measuring the strangeness of strange attractors we study the correlation exponent v introduced recently as a characteristic measure of strange attractors which allows one to distinguish between deterministic chaos and random noise the exponent v is closely related to the fractal dimension and the information dimension but its computation is considerably easier its usefulness in characterizing experimental data which stem from very high dimensional systems is stressed algorithms for extracting v from the time series of a single variable are proposed the relations between the various measures of strange attractors and between them and the lyapunov exponents are discussed it is shown that the conjecture of kaplan and yorke for the dimension gives an upper bound for v various examples of finite and infinite dimensional systems are treated both numerically and analytically

a class of markov type operators which preserve e j j 1 abstract in this paper we construct a class of markov type operators which preserve e j j 1 we give a recurrence relation for the moments of this operator and study the convergence we show the uniform convergence of the derivative of order r 0 of the operator a voronovskaya formula and some inequalities are presented

optimal shadowing and noise reduction abstract the shadowing problem is that of finding a deterministic orbit as close as possible to a given noisy orbit we present an optimal solution to this problem in the sense of least mean squares which also provides an effective and convenient numerical method for noise reduction for data generated by a dynamical system given a noisy orbit y and a dynamical system we derive a set of nonlinear equations whose solution x is the deterministic orbit with the smallest possible euclidean distance to y we present a numerical method for solving these equations the quality of the solution depends on the initial noise level when is known exactly the noise can be reduced to machine precision over long trajectory segments with higher noise levels there are regions where the algorithm has difficulty but significant overall noise reductions are still achieved if must be learned from the data the noise reduction is limited by the accuracy of the learning algorithm and the number of available data points but large reductions are still possible in some cases

sufficient matrices and the linear complementarity problem abstract we pose and answer two questions about solutions of the linear complementarity problem lcp the first question is concerned with the conditions on a matrix m which guarantee that for every vector q the solutions of the lcp q m are identical to the karush kuhn tucker points of the natural quadratic program associated with q m in answering this question we introduce the class of row sufficient matrices the transpose of such a matrix is what we call column sufficient the latter matrices turn out to furnish the answer to our second question which asks for the conditions on m under which the solution set of q m is convex for every q in addition to these two main results we discuss the connections of these twonew matrix classes with other well known matrix classes in linear complementarity theory

on the uniqueness of solutions to linear complementarity problems this paper characterizes the classu of all realn n matricesm for which the linear complementarity problem q m has a unique solution for all realn vectorsq interior to the conek m of vectors for which q m has any solution at all it is shown that restricting the uniqueness property to the interior ofk m is necessary because whenu the problem q m has infinitely many solutions ifq belongs to the boundary of intk m it is shown thatm must have nonnegative principal minors whenu andk m is convex finally it is shown that whenm has nonnegative principal minors only one of which is 0 andk m r n thenu andk m is a closed half space

calculation of lyapunov exponents avoiding spurious elements abstract a new approach to evaluate lyapunov exponents from time series is discussed with the help of this approach the number of calculated lyapunov exponents can be reduced to the physically relevant ones calculations in high dimensional embedding spaces are performed on smaller data bases with improved speed more direct information is obtained from the dynamics of the underlying dynamical system

asymptotic formulas for generalized szasz mirakyan operators in the present paper we consider the general szasz mirakyan operators and investigate their asymptotic behaviours we obtain quantitative voronovskaya and quantitative gruss type voronovskaya theorems using the weighted modulus of continuity the particular cases are presented for classical szasz mirakyan operators

approximation and geometric properties of complex favard szasz mirakjan operators in compact disks in this paper first we obtain quantitative estimates of the convergence and of the voronovskaja s theorem in compact disks for complex favard szasz mirakjan operators attached to analytic functions satisfying some suitable exponential type growth condition then we prove that beginning with an index these operators preserve the starlikeness convexity and spirallikeness in the unit disk

bernstein type operators with a better approximation for some functions in this paper we construct new operators of bernstein type with a better approximation than the classical bernstein operator for some classes of functions on the whole interval 0 1 convergence of these operators and their shape preserving properties are discussed we determine the subintervals in 0 1 in which the approximation order of constructed operators is better than that of the bernstein operator for an arbitrary continuous function on the interval 0 1 finally we present comparisons with other two bernstein type operators

