c2 quadratic trigonometric polynomial curves with local bias quadratic trigonometric polynomial curves with local bias are presented in this paper the quadratic trigonometric polynomial curves have c 2 continuity with a non uniform knot vector and any value of the bias while the quadratic b spline curves have c 1 continuity the changes of a local bias parameter will only affect two curve segments with the bias parameters the quadratic trigonometric polynomial curves can move locally toward or against a control vertex a quadratic trigonometric bezier curve is also introduced as special case of the given trigonometric polynomial curves

sensitivity analysis for certain permutation inferences in matched observational studies summary in observational studies treatments are not randomly assigned to experimental units so that randomization tests and their associated interval estimates are not generally applicable in an effort to compensate for the lack of randomization treated and control units are often matched on the basis of observed covariates however the possibility remains of bias due to residual imbalances in unobserved covariates a general though simple method is proposed for displaying the sensitivity of permutation inferences to a range of assumptions about unobserved covariates in matched observational studies the sensitivity analysis is applicable to wilcoxon s signed rank test to the mcnemar cox test for paired binary responses and to some matching problems with a variable number of controls

explicit representations of changeable degree spline basis functions changeable degree spline cd spline for short basis functions defined by an iterative integral method are extensions of b spline basis functions a cd spline basis function is a piecewise function made up of polynomials of different degrees in this paper we will give the explicit representations of cd spline basis functions from which the spanned linear space can be seen clearly our method is also feasible for the explicit representations of the other basis functions given in analogous integral ways

geometric analysis of impulse controllability for descriptor system for descriptor linear system this paper presents three new concepts impulsive direction controllability of impulsive direction and order of impulsive direction controllability at infinity is proved to be equivalent to the controllability of impulsive directions of zero order which guarantees the controllability of impulsive directions of any order unlike what one expects the controllability of impulsive free response modes does not guarantee impulse controllability

feedback and pole placement in descriptor variable systems the effects and uses of applying linear feedback to continuous time descriptor systems are studied structural changes resulting from feeding back the slow and fast parts of the trajectory separately are characterized it is shown that under certain conditions related to controllability the poles of the slow subsystem may be shifted arbitrarily and the impulsive behaviour of the fast subsystem may be eliminated

brief paper output feedback controller synthesis for descriptor systems satisfying closed loop dissipativity this paper is concerned with synthesis of output feedback controllers for descriptor systems to attain dissipativity of the closed loop system a necessary and sufficient condition is provided in terms of lmis for the existence of a controller satisfying dissipativity and admissibility an internal stability of the closed loop system unlike previous results the condition does not depend on the choice of the descriptor realization the derived lmi condition with a rank constraint for synthesis is a generalization of those for lmi based h control of state space systems to descriptor systems

the g2 and c2 rational quadratic trigonometric bezier curve with two shape parameters with applications the rational quadratic trigonometric bezier curve with two shape parameters is presented in this paper which is new in literature the purposed curve inherits all the geometric properties of the traditional rational quadratic bezier curve the presence of shape parameters provides a control on the shape of the curve more than that of traditional bezier curve moreover the weight offers an additional control on the curve simple constraints for shape parameters are derived using the end points curvature so that their values always fall within the defined range the composition of two segments of curve using g 2 and c 2 continuity is given the new curves can accurately represent some conics and best approximates the traditional rational quadratic bezier curve

h control for descriptor systems a matrix inequalities approach abstract this paper considers the h control problem for descriptor systems that possibly have impulsive modes and or j axis zeros first we propose matrix inequalities that give a generalized stability condition and an h norm condition for descriptor systems using these matrix inequalities we show that the solvability of a set of matrix inequalities is necessary and sufficient to the existence of a proper controller that satisfies a prescribed h norm condition as well as stabilizing the closed loop system and eliminating all impulsive modes these inequalities are equivalent to certain linear matrix inequalities to which we can get solutions whenever they exist using efficient polynomial time algorithms

