has less computational cost than the cmf ukf does with the increase of the number of sensors two examples are given to show the effectiveness of the proposed algorithms

distributed estimation constraints on the choice of the local models the following estimation problem is considered a coordinator must reconstruct the global probability density of a nonlinear random process conditioned on the noise corrupted observation history the coordinator can only access the local probability density produced by local processing of the observation history using a local model different from the process model it is shown that if the local model satisfies an algebraic constraint the coordinator can reconstruct the same conditional density of the state process as the one obtained if the observations were processed using the coordinator process model it is assumed that the random process is a nonlinear stochastic differential equation driven by a brownian motion and the observation process is corrupted by additive brownian motion which is identically modeled by the coordinator and the local processor

on kamenev type oscillation theorems for second order differential equations with damping abstract oscillation criteria for the nonlinear second order ordinary differential equation with damping x p t x f x 0 are given the results are extensions of integral averaging technique of kamenev and include earlier results of yeh yan and chen

whittaker hill equation and semifinite gap schrodinger operators a periodic one dimensional schrodinger operator is called semifinite gap if every second gap in its spectrum is eventually closed we construct explicit examples of semifinite gap schrodinger operators in trigonometric functions by applying darboux transformations to the whittaker hill equation we give a criterion for the regularity of the corresponding potentials and investigate the spectral properties of the new operators