rate of convergence of baskakov bezier type operators for locally bounded functions abstract in this paper we introduce baskakov bezier operator b n which is an operator of probabilistic type we study the rate of convergence of the operator b n for locally bounded functions by using some inequalities and results of probability theory our estimate is essentially the best possible

simultaneous approximation for bezier variant of szasz mirakyan durrmeyer operators abstract we study the rate of convergence in simultaneous approximation for the bezier variant of szasz mirakyan durrmeyer operators by using the decomposition technique of functions of bounded variation

rate of convergence by chlodowsky taylor polynomials approximation on an unbounded interval is studied in this work by means of a newly defined two parameter polynomial operator based on chlodowsky polynomials the operator s properties including convergence rate are investigated using the weighted modulus of continuity an example is given to illustrate the effect of the parameters some basic results are presented

control and synchronize a novel hyperchaotic system the control and hybrid projective synchronization hps strategies for a novel hyperchaotic system are investigated firstly the novel hyperchaotic system is controlled to the unsteady equilibrium point or limit cycle via only one scalar controller which includes two state variables secondly based on lyapunov s direct method hps between two novel hyperchaotic systems is studied a new nonlinear feedback vector controller is designed to guarantee hps which can be simplified ulteriorly into a single scalar controller to achieve complete synchronization between two novel hyperchaotic systems finally numerical simulations are given to verify the effectiveness of these strategies the proposed methods have certain significances for reducing the cost and complexity for controller implementation

adaptive added order anti synchronization of chaotic systems with fully unknown parameters this work investigates the chaos anti synchronization between two different dimensional chaotic systems with fully unknown parameters via added order based on the lyapunov stability theory the adaptive controllers with corresponding parameter update laws are designed such that the two different chaotic systems with different dimensions can be synchronized asymptotically finally two illustrative numerical simulations are given to demonstrate the effectiveness of the proposed scheme

the bezier variant of kantorovitch operators in the present paper we define generalized kantorovitch type operators for particular values our operators reduce to the well known szasz kantorovitch operators and baskakov kantorovitch operators we estimate the rate of convergence of the bezier variant of these generalized operators for bounded variation functions here we also remark that for a particular value c 0 the second central moment was not estimated correctly in 1 which leads to the major error in the main results of 1

an asymptotic closed form microstrip surface green s function for the efficient moment method analysis of mutual coupling in microstrip antennas a relatively simple closed form asymptotic representation for the single layer microstrip dyadic surface green s function is developed the large parameter in this asymptotic development is proportional to the lateral separation between the source and field points along the air dielectric interface this asymptotic solution remains surprisingly accurate even for very small a few tenths of a free space wavelength lateral separation of the source and field points thus using the present asymptotic approximation of the green s function can lead to a very efficient moment method mm solution for the currents on an array of microstrip antenna patches and feed lines numerical results based on the efficient mm analysis using the present closed form asymptotic approximation to the microstrip surface green s function are given for the mutual coupling between a pair of printed dipoles on a single layer grounded dielectric slab the accuracy of the latter calculation is confirmed by comparison with numerical results based on a mm analysis which employs an exact integral representation for the microstrip green s function

an estimate on the convergence of mkz bezier operators the pointwise approximation properties of the mkz bezier operators m n a f x for a 1 have been studied in x m zeng rates of approximation of bounded variation functions by two generalized meyer konig zeller type operators comput math appl 39 2000 1 13 the aim of this paper is to study the pointwise approximation of the operators m n a f x for the other case 0 a 1 by means of some new estimate techniques and a result of guo and qi s guo q qi the moments for the meyer konig and zeller operators appl math lett 20 2007 719 722 we establish an estimate formula on the rate of convergence of the operators m n a f x for the case 0 a 1

rate of pointwise approximation for locally bounded functions by szasz operators abstract in this paper the asymptotic behavior of szasz operators for locally bounded functions f is studied at points x where f x and f x exist an asymptotic estimate of this type approximation is obtained by using some techniques and results of probability theory the estimate essentially is the best possible for continuous points of f

an estimate on the convergence of baskakov bezier operators abstract in the present paper we estimate the rate of convergence on functions of bounded variation for the bezier variant of the baskakov operators b n f x here we have studied the rate of convergence of b n f x for the case 0 1

