Permanence of stability for a class of system of differential equations with two delays

The paper studies a class of a system of linear retarded differential difference equations with several parameters. It presents some sufficient conditions under which no stability changes for an equilibrium point occurs. Application of these results is given.     

Calorimetry to Evaluate Inclusion Mechanism in the Complexation Between 2-hydroxypropyl-β-cyclodextrin and Barbiturates in Aqueous Solution

Two different types (structures) of inclusion complexes with a 1:1 stoichiometry between barbiturates and 2-hydroxypropyl-β-cyclodextrin (HPCyD) were realized in aqueous solution using isothermal titration calorimetry and molecular dynamics simulation. The first type of complex with a higher association constant was entropy driven and the substituent R ₂ was inserted into the HPCyD cavity by hydrophobic interaction. The barbituric acid ring contributed to the second type of complex, which was characterized by large negative values of ΔH and small positive ΔS reflecting van der Waals interaction and/or hydrogen bonding formation between the hetero atoms in the barbituric acid ring and the secondary hydroxyl groups of HPCyD. This revised version was published online in July 2006 with corrections to the Cover Date.     

Grade 3 students’ mathematization through modeling: Situation models and solution models with mutli-digit subtraction problem solving

In considering mathematics problem solving as a model-eliciting activity ( [Lesh and Doerr, 2003], [Lesh and Harel, 2003] and [Lesh and Zawojewski, 2008]), it is important to know what students are modeling for the problems: situations or solutions. This study investigated Grade 3 students’ mathematization process by examining how they modeled different types of multi-digit subtraction situation problems. Students’ modeling processes differed from one problem type to another due to their prior experiences and the complexity of the problems. This study showed that students make their own distinctions between solution and situation models in their mathematization process. Mathematics curricula and teaching should consider these distinctions to carefully facilitate different model development of and support student understanding of a content topic.     

Mass probe-assisted ionization method for total analysis of biomolecules with electrospray ionization-mass spectrometry

In this paper, we review the mass probes used for the derivation of a variety of biomolecules efficiently detected by the electrospray ionization-mass spectrometry and mass probe-assisted ionization method for total analysis and determination by consecutive detection with a single instrument. We describe mass probes for a variety of molecules including proteins, nucleobases, metallic cations, and other small molecules.     

A generalized Pólya urn model and related multivariate distributions

In this paper, we study of Pólya urn model containing balls of (m+1) different labels under a general replacement scheme, which is characterized by an (m+1) × (m+1) addition matrix of integers without constraints on the values of these (m+1)² integers other than non-negativity. LetX ₁,X ₂,...,X _n be trials obtained by the Pólya urn scheme (with possible outcomes: “O”, “1”,...“m”). We consider the multivariate distributions of the numbers of occurrences of runs of different types arising from the various enumeration schemes and give a recursive formula of the probability generating function. Some closed form expressions are derived as special cases, which have potential applications to various areas. Our methods for the derivation of the multivariate run-related distribution are very simple and suitable for numerical and symbolic calculations by means of computer algebra systems. The results presented here develop a general workable framework for the study of Pólya urn models. Our attempts are very useful for understanding non-classic urn models. Finally, numerical examples are also given in order to illustrate the feasibility of our results. This research was partially supported by the ISM Cooperative Research Program (2003-ISM·CRP-2007).     

Start-Up Demonstration Tests Under Markov Dependence Model with Corrective Actions

A general probability model for a start-up demonstration test is studied. The joint probability generating function of some random variables appearing in the Markov dependence model of the start-up demonstration test with corrective actions is derived by the method of probability generating function. By using the probability generating function, several characteristics relating to the distribution are obtained.     

On the Waiting Time for the First Success Run

Let k and m are positive integers with k ≥ m. The probability generating function of the waiting time for the first occurrence of consecutive k successes in a sequence of m-th order Markov dependent trials is given as a function of the conditional probability generating functions of the waiting time for the first occurrence of consecutive m successes. This provides an efficient algorithm for obtaining the probability generating function when k is large. In particular, in the case of independent trials a simple relationship between the geometric distribution of order k and the geometric distribution of order k−1 is obtained. This research was partially supported by the ISM Cooperative Research Program(2004-ISM-CRP-2006) and by a Grant-in-Aid for Scientific Research (C) of the JSPI (Grant Number 16500183)     

Automatic polymerase chain reaction product detection system for food safety monitoring using zinc finger protein fused to luciferase

An automatic polymerase chain reaction (PCR) product detection system for food safety monitoring using zinc finger (ZF) protein fused to luciferase was developed. ZF protein fused to luciferase specifically binds to target double stranded DNA sequence and has luciferase enzymatic activity. Therefore, PCR products that comprise ZF protein recognition sequence can be detected by measuring the luciferase activity of the fusion protein. We previously reported that PCR products from Legionella pneumophila and Escherichia coli (E. coli) O157 genomic DNA were detected by Zif268, a natural ZF protein, fused to luciferase. In this study, Zif268–luciferase was applied to detect the presence of Salmonella and coliforms. Moreover, an artificial zinc finger protein (B2) fused to luciferase was constructed for a Norovirus detection system. In the luciferase activity detection assay, several bound/free separation process is required. Therefore, an analyzer that automatically performed the bound/free separation process was developed to detect PCR products using the ZF–luciferase fusion protein. By means of the automatic analyzer with ZF–luciferase fusion protein, target pathogenic genomes were specifically detected in the presence of other pathogenic genomes. Moreover, we succeeded in the detection of 10 copies of E. coli BL21 without extraction of genomic DNA by the automatic analyzer and E. coli was detected with a logarithmic dependency in the range of 1.0 × 10 to 1.0 × 10⁶ copies.     

On nonparametric tests for symmetry inRm

This paper considers the problem for testing symmetry of a distribution inR ^m based on the empirical distribution function. Limit theorems which play important roles for investigating asymptotic behavior of such tests are obtained. The limit processes of the theorems are multiparameter Wiener process. Based on the limit theorems, nonparametric tests are proposed whose asymptotic distributions are functionals of a multiparameter standard Wiener process. The tests are compared asymptotically with each other in the sense of Bahadur.