controllability observability and duality in singular systems the concepts of controllability and observability for systems of the form e dot x ax bu y cx e singular are considered a theory is presented which unifies the three main approaches to this topic already existing in the literature the development includes a generalization of the duality theorem from state space theory

which spaces for design we determine the largest class of spaces of sufficient regularity which are suitable for design in the sense that they do possess blossoms it is the class of all spaces containing constants of which the spaces derived under differentiation are quasi extended chebyshev spaces i e they permit hermite interpolation taylor interpolation excepted it is also the class of all spaces which possess bernstein bases or of all spaces for which any associated spline space does possess a b spline basis note that blossoms guarantee that such bases are normalised totally positive bases they even are the optimal ones

the pencil se a and controllability observability for generalized linear systems a geometric approach in the first part of the paper we study the pencil se a by using some geometric concepts given by bernhard siam j control optim 20 1982 pp 612 6331 and some new ones which are introduced here such concepts are then used to obtain an alternative characterization for the finite and infinite zero structure of the pencil and to construct a polynomial basis for ker se a necessary and sufficient conditions for the rows or and the columns of the pencil to be linearly independent over the ring of the polynomials are also given the main geometric properties of a regular pencil are presented including the identification of the subspace in which the impulsive response of the autonomous generalized linear system e dot x ax takes place in the second part we consider the generalized linear system e dot x ax bu y cx and we give necessary and sufficient conditions for the infinite zeros of the regular pencil se a to be controllable and observable

derivative and proportional state feedback for linear descriptor systems with variable coefficients abstract we study linear descriptor systems with rectangular variable coefficient matrices using local and global equivalence transformations we introduce normal and condensed forms and get sets of characteristic quantities these quantities allow us to decide whether a linear descriptor system with variable coefficients is regularizable by derivative and or proportional state feedback or not regularizable by feedback means for us that there exists a feedback which makes the closed loop system uniquely solvable for every consistent initial vector

piecewise trigonometric hermite interpolation based on the symmetric nonnegative and normalized basis of the trigonometric polynomial space the piecewise trigonometric hermite interpolation methods are presented the c n 1 and cn continuous piecewise trigonometric hermite interpolants of degree n are constructed and the interpolation methods are local the integral and the differential representations of the errors of the trigonometric hermite interpolants are given several examples are supplied to support the practical value of the given interpolation methods

solvability conditions consistency and weak consistency for linear differential algebraic equations and time invariant singular systems the general case we present several solvability concepts for linear differential algebraic equations daes with constant coefficients on the positive time axis as well as for the associated singular systems and investigate under which conditions these concepts are met next we derive necessary and sufficient conditions for global consistency of initial conditions for the dae as well as for the system and generalize these conditions with respect to our concept of weak consistency our distributional approach enables us to generalize results in an earlier paper where singular systems are assumed to have a regular pencil in the sense of gantmacher in particular we establish that global weak consistency in the system sense is equivalent to impulse controllability

the cross cut statistic and its sensitivity to bias in observational studies with ordered doses of treatment a common practice with ordered doses of treatment and ordered responses perhaps recorded in a contingency table with ordered rows and columns is to cut or remove a cross from the table leaving the outer corners that is the high versus low dose high versus low response corners and from these corners to compute a risk or odds ratio this little remarked but common practice seems to be motivated by the oldest and most familiar method of sensitivity analysis in observational studies proposed by cornfield et al 1959 which says that to explain a population risk ratio purely as bias from an unobserved binary covariate the prevalence ratio of the covariate must exceed the risk ratio quite often the largest risk ratio hence the one least sensitive to bias by this standard is derived from the corners of the ordered table with the central cross removed obviously the corners use only a portion of the data so a focus on the corners has consequences for the standard error as well as for bias but sampling variability was not a consideration in this early and familiar form of sensitivity analysis where point estimates replaced population parameters here this cross cut analysis is examined with the aid of design sensitivity and the power of a sensitivity analysis

