the laguerre and legendre polynomials from an operational point of view the use of the monomiality principle and of the associated operational calculus allows to reformulate the theory of laguerre and legendre polynomials from a unified point of view they are indeed shown to be particular cases of more general polynomials whose usefulness in purely mathematical and applied contexts is discussed the concepts introduced in the paper are also exploited to develop an elementary point of view on the theory of legendre and laguerre bessel functions

associated laguerre konhauser polynomials quasi monomiality and operational identities abstract in this paper we exploit the monomiality principle to discuss and introduce a new class of laguerre konhauser polynomials we study their properties differential equations generating functions recurrence relations expansions and so on and discuss the link with ordinary case

integral transforms and chebyshev like polynomials we use the integral representation method to derive the properties of chebyshev polynomials and of their generalized forms

multivariate meta analysis a robust approach based on the theory of u statistic meta analysis is the methodology for combining findings from similar research studies asking the same question when the question of interest involves multiple outcomes multivariate meta analysis is used to synthesize the outcomes simultaneously taking into account the correlation between the outcomes likelihood based approaches in particular restricted maximum likelihood reml method are commonly utilized in this context reml assumes a multivariate normal distribution for the random effects model this assumption is difficult to verify especially for meta analysis with small number of component studies the use of reml also requires iterative estimation between parameters needing moderately high computation time especially when the dimension of outcomes is large a multivariate method of moments mmm is available and is shown to perform equally well to reml however there is a lack of information on the performance of these two methods when the true data distribution is far from normality in this paper we propose a new nonparametric and non iterative method for multivariate meta analysis on the basis of the theory of u statistic and compare the properties of these three procedures under both normal and skewed data through simulation studies it is shown that the effect on estimates from reml because of non normal data distribution is marginal and that the estimates from mmm and u statistic based approaches are very similar therefore we conclude that for performing multivariate meta analysis the u statistic estimation procedure is a viable alternative to reml and mmm easy implementation of all three methods are illustrated by their application to data from two published meta analysis from the fields of hip fracture and periodontal disease we discuss ideas for future research based on u statistic for testing significance of between study heterogeneity and for extending the work to meta regression setting copyright 2011 john wiley sons ltd

the design of a precompensator for multivariable adaptive control a network theoretic approach a network theoretic approach to the design of a dynamic precompensator c s for a multiinput multioutput plant t s is considered the design is based on the relative degree of each element of t s specifically an efficient algorithm is presented for determining whether a given plant t s has a diagonal precompensator c s such that for almost all cases t s c s has a diagonal interactor the algorithm also finds any optimal precompensator in the sense that the total relative degree is minimal the algorithm can be easily modified to work even when a t s represented by a nonsquare matrix is given

missing data methods for generalized linear models a comparative review missing data is a major issue in many applied problems especially in the biomedical sciences we review four common approaches for inference in generalized linear models glms with missing covariate data maximum likelihood ml multiple imputation mi fully bayesian fb and weighted estimating equations wees there is considerable interest in how these four methodologies are related the properties of each approach the advantages and disadvantages of each methodology and computational implementation we examine data that are missing at random and nonignorable missing for ml we focus on techniques using the em algorithm and in particular discuss the em by the method of weights and related procedures as discussed by ibrahim for mi we examine the techniques developed by rubin for fb we review approaches considered by ibrahim et al for wee we focus on the techniques developed by robins et al we use a real dataset and a detailed simulation study to compare the four methods

bayesian measures of model complexity and fit summary we consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined using an information theoretic argument we derive a measure pd for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest in general pd approximately corresponds to the trace of the product of fisher s information and the posterior covariance which in normal models is the trace of the hat matrix projecting observations onto fitted values its properties in exponential families are explored the posterior mean deviance is suggested as a bayesian measure of fit or adequacy and the contributions of individual observations to the fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages adding pd to the posterior mean deviance gives a deviance information criterion for comparing models which is related to other information criteria and has an approximate decision theoretic justification the procedure is illustrated in some examples and comparisons are drawn with alternative bayesian and classical proposals throughout it is emphasized that the quantities required are trivial to compute in a markov chain monte carlo analysis