optimality of piecewise τ linear interpolating operators we show an optimality property of the piecewise t linear interpolating operator within a general class of linear positive operators

new characterizations of row sufficient matrices in dealing with a linear complementarity problem much depends on knowing that the matrix through which the particular lcp is defined belongs to a suitable matrix class two such classes are su the so called sufficient matrices and l which were introduced in r w cottle j s pang v venkateswaran sufficient matrices and the linear complementarity problem linear algebra appl 114 115 1989 231 249 b c eaves the linear complementarity problem manage sci 17 1971 612 634 respectively in an earlier article i adler r w cottle s verma sufficient matrices belong to l math prog 106 2006 391 401 the authors proved that su is a subclass of l by definition the class su is the intersection of two distinct classes rsu the row sufficient matrices and csu the column sufficient matrices in the present work we strengthen the aforementioned inclusion by showing that all row sufficient matrices belong to l using what we call structural properties of certain matrix classes we add to the existing characterizations of rsu in r w cottle s m guu two characterizations of sufficient matrices linear algebra appl 170 1992 65 74 s m guu r w cottle on a subclass of p0 linear algebra appl 223 224 1995 325 335 h valiaho criteria for sufficient matrices linear algebra appl 233 1996 109 129 this line of inquiry was inspired by asking what must be true of a row sufficient l matrix we establish three new characterizations of rsu in terms of the matrix classes l e0 and q0 and the structural properties of sign change invariance completeness and fullness the new characterizations of rsu provide new characterizations of su by adjoining a fourth structural property we call reflectiveness

counterexamples to q matrix conjectures abstract a matrix m r n n is in the class q if for all q r n there exist w z r n such that w mz q wtz 0 it has been conjectured that it is possible to tell if a matrix m is in q solely by considering the signs of subdeterminants of m we present two matrices that have the same signs of corresponding subdeterminants but are such that one is in q and the other is not the second of these two matrices has the property that every column of the matrix i m is in the interior of the union of the complementary cones associated with i m

fully copositive matrices the class of fully copositive c 0 f matrices introduced in g s r murthy t parthasarathy siam journal on matrix analysis and applications 16 4 1995 1268 1286 is a subclass of fully semimonotone matrices and contains the class of positive semidefinite matrices it is shown that fully copositive matrices within the class ofq 0 matrices arep 0 matrices as a corollary of this main result we establish that a bisymmetricq 0 matrix is positive semidefinite if and only if it is fully copositive another important result of the paper is a constructive characterization ofq 0 matrices within the class ofc 0 f while establishing this characterization it will be shown that graves s principal pivoting method of solving linear complementarity problems lcps with positive semidefinite matrices is also applicable toc 0 f q 0 class as a byproduct of this characterization we observe that ac 0 f matrix is inq 0 if and only if it is completelyq 0 also from aganagic and cottle s m aganagic r w cottle mathematical programming 37 1987 223 231 result it is observed that lcps arising fromc 0 f q 0 class can be processed by lemke s algorithm 1998 the mathematical programming society inc published by elsevier science b v

a constructive characterization of q 0 matrices with nonnegative principal minors in 2 we characterized the class of matrices with nonnegative principla minors for which the linear complementarity problem always has a solution that class is contained in the one we study here our main result gives a finitely testable set of necessary and sufficient conditions under which a matrix with nonnegative principal minors has the property that if a corresponding linear complementarity problem is feasible then it is solvable in short we constructively characterize the matrix class known asqo po

sufficient matrices belong to l in this paper we establish a significant matrix class inclusion that seems to have been overlooked in the literature of the linear complementarity problem we show that p the class of sufficient matrices is a subclass of l in the course of demonstrating this inclusion we introduce other new matrix classes that forge interesting new connections between known matrix classes