feedback design for regularizing descriptor systems this paper surveys numerical techniques for the regularization of descriptor generalized state space systems by proportional and derivative feedback we review generalizations of controllability and observability to descriptor systems along with definitions of regularity and index in terms of the weierstras canonical form three condensed forms display the controllability and observability properties of a descriptor system the condensed forms are obtained through orthogonal equivalence transformations and rank decisions so they may be computed by numerically stable algorithms in addition the condensed forms display whether a descriptor system is regularizable i e when the system pencil can be made to be regular by derivative and or proportional output feedback and if so what index can be achieved also included is a a new characterization of descriptor systems that can be made to be regular with index 1 by proportional and derivative output feedback

descriptor systems without controllability at infinity this paper concerns the structure that can be achieved by feedback in descriptor systems that lack controllability at infinity staircase and double staircase condensed forms obtained through a sequence of orthogonal state transformations display when and how feedback can be used to achieve minimal index furthermore they reveal that the modes that are uncontrollable at infinity have a fixed minimal index that cannot be reduced by feedback however this fixed higher index part of the control system is constrained to be zero in an appropriate coordinate system provided the initial conditions are consistent the remainder is a reduced order system that is controllable at infinity that can be made to have index one by feedback

solvability controllability and observability of continuous descriptor systems in this paper we investigate the properties of the continuous descriptor system e dot x t ax t bu t 0 leqt leqb where e a and b are complex and possibly singular matrices and u t is a complex function differentiable sufficiently many times the traditional approach to such systems is to separate the state equations from the algebraic equations however such algorithms usually destroy the natural physically based sparsity and structure of the original system therefore we consider descriptor systems in their original form such systems possess numerous properties not shared by the well known state variable systems first we relate classical theories of matrix pencils to the solvability of descriptor systems then we extend the concepts of reachability controllability and observability of state variable systems to descriptor systems and describe the set of reachable states for descriptor systems

impulse controllability and observability of rectangular descriptor systems the presence of impulsive responses in descriptor systems and how it relates to impulse controllability and impulse observability is considered it is shown that the equivalence between impulse controllability observability and the existence of an impulse eliminating semistate feedback output injection gain although true for square descriptor systems does not hold for rectangular descriptor systems in general hence necessary and sufficient conditions for the existence of an impulse eliminating semistate feedback output injection gain are presented

causal observability of descriptor systems observability analysis for descriptor systems by using a matrix pencil approach is presented systems under consideration are the most general class of linear continuous descriptor systems a few practically relevant notions of observability particularly the causal observability which corresponds to the existence of a luenberger observer and the corresponding necessary and sufficient test conditions are provided the interpretation of various observabilities in terms of matrix pencils offers insights into the physical meaning of these concepts

impulsive modes and causality in singular systems the concepts of impulsive modes and causality in singular systems are considered their properties relations and applications are studied matrix rank criteria are presented thus all controllabilities and observabilities and related concepts have matrix rank criteria based on the original system coefficient matrices

controllability and observability of second order descriptor systems we analyze controllability and observability conditions for second order descriptor systems and show how the classical conditions for first order systems can be generalized to this case we show that performing a classical transformation to first order form may destroy some controllability and observability properties as an example we demonstrate that the loss of impulse controllability in constrained multibody systems is due to the representation as a first order system to avoid this problem we will derive a canonical form and new first order formulations that do not destroy the controllability and observability properties

on a class of weak tchebycheff systems in this paper we study the approximation power the existence of a normalized b basis and the structure of a degree raising process for spaces of the form requiring suitable assumptions on the functions u and v the results about degree raising are detailed for special spaces of this form which have been recently introduced in the area of cagd

