sharp inequalities that generalize the divergence theorem an extension of the notion of quasi convexity subject to suitable boundary conditions being imposed sharp inequalities are obtained on integrals over a region of certain special quadratic functions f e where e x derives from a potential u

semigroup structural form for bernstein type operators and its applications in this note we provide a semigroup viewpoint for bernstein type operators a main ingredient of our approach is to obtain some explicit semigroup representation formulae which as simple forms are proposed for the fist time as direct applications we improve the corresponding results of de la cal and luquin 1992 1994 moreover some kinds of voronovskaja type results are made by using general semigroup expansion in the end we discuss corresponding generalizations of integral operators with some examples of hybrid durrmeyer type operators

an identification algorithm for polynomial narx models based on simulation error minimization classical prediction error approaches for the identification of non linear polynomial narx narmax models often yield unsatisfactory results for long range prediction or simulation purposes mainly due to incorrect or redundant model structure selection the paper discusses some limitations of the standard approach and suggests two modifications namely a new index based on the simulation error is employed as the regressor selection criterion and a pruning mechanism is introduced in the model selection algorithm the resulting algorithm is shown to be effective in the identification of compact and robust models generally yielding model structures closer to the correct ones computational issues are also discussed finally the identification algorithm is tested on a long range prediction benchmark application

stancu kantorovich operators based on inverse polya eggenberger distribution the purpose of this paper is to investigate approximation properties of stancu kantorovich operators based on inverse polya eggenberger distribution for these new operators we establish some approximation properties including uniform convergence asymptotic formula and degree of approximation

approximation by kantorovich form of modified szszmirakyan operators in the present article we consider the kantorovich type generalized szszmirakyan operators based on jain and pethe operators 32 we study local approximation results in terms of classical modulus of continuity as well as ditziantotik moduli of smoothness further we establish the rate of convergence in class of absolutely continuous functions having a derivative coinciding a e with a function of bounded variation

towards characterization of all 3 3 extremal quasiconvex quadratic forms given a d d quasiconvex quadratic form d 3 we prove that if the determinant of its acoustic tensor is an irreducible extremal polynomial that is not identically zero then the form itself is an extremal quasiconvex quadratic form i e it loses its quasiconvexity whenever a convex quadratic form is subtracted from it in the special case d 3 we slightly weaken the condition namely we prove that if the determinant of the acoustic tensor of the quadratic form is an extremal polynomial that is not a perfect square then the form itself is an extremal quadratic form in the case d 3 we also prove that if the determinant of the acoustic tensor of the form is identically zero then the form is either extremal or polyconvex also if the determinant of the acoustic tensor of the form is a perfect square then the form is either extremal or polycovex or is a sum of a rank 1 form and an extremal whose acoustic tensor determinant is identically zero here we use the notion of extremality introduced by milton in 1990 2017 wiley periodicals inc

some approximation properties of q durrmeyer operators in the present paper we introduce a simple q analogue of well known durrmeyer operators we first estimate moments of q durrmeyer operators we also establish the rate of convergence for q durrmeyer operators

system impulse response identification using a multiresolution neural network abstract this paper proposes a new identification method for the discrete time impulse response model of a linear system from sampled input output data our attention is especially focused on identification of the impulse response which includes high frequency components locally the continuous time impulse response of the system is approximated by a multiresolution neural network composed of the scaling and wavelet functions hence the system under study can be viewed as the weighted sum of a group of subsystems in which the scaling functions and wavelet functions are interpreted as their impulse responses respectively then the genetic algorithm and the aic are introduced to select significant subsystems at each resolution level such that some redundant subsystems that are sensitive to the noise effects are discarded it is shown through a simulation that the proposed method yields accurate estimate of the impulse response even in the ill conditioned cases 1997 elsevier science ltd