approximation of unbounded functions by a new sequence of linear positive operators in the present paper we introduce a new sequence of linear positive operators to study the simultaneous approximation of unbounded functions

synchronization of delay bursting neuron system with stochastic noise via linear controllers abstract synchronization of bursting neuron system with stochastic noise is investigated when parameters are known based on lyapunov stability theory via appropriate controllers synchronization of delay hindmarsh rose system with stochastic noise is obtained when parameters are unknown by adaptive control technique corresponding parameter update laws are proposed to achieve synchronization of hindmarsh rose system with stochastic noise finally numerical simulations are given to demonstrate the effectiveness of the proposed schemes

bounds for bernstein basis functions and meyer konig and zeller basis functions abstract in this paper the inequality estimates of bernstein basis functions and meyer konig and zeller basis functions are studied exact bounds for these two basis functions are obtained moreover some application results of the new estimates in estimating the rate of convergence of durrmeyer operators and meyer koning and zeller operators for functions of bounded variation are also given

convergence rate of a new bezier variant of chlodowsky operators to bounded variation functions in the present paper we estimate the rate of pointwise convergence of the bezier variant of chlodowsky operators c n a for functions defined on the interval extending infinity of bounded variation to prove our main result we have used some methods and techniques of probability theory

approximation by stancu chlodowsky polynomials in this paper we investigate convergence and approximation properties of a chlodowsky type generalization of stancu polynomials we called stancu chlodowsky polynomials the rates of convergence of this generalization are obtained by means of modulus of continuity and by using the k functional of peetre we also present and prove theorems on weighted approximation and the order of approximation of continuous functions by these operators on all positive semi axis

rate of approximation by a new sequence of linear positive operators abstract in the present paper we study the rate of pointwise approximation by a new sequence of linear positive operators for functions of bounded variation to prove the main result we have used some results of probability theory in the end we also introduce the bezier variant of these newly introduced sequences of linear positive operators

on the durrmeyer type modification of the q baskakov type operators abstract this paper deals with durrmeyer type generalization of q baskakov type operators using the concept of q integral which introduces a new sequence of positive q integral operators we show that this sequence is an approximation process in the polynomial weighted space of continuous functions defined on the interval 0 an estimate for the rate of convergence and weighted approximation properties are also obtained

analytical technique to evaluate the asymptotic part of the impedance matrix of sommerfeld type integrals the propagation of electromagnetic waves in a grounded dielectric slab has numerous applications in printed antenna technology and in the analysis of microwave and millimeter wave integrated circuits for the accurate analysis of microstrip dipoles and circuits based on the moment of method mom a crucial step is the precise evaluation of the impedance matrix elements which contain the integration of sommerfeld type integrals the integral transform method with the asymptotic extraction technique is formulated for calculating a sommerfeld type integral problem this formulation allows the infinite double integral of the asymptotic part of the impedance matrix to be transformed into a finite one dimensional 1 d integral this finite 1 d integral contains a spherical legendre function and can be easily evaluated numerically after the singular part of the integral is performed analytically it is shown that the proposed method dramatically reduces the computation time and improves the accuracy over the conventional method to evaluate the asymptotic part of impedance matrix

rate of convergence of bernstein polynomials for functions with derivatives of bounded variation abstract for any x 0 1 we first prove that if x t t x on 0 1 then the bernstein polynomials of x satisfy the asymptotic relation k 0 n k n x k n x k 1 x n k 2x 1 x 1 2 1 n o 1 n this asymptotic relation is then used to study the rate of convergence of bernstein polynomials for functions with derivatives of bounded variation an estimate of the rate of convergence is given this estimate is asymptotically the best possible at points where is continuous

rates of approximation of bounded variation functions by two generalized meyer konig and zeller type operators abstract in this paper the approximation behaviours of two generalized meyer konig and zeller type operators m n and m n are studied by means of the decomposition technique of functions of bounded variation and the method of bojanic 1 bojanic and vuilleumier 2 and cheng 3 together with some results from probability theory and the exact bound of meyer konig and zeller operators basis functions the rates of convergence of these two operators for functions of bounded variation are obtained