cone order association and stochastic cone ordering with applications to order restricted testing cohen sackrowitz and samuel cahn introduced the notion of cone order association and established a necessary and sufficient condition for a normal random vector to be cone order associated coa in this paper we provide the following 1 a necessary and sufficient condition for a multinomial distribution to be coa when the cone is a pairwise contrast cone 2 a relationship between coa and regular association 3 a notion of stochastic cone ordering sco of random vectors along with two preservation theorems indicating monotonicity properties of expectations as functions of parameters and 4 applications to unbiasedness of tests and monotonicity of power functions of tests in cone order restricted hypothesis testing problems in particular the matrix order alternative hypothesis testing problem is treated when the underlying distributions are independent poisson or the joint distribution is multinomial

on the solutions of linear differential equations with singular coefficients abstract equations of the form e ax u with e and a square matrices and e singular are considered the controversy that exists in the literature concerning the solutions of such equations is investigated solutions are arrived at through an application of singular perturbation theory

time domain solution to descriptor variable systems the time domain solution to the fast subsystem of the descriptor variable system of the form ex spl dot ax bu with e singular is given by laplace inverse transformation a new and significant feature of the solution is that it contains impulse terms excited by the values of sufficiently smooth input u and its derivatives at the initial time point based on the solution the notions of consistent initial conditions classical solutions and impulse free solutions are discussed perfectly the impulse controllability is discussed also which admits the same interpretation as the controllability at infinity in frequency domain

convergence in the boundary layer for singularly perturbed equations a singularly perturbed linear finite dimensional ordinary differential equation is considered on the half line 0 the reduced system is assumed to have a unique solution in the sense of distributions it is proved that under reasonable conditions the solution of the full system converges to that of the reduced in the distributional sense and the order of the limiting distribution is computed an application to the optimal linear quadratic regulator with cheap control is described

conditional association and unidimensionality in monotone latent variable models latent variable models represent the joint distribution of observable variables in terms of a simple structure involving unobserved or latent variables usually assuming the conditional independence of the observable variables given the latent variables these models play an important role in educational measurement and psychometrics in sociology and in population genetics and are implicit in some work on systems reliability we study a broad class of latent variable models namely the monotone unidimensional models in which the latent variable is a scalar the observable variables are conditionally independent given the latent variable and the conditional distribution of the observables given the latent variable is stochastically increasing in the latent variable all models in this class imply a new strong form of positive dependence among the observable variables namely conditional positive association this positive dependence condition may be used to test whether any model in this class can provide an adequate fit to observed data various applications generalizations and a numerical example are discussed

a generalized state space for singular systems systems of the form e dot x ax bu y cx with e singular are studied of particular interest are the impulsive modes that may appear in the free response of such systems when arbitrary initial conditions are permitted modes that are associated with natural system frequencies at infinity a generalized definition of system order that incorporates these impulsive degrees of freedom is proposed and concepts of controllability and observability are defined for the impulsive modes allowable equivalence transformations of such singular systems are specified the present framework is shown to overcome several difficulties inherent in other treatments of singular systems and to extend in a natural and satisfying way many results previously known only for regular state space systems

a tutorial on the geometric analysis of linear time invariant implicit systems abstract a background of recent work in nonregular and regular implicit systems of the form e x ax bu is provided then the output nulling unknown input and composite subspaces are defined for singular systems with recursions given for their computation inner subspaces that is those in the domain of e and a are distinguished from outer subspaces those in the codomain of e and a the notions of composite preimage and composite image are introduced the result is a framework that unifies some of the recent work in the geometric theory of implicit systems system properties are discussed for both regular and nonregular systems and duality is investigated

impulse analysis of linear time varying singular systems impulsive part of solution to initial value problem of linear time varying singular systems is given explicitly impulse observability and impulse controllability for the systems are redefined

high order data sharpening for density estimation it is shown that data sharpening can be used to produce density estimators that enjoy arbitrarily high orders of bias reduction practical advantages of this approach relative to competing methods are demonstrated they include the sheer simplicity of the estimators which makes code for computing them particularly easy to write very good mean squared error performance reduced wiggliness of estimates and greater robustness against undersmoothing

