Numbers of Success-Runs of Specified Length Until Certain Stopping Time Rules and Generalized Binomial Distributions of Order k

A new distribution called a generalized binomial distribution of order k is defined and some properties are investigated. A class of enumeration schemes for success-runs of a specified length including non-overlapping and overlapping enumeration schemes is rigorously studied. For each nonnegative integer less than the specified length of the runs, an enumeration scheme called -overlapping way of counting is defined. Let k and be positive integers satisfying < k. Based on independent Bernoulli trials, it is shown that the number of (– 1)-overlapping occurrences of success-run of length k until the n-th overlapping occurrence of success-run of length follows the generalized binomial distribution of order (k–). In particular, the number of non-overlapping occurrences of success-run of length k until the n-th success follows the generalized binomial distribution of order (k– 1). The distribution remains unchanged essentially even if the underlying sequence is changed from the sequence of independent Bernoulli trials to a dependent sequence such as higher order Markov dependent trials. A practical example of the generalized binomial distribution of order k is also given.     

Synthesis and evaluation of 1-arylsulfonyl-3-piperazinone derivatives as a factor Xa inhibitor II. Substituent effect on biological activities

Intravascular clot formation is an important event in a number of cardiovascular diseases. The prevention of blood coagulation has become a major target for new therapeutic agents. Factor Xa (FXa) is a trypsin-like serine protease that plays a key role in the blood coagulation cascade and represents an attractive target for anticoagulant drug development. We have investigated substituents in the central part of a lead compound (3: M55113), and discovered that compound M55551 (34: (R)-4-[(6-Chloro-2-naphthalenyl)sulfonyl]-6-oxo-1-[[1-(4-pyridinyl)-4-