extended model set global data and threshold model identification of severely non linear systems abstract new parameter estimation algorithms based on an extended model set a global data model and a threshold model formulation are derived for identifying severely non linear systems it is shown that in each case an integrated structure determination and parameter estimation algorithm based on an orthogonal decomposition of the regression matrix can be derived to provide procedures for identifying parsimonious models of unknown systems with complex structure simulation studies are included to illustrate the techniques discussed

approximation properties of bezier summation integral type operators based on polya bernstein functions in this article we introduce the bezier variant of summation integral type operators having polya and bernstein basis functions we give a direct approximation theorem by means of the first order modulus of smoothness and the rate of convergence for absolutely continuous functions having a derivative equivalent to a function of bounded variation

on the relation between extremal elasticity tensors with orthotropic symmetry and extremal polynomials we prove that an elasticity tensor with orthotropic symmetry is extremal if the determinant of its acoustic tensor is an extremal polynomial that is not a perfect square

persistent excitation in bilinear systems discrete time systems described by difference equations which are polynomial in the input and linear in the output are discussed bilinear systems are special members of this class two issues are examined first a multidimensional polynomial based algebraic condition which is necessary and sufficient for such systems to be identifiable is given second subject to an identifiability assumption a condition on the input sequence which guarantees persistent excitation is given the principle analytic tool used in this study involves multidimensional polynomials

identification of a class of nonlinear continuous time systems using hartley modulating functions most of the existing approaches to identification of nonlinear dynamic systems involve matching a given input output behaviour with empirical discrete time approximations such as artificial neural networks kolmogorov gabor polynomials radial basis function networks etc techniques for dealing with physically based continuous time models are either applicable to only a restricted class of systems or are computationally very demanding in this paper a new methodology is presented that is applicable to a large class of nonlinear continuous time systems by defining a set of hartley modulating functions for characterizing the continuous process signals the advantages of this new class of modulating functions are that a set of algebraic equations with real coefficients results the formulations are free from boundary conditions and the computations can be made using fast algorithms for the discrete hartley transformation the resulting estimation scheme is applied to different categories of nonlinear syst

szasz durrmeyer type operators based on charlier polynomials in the present paper we introduce a durrmeyer type modification of szasz operators based on charlier polynomials and study a voronovskaja type asymptotic theorem local approximation theorem weighted approximation statistical convergence and approximation of functions with derivatives of bounded variation for these operators

certain new classes of durrmeyer type operators in the present paper we estimate the rate of convergence for functions having bounded derivatives for certain durrmeyer type generalization of jain and pethe operators in the last section we also propose a new modification of the lupas operators and study some direct results we also give some open problems for the readers

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

identification of non linear system structure and parameters using regime decomposition abstract an off line algorithm for empirical modeling and identification of non linear dynamic systems is presented the minimal input to the algorithm is a sequence of empirical data and the model order using this information the algorithm searches for an optimal model structure and parameters within a rich non linear model set the model representation is based on the interpolation of a number of simple local models where each local model has a limited range of validity but the local models yield a complete global model when interpolated the method is illustrated using simulated data

a new route to finding bounds on the generalized spectrum of many physical operators here we obtain bounds on the generalized spectrum of that operator whose inverse when it exists gives green s function we consider the wide range of physical problems that can be cast in a form where a constitutive equation j x l x e x h x with a source term h x holds for all x in some domain and relates fields e and j that satisfy appropriate differential constraints symbolized by e e 0 and j j where e 0 and j are orthogonal spaces that span the space h of square integrable fields in which h lies boundedness and coercivity conditions on the moduli l x ensure that there exists a unique e for any given h i e e g h which then establishes the existence of green s function g we show that the coercivity condition is guaranteed to hold if weaker conditions involving generalized quasiconvex functions are satisfied the advantage is that these weaker conditions are easier to verify and for multiphase materials they can be independent of the geometry of the phases for l x depending linearly on a vector of parameters z z1 z2 zn we obtain constraints on z that ensure that green s function exists and hence which provide bounds on the generalized spectrum here we obtain bounds on the generalized spectrum of that operator whose inverse when it exists gives green s function we consider the wide range of physical problems that can be cast in a form where a constitutive equation j x l x e x h x with a source term h x holds for all x in some domain and relates fields e and j that satisfy appropriate differential constraints symbolized by e e 0 and j j where e 0 and j are orthogonal spaces that span the space h of square integrable fields in which h lies boundedness and coercivity conditions on the moduli l x ensure that there exists a unique e for any given h i e e g h which then establishes the existence of green s function g we show that the coercivity condition is guaranteed to hold if weaker conditions involving generalized quasiconvex functions are satisfied the advantage is that these weaker conditions are easier to verify and for multiphase materials they can be independent of the geometry of the phases for l x depend