an extension of the bezier model abstract in this paper we first construct a new kind of basis functions by a recursive approach based on these basis functions we define the bezier like curve and rectangular bezier like surface then we extend the new basis functions to the triangular domain and define the bernstein bezier like surface over the triangular domain the new curve and surfaces have most properties of the corresponding classical bezier curve and surfaces moreover the shape parameter can adjust the shape of the new curve and surfaces without changing the control points along with the increase of the shape parameter the new curve and surfaces approach the control polygon or control net in addition the evaluation algorithm for the new curve and triangular surface are provided

families of multivariate distributions abstract for many years there has been an interest in families of bivariate distributions with marginals as parameters genest and mackay 1986a b showed that several such families that appear in the literature can be derived by a unified method a similar conclusion is obtained in this article through the use of mixture models these models might be regarded as multivariate proportional hazards models with random constants of proportionality the mixture models are useful for two purposes first they make some properties of the derived distributions more transparent the positive dependency property of association is sometimes exposed and a method for simulation of data from the distributions is suggested but the mixture models also allow derivation of several new families of bivariate distributions with marginals as parameters and they indicate obvious multivariate extensions some of the new families of bivariate distributions given in this article extend known distributions by adding a parameter

on dimension elevation in quasi extended chebyshev spaces via blossoms we analyse the dimension elevation process from mathcal e n p q to mathcal e n 1 p q where mathcal e n p q is spanned over 0 1 by 1 x xn 2 xp 1 x q p q being any convenient real numbers such spaces are not extended chebyshev spaces but quasi extended chebyshev spaces they were recently introduced in cagd for shape preservation purposes costantini in math comp 46 203 214 1986 costantini in advanced course on fairshape pp 87 114 in 1996 costantini in curves and surfaces with applications in cagd pp 85 94 1997 our results give a new insight into the special case p q for which dimension elevation had already been considered first when p q was supposed to be an integer goodman and mazure in j approx theory 109 48 81 2001 then without the latter requirement costantini et al in numer math 101 333 354 2005 the question of dimension elevation in more general quasi extended chebyshev spaces is also addressed

curve construction based on four αβ bernstein like basis functions a b s t r a c t four new bernstein like basis functions with two exponential shape parameters are constructed in this paper which include the cubic said ball basis functions and the cubic bernstein basis functions within the general framework of quasi extended chebyshev space we prove that the proposed bernstein like basis is an optimal normalized totally positive basis in order to compute the corresponding bezier like curves stably and efficiently a new corner cutting algorithm is developed necessary and sufficient conditions are derived for the planar bezier like curve having single or double inflection points a loop or a cusp or be locally or globally convex in terms of the relative position of its control polygons side vectors based on the new proposed bernstein like basis a class of b spline like basis functions with two local exponential shape parameters is constructed their totally positive property is also proved the associated b splinelike curves have c 2 continuity at single knots and include the cubic non uniform b spline

shape analysis of cubic trigonometric bezier curves with a shape parameter abstract for the cubic trigonometric polynomial curves with a shape parameter tb curves for short the effects of the shape parameter on the tb curve are made clear the shape features of the tb curve are analyzed the necessary and sufficient conditions are derived for these curves having single or double inflection points a loop or a cusp or be locally or globally convex the results are summarized in a shape diagram of tb curves which is useful when using tb curves for curve and surface modeling furthermore the influences of shape parameter on the shape diagram and the ability for adjusting the shape of the curve are shown by graph examples respectively

controllability and elimination of impulsive modes in descriptor systems as a refined notion impulsive mode controllability is suggested for the general class of linear continuous descriptor systems this notion reveals rich properties of the general descriptor systems in terms of admissibility of initial conditions admissibility of feedback control and impulsive mode elimination the condition for impulsive mode controllability is derived and proved to be necessary and sufficient for the existence of admissible feedback controls eliminating impulsive modes under impulsive mode controllability admissible feedback controls are constructed for eliminating impulsive modes on the basis of numerically reliable decompositions of the system s coefficient matrices

