Joint distributions of numbers of success-runs and failures until the first consecutivek successes

Joint distributions of the numbers of failures, successes and success-runs of length less thank until the first consecutivek successes are obtained for some random sequences such as a sequence of independent and identically distributed integer valued random variables, a {0, 1}-valued Markov chain and a binary sequence of orderk. There are some ways of counting numbers of runs with a specified length. This paper studies the joint distributions based on three ways of counting numbers of runs, i.e., the number of overlapping runs with a specified length, the number of non-overlapping runs with a specified length and the number of runs with a specified length or more. Marginal distributions of them can be derived immediately, and most of them are surprisingly simple.This research was partially supported by the ISM Cooperative Research Program (93-ISM-CRP-8).     

Behavior of thin rectangular ANCF shell elements in various mesh configurations

The absolute nodal coordinate formulation (ANCF) is characterized by being developed specifically for dynamic analysis of large deformation problems. The objective of the study is to investigate how the shape of the initial mesh configuration influences the obtained numerical solution. After a thorough review of three available formulations, they are used in three different convergence studies. Initially a reference study is conducted to determine how the ANCF performs in an uniform and rectangular mesh. Subsequently, the ANCF methods sensitivity to irregular mesh is investigated and finally, the ability of the ANCF method to describe curved structures is evaluated. This study concludes that thin ANCF shell elements are sensitive to both the initial shape and their loading condition. Furthermore, both the initial configuration and the loading condition affect how the ANCF-based models converge. It is suggested that models containing thin ANCF shell elements are subjected to extensive validation studies, before they are used in a design process.     

Chemical Dynamic Kinetic Resolution and S/R Interconversion of Unprotected α‐Amino Acids

Reported herein is the first purely chemical method for the dynamic kinetic resolution (DKR) of unprotected racemic α‐amino acids (α‐AAs), a method which can rival the economic efficiency of the enzymatic reactions. The DKR reaction principle can be readily applied for S/R interconversions of α‐AAs, the methodological versatility of which is unmatched by biocatalytic approaches. The presented process features a virtually complete stereochemical outcome, fully recyclable source of chirality, and operationally simple and convenient reaction conditions, thus allowing its ready scalability. A quite unique and novel mode of the thermodynamic control over the stereochemical outcome, including an exciting interplay between axial, helical, and central elements of chirality is proposed.     

Zamamidine C, 3,4-dihydro-6-hydroxy-10,11-epoxymanzamine A, and 3,4-dihydromanzamine J N-oxide, new manzamine alkaloids from sponge Amphimedon sp.

New manzamine alkaloids, zamamidine C (1), 3,4-dihydro-6-hydroxy-10,11-epoxymanzamine A (2), and 3,4-dihydromanzamine J N-oxide (3), have been isolated from an Okinawan marine sponge Amphimedon species. The structures and stereochemistries of 1-3 were elucidated from the spectroscopic data and chemical derivatization. Zamamidine C (1) is a new manzamine alkaloid possessing a second β-carboline ring via an ethylene unit at N-2 of manzamine D, while 3,4-dihydro-6-hydroxy-10,11-epoxymanzamine A (2) is the first manzamine alkaloid possessing an epoxide ring at C-10 and C-11. Zamamidine C (1) showed significant antitrypanosomal activity against Trypanosoma brucei brucei, the parasite associated with sleeping sickness, and antimalarial activity against Plasmodium falciparum, the causative agent of malaria in vitro.     

Carbohydrate recognition of C3-symmetrical tripodal receptor-type 2,4,6-trisubstituted 1,3,5-triazine derivatives with antiviral activities

Journal of Thermal Analysis and Calorimetry - In our search for new bioactive compounds that interfere with the sugar recognition process, we have designed and synthesized C3- and Cs-symmetrical...     

Effect of solution pH on complex formation between epi-type catechin and β-cyclodextrin

Journal of Thermal Analysis and Calorimetry - The effect of solution pH on the formation of an inclusion complex between (?)-epigallocatechin gallate (EGCg: pKa?=?7.5) and...     

Nucleophilic addition of benzenethiol to 1',2'-unsaturated nucleosides: 1'-C-phenylthio-2'-deoxynucleosides as anomeric radical precursors

The addition reaction of benzenethiol to the glycal portion of 1',2'-unsaturated uridine proceeds efficiently in the presence of Et(3)N. The mechanism involves nucleophilic attack of thiolate at the anomeric position in the rate-determining step, wherein conjugation between the nucleobase and the glycal portion is crucial. The derivative having a methyl group either at the 2'- or 6-position did not undergo this addition reaction, due to their sterically prohibited coplanarity. The 1',2'-unsaturated derivatives of thymine and adenine can also be used as substrates for this addition reaction. It was also shown that the resulting 1'-C-phenylthio-2'-deoxynucleosides serve as precursors for radical-mediated C-C bond formation at the anomeric position.     

Generalized Waiting Time Problems Associated with Pattern in Polya's Urn Scheme

Let X ₁, X ₂, ... be a sequence obtained by Polya's urn scheme. We consider a waiting time problem for the first occurrence of a pattern in the sequence X ₁, X ₂, ... , which is generalized by a notion score. The main part of our results is derived by the method of generalized probability generating functions. In Polya's urn scheme, the system of equations is composed of the infinite conditional probability generating functions, which can not be solved. Then, we present a new methodology to obtain the truncated probability generating function in a series up to an arbitrary order from the system of infinite equations. Numerical examples are also given in order to illustrate the feasibility of our results. Our results in this paper are not only new but also a first attempt to treat the system of infinite equations.