approximation properties of bernstein durrmeyer type operators abstract this paper deals with the approximation of continuous functions by sequences of some modified bernstein durrmeyer type operators that reproduce certain test functions the orders of approximation of the new versions turn to be at least as good as the one of the genuine bernstein durrmeyer operators moreover by extrapolating techniques recently applied to the classical bernstein operators we present a one parameter family of modified sequences of operators that reproduce certain polynomials and possess that popular genuine sequence as a limit case comparisons and some illustrative graphics are also presented

the norm estimates of the q bernstein operators for varying q 1 the aim of this paper is to present norm estimates in c 0 1 for the q bernstein basic polynomials and the q bernstein operators b n q in the case q 1 while for 01 the norm b n q increases rather rapidly as q in this study it is proved that b n q c nq n n 1 2 q withc n 2n 1 1n n 1 moreover it is shown that b n q 2q n n 1 2ne as n q the results of the paper are illustrated by numerical examples

a partial characterization of a class of matrices defined by solutions to the linear complementarity problem in this paper we analyze the class of matrices q0 characterized as all n n matrices m for which the linear complementarity problem w mz q w z 0 w z 0 has a solution whenever q is feasible the method is to analyze the faces of the linear cone cone i m where i is the n n identity essentially a labelling requirement for the faces is shown necessary for m to be in q0 with proper restrictions and nondegenerate assumptions sufficiency is also shown these results arc related to the signs of the minors of m and some conjectures in this area are also discussed

a note on approximation properties of q durrmeyer operators in this paper the approximation properties of q durrmeyer operators d n q f x for f c 0 1 are discussed the exact class of continuous functions satisfying approximation process lim n d n q f x f x is determined the results of the paper provide an elaboration of the previously known ones on operators d n q

a finite improvement algorithm for the linear complementarity problem abstract this paper is concerned with the development of an improvement algorithm for the linear complementarity problem lcp our approach to find a solution to lcp is to solve the equivalent constrained optimization problem cop of maximizing the sum of the minimum of each complementary pair of variables subject to the constraints that each such minimum is nonpositive the algorithm ascent in nature is similar to the simplex method in the sense that it moves between basic points of an associated system of linear equations these basic points are feasible to our cop whose objective function is piecewise linear and concave classes of matrices are characterized for which our algorithm processes lcp for every right hand side vector and every matrix in the class a computational study shows that our algorithm is clearly superior to a previos improvement algorithm computational comparisons with lemke s well known algorithm are also presented

bifurcations with imperfect so 2 symmetry and pinning of rotating waves rotating waves are periodic solutions in so 2 equivariant dynamical systems their precession frequency changes with parameters and it may change sign passing through zero when this happens the

dunkl analogue of szasz operators abstract the main purpose of this paper is to construct linear positive operators generated by dunkl generalization of exponential function we present qualitative result with the help of universal korovkin type theorem and weighted korovkin type theorem and also get quantitative estimates in terms of classical modulus of continuity the class of lipschitz functions peetre s k functional second order modulus of continuity and weighted modulus of continuity by dunkl analogue of szasz operators

the basic theorem of complementarity revisited the basic theorm of linear complementarity was stated in a 1971 paper 6 by b c eaves who credited c e lemke for giving a constructive proof based on his almost complementary pivot algorithm this theorem asserts that associated with an arbitrary linear complementarity problem a certain augmented problem always possesses a solution many well known existence results pertaining to the linear complementarity problem are consequences of this fundamental theorem in this paper we explore some further implications of the basic theorem of complementarity and derive new existence results for the linear complementarity problem based on these results conditions for the existence of a solution to a linear complementarity problem with a fully semimonotone matrix are examined the class of the linear complementarity problems with ag matrix is also investigated

properties of convergence for ω q bernstein polynomials in this paper we discuss properties of the q bernstein polynomials bn q f x introduced by s lewanowicz and p wo ny in s lewanowicz p wo ny generalized bernstein polynomials bit 44 1 2004 63 78 where f c 0 1 q 0 1 q 1 q n 1 when 0 we recover the q bernstein polynomials introduced by g m phillips bernstein polynomials based on the q integers ann numer math 4 1997 511 518 when q 1 we recover the classical bernstein polynomials we compute the second moment of bn q t2 x and demonstrate that if f is convex and q 0 1 or 1 then bn q f x are monotonically decreasing in n for all x 0 1 we prove that for 0 1 qn 0 1 the sequence bn qn f n 1 converges to f uniformly on 0 1 for each f c 0 1 if and only if limn qn 1 for fixed q 0 1 we prove that the sequence bn q f converges for each f c 0 1 and obtain the estimates for the rate of convergence of bn q f by the modulus of continuity of f and the estimates are sharp in the sense of order for lipschitz continuous functions