some convergence considerations in space domain moment method analysis of a class of wide band microstrip antennas the method of moments mom analysis of probe fed rectangular microstrip patches requires the inclusion of a probe to patch attachment mode expansion function when the substrate thickness d spl ges 0 02 spl lambda where spl lambda is the free space wavelength the results for the input impedance showed increased divergence with measurements when the attachment mode was omitted from the full wave analysis the attachment mode can be expressed as an infinite eigenfunction series that increases the fill time of the impedance matrix in an mom analysis in an earlier investigation the infinite eigenfunction series was reduced to a residue series that required one or two terms compared to about 55 terms for the eigenfunction series in this paper the convergence properties of the eigenfunction and residue series are investigated in view of rigorous mom analysis the relative errors resulting from replacing the eigenfunction by the residue series for the attachment mode are compared by numerically evaluating a class of two dimensional 2 d spatial integrals shown to be closely related to the elements of an mom impedance matrix additionally the computation times for the evaluation of these integrals for the two forms of the attachment mode expansion function are also included based on the superior convergence properties of the residue series for the attachment mode expansion function it is mathematically justified that this form can readily be used for analytic reduction of the spatial reaction integrals from four to 2 d forms this feature allows further reduction of the fill time of the mom impedance matrix suggesting the possibility of developing an efficient space domain mom technique for modeling of wide band microstrip antennas

analysis of printed antennas mounted on a coated circular cylinder of arbitrary size an efficient numerical algorithm for the analysis of printed antennas on a dielectric coated circular cylinder is presented the formulation employs the spectral domain approach green s function is evaluated via olver s uniform asymptotic expansions the fourier summation is transformed into integration and the asymptotic part of the integral is evaluated in closed form the whole procedure results in a numerical algorithm that is at least as accurate and efficient as the respective one for the planar structure the present approach can be applied for any source receiver position and any cylinder radius

degree of approximation to function of bounded variation by bezier variant of mkz operators abstract guo approx theory appl 4 1988 9 18 introduced the integral modification of meyer konig and zeller operators m n and studied the rate of convergence for functions of bounded variation in this paper we introduce the bezier variant of these integrated mkz operators and study the rate of convergence by means of the decomposition technique of functions of bounded variation together with some results of probability theory and the exact bound of mkz basis functions recently zeng j math anal appl 219 1998 364 376 claimed to improve the results of guo and gupta approx theory appl 11 1995 106 107 but there is a major mistake in the paper of zeng for special case our main theorem gives the correct estimate on the rate of convergence over the result of zeng

direct estimates in simultaneous approximation for bbs operators abstract the summation integral type baskakov beta operator were introduced by gupta v gupta a note on modified baskakov type operators approx theory appl 10 3 1994 74 78 in the present paper we extend our studies and introduce the baskakov beta stancu abbr bbs operator we give the moments of these operators using hypergeometric series in the next section we derive the asymptotic formula and error estimation in simultaneous approximation in the end we propose an open problem to the readers

rate of convergence for certain families of summation integral type operators in this paper we study the rate of convergence for the iterative combinations of a certain family of linear positive operators in terms of higher order integral modulus of smoothness we have used the technique of linear approximating method namely steklov mean to prove the main result in the end we propose some other sequences of linear positive operators and obtain the recurrence formulae for the central moments voronovskaja type asymptotic formulae and error estimations

convergence rate for generalized baskakov type operators we introduce the bezier variant of certain integral modification of the baskakov type operators bn 1 0 and estimate the rate of convergence of these operators for bounded functions satisfying certain growth condition

a hybrid evaluation method for the full wave analysis of microstrip structures a hybrid evaluation method using both the spectral and the spatial domain techniques is proposed for the evaluation of the sommerfeld type integrals resulting from the full wave analysis of microstrip structures this method combines the advantages of the spectral domain for the evaluation of near fields and the spatial domain method for the evaluation of far fields this method is simple and needs no additional formulations it also provides an easy alternative method to handle the inefficiency of calculation with the singularity of the green s function numerical results are used to demonstrate the simplicity and the accuracy of this method

a note on the convergence of baskakov type operators in the present paper we estimate the rate of convergence on functions of polynomial type for some variant of the baskakov operators the form of the operator discussed in the present paper makes results helpful from the computational point of view

