sequential composition of linear systems clans when using petri nets to investigate deadlock control structural analysis techniques are applied which are based on solving systems of linear algebraic equations to gain an extra computational speed up when solving sparse linear systems we examine a sequential clan composition process represented by a weighted graph the system decomposition into clans is represented by a weighted graph the comparative analysis of sequential composition for subgraphs and edges pairwise is presented the task of constructing a sequence of systems of lower dimension is called an optimal collapse of a weighted graph the question whether it is np complete remains open upper and lower bounds for the collapse width corresponding to the maximal dimension of systems are derived a heuristic greedy algorithm of quasi optimal collapse is presented and validated statistically the technique is applicable for solving sparse systems over arbitrary rings fields with sign

numerical range circumscribed by two polygons abstract we show that for any 2 n 2 distinct points a 1 a 1 a 2 a 2 a n 1 a n 1 in this order on the unit circle there is an n by n matrix a unique up to unitary equivalence which has norm one and satisfies the conditions that it has all its eigenvalues in the open unit disc i n a a has rank one and its numerical range is circumscribed by the two n 1 gons a 1 a 2 a n 1 and a 1 a 2 a n 1 this generalizes the classical result of the existence of a conical curve circumscribed by two triangles which are already inscribed on another conical curve

a characterization of complex plane poncelet curves abstract we consider algebraic curves in the complex affine plane a natural extension of the existing definition of poncelet curves in the real plane to the complex plane is presented three equivalent polynomial equations in tangent coordinates are given for complex plane poncelet curves a the polynomial which generates the bezoutian form with parameters the foci of the curve b the darboux equation with parameters the vertices of a poncelet polygon c the determinant equation involving matrices having certain specific properties we use these polynomials in order to solve poncelet type problems namely criteria are proved for real poncelet curves to be generated by matrices that admit unitary bordering these criteria answer the question when a convex poncelet curve which is inscribed in a convex polygon is the boundary of a numerical range of a matrix we also demonstrate that the general theorems of the first three sections may shorten the proofs of some known results

poncelet s theorem paraorthogonal polynomials and the numerical range of compressed multiplication operators abstract there has been considerable recent literature connecting poncelet s theorem to ellipses blaschke products and numerical ranges summarized for example in the recent book 16 we show how those results can be understood using ideas from the theory of orthogonal polynomials on the unit circle opuc and in turn can provide new insights to the theory of opuc

density estimation under random censorship and order restrictions from asymptotic to small samples do a random censorship and or order restrictions e g nonnegativity monotonicity convexity affect estimation of a smooth density under mean integrated squared error mise under mild assumptions the known asymptotic results which are concerned only with rates answer no this answer especially for censored data contradicts practical experience and statistical intuition so what can be said about constants of mise convergence it is shown that asymptotically a censorship does affect the constant and this allows one to find a relationship between sample sizes of directly observed and censored datasets that implies the same precision of estimation and b an order restriction does not affect the constant and thus no isotonic estimation is needed intensive monte carlo simulations show that the lessons of the sharp asymptotics are valuable for small sample sizes also the estimator developed is illustrated both on simulated data and a dataset of lifetimes of conveyer blades used at wastewate

exact mean integrated squared error an exact and easily computable expression for the mean integrated squared error mise for the kernel estimator of a general normal mixture density is given for gaussian kernels of arbitrary order this provides a powerful new way of understanding density estimation which complements the usual tools of simulation and asymptotic analysis the family of normal mixture densities is very flexible and the formulae derived allow simple exact analysis for a wide variety of density shapes a number of applications of this method giving important new insights into kernel density estimation are presented among these is the discovery that the usual asymptotic approximations to the mise can be quite inaccurate especially when the underlying density contains substantial fine structure and also strong evidence that the practical importance of higher order kernels is surprisingly small for moderate sample sizes 1 introduction substantial research has been devoted to kernel density estimation this is because it provides a simple yet appealing context in which to study problems and issues that arise in all types of nonparametric curve estimation this includes regression spectral density and hazard estimation and also a variety of other estimators including histograms splines and orthogonal series three important and useful tools for understanding the behavior of nonparametric curve estimators are asymptotic analysis simulation and numerical calculation of error criteria each of these methods provides many useful insights into the complicated structure present in the study of curve estimation however each has its limitations as well rhe strength of asymptotic analysis is that it frequently allows simultaneous study of many different specific examples through general results applying to entire classes of settings the weakness of asymptotics is that they only describe behavior in the limit this is still very useful in many situations because the asymptotics describe the actual situation quite well however it is less useful when the asymptotics have not yet kicked in that is in studying situations where the asymptotically dominant effect has not taken over yet perhaps the biggest drawback to asymptotics is that it is very difficult to determine in a given situation which of these possibilities is occurring