approximation properties of complex q szasz mirakjan operators in compact disks this paper deals with approximating properties of the newly defined q generalization of the szasz mirakjan operators in the case q 1 quantitative estimates of the convergence the voronovskaja s theorem and saturation of convergence for complex q szasz mirakjan operators attached to analytic functions in compact disks are given in particular it is proved that for functions analytic in email protected c z 2q the rate of approximation by the q szasz mirakjan operators q 1 is of order q n versus 1 n for the classical szasz mirakjan operators

on hidden z matrices and the linear complementarity problem abstract in this paper we explore various matrix theoretic aspects of the hidden z class and demonstrate how the concept of principal pivot transform can be effectively used to extend many existing results in fact we revisit various results obtained for hidden z class by mangasarian cottle and pang in context of solving linear complementarity problems as linear programs we identify hidden z matrices of special category and discuss the number of solutions of the associated linear complementarity problems we also present game theoretic interpretation of various results related to hidden z class and obtain proofs following the game theoretic approach of raghavan for a subclass of z matrices

a finite characterization of k matrices in dimensions less than four the class of real n n matrices m known as k matrices for which the linear complementarity problem w mz q w 1 o z 1 o wtz 0 has a solution whenever w mz q w i o z 1 0 has a solution is characterized for dimensions n 4 the characterization is finite and practical several necessary conditions sufficient conditions and counterexamples pertaining to k matrices are also given a finite characterization of completely k matrices k matrices all of whose principal submatrices are also k matrices is proved for dimensions 4

q bernstein polynomials of the cauchy kernel due to the fact that in the case q 1 q bernstein polynomials are not positive linear operators on c 0 1 the study of their approximation properties is essentially more difficult than that for 0 1 is still open in this paper the q bernstein polynomials bn q fa z of the cauchy kernel fa 1 z a a c 0 1 are found explicitly and their properties are investigated in particular it is proved that if q 1 then polynomials bn q fa z converge to fa uniformly on any compact set k z z a the sequence bn q fa z is not even uniformly bounded

on the transpose of a pseudomonotone matrix and the lcp abstract in the study of linear complementary problem it is known that pseudomonotone matrices belong to the class p 0 q 0 in this note we show that under certain conditions such as invertibility or normality the transpose of a pseudomonotone matrix belongs to the class q 0

a nonlinear dynamical systems analysis of fricative consonants acoustic waveforms of the strident fricatives s z sh and yog spoken by two native american english speakers are analyzed using modern chaotic analysis techniques fricative data are extracted from both intervocalic and sustained utterances for comparison acoustic waveforms of the vowels a i and u are also analyzed for 44 of the unvoiced fricative tokens in vcv contexts and 59 of the sustained voiced fricatives indications of low dimensional dynamics could be found with the given limitations of stationarity the low dimensional chaotic behavior is exhibited by a correlation dimension d2 ranging between 3 and 7 2 and by positive maximum lyapunov exponents les for the remaining fricatives results suggest that the dimensional complexity therein is greater than the maximum d2 value that could be reliably estimated from the available data about 7 8 for the intervocalic cases and 9 for the sustained cases intervocalic voiced fricatives are excluded from the analysis due to stat

q matrix recognition via secondary and universal polytopes mx q 0 mx q 0 x 0 has a solution we explain how one can use the polyhedral structure of the set of all triangulations of a finite point set to determine if an n n matrix m is a q matrix our implementation of the algorithm is practical for deciding the q nature for all m with n 8

