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Growth Curve Models and Statistical Diagnostics
Get PDFGrowth-curve models are generalized multivariate analysis-of-variance models. The basic idea of the models is to use different polynomials to fit different treatment groups involved in the longitudinal study. It is not uncommon, however, to find outliers and influential observations in growth data that heavily affect statistical inference in growth curve models. This book provides a comprehensive introduction to the theory of growth curve models with an emphasis on statistical diagnostics. A variety of issues on model fittings and model diagnostics are addressed, and many criteria for outlier detection and influential observation identification are created within likelihood and Bayesian frameworks. This book is intended for postgraduates and statisticians whose research involves longitudinal study, multivariate analysis and statistical diagnostics, and also for scientists who analyze longitudinal data and repeated measures. The authors provide theoretical details on the model fittings and also emphasize the application of growth curve models to practical data analysis, which are reflected in the analysis of practical examples given in each chapter. The book assumes a basic knowledge of matrix algebra and linear regression. Jian-Xin Pan is a lecturer in Medical Statistics of Keele University in the U.K. He has published more than twenty papers on growth curve models, statistical diagnostics and linear/non-linear mixed models. He has a long-standing research interest in longitudinal data analysis and repeated measures in medicine and agriculture. Kai-Tai Fang is a chair professor in Statistics of Hong Kong Baptist University and a fellow of the Institute of Mathematical Statistics. He has published several books with Springer-Verlag, Chapman & Hall, and Science Press and is an author or co-author of over one hundred papers. His research interest includes generalized multivariate analysis, elliptically contoured distributions and uniform design
New relations in the algebra of the Baxter Q-operators
No full textWe consider irreducible cyclic representations of the algebra of monodromy matrices corresponding to the R-matrix of the six-vertex model. At roots of unity, the Baxter Q-operator can be represented as a trace of a tensor product of L-operators corresponding to one of these cyclic representations, and this operator satisfies the TQ equation. We find a new algebraic structure generated by these L-operators and consequently by the Q-operators
Lie powers of modules for groups of prime order
No full textLet be the free Lie algebra on a finite-dimensional vector space over a field , with homogeneous components for . If is a group and is a -module, the action of extends naturally to , and the become finite-dimensional -modules, called the Lie powers of . In the decomposition problem, the aim is to identify the isomorphism types of indecomposable -modules, with their multiplicities, in unrefinable direct decompositions of the Lie powers. This paper is concerned with the case where has prime order , and has characteristic . As is well known, there are indecomposables, denoted here by , where has dimension . A theory is developed which provides information about the overall module structure of and gives a recursive method for finding the multiplicities of in the Lie powers . For example, the theory yields decompositions of as a direct sum of modules isomorphic either to or to an infinite sum of the form with . Closed formulae are obtained for the multiplicities of in and . For , the indecomposables which occur with non-zero multiplicity in are identified for all sufficiently large
Elliptic algebras
No full textThis survey is devoted to associative -graded algebras presented by n generators and quadratic relations and satisfying the so-called Poincaré–Birkhoff–Witt condition (PBW-algebras). Examples are considered of such algebras, depending on two continuous parameters (namely, on an elliptic curve and a point on it), that are flat deformations of the polynomial ring in n variables. Diverse properties of these algebras are described, together with their relations to integrable systems, deformation quantization, moduli spaces, and other directions of modern investigations
Fluctuations in viscous fingering
No full textOur experiments on viscous (Saffman-Taylor) fingering in Hele-Shaw channels reveal finger width fluctuations that were not observed in previous experiments, which had lower aspect ratios and higher capillary numbers Ca. These fluctuations intermittently narrow the finger from its expected width. The magnitude of these fluctuations is described by a power law, Ca-0.64, which holds for all aspect ratios studied up to the onset of tip instabilities. Further, for large aspect ratios, the mean finger width exhibits a maximum as Ca is decreased instead of the predicted monotonic increase
The hit problem for symmetric polynomials over the Steenrod algebra
No full textWe cite [18] for references to work on the hit problem for the polynomial algebra P(n) = [open face F]2[x1, ;…, xn] = [oplus B: plus sign in circle]d[gt-or-equal, slanted]0 Pd(n), viewed as a graded left module over the Steenrod algebra [script A] at the prime 2. The grading is by the homogeneous polynomials Pd(n) of degree d in the n variables x1, …, xn of grading 1. The present article investigates the hit problem for the [script A]-submodule of symmetric polynomials B(n) = P(n)[sum L: summation operator]n , where [sum L: summation operator]n denotes the symmetric group on n letters acting on the right of P(n). Among the main results is the symmetric version of the well-known Peterson conjecture. For a positive integer d, let [mu](d) denote the smallest value of k for which d = [sum L: summation operator]ki=1(2[lambda]i[minus sign]1), where [lambda]i [gt-or-equal, slanted] 0
On the existence of flexural edge waves on thin orthotopic plates
No full textThis paper is concerned with an investigation into the existence of waves propagating along a free
edge of an orthotropic plate, where the edge is inclined at arbitrary angle to a principal direction of
the material. After deriving the governing equation and edge conditions, an edge wave ansatz is
substituted into this system to reduce it to a set of algebraic equations for the edge wave wave
number and wave vector. These are solved numerically for several typical composite materials
although analytic expressions can be obtained in the case of special values of the material
parameters and inclination angle. It is found that a unique edge wave solution, which generally
exhibits oscillation as well as decay away from the free edge, exists in all cases, and its wave speed
is independent of its direction of propagation along the plate
Influence of conductive heat-losses on the propagation of premixed flames in channels
No full textWe study the propagation of premixed flames in two-dimensional channels accounting for heat-losses by conduction to the channel’s walls and a prescribed Poiseuille flow. A diffusive-thermal model is used and the calculations reported are based on Arrhenius-type chemistry. Attention is focused on the influence of the magnitude of heat losses, the channel width, and the mean flow velocity. Special attention is devoted to the determination of the global burning rate and to extinction conditions. Depending on the channel width we discuss two possible modes of extinction: total flame extinction brought about in narrow channels by excessive losses, and partial flame extinction near the walls of wider channels. Our predictions of the quenching distance, namely the smallest channel’s width that permits flame propagation, and the dead space in the case of partial extinction are in agreement with experimentally reported values. The sensitivity of the flame to an imposed flow, being directed either towards the fresh mixture or towards the burned gas, is examined with some details
Pure injective envelopes of finite length modules over a generalized Weyl algebra
No full textWe investigate certain pure injective modules over generalised Weyl algebras. We consider pure injective hulls of finite length modules, the elementary duals of these, torsionfree pure injective modules, and the closure in the Ziegler spectrum of the category of finite length modules supported on a nondegenerate orbit of a generalized Weyl algebra. We also show that this category is a direct sum of uniserial categories and admits almost split sequences. We find parallels to but also marked contrasts with the behaviour of pure injective modules over finite-dimensional algebras and hereditary orders