markov chain monte carlo convergence diagnostics a comparative review abstract a critical issue for users of markov chain monte carlo mcmc methods in applications is how to determine when it is safe to stop sampling and use the samples to estimate characteristics of the distribution of interest research into methods of computing theoretical convergence bounds holds promise for the future but to date has yielded relatively little of practical use in applied work consequently most mcmc users address the convergence problem by applying diagnostic tools to the output produced by running their samplers after giving a brief overview of the area we provide an expository review of 13 convergence diagnostics describing the theoretical basis and practical implementation of each we then compare their performance in two simple models and conclude that all of the methods can fail to detect the sorts of convergence failure that they were designed to identify we thus recommend a combination of strategies aimed at evaluating and accelerating mcmc sampler convergence including ap

multi variable hermite matrix polynomials properties and applications abstract in this paper the multi variable hermite matrix polynomials are introduced by algebraic decomposition of exponential operators their properties are established using operational methods the matrix forms of the chebyshev and truncated polynomials of two variable are also introduced which are further used to derive certain operational representations and expansion formulae

finding mixed families of special polynomials associated with appell sequences abstract in this paper certain mixed special polynomial families associated with appell sequences are introduced and their properties are established further operational rules providing connections between these families and known special polynomials are established which are used to derive the identities and results for the members of these new families determinantal definitions of the polynomials associated with appell family are also derived the approach presented is general

bayesian inference for multivariate meta regression with a partially observed within study sample covariance matrix multivariate meta regression models are commonly used in settings where the response variable is naturally multidimensional such settings are common in cardiovascular and diabetes studies where the goal is to study cholesterol levels once a certain medication is given in this setting the natural multivariate endpoint is low density lipoprotein cholesterol ldl c high density lipoprotein cholesterol hdl c and triglycerides tg ldl c hdl c tg in this article we examine study level aggregate multivariate meta data from 26 merck sponsored double blind randomized active or placebo controlled clinical trials on adult patients with primary hypercholesterolemia our goal is to develop a methodology for carrying out bayesian inference for multivariate meta regression models with study level data when the within study sample covariance matrix s for the multivariate response data is partially observed specifically the proposed methodology is based on postulating a multivariate random effects re

certain results for the 2 variable apostol type and related polynomials in this article the 2 variable general polynomials are taken as base with apostol type polynomials to introduce a family of 2 variable apostol type polynomials these polynomials are framed within the context of monomiality principle and their properties are established certain summation formulae for these polynomials are also derived examples of some members belonging to this family are considered and numbers related to some mixed special polynomials are also explored

generating functions involving hermite laguerre polynomials using operational methods in this paper some generating functions involving 3 variable hermite laguerre polynomials are derived by using operational methods further generating functions for the polynomials related to hermite laguerre polynomials are also obtained as applications of the main results

an algorithm for the calculation of a nilpotent interactor matrix for linear multivariable systems a new algorithm for the calculation of the delay structure for a linear multivariable system is presented the algorithm evaluates a nilpotent interactor matrix from the matrix of coefficients of the numerator of a right matrix fraction description of the system the resulting nilpotent interactor is a product of first degree nilpotent polynomial matrices

on the role of the interactor matrix in multiinput multioutput adaptive control recent papers have shown that the system interactor matrix plays an important role in the multiinput multioutput adaptive control in these papers however the impression may have been inadvertently conveyed that the interactor matrix can be taken to be diagonal in almost all cases this note shows that this impression is false and that in general a nondiagonal interactor matrix should be considered

operational methods and laguerre gould hopper polynomials abstract in this paper the authors introduce the laguerre gould hopper polynomials by combining the operational methods with the principle of monomiality generating function series definition differential equation and certain other properties of laguerre gould hopper polynomials are derived further operational representations of these polynomials are established which are used to get integral representations and expansion formulae for these polynomials

multivariable adaptive control as a natural extension of siso adaptive control the concepts of a potentially structural non singularity and a structural non singularity are introduced in this paper using these concepts we derive the result that for almost all cases the plant to be controlled has a diagonal interactor by using an appropriate diagonal proper precompensator furthermore both the precom pensator and the interactor can be determined only from the structural information of t s the relative degrees of each element of t s without requiring any parametric information about t s therefore by assuming that the a priori knowledge of the plant consists of the relative degrees of each element of t s as well as the observability index of t s we can make mi mo adaptive control be quite a natural extension of siso adaptive control

global convergence for adaptive one step ahead optimal controllers based on input matching this paper establishes global convergence for adaptive one step ahead optimal controllers applied to a class of linear discrete time single input single output systems the class of systems includes all stable systems whether they are minimum phase or not all minimum phase systems whether they are stable or not and some unstable nonminimum phase systems the key substantive assumption is that the one step ahead optimal controller designed using the true system parameters leads to a stable closed loop system subject to this natural restriction it is shown that a simple adaptive control algorithm based on input matching is globally convergent in the sense that the system inputs and outputs remain bounded for all time and the input converges to the one step ahead optimal input both deterministic and stochastic cases are treated

the collapsed gibbs sampler in bayesian computations with applications to a gene regulation problem abstract this article describes a method of grouping and collapsing in using the gibbs sampler and proves from an operator theory viewpoint that the method is in general beneficial the norms of the forward operators associated with the corresponding nonreversible markov chains are used to discriminate among different simulation schemes when applied to bayesian missing data problems the idea of collapsing suggests skipping the steps of sampling parameter s values in standard data augmentation by doing this we obtain a predictive update version of the gibbs sampler a procedure of calculating the posterior odds ratio via the collapsed gibbs sampler when incomplete observations are involved is presented as an illustration of possible applications three examples along with a bayesian treatment for identifying common protein binding sites in unaligned dna sequences are provided

generalized polynomials and associated operational identities we use operational identities to introduce multivariable laguerre polynomials we explore the wealth of differential equations they satisfy we analyze their properties and the link with legendre type polynomials

design of g interactor and its application to direct multivariable adaptive control in the design of multi input multi output mimo adaptive control systems an interactor plays an important role the derivation of the interactor requires system parameter values unless the interactor is in diagonal form this is a considerable restriction when the interactor is applied to the adaptive control system design in mimo adaptive control many parameters must be estimated to achieve good tracking over parametrization causes many problems e g bad tracking performance and long calculation time of control input a design of interactor called a g interactor for unknown mimo plants is given it is applied to mimo adaptive control systems the g interactor requires minimum information on the plant such as the relative degree of each element of the plant transfer matrix for this design a canonical form called the g canonical form of a matrix a is investigated the canonical form is also used to eliminate redundant parameters of mimo adaptive control systems numerical examples show the effect

bivariate mittag leffler functions arising in the solutions of convolution integral equation with 2d laguerre konhauser polynomials in the kernel abstract recently the 2d laguerre konhauser polynomials were introduced in 1 in the present paper first of all we propose another bivariate polynomial family which is bi orthonormal with the 2d laguerre konhauser polynomials then we consider a convolution integral equation with 2d laguerre konhauser polynomials in the kernel and we obtain its solution by introducing a new family of bivariate mittag leffler functions furthermore we introduce a double fractional integral operator including bivariate mittag leffler functions in the kernel this integral operator includes the double riemann liouville fractional integral operator we investigate its transformation properties on the continuous function and lebesgue summable function spaces also the semigroup property of the operator is investigated we further study some miscelenenous properties of 2d laguerre konhauser polynomials and bivariate mittag leffler functions such as generating function schlafli s integral represantation finally we approximate to the image of any bivariate continuous function under the action of the proposed double integral operators

some properties of hermite based sheffer polynomials abstract in this paper the concepts and the formalism associated with monomiality principle and sheffer sequences are used to introduce family of hermite based sheffer polynomials some properties of hermite sheffer polynomials are considered further an operational formalism providing a correspondence between sheffer and hermite sheffer polynomials is developed furthermore this correspondence is used to derive several new identities and results for members of hermite sheffer family

some properties of legendre gould hopper polynomials and operational methods abstract in this paper the author introduces the legendre gould hopper polynomials by combining the operational methods with the principle of monomiality generating functions series definition differential equation and certain other properties of legendre gould hopper polynomials are derived further operational representations of these polynomials are established which are used to get integral representations and expansion formulae certain summation formulae for these polynomials are also obtained

multivariable adaptive control without a prior knowledge of the delay matrix this paper is concerned with the structure and role of the time delay matrix in discrete time multivariable processes interpretations and properties of this matrix as a multivariable generalization of the siso delay term are discussed it is formally shown that a finite time horizon or multi step cost function for the multivariable case can be minimized subject to a suitable choice of output and control horizons and without prior knowledge of the system delay matrix

bilateral generating functions and operational methods bilateral generating functions are those involving products of different types of polynomials we show that operational methods offer a powerful tool to derive these families of generating functions we study cases relevant to products of hermite polynomials with laguerre legendre and other polynomials we also propose further extensions of the method which we develop here

generalized and mixed type gegenbauer polynomials abstract in this paper a new generalized form of the gegenbauer polynomials is introduced by using the integral representation method further the hermite gegenbauer and the laguerre gegenbauer polynomials are introduced by using the operational identities associated with the generalized hermite and laguerre polynomials of two variables