saturation of convergence for q bernstein polynomials in the case q 1 abstract in the note we discuss voronovskaya type theorem and saturation of convergence for q bernstein polynomials for a function analytic in the disc u r z z r r q for arbitrary fixed q 1 we give explicit formulas of voronovskaya type for the q bernstein polynomials for q 1 we show that the rate of convergence for the q bernstein polynomials is o q n q 1 for infinite number of points having an accumulation point on u r q if and only if f is linear

asymptotic properties of powers of linear positive operators which preserve e2 in this paper we prove korovkin type theorem for iterates of general positive linear operators t c 0 1 c 0 1 which preserve e 2 and derive quantitative estimates in terms of moduli of smoothness the results can be applied to several well known operators we present here the bernstein the q bernstein the genuine bernstein durrmeyer and the genuine q bernstein durrmeyer operators

necessary and sufficient conditions for the existence of complementary solutions and characterizations of the matrix classes q and q q we simplify a result by mangasarian on the existence of solutions to the linear complementarity problem the simplified condition gives a new geometric interpretation of the result when used to characterize the matrix classesq andq0 our condition suggests a finitely checkable sufficient condition forp andp0

approximation in compact sets by q stancu faber polynomials q 1 we prove that the q stancu faber polynomials q 1 attached to a compact set email protected c and to an analytic function on g can represent good alternatives to the partial sums of the faber series attached to the same function and subset both giving the geometric progression order of approximation q n

shape preserving properties of generalized bernstein operators on extended chebyshev spaces we study the existence and shape preserving properties of a generalized bernstein operator b n fixing a strictly positive function f 0 and a second function f 1 such that f 1 f 0 is strictly increasing within the framework of extended chebyshev spaces u n the first main result gives an inductive criterion for existence suppose there exists a bernstein operator b n c a b u n with strictly increasing nodes fixing f 0 f 1 in u n if u n subset u n 1 and u n 1 has a non negative bernstein basis then there exists a bernstein operator b n 1 c a b u n 1 with strictly increasing nodes fixing f 0 and f 1 in particular if f 0 f 1 f n is a basis of u n such that the linear span of f 0 f k is an extended chebyshev space over a b for each k 0 n then there exists a bernstein operator b n with increasing nodes fixing f 0 and f 1 the second main result says that under the above assumptions the following inequalities hold b n f geq b n 1 f geq f furthermore b nf is f0 f1 convex for all f0 f1 convex functions f in c a b

a homological characterization of q matrices a real square matrix m is said to be a q matrix if the linear complementarity problem q m has a solution for every vector q there is as yet no characterization of q matrices which makes it easy to determine whether or not a given matrix is q ideas from topology in particular degreetheory have previously been used to obtain sufficient conditions for when a matrix is q in this paper we will apply some other ideas from topology to give a homological characterization of q matrices continuing to borrow from topology we define the nerve of a matrix which along with our characterization leads to an algorithm for checking whether or not a matrix is q this algorithm has smaller bounds on its worst case time complexity than previous methods

some perturbation results for the linear complementarity problem it has been shown previously that the linear complementarity problem is stable when the defining matrix is positive semidefinite and when locally the set of solutions is nonempty and bounded we enlarge the class of matrices for which this is true and also demonstrate how the boundedness condition leads to other stability type questions

the principal pivoting method revisited the principal pivoting method ppm for the linear complementarity problem lcp is shown to be applicable to the class of lcps involving the newly identified class of sufficient matrices

convergence properties and iterations for q stancu polynomials in compact disks this paper deals with approximating properties and convergence results of the iterates for complex q stancu polynomials attached to analytic functions on compact disks in the case q 1 some estimates on the rate of convergence are given

a note on sufficient conditions for q 0 and q 0 p 0 matrices in this note we settle an open problem posed by al khayyal on a condition being sufficient for a matrix to belong to the class ofq0 matrices the answer is in the affirmative and we further relax the condition and obtain a sufficient condition forq0 matrices the results yield a class of matrices for which the linear complementarity problems can be solved as simple linear programs

