Generalizations of Cole's Systems

There are four resolvable Steiner triple systems on fifteen elements. Some generalizations of these systems are presented here.

A Note on Coercivity of Lower Semicontinuous Functions and Nonsmooth Critical Point Theory

The first motivation for this note is to obtain a general version of the following result: let E be a Banach space and f : E → R be a differentiable function, bounded below and satisfying the Palais-Smale condition; then, f is coercive, i.e., f(x) goes to infinity as ||x|| goes to infinity. In recent years, many variants and extensions of this result appeared, see [3], [5], [6], [9], [14], [18], [19] and the references therein. A general result of this type was given in [3, Theorem 5.1] for a lower semicontinuous function defined on a Banach space, through an approach based on an abstract notion of subdifferential operator, and taking into account the “smoothness” of the Banach space. Here, we give (Theorem 1) an extension in a metric setting, based on the notion of slope from [11] and coercivity is considered in a generalized sense, inspired by [9]; our result allows to recover, for example, the coercivity result of [19], where a weakened version of the Palais-Smale condition is used. Our main tool (Proposition 1) is a consequence of Ekeland’s variational principle extending [12, Corollary 3.4], and deals with a function f which is, in some sense, the “uniform” Γ-limit of a sequence of functions.

A Computational Approach for the Statistical Estimation of Discrete Time Branching Processes with Immigration

2010 Mathematics Subject Classification: 60J80.

Classification of Texts' Authorship Using a Regression Model on Compressed Data

2010 Mathematics Subject Classification: 68T50,62H30,62J05.

Group Comparisons on Cognitive Attributes Using the Least Squares Distance Model of Cognitive Diagnosis

2010 Mathematics Subject Classification: 62P15.

Implementation of the EM Algorithm for Maximum Likelihood Estimation of a Random Effects Model for One Longitudinal Ordinal Outcome

2010 Mathematics Subject Classification: 62J99.

Lp Microlocal Supercritical Markov Branching Processes with Non-Homogeneous Poisson Immigration

2010 Mathematics Subject Classification: 60J80.

A Generalized Quasi-Likelihood Estimator for Nonstationary Stochastic Processes−Asymptotic Properties and Examples

2010 Mathematics Subject Classification: 62F12, 62M05, 62M09, 62M10, 60G42.

On Estimation and Testing for Pareto Tails

2010 Mathematics Subject Classification: 62F10, 62F12.

Sub- and Super-solutions of a Nonlinear PDE, and Application to a Semilinear SPDE

2010 Mathematics Subject Classification: 35R60, 60H15, 74H35.

On the Poisson Process of Order k Space

2010 Mathematics Subject Classification: 60E05, 62P05.

Minimum Description Length Principle in Discriminating Marginal Distributions

2010 Mathematics Subject Classification: 94A17, 62B10, 62F03.

Modeling Data for Complications in Diabetics Using Logistic Regression

2010 Mathematics Subject Classification: 62P10.

On Supra-Bayesian Weighted Combination of Available Data Determined by Kerridge Inaccuracy and Entropy

2010 Mathematics Subject Classification: 94A17.