In [5] and [10], statistical-conservative and $\sigma $-conservative matrices were characterized. In this note we have determined a class of statistical and $\sigma $-conservative matrices studying some inequalities which are analogous to Knopp’s Core Theorem.
In this paper, we study the limit properties of countable nonhomogeneous Markov chains in the generalized gambling system by means of constructing compatible distributions and martingales. By allowing random selection functions to take values in arbitrary intervals, the concept of random selection is generalized. As corollaries, some strong limit theorems and the asymptotic equipartition property (AEP) theorems for countable nonhomogeneous Markov chains in the generalized gambling system are established. Some results obtained are extended.
The empirical moment process is utilized to construct a family of tests for the null hypothesis that a random variable is exponentially distributed. The tests are consistent against the 'new better than used in expectation' (NBUE) class of alternatives. Consistency is shown and the limit null distribution of the test statistic is derived, while efficiency results are also provided. The finite-sample properties of the proposed procedure in comparison to more standard procedures are investigated via simulation.
This paper obtains a class of tight framelet packets on $L^2(\mathbb R^d)$ from the extension principles and constructs the relationships between the basic framelet packets and the associated filters.
Butler groups formed by factoring a completely decomposable group by a rank one group have been studied extensively. We call such groups, bracket groups. We study bracket modules over integral domains. In particular, we are interested in when any bracket $R$-module is $R$ tensor a bracket group.
A graph is called weakly perfect if its chromatic number equals its clique number. In this note a new class of weakly perfect graphs is presented and an explicit formula for the chromatic number of such graphs is given.
The aim of this paper is to rank the words of the Chinese language of the III-V centuries in a number of classes that differ in their grammatical characteristics. The classification undertaken is based on syntactic criteria.
(i) The procedure introduced here for the clustering of frequency vectors takes into account the uncertainty arising from dealing with small observed frequencies. The smaller observed absolute frequencies, the more uncertainty about the “true” probability vector. The object is not represented by a single point in the multidimensional space but rather by the fuzzy set spread around this point. Consequently, the distance between two such objects is a fuzzy value, too. The expected mean distance between two objects generally differs from the simple distance: for instance, two objects with the same frequency vectors have a positive mean distance. The exact formula for estimation of the mean distance is given; this makes the algorithmization of the proposed procedure possible. The approach corresponds to that of the Bayesian estimation. The matrix of expected mean distances is an input to the hierarchical cluster analysis. (ii) The conventional hierarchical cluster analysis investigates similarities between objects from a given class. A modified general procedure is proposed seeking analogies between two classes of objects. The “two-class cluster analysis” is applicable to any kind of objects to be clustcred; it is not confined to the herein discussed special case of frequency vectors. (iii) The development of the procedure was developed initially for the field of the psychotherapy research - investigation of relationship patterns found within verbatirn protocols of sessions using the “guided imagery”, a psychotherapy technique dealing with evoked daydrearns. This constitutes an application example.