the norm estimates for the q bernstein operator in the case q 1 the q bernstein basis with 0 1 the behavior of the q bernstein basic polynomials on 0 1 combines the fast increase in magnitude with sign oscillations this seriously complicates the study of q bernstein polynomials in the case of q 1 the aim of this paper is to present norm estimates in c 0 1 for the q bernstein basic polynomials and the q bernstein operator b n q in the case q 1 while for 0 1 the norm b n q increases rather rapidly as n oo we prove here that b n q c q q n n 1 2 n n oo with c q 2 q 2 q 2 e such a fast growth of norms provides an explanation for the unpredictable behavior of q bernstein polynomials q 1 with respect to convergence

noise reduction finding the simplest dynamical system consistent with the data abstract a novel method is described for noise reduction in chaotic experimental data whose dynamics are low dimensional in addition we show how the approach allows experimentalists to use many of the same techniques that have been essential for the analysis of nonlinear systems of ordinary differential equations and difference equations

constructive characterization of lipschitzian q0 matrices abstract a matrix m r n n has property if m and all its principal pivotal transforms ppts satisfy the property that the rows corresponding to the nonpositive diagonal entries are nonpositive it has been shown that every lipschitzian q 0 matrix satisfies property in this paper it is shown that property is also sufficient for a lipschitzian matrix to be in q 0 property has several consequences if a has this property then a and all its ppts must be completely q 0 further for any q the linear complementarity problem q a can be processed by a simple principal pivoting method it is shown that a negative matrix is an n matrix if and only if it has property a matrix is a p matrix if and only if it has property and its value is positive property also yields a nice decomposition structure of lipschitzian matrices this paper also studies properties of lipschitzian matrices in general for example we show that the lipschitzian property is inherited by all the principal submatrices

generalized szasz mirakjan type operators via q calculus and approximation properties abstract the aim of this paper is to construct q analogue of generalized szasz mirakjan type operators whose construction depend on a real valued function we prove that the new operators provide better weighted uniform approximation over 0 in terms of weighted moduli of smoothness we obtain degrees of approximation associated with the function also a voronovskaya type result is obtained finally we give some graphical examples for these operators and show that the new operators are more flexible in view of rate of convergence to the function f which depends on the selection of un q and vn q

on spherically convex sets and q matrices abstract let k be a closed spherically convex subset of sn 1 that is contained in a hemisphere and x k the radial projection onto sn 1 of the centroid of k then ptx k 0 for all p k a specialization of this result to spherical simplices is used to derive a necessary condition for q matrices i e matrices for which every corresponding linear complementarity problem has at least one solution

bernstein type operators which preserve polynomials abstract in this paper we present the sequence of linear bernstein type operators defined for f c 0 1 by b n f 1 b n being the classical bernstein operators and being any function that is continuously differentiable times on 0 1 such that 0 0 1 1 and x 0 for x 0 1 we investigate its shape preserving and convergence properties as well as its asymptotic behavior and saturation moreover these operators and others of king type are compared with each other and with b n we present as an interesting byproduct sequences of positive linear operators of polynomial type with nice geometric shape preserving properties which converge to the identity which in a certain sense improve b n in approximating a number of increasing functions and which apart from the constant functions fix suitable polynomials of a prescribed degree the notion of convexity with respect to plays an important role

asymptotic expansion of multivariate conservative linear operators in this paper we study the asymptotic expansion of the partial derivatives of a sequence of linear conservative operators we find sufficient conditions on the sequence that guarantee that such an expansion can be derived from the asymptotic formula for the nondifferentiated sequence our results are valid even if the operators of the sequence present difficult conservative properties different form the classical preservation of the usual convexities we use our theorems to obtain the complete asymptotic expansions and voronovskaja formulae for the partial derivatives of multivariate versions of the meyer konig and zeller operators and the bleimann butzer and hahn operators

on a subclass of p0 abstract in 1966 fiedler and ptak wrote the first systematic investigation of the matrix class p 0 consisting of all real square matrices with nonnegative principal minors in this note we focus on a particular subclass of p 0 that has arisen within the field of linear complementarity theory namely the class su of sufficient matrices our principal result is that su contains another class p we conjecture that the latter two classes are in fact the same