new method for the efficient summation of double infinite series arising from the spectral domain analysis of frequency selective surfaces when the method of moments mom in the spectral domain is applied to the analysis of frequency selective surfaces the entries of the mom matrix are slowly convergent double infinite series in this paper a two step acceleration technique is developed which makes it possible the fast and accurate computation of these double series in the particular case where subsectional rooftops are used as basis functions the technique is based on a combination of the use of kummer s transformation the use of poisson s transformation and the determination of judicious chebyshev polynomial interpolations of some of the spectral discrete functions involved in the infinite series the results obtained show that when all the double series of the mom matrix are to be computed with an accuracy of three significant figures the new acceleration technique turns out to be about one thousand times faster than brute force computation and a few times faster than the acceleration technique based on fast fourier transform

real axis integration of sommerfeld integrals with applications to printed circuit antennas printed circuit antennas are becoming an integral part of imaging arrays in microwave millimeter and submillimeter wave frequencies the electrical characteristics of such antennas can be analyzed by solving integral equations of the fredholm first kind the kernel involves sommerfeld integrals which are particularly difficult to solve when source and field points lie on an electrical discontinuity as it occurs in the determination of the characteristics of printed circuit antennas an analytic numeric real axis integration technique has been developed for such integrals and it is combined with piece wise sinusoidal expansions to solve the fredholm integral equation for the unknown current density

local approximation by a variant of bernstein durrmeyer operators abstract this paper deals with the local approximation properties of a certain variant m n of the bernstein durrmeyer operators firstly we obtain an estimate on the rate of convergence of m n by means of the decomposition technique for functions of bounded variation it will be shown that our estimate in its most convenient form corollary 2 is asymptotically optimal furthermore we derive the complete asymptotic expansion for the sequence of the operators m n as n tends to infinity

the generalized baskakov type operators the use of baskakov type operators is difficult for numerical calculation because these operators include infinite series do the operators expressed as a finite sum provide the approximation properties furthermore are they appropriate for numerical calculation in this paper in connection with these questions we define a new family of linear positive operators including finite sum by using the baskakov type operators we also give some numerical results in order to compare baskakov type operators with this new defined operator

improved formulation for investigation of proximity coupled microstrip antenna in homogeneous dielectric half space analytical evaluation of asymptotic part of the green s function in product with piece wise sinusoidal entire domain and travelling wave mode basis functions is presented the sommerfeld type double integral in spectral domain is solved and reduced into a single integral in spatial domain with very short integration range the derived results lead to develop a computational efficiency improved code which has been found 27 times faster than the earlier validated common method of moments code

chaos control and hybrid projective synchronization of several new chaotic systems abstract the problems on purposefully creating and controlling chaos are investigated first several new 4d chaotic systems are presented based on a 3d chaotic system and three dynamical characteristics are verified second it is demonstrated that they can be stabilized to their equilibrium points by a same single scalar adaptive feedback control law third two of the chaotic systems with constant parameters are in hybrid projective synchronization hps by presented adaptive feedback control strategies which can be simplified into a scalar form for identical drive response systems to achieve complete synchronization furthermore hps between two of the chaotic systems with response system parameters unknown is also considered and adaptive parameter update laws are developed numerical simulations show their characteristics and verify the effectiveness of the strategies

rate of convergence in simultaneous approximation for szasz mirakyan durrmeyer operators abstract in the present paper we study the rate of convergence in simultaneous approximation for the szasz mirakyan durrmeyer operators by using the decomposition technique of functions of bounded variation

cooperative behavior of a chain of synaptically coupled chaotic neurons abstract a coupled linear chain of hindmarsh rose model neurons with reciprocal inhibition between neighboring neurons exhibited synchronous oscillations in which neighboring neurons burst out of phase and next nearest neighbor neurons burst in phase the bifurcations observed inside this out of phase regime were qualitatively the same for all chains with an even number of neurons and were similar to those observed in a single isolated cell although the organization of the behavior of a chain of coupled neurons was more regular than that of an isolated cell when noise was added to the synaptic coupling strengths there was less hysteresis in the system and many of the bifurcations with smaller basins of attraction were eliminated making the system even more regular these results suggest that in populations of bursting neurons with reciprocal inhibition the chaotic behavior found in single cells is suppressed

exponential synchronization of a new lorenz like attractor with uncertain parameters via single input the new lorenz like attractor reported by li et al 2009 1 includes a product term of system parameters it can be predicted that chaotic synchronization of this new chaotic system becomes more complicated by taking account of uncertain system parameters in this paper the exponential synchronization between two nearly identical lorenz like attractors by applying single input controller associated with system parameter update laws is proposed unlike multiple control inputs and state variable feedbacks required in chaotic synchronization in the literature the proposed single input controller includes only one state variable proportional feedback two kinds of system parameter update laws are introduced and sufficient conditions are provided to guarantee exponential stability of both synchronous errors and system parameter errors in addition numerical simulations are also performed to verify the effectiveness of presented schemes

synchronization transition in degenerate optical parametric oscillators induced by nonlinear coupling in this paper the synchronization of certain degenerate optical parametric oscillators is investigated in detail complete and or partial synchronization can be reached when linear controller constructed by the real part or imaginary part of the subharmonic mode is imposed on the chaotic degenerate optical parametric oscillators with appropriate coupling intensity the lyapunov exponents under different coupling coefficients are calculated to find the critical condition for complete synchronization transition from complete synchronization to partial synchronization is observed when nonlinear coupling is introduced into the two chaotic oscillators it is found that synchronization of chaotic oscillators keeps robust when the intensity of the nonlinear coupling is less than the intensity of the linear coupling the complete synchronization state is destructed and transient period for partial synchronization is in certain delay when the intensity of the nonlinear coupling is beyond the intensity of the linear coupling

an asymptotic extraction technique for evaluating sommerfeld type integrals an asymptotic extraction process is developed which leads to an efficient method for the evaluation of the electric field from a hertzian dipole in a layered geometry this technique allows for a rapidly converging expression for the electric field which remains well behaved as the source and observation heights z z coincide a useful application of this method is in the calculation of mutual impedance between printed dipoles

rate of convergence for the modified szasz mirakyan operators on functions of bounded variation in this paper we obtain an estimate of the rate of convergence of modified szasz mirakyan operators on functions of bounded variation our result essentially improves the results due to a sahai and g prasad 1993 publ inst math beograd n s 53 73 80 and v gupta and p n agrawal 1991 publ inst math beograd n s 49 97 103

hybrid projective synchronization and control of the baier sahle hyperchaotic flow in arbitrary dimensions with unknown parameters the problem of hybrid projective synchronization hps strategies and control for the baier sahle hyperchaotic flow in arbitrary dimensions with unknown parameters is considered based on the lasalle invariance principle and adaptive control method adaptive controllers and parameters update laws are given for the hps between two identical hyper chaotic systems with fully unknown parameters using this method the baier sahle hyperchaotic flow in arbitrary dimensions is controlled to the unsteady equilibrium points the baier sahle hyperchaotic flow is a useful choice for this analysis since it is a standard model of hyperchaos yet it is simple enough to be analytically tractable in particular the baier sahle hyperchaotic flow has been proposed as an n dimensional nonlinear system model giving the maximal number of positive lyapunov exponents n 2 both a rigorous theoretical analysis and direct numerical simulations are provided to demonstrate the control of hyperchaos in this model the results suggest that the methods used here can be applied to more complicated models from which hyperchaos arises

analytical evaluation of the asymptotic impedance matrix of a grounded dielectric slab with roof top functions an analytical technique is derived to solve the asymptotic part of impedance matrix elements for printed circuit structures using roof top subdomain expansions the key to this problem is the analytical transformation from an infinite double integral to a suitable finite one dimensional 1 d integral the newly developed formula is applied to the monostatic radar cross section rcs of a microstrip patch comparisons are made with measurements and conventional method of moments predictions

on the rate of convergence of the generalized szasz type operators for functions of bounded variation abstract in this article we introduce the szasz bezier operatorsn which is the modified form of the szasz mirakyan operator by means of construction of suitable functions and the methods of bojanic vuillemier j approx theory31 1981 67 79 and cheng j approx theory40 1984 226 241 using some results and techniques of probability theory we obtain the rate of convergence ofsn for functions of bounded variation our results extend and sharpen the results of cheng j approx theory40 1984 226 241 guo and khan j approx theory58 1989 90 101 for the szasz mirakyan operator