On correspondence between solutions of a family of cubic Thue equations and isomorphism classes of the simplest cubic fields

Let m?−1 be an integer. We give a correspondence between integer solutions to the parametric family of cubic Thue equations

X³−mX²Y−(m+3)XY²−Y³=λ     

On uniqueness of characteristic classes

We give an axiomatic characterization of maps from algebraic K-theory. The results apply to a large class of maps from algebraic K-theory to any suitable cohomology theory or to algebraic K-theory. In particular, we obtain comparison theorems for the Chern character and Chern classes and for the Adams operations and λ-operations on higher algebraic K-theory. We show that the Adams operations and λ-operations defined by Grayson agree with the ones defined by Gillet and Soulé.     

Inversion of regular analytic matrix functions: Local Smith form and subspace duality

This paper analyzes the relation between the local rank-structure of a regular analytic matrix function and the one of its inverse function. The local rank factorization (lrf) of a matrix function is introduced, which characterizes extended canonical systems of root functions and the local Smith form. An interpretation of the local rank factorization in terms of Jordan chains and Jordan pairs is provided. Duality results are shown to hold between the subspaces associated with the lrf of the matrix function and the one of its reduced adjoint.     

On consensus speed of multi-agent systems with double-integrator dynamics

The performance of multi-agent systems is an important issue. In this paper, it is focused on consensus speed for multi-agent systems with double-integrator dynamics and fixed undirected graphes under a kind of consensus protocols. It is revealed that, under some conditions, the maximum consensus speed is determined by the largest and the smallest nonzero eigenvalues of the Laplacian matrix of the undirected connected graph. Based on the mentioned results, arbitrary desired consensus speed can be achieved by choosing suitable feedback gains. Numerical simulations are given to illustrate the main results.     

On the sequences of the Weyl semi-radii associated with matricial Carathéodory and Schur sequences in both nondegenerate and degenerate cases

In this paper we discuss Weyl matrix balls in the context of the matricial versions of the classical interpolation problems named after Carathéodory and Schur. Our particular focus will be on studying the monotonicity of suitably normalized semi-radii of the corresponding Weyl matrix balls. We, furthermore, devote a fair bit of attention to characterizing the case in which equality holds for particular matricial inequalities. Solving these problems will provide us with a new perspective on the role of the central functions for the classes of Carathéodory and Schur.     

Turkish Preservice Primary School Teachers' Science Teaching Efficacy Beliefs and Attitudes Toward Science: The Effect of a Primary Teacher Education Program

The main purpose of this study was to investigate the effectiveness of a primary teacher education program in improving science teaching efficacy beliefs (personal science teaching efficacy beliefs and outcome expectancy beliefs) of preservice primary school teachers. The study also investigated whether the program has an effect on student teachers' attitudes toward science. Data were collected by administering the “Science Teaching Efficacy Beliefs Instrument” and “Attitudes toward Science Scale” to 282 preservice primary teachers (147 freshmen, 135 seniors). Statistical techniques such as means and t‐test were used to analyze the data. Results of the study showed that the primary teacher education program has a medium positive effect on science teaching efficacy beliefs of the primary preservice teachers (t = 4.791, p = .000) and that there were no gender differences in terms of efficacy beliefs. Results also indicated that preservice primary teachers' attitudes toward science were moderately positive and differ by class level. Fourth‐year preservice teachers' attitudes toward science were found to be significantly more positive than the first years (t = 5.494, p = .000). There were no gender differences in attitudes toward science.     

Principal points of a multivariate mixture distribution

A set of n-principal points of a distribution is defined as a set of n points that optimally represent the distribution in terms of mean squared distance. It provides an optimal n-point-approximation of the distribution. However, it is in general difficult to find a set of principal points of a multivariate distribution. Tarpey et al. [T. Tarpey, L. Li, B. Flury, Principal points and self-consistent points of elliptical distributions, Ann. Statist. 23 (1995) 103-112] established a theorem which states that any set of n-principal points of an elliptically symmetric distribution is in the linear subspace spanned by some principal eigenvectors of the covariance matrix. This theorem, called a “principal subspace theorem”, is a strong tool for the calculation of principal points. In practice, we often come across distributions consisting of several subgroups. Hence it is of interest to know whether the principal subspace theorem remains valid even under such complex distributions. In this paper, we define a multivariate location mixture model. A theorem is established that clarifies a linear subspace in which n-principal points exist.     

Analysis of NMAR missing data without specifying missing-data mechanisms in a linear latent variate model

It is natural to assume that a missing-data mechanism depends on latent variables in the analysis of incomplete data in latent variate modeling because latent variables are error-free and represent key notions investigated by applied researchers. Unfortunately, the missing-data mechanism is then not missing at random (NMAR). In this article, a new estimation method is proposed, which leads to consistent and asymptotically normal estimators for all parameters in a linear latent variate model, where the missing mechanism depends on the latent variables and no concrete functional form for the missing-data mechanism is used in estimation. The method to be proposed is a type of multi-sample analysis with or without mean structures, and hence, it is easy to implement. Complete-case analysis is shown to produce consistent estimators for some important parameters in the model.     

Normality of products of monotonically normal spaces with compact spaces

Let S be the class of all spaces, each of which is homeomorphic to a stationary subset of a regular uncountable cardinal (depending on the space). In this paper, we prove the following result: The product X×C of a monotonically normal space X and a compact space C is normal if and only if S×C is normal for each closed subspace S in X belonging to S. As a corollary, we obtain the following result: If the product of a monotonically normal space and a compact space is orthocompact, then it is normal.