voronovskaya type results for bernstein chlodovsky operators preserving e 2x abstract in this paper we continue the study of certain bernstein chlodovsky operators b n preserving the exponential function e 2 x x 0 recently introduced in 4 in particular we prove some voronovskaya type theorems and we deduce some properties of the b n s such as saturation results we also compare this new class of operators with the classical bernstein chlodovsky ones proving that the operators b n provide better approximation results for certain functions

approximation of functions by a new family of generalized bernstein operators abstract the main object of this paper is to construct a new generalization of the bernstein operator depending on a non negative real parameter we investigate some elementary properties of this operator such as end point interpolation linearity and positivity etc by using these generating operators we provide another proof of the weierstrass approximation theorem we give the detailed proofs to the rate of convergence and voronovskaja type asymptotic estimate formula for the operators moreover an upper bound for the error is obtained in terms of the usual modulus of continuity shape preserving properties of the generalized bernstein operators are also studied it is proved that monotonic or convex functions produce monotonic or convex generalized bernstein polynomials

structure properties of w matrices abstract we continue an investigation of the class w of real square matrices a matrix belongs to w if and only if certain pairs of its complementary cones intersect in the zero vector only we show that a w matrix with no zero diagonal entries is a p 0 matrix each principal minor is nonnegative and a w matrix with no nonzero diagonal entries is a nonnegative matrix which either is monomial or has a zero column lastly we show how these two results impose certain necessary conditions on the structure of a w matrix

comparison of algorithms calculating optimal embedding parameters for delay time coordinates the success of noise reduction processes and forecasting methods as well as accurate calculations of fractal dimensions and lyapunov exponents from scalar time series depends strongly on the quality of the reconstructed phase space we present a comparison of four methods which simultaneously estimate the two embedding parameters delay time and sufficiently large embedding dimension dime for takens delay time coordinates recently we introduced a global geometrical measure the fill factor and a local dynamical measure the averaged integral local deformation we will discuss these methods briefly and compare them to the topological wavering product in addition a simple algorithm is presented which observes the spreading of trajectories at the transition from dime to dime 1 and gives the opportunity to estimate the correlation entropy k2 we applied these algorithms to experimental data series measured from a rotational taylor couette experiment and verified the quality of the obtained embedding parameters by the estimation of correlation dimensions for different reconstructed attractors

the saturation of convergence on the interval 0 1 for the q bernstein polynomials in the case q 1 abstract in the note we consider saturation of convergence on the interval 0 1 for the q bernstein polynomials of a continuous function f for arbitrary fixed q 1 we show that the rate of uniform convergence on 0 1 is o q n if and only if f is linear the result is sharp in the following sense it ceases to be true if we replace o by o

approximation by q durrmeyer type polynomials in compact disks in the case q 1 abstract recently agarwal and gupta 2012 1 studied some approximation properties of the complex q durrmeyer type operators in the case 0 q 1 in this paper this study is extended to the case q 1 more precisely approximation properties of the newly defined generalization of this operators in the case q 1 are studied quantitative estimates of the convergence the voronovskaja type theorem and saturation of convergence for complex q durrmeyer type polynomials attached to analytic functions in compact disks are given in particular it is proved that for functions analytic in z c z r r q the rate of approximation by the q durrmeyer type polynomials q 1 is of order q n versus 1 n for the classical q 1 durrmeyer type polynomials explicit formulas of voronovskaya type for the q durrmeyer type operators for q 1 are also given this paper represents an answer to the open problem initiated by gal 2013 6

pc matrices and the linear complementarity problem abstract we introduce a new matrix class pc which consists of those matrices m for which the solution set of the corresponding linear complementarity problem is connected for every q rn we consider lemke s pivotal method from the perspective of piecewise linear homotopies and normal maps and show that lemke s method processes all matrices in pc q0 we further investigate the relationship of the class pc to other known matrix classes and show that column sufficient matrices are a subclass of pc as are 2 2 p0 matrices