dual and simultaneous sensitivity analysis for matched pairs summary when a study shows an association between a treatment and a response before concluding that there is a causal relationship it is useful to assess whether or not an unobserved variable u might explain the observed association sensitivity analysis clarifies the properties u must have in terms of its relationship to the response and its imbalance in the groups being compared a substantial literature has investigated the imbalance or association between u and group assignment this paper develops a dual sensitivity analysis for matched pairs focusing on the strength of the relationship between u and the response required to reduce an observed association to non significance a third simultaneous form of sensitivity analysis models both relationships between u and treatment assignment and u and response the simultaneous form allows one to compare results from the sensitivity analysis to subject matter knowledge about both relationships the methods are illustrated by several examples

studentized sensitivity analysis for the sample average treatment effect in paired observational studies abstracta fundamental limitation of causal inference in observational studies is that perceived evidence for an effect might instead be explained by factors not accounted for in the primary analysi

dissipativity inequalities for continuous time descriptor systems with applications to synthesis of control gains this paper is concerned with a kyp type result for descriptor systems matrix inequalities are shown that provide necessary and sufficient conditions of dissipativity of descriptor systems without such restriction on the realization of descriptor systems as in many of previous results furthermore lmi conditions are presented for synthesis of control gains to attain dissipativity of feedback systems represented in the descriptor form

a class of algebraic trigonometric blended splines this paper presents a new kind of algebraic trigonometric blended spline curve called xyb curves generated over the space 1 t sint cost sin 2t sin 3t cos 3t the new curves not only inherit most properties of usual cubic b spline curves in polynomial space but also enjoy some other advantageous properties for modeling for given control points the shape of the new curves can be adjusted by using the parameters x and y when the control points and the parameters are chosen appropriately the new curves can represent some conics and transcendental curves in addition we present methods of constructing an interpolation xyb spline curve and an xyb spline curve which is tangent to the given control polygon the generation of tensor product surfaces by these new spline curves is straightforward many properties of the curves can be easily extended to the surfaces the new surfaces can exactly represent the rotation surfaces as well as the surfaces with elliptical or circular sections

piecewise quartic polynomial curves with a local shape parameter piecewise quartic polynomial curves with a local shape parameter are presented in this paper the given blending function is an extension of the cubic uniform b splines the changes of a local shape parameter will only change two curve segments with the increase of the value of a shape parameter the curves approach a corresponding control point the given curves possess satisfying shape preserving properties the given curve can also be used to interpolate locally the control points with gc2 continuity thus the given curves unify the representation of the curves for interpolating and approximating the control polygon as an application the piecewise polynomial curves can intersect an ellipse at different knot values by choosing the value of the shape parameter the given curve can approximate an ellipse from the both sides and can then yield a tight envelope for an ellipse some computing examples for curve design are given

disturbance impulse controllability in descriptor system the descriptor system ex ax gu hv with external disturbance v is considered to characterize the possibility to cancel the impulses produced by external disturbance v through using control u the concept of disturbance impulse controllability is introduced

piecewise quadratic trigonometric polynomial curves analogous to the quadratic b spline curve a piecewise quadratic trigonometric polynomial curve is presented in this paper the quadratic trigonometric polynomial curve has c2 continuity while the quadratic b spline curve has c1 continuity the quadratic trigonometric polynomial curve is closer to the given control polygon than the quadratic b spline curve

brief paper stability and stabilization of continuous time singular hybrid systems in this paper the problems of stability and state feedback stabilization for a class of continuous time singular hybrid systems are investigated a new sufficient and necessary condition for a continuous time singular hybrid system to be regular impulse free and stochastically stable is proposed in terms of a set of coupled strict linear matrix inequalities lmis moreover a new sufficient and necessary condition is presented for the existence of the state feedback controller in terms of a set of coupled strict matrix inequalities finally a numerical example is given to illustrate the effectiveness of the obtained theoretical results