numerical ranges poncelet curves invariant measures abstract a class of closed algebraic curves circuits is considered these circuits have the property of poncelet quadrics the circuits are generated by matrices which admit unitary bordering the link between spectral properties of the matrices and geometrical properties of the circuits is studied

mobius transformations and blaschke products the geometric connection abstract let b be a degree n blaschke product and for t let z 1 z n ordered according to increasing argument denote the distinct solutions to b z 0 then there is a smooth curve c such that for each the line segments joining z j and z j 1 are tangent to c we study the situation in which c is an ellipse and describe the relation to the action of the points z j under elliptic disk automorphisms these results provide a condition for the numerical range of a compressed shift operator with finite blaschke symbol to be an elliptical disk we also consider infinite blaschke products and the action of parabolic and hyperbolic disk automorphisms

an efficient incremental algorithm for solving systems of linear diophantine equations abstract in this paper we describe an algorithm for solving systems of linear diophantine equations based on a generalization of an algorithm for solving one equation due to fortenbacher it can solve a system as a whole or be used incrementally when the system is a sequential accumulation of several subsystems the proof of termination of the algorithm is difficult whereas the proofs of completeness and correctness are straightforward generalizations of fortenbacher s proof

quasi linear wavelet estimation abstract the main paradigm of the modern wavelet theory of spatial adaptation formulated by donoho and johnstone is that there is a divergence between the linear minimax adaptation theory and the heuristic guiding algorithm development that leads to the necessity of using strongly nonlinear adaptive thresholded methods on the other hand it is well known that linear adaptive estimates are the best whenever an estimated function is smooth is it possible to suggest a quasi linear wavelet estimate by adding to a linear adaptive estimate a minimal number of nonlinear terms on finest scales that offers advantages of linear adaptive estimates and at the same time matches asymptotic properties of strongly nonlinear procedures like the benchmark sureshrink the answer is yes and we discuss quasi linear estimation both theoretically and via a monte carlo study in particular i show that asymptotically a quasi linear procedure not only matches properties of sureshrink over the besov scale but also allows

numerical range of a normal compression ii as in the predecessor numerical range of a normal compression linear and multilinear algebra in press of this paper we consider properties of matrices of the form v nv where n diag a1 a n 1 is a diagonal matrix with distinct eigenvalues aj s such that each of them is a corner of the convex hull they generate and v is an n 1 by n matrix with v v in such that any nonzero vector orthogonal to the range space of v has all its components nonzero we obtain that such a matrix a is determined by its eigenvalues up to unitary equivalence is irreducible and cyclic and the boundary of its numerical range is a differentiable curve which contains no line segment we also consider the condition for the existence of another matrix of the above type which dilates to a such that their numerical ranges share some common points with the boundary of the n 1 gon a1 an 1

numerical ranges and poncelet curves abstract convex circuits which have the property of circles of the great poncelet theorem are introduced the circuits are generated as boundaries of numerical ranges of specially constructed matrices algebraic and geometric properties of such matrices and their numerical ranges are obtained these properties lead to a new proof of the poncelet theorem the proposed approach illustrates the fact that complex relations between geometrical figures in a plane may have simple interpretation in a space of higher dimension

the group of invariants of an inner function with finite spectrum abstract this paper determines the group of continuous invariants corresponding to an inner function with finitely many singularities on the unit circle t that is the continuous mappings g t t such that g on t these mappings form a group under composition

decomposing finite blaschke products abstract we present four algorithms to determine whether or not a blaschke product is a composition of two non trivial blaschke products and if it is the algorithms suggest what the composition must be the initial algorithm is a naive counting argument the second considers critical values and the counting argument the third is a geometric argument that exploits the relationship between blaschke products and curves with the poncelet property and it can also be expressed in terms of a group associated with the blaschke product the final algorithm looks at inverse images under the blaschke product our algorithms are accompanied by an applet that implements them

a new poncelet curve for the boundary generating curve of a numerical range abstract in this paper a geometrical method is developed to obtain a new poncelet curve for the boundary generating curve of the numerical range of a certain class of contractions an algorithm is provided for producing the equation of the new poncelet curve several examples of experimental results are also presented to illustrate such new poncelet curves

maximum likelihood estimation of smooth monotone and unimodal densities we study the nonparametric estimation of univariate monotone and unimodal densities using the maximum smoothed likelihood approach the monotone estimator is the derivative of the least concave majorant of the distribution corresponding to a kernel estimator we prove that the mapping on distributions with density the derivative of the least concave majorant of is a contraction in all l p norms 1 p and some other distances such as the hellinger and kullback leibler distances the contractivity implies error bounds for monotone density estimation almost the same error bounds hold for unimodal estimation

ub matrices and conditions for poncelet polygon to be closed a sufficient condition for the generation of a package of algebraic poncelet curves is presented the condition is obtained via the link between the parameters of the nested poncelet curves and the eigenvalues of matrices which admit unitary bordering this condition results in an example refuting the conjecture raised in linear and multilinear algebra 45 1998 49 linear algebra appl 329 2001 61 that algebraic poncelet curves are always generated by such matrices then the condition is applied to the case of nested quadrics in order to determine whether they form the poncelet configuration i e whether there exists a closed polygon inscribed in the outer quadric and circumscribed about the inner one the classical cayley criterion answers this question for a given number n of sides of a polygon in this paper a different kind of criterion in the form of rational recurrent equations is developed moreover sufficient conditions are derived for the case when a closed poncelet polygon with any number of sides does not exist

ellipses and compositions of finite blaschke products abstract we provide a new proof of a theorem of fujimura characterizing blaschke products of degree 4 that are compositions of two degree 2 blaschke products connect this result to the numerical ranges of certain operators and characterize poncelet ellipses that are inscribed in quadrilaterals geometrically and algebraically

on parallel multisplitting block iterative methods for linear systems arising in the numerical solution of euler equations the paper studies the convergence of some parallel multisplitting block iterative methods for the solution of linear systems arising in the numerical solution of euler equations some sufficient conditions for convergence are proposed as special cases the convergence of the parallel block generalized aor bgaor the parallel block aor baor the parallel block generalized sor bgsor the parallel block sor bsor the extrapolated parallel baor and the extrapolated parallel bsor methods are presented furthermore the convergence of the parallel block iterative methods for linear systems with special block tridiagonal matrices arising in the numerical solution of euler equations are discussed finally some examples are given to demonstrate the convergence results obtained in this paper

brief paper design of a maximally permissive liveness enforcing supervisor with a compressed supervisory structure for flexible manufacturing systems in this paper a deadlock prevention policy for flexible manufacturing systems fms is proposed which can obtain a maximally permissive liveness enforcing petri net supervisor while the number of control places is compressed by using a vector covering approach the sets of legal markings and first met bad markings fbm are reduced to two small ones i e the minimal covering set of legal markings and the minimal covered set of fbm a maximally permissive control purpose can be achieved by designing control places such that all markings in the minimal covered set of fbm are forbidden and no marking in the minimal covering set of legal markings is forbidden an integer linear programming problem is designed to minimize the number of control places under an assumption that a control place is associated with a p semiflow the resulting net has the minimal number of control places on the premise that the assumption holds and possesses all permissive states of a plant the only problem of the proposed method is its computational complexity that makes it inapplicable to large scale petri net models an fms example from the literature is presented to illustrate the proposed method

poncelet s theorem sendov s conjecture and blaschke products by connecting blaschke products unitary dilations of matrices numerical range poncelet s theorem and interpolation we extend and simplify gau and wu s work gau and wu 2004 10 we look at blaschke products role in the sendov conjecture