the linear complimentarity problem sufficient matrices and the criss cross method specially structured linear complementarity problems lcps and their solution by the criss cross method are examined the criss cross method is known to be finite for lcps with positive semidefinite bisymmetric matrices and with p matrices it is also a simple finite algorithm for oriented matroid programming problems recently cottle pang and venkateswaran identified the class of column row sufficient matrices they showed that sufficient matrices are a common generalization of p and psd matrices cottle also showed that the principal pivoting method with a clever modification can be applied to row sufficient lcps in this paper the finiteness of the criss cross method for sufficient lcps is proved further it is shown that a matrix is sufficient if and only if the criss cross method processes all the lcps defined by this matrix and all the lcps defined by the transpose of this matrix and any parameter vector

stability of the linear complementarity problem at a solution point in this paper we study the behavior of a solution of the linear complementarity problem when data are perturbed we give characterizations of strong stability of the linear complementarity problem at a solution in the case of stability we give sufficient and necessary conditions

bivariate bernstein type operators in this paper we introduce bivariate extension of bernstein type operators defined in 11 we show that these operators preserve some properties of the original function f such as lipschitz constant and monotonicity furthermore we present the monotonicity of the sequence of bivariate bernstein type operators for n when f is convex

stancu type generalization of modified schurer operators based on q integers in the present paper we introduce the stancu type generalization s n p a b q x of the modified schurer operators based on q integers first we prove the basic convergence of the operators s n p a b q x and then obtain the voronovskaja type theorem next we discuss local direct results for these operators finally we study the statistical convergence of s n p a b q x and also obtain some convergence properties of the limit q modified schurer stancu operators

shape preserving approximation by bernstein type operators which fix polynomials in this paper we present a family of sequences of linear bernstein type operators an element of which was recently introduced by j p king as well as showing that they fix certain polynomials and studying some shape preserving and convergence properties we make a comparison with bernstein polynomials which shows that for certain usual situations and without too much additional computational cost the elements of the family represent a good shape preserving approximation process versus that of the referred polynomials the notion of convexity with respect to a function plays an important role

mutual information and global strange attractors in taylor couette flow abstract we apply a new method for the estimation of the mutual information m to experimental time series from different locations in weakly turbulent taylor couette flow we observe a dependence of m on the partition scale e and find m e dm log 1 e for small e and sufficient embedding dimension m our results confirm that the overall dynamics of the taylor couette flow is dominated by a global strange attractor of fractal information dimension d 1 d m at moderate reynolds numbers the dimension estimates obtained by our method are found to be more reliable than results from dimension algorithms based on single measurements alone a fact which makes our method most attractive for dimension analysis in extended systems

almost p 0 matrices and the class q this paper demonstrates that within the class of thosen n real matrices each of which has a negative determinant nonnegative proper principal minors and inverse with at least one positive entry the class ofq matrices coincides with the class of regular matrices each of these classes of matrices plays an important role in the theory of the linear complementarity problem lastly analogous results are obtained for nonsingular matrices which possess only nonpositive principal minors

on the q bernstein polynomials of rational functions with real poles abstract the paper aims to investigate the convergence of the q bernstein polynomials b n q f x attached to rational functions in the case q 1 the problem reduces to that for the partial fractions x j j n the already available results deal with cases where either the pole is simple or q m m n 0 consequently the present work is focused on the polynomials b n q f x for the functions of the form f x x q m j with j 2 for such functions it is proved that the interval of convergence of b n q f x depends not only on the location but also on the multiplicity of the pole a phenomenon which has not been considered previously

characterization of experimental time series from taylor couette flow abstract rotational taylor couette flow shows a rich variety of well defined and controllable scenarios even for short cylinders where the number of possible flow states is found to be very small period doubling cascades intermittencies homoclinic orbits and n tori can be found depending on boundary conditions we characterize these flow states by fractal dimensions lyapunov spectra and entropies in the experiments the axial velocity component was measured using laser doppler anemometry and the phase space was reconstructed by using delay time coordinates a simple noise reduction algorithm was applied to the noisy data set to improve the accuracy of the estimation of the dynamical variables

linear complementarity problems with an invariant number of solutions this paper studies the class ins of all realn n matricesm for which the linear complementarity problem q m has exactlyk solutions k depending only onm for all realn vectorsq interior to the conek m of vectors for which q m has any solution at all this generalizes the results in cottle and stone 1983 which deal with the subclassu in ins wherek equals one