application and comparison of different identification schemes under industrial conditions two new identification procedures based on different strategies are presented to determine a mathematical model for the crude iron quality of a blast furnace process the first algorithm estimates the parameters of a common linear difference equation model based on identification results obtained from separate series of data with given model structure prior to complete estimation of the parameters the second method automatically detects the significant terms of a general model to optimally characterize a linear or non linear system the process is described by a general discrete polynomial expansion of past and present input signals and past output signals this algorithm is based on orthogonalization and application of several information criteria a comparison of the prediction accuracy of the linear model obtained from the first method with the linear and non linear model resulting from the second algorithm and with models developed by other identification procedures is presented and some experiences

bounds on the volume fractions of two materials in a three dimensional body from boundary measurements by the translation method using the translation method of tartar murat lurie and cherkaev bounds are derived on the volume occupied by an inclusion in a three dimensional conducting body the bounds assume that electrical impedance tomography measurements have been made for three sets of pairs of current flux and voltage measurements around the boundary additionally the conductivity of the inclusion and the conductivity of the surrounding medium are assumed to be known if the boundary data dirichlet or neumann is special i e such that the fields inside the body would be uniform were the body homogeneous then the bounds reduce to those of milton and thus when the volume fraction is small to those of capdeboscq and vogelius

on certain q durrmeyer type operators very recently gupta and heping v gupta w heping the rate of convergence of q durrmeyer operators for 0 q 1 math meth appl sci 31 16 2008 1946 1955 introduced certain q durrmeyer type operators and established some approximation properties in the present paper we study some direct results for the certain q durrmeyer type operators

direct estimates for certain szasz type operators we deal with the modified forms of the szasz basis functions we introduce a new sequence of linear positive operators of durrmeyer type direct estimates for the new sequence have been discussed an open problem is also proposed the present paper deals with the modified forms of the szasz basis functions we propose a durrmeyer type operator having the basis functions in summation and integration due to jain 1972 and pa lta nea 2008 we establish some direct results which include the asymptotic formula and error estimation in terms of the modulus of continuity and weighted approximation in the end we give an open problem for the readers

statistical approximation of a kind of kantorovich type q szasz mirakjan operators abstract in the present paper we introduce a kantorovich type generalization of the q szasz mirakjan operators and investigate their a statistical approximation properties also the rate of a statistical convergence of the proposed sequence of linear positive operators is obtained by a weighted modulus of continuity

addendum to sharp inequalities that generalize the divergence theorem an extension of the notion of quasi convexity the paper sharp inequalities that generalize the divergence theorem an extension of the notion of quasi convexity published in proc r soc a 2013 469 20130075 doi 10 1098 rspa 2013 0075 is c

on statistical approximation of a general class of positive linear operators extended in q calculus in this paper we present a general class of positive linear operators of discrete type based on q calculus and we investigate their weighted statistical approximation properties by using a bohman korovkin type theorem we also mark out two particular cases of this general class of operators

bounds on the size of an inclusion using the translation method for two dimensional complex conductivity the size estimation problem in electrical impedance tomography is considered when the conductivity is a complex number and the body is two dimensional upper and lower bounds on the volume fraction of the unknown inclusion embedded in the body are derived in terms of two pairs of voltage and current data measured on the boundary of the body these bounds are derived using the translation method we then show by numerical examples that these bounds are quite tight and stable under measurement noise

weighted statistical approximation by kantorovich type q szasz mirakjan operators abstract in the present paper we introduce a kantorovich type modification of q szasz mirakjan operators and obtain weighted statistical approximation properties of these operators also for introduced operators we give a voronovskaja type theorem related to q derivatives

jain durrmeyer operators associated with the inverse polya eggenberger distribution the present paper deals with the jain durrmeyer operators based on inverse polya eggenberger distribution first we give the moments with the help of vandermonde convolution formula and then study approximation properties of these operators which include uniform convergence and degree of approximation

the inverse conductivity problem with one measurement bounds on the size of the unknown object we consider the problem of determining within an electrically conducting body omega of conductivity sigma equiv 1 an unknown inclusion d whose conductivity is sigma equiv k neq 1 when one pair of current density and voltage measurements from the exterior of omega is available we prove upper and lower bounds on the size of the unknown inclusion d we also consider the case of nonuniform and nonisotropic conductivities in omega and in d

on the integrated baskakov type operators the present paper deals with the study of the rate of convergence of the integrated baskakov durrmeyer type operators in simultaneous approximation we also mention some of the improvements on the recent paper of deo n deo direct results on exponential type operators applied mathematics and computation 204 1 2008 109 115

rate of convergence of lupas kantorovich operators based on polya distribution in the present paper we consider the kantorovich modification of lupas operators based on polya distribution we estimate the rate of convergence for absolutely continuous functions having a derivative coinciding a e with a function of bounded variation

stancu type generalization of q favard sziasz operators in this paper we introduce a stancu type generalization of q favard szi sz operators estimate the rates of convergence and study the local approximation properties of these operators

application of a general multi model approach for identification of highly nonlinear processes a case study an identification method for highly nonlinear processes is proposed based on a multi model approach and kolmogorov gabor polynomials owing to the large number of possible terms in this general model structure the significant terms are selected by several statistical test procedures leading automatically to a minimal order model realization the performance of this method is evaluated in an in depth case study using a simulated ph neutralization process the effects of important variables such as range of operating conditions signal noise ratio and data length are discussed

quantitative convergence results for a family of hybrid operators we introduce a one parameter family of hybrid operators and study quantitative convergence theorems for these operators e g local and weighted approximation results and simultaneous approximation of derivatives further we discuss the statistical convergence of these operators lastly we show the rate of convergence of these operators to a certain function by illustrative graphics in matlab

approximation for genuine summation integral type link operators in the present article we extend the studies on recently introduced sequence of the genuine summation integral type operators 7 here we establish a link between the genuine operators and the discrete operators we also establish a quantitative asymptotic formula a direct estimate in terms of ditzian totik modulus of smoothness and finally we present the rate of convergence for functions having derivatives of bounded variation

generalized baskakov szasz type operators abstract in the present paper we introduce generalized baskakov szasz type operators and study some approximation properties of these operators e g rate of convergence in ordinary and simultaneous approximation statistical convergence and the estimate of the rate of convergence for absolutely continuous functions having a derivative coinciding a e with a function of bounded variation

on characterizing the set of possible effective tensors of composites the variational method and the translation method a general algebraic framework is developed for characterizing the set of possible effective tensors of composites a transformation to the polarization problem simplifies the derivation of the hashin shtrikman variational principles and simplifies the calculation of the effective tensors of laminate materials a general connection is established between two methods for bounding effective tensors of composites the first method is based on the variational principles of hashin and shtrikman the second method due to tartar murat lurie and cherkaev uses translation operators or equivalently quadratic quasiconvex functions a correspondence is established between these translation operators and bounding operators on the relevant non local projection operator t1 an important class of bounds namely trace bounds on the effective tensors of two component media are given a geometrical interpretation after a suitable fractional linear transformation of the tensor space each bound corresponds to a tangent plane to the set of possible tensors a wide class of translation operators that generate these bounds is found the extremal translation operators in this class incorporate projections onto spaces of antisymmetric tensors these extremal translations generate attainable trace bounds even when the tensors of the two components are not well ordered in particular they generate the bounds of walpole on the effective bulk modulus the variational principles of gibiansky and cherkaev for bounding complex effective tensors are reviewed and used to derive some rigorous bounds that generalize the bounds conjectured by golden and papanicolaou an isomorphism is shown to underlie their variational principles this isomorphism is used to obtain dirichlet type variational principles and bounds for the effective tensors of general non selfadjoint problems it is anticipated that these variational principles which stem from the work of gibiansky and cherkaev will have applications in many fields of science

durrmeyer type modification of generalized baskakov operators abstract in the present paper durrmeyer type modification of generalized baskakov operators is introduced and some direct results are established for these operators

weighted approximation by a certain family of summation integral type operators in this study we investigate the weighted approximation properties of a general sequence of summation integral type operators introduced by srivastava and gupta 1 we estimate the rate of convergence of these operators for functions of polynomial growth in terms of weighted modulus of continuity on the interval 0

approximation of discontinuous signals by sampling kantorovich series abstract in this paper the behavior of the sampling kantorovich operators has been studied when discontinuous functions signals are considered in the above sampling series moreover the rate of approximation for the family of the above operators is estimated when uniformly continuous and bounded signals are considered finally several examples of duration limited kernels which satisfy the assumptions of the present theory have been provided and also the problem of the linear prediction by sampling values from the past is analyzed

approximation of baskakov type polya durrmeyer operators in the present paper we propose the durrmeyer type modification of baskakov operators based on inverse polya eggenberger distribution first we estimate a recurrence relation by using hypergeometric series we give a global approximation theorem in terms of second order modulus of continuity a direct approximation theorem by means of the ditzian totik modulus of smoothness and a voronovskaja type theorem some approximation results in weighted space are obtained also we show the rate of convergence of these operators to certain functions by illustrative graphics using the maple algorithms

identification of mimo non linear systems using a forward regression orthogonal estimator abstract an orthogonal least squares estimator which was originally derived for single input single output systems is extended to multi input multi output non linear systems the estimator can provide information about the structure or which terms to include in the model and final parameter estimates in a very simple and efficient manner multivariable non linear model validity tests are also discussed and the results of applying the orthogonal estimator to both simulated and real data are included

structure identification of nonlinear dynamic systems a survey on input output approaches abstract in the past several methods have been elaborated for the identification of nonlinear dynamic systems most of the methods assume that the structure of the system is given a priori therefore they are in reality parameter estimation algorithms and structure identification is thus usually performed by repeated parameter estimation however in nonlinear system theory several methods are known to determine the structure of a system in this paper structure identification of block oriented especially cascade models of semi linear dynamic models with signal dependent parameters and of nonlinear dynamic models being linear in the parameters will be considered different structure selection methods are summarized based on step and impulse tests frequency response measurements correlation analysis repeated reproducible tests and normal operating data

pointwise approximation by bernstein type operators in mobile interval abstract in the present paper we study pointwise approximation by bernstein durrmeyer type operators in the mobile interval x 0 1 1 n 1 with use of peetre s k functional and 2 f t 0 1 we give its properties and obtain the direct and inverse theorems for these operators

efficient algorithms for volterra system identification in this paper nonlinear filtering and identification based on finite support volterra models are considered the volterra kernels are estimated via input output statistics or directly in terms of input output data it is shown that the normal equations for a finite support volterra system excited by zero mean gaussian input have a unique solution if and only if the power spectral process of the input signal is nonzero at least at m distinct frequencies where m is the memory of the system a multichannel embedding approach is introduced a set of primary signals defined in terms of the input signal serve to map efficiently the nonlinear process to an equivalent multichannel format efficient algorithms for the estimation of the volterra parameters are derived for batch as well as for adaptive processing an efficient order recursive method is presented for the determination of the volterra model structure the proposed methods are illustrated by simulations