quantiles in nonrandom samples and observational studies abstract in a nonrandom sample or a nonrandomized comparison of treated and control groups methods are developed for displaying the sensitivity of confidence intervals for population quantiles to the magnitude of the departure from random selection quantiles of a single distribution and for a shift in two distributions are both discussed these confidence intervals are based on a new inequality for the distribution of the number of successes in a nonrandom sample or nonrandomized comparison the inequality has additional applications in particular it greatly accelerates the computations in a sensitivity analysis for the mantel haenszel statistic in a 2 2 s contingency table examples include a nonrandom collection of blood samples from a town with comparatively high levels of radon gas an observational study of chromosome damage from mercury and a study of the drug allopurinol as a cause of skin rash the proof of the inequality makes use of savage s lattice for ranks and holley s inequality wh

amplification of sensitivity analysis in matched observational studies a sensitivity analysis displays the increase in uncertainty that attends an inference when a key assumption is relaxed in matched observational studies of treatment effects a key assumption in some analyses is that subjects matched for observed covariates are comparable and this assumption is relaxed by positing a relevant covariate that was not observed and not controlled by matching what properties would such an unobserved covariate need to have to materially alter the inference about treatment effects for ease of calculation and reporting it is convenient that the sensitivity analysis be of low dimension perhaps indexed by a scalar sensitivity parameter but for interpretation in specific contexts a higher dimensional analysis may be of greater relevance an amplification of a sensitivity analysis is defined as a map from each point in a low dimensional sensitivity analysis to a set of points perhaps a curve in a higher dimensional sensitivity analysis such that the possible inferences are

analysis of impulsive modes and luenberger observers for descriptor systems abstract in this paper the distinction between impulsive modes that can be generated by inputs and impulsive modes that can only be generated by initial conditions is investigated for linear time invariant descriptor systems it reveals that the input generatable impulsive modes are very crucial to the existence of normal luenberger observers of the systems based on this observation an earlier known concept called strongly detectability for regular descriptor systems is extended to irregular case that is shown to be of much clearer physical meanings in classical sense than a recently proposed equivalent notion of causal detectability does thus similar to the regular case strong detectability is also a sufficient and necessary condition for the existence of normal luenberger observers of irregular descriptor systems

positivity of discrete singular systems and their stability in this paper we present an efficient approach to the analysis of discrete positive singular systems one of our main objectives is to investigate the problem of characterizing positivity of such systems previously this issue was not completely addressed we provide easily checkable necessary and sufficient conditions for such problem to be solved on the other hand we study the stability of discrete positive singular systems note that this is not a trivial problem since the set of admissible initial conditions is not the whole space but it is represented by a special cone all the conditions we provide are necessary and sufficient and are based on a reliable computational approach via linear programming

changeable degree spline basis functions a b spline basis function is a piecewise function of polynomials of equal degree on its support interval this paper extends b spline basis functions to changeable degree spline cd spline for short basis functions each of which may consist of polynomials of different degrees on its support interval the cd spline basis functions possess many b spline like properties and include the b spline basis functions as subcases their corresponding parametric curves called cd spline curves are like b spline curves and also have many good properties if we use the cd spline basis functions to design a curve made up of polynomial segments of different degrees the number of control points may be decreased

stochastic order in dichotomous item response models for fixed adaptive and multidimensional tests dichotomous irt models can be viewed as families of stochastically ordered distributions of responses to test items this paper explores several properties of such distributions in particular it is examined under what conditions stochastic order in families of conditional distributions is transferred to their inverse distributions from two families of related distributions to a third family or from multivariate conditional distributions to a marginal distribution the main results are formulated as a series of theorems and corollaries which apply to dichotomous irt models one part of the results holds for unidimensional models with fixed item parameters the other part holds for models with random item parameters as used for example in adaptive testing or for tests with multidimensional abilities