Pseudocomplemented lattice effect algebras and existence of states

We prove that in every pseudocomplemented atomic lattice effect algebra the subset of all pseudocomplements is a Boolean algebra including the set of sharp elements as a subalgebra. As an application, we show families of effect algebras for which the existence of a pseudocomplementation implies the existence of states. These states can be obtained by smearing of states existing on the Boolean algebra of sharp elements.     

Some types of filters in BL algebras

In this paper we introduce some types of filters in a BL algebra A, and we state and prove some theorems which determine the relationship between these notions and other filters of a BL algebra, and by some examples we show that these notions are different. Also we consider some relations between these filters and quotient algebras that are constructed via these filters.     

The pasting constructions of lattice ordered effect algebras

The aim of this paper is to present some ways of constructing a lattice ordered effect algebra from the given family of MV-algebras. The loop lemma of lattice ordered effect algebras is proved. Then the definitions of Greechie diagrams of effect algebras are given. All these results have generalized those of orthomodular lattices. As applications of loop lemma and Greechie diagrams, some lattice ordered effect algebras without states are presented.     

?ukasiewicz transform and its application to compression and reconstruction of digital images

We define the ?ukasiewicz transform as a residuated map and a homomorphism between semimodules over the semiring reducts of an MV-algebra. Then we describe the “?ukasiewicz Transform Based” (?TB) algorithm for image processing, demonstrating its applicability.     

Partial quasi-metrics

In this article we introduce and investigate the concept of a partial quasi-metric and some of its applications. We show that many important constructions studied in Matthews's theory of partial metrics can still be used successfully in this more general setting. In particular, we consider the bicompletion of the quasi-metric space that is associated with a partial quasi-metric space and study its applications in groups and BCK-algebras.     

Notes on redefined fuzzy implicative filters of lattice implication algebras

The concept of -fuzzy implicative filters of lattice implication algebras is introduced and some of its related properties are investigated. In particular, the relationships among the ordinary fuzzy implicative filters, the (∈,∈∨q)-fuzzy implicative filters and the -fuzzy implicative filters of lattice implication algebras will be studied.     

Bootstrap based tests for generalized negative binomial distribution

Goodness of fit test statistics based on the empirical distribution function (EDF) are considered for the generalized negative binomial distribution. The small sample levels of the tests are found to be very close to the nominal significance levels. For small sample sizes, the tests are compared with respect to their simulated power of detecting some alternative hypotheses against a null hypothesis of generalized negative binomial distribution. The discrete Anderson—Darling test is the most powerful among the EDF tests. Two numerical examples are used to illustrate the application of the goodness of fit tests. The support received from the Research Professorship Program at Central Michigan University under the grant #22159 is gratefully acknowledged.     

Testing equality of inverse Gaussian means under heterogeneity, based on generalized test variable

The inverse Gaussian (IG) distribution is an ideal candidate for modelling positive, right-skewed data due to the fact that its inference theory and methodology bear a striking resemblance to the normal theory and methods. For testing equality of several IG means under the assumption of equal scale parameters, there exists the ANORE (analysis of reciprocal) F test, which is analogous to the ANOVA F test for the normal distribution. In this article, the concept of generalized P-value, introduced by Tsui and Weerahandi [1989. Generalized P-values in significance testing of hypotheses in the presence of nuisance parameters. J. Amer. Statist. Assoc. 84, 602-607], is applied for testing equality of several IG means for the general cases without the assumption of homogeneity. Simulation results indicate that the proposed test has excellent type I error control under both heterogeneity and homogeneity, whereas the type I error probabilities of the ANORE test can be much larger than the nominal level under heterogeneity. The proposed procedure is illustrated using two examples.     

一种基于单片机的可自动关闭音乐的耳机装置

设计了一种基于单片机的可以自动关闭手机音乐播放器的耳机装置。该装置以STC12LE2052单片机为主控器,以三轴数字陀螺仪L3G4200D为位置检测传感器,通过检测耳机使用者头部的运动状态,由主控器判断人是否进入睡眠状态,如进入睡眠状态则向手机发送信号,将音乐停止。     

A Proof of the Consistency of the Finite Difference Technique on Sparse Grids

In this paper, we give a proof of the consistency of the finite difference technique on regular sparse grids [7, 18]. We introduce an extrapolation-type discretization of differential operators on sparse grids based on the idea of the combination technique and we show the consistency of this discretization. The equivalence of the new method with that of [7, 18] is established. Received February 8, 2000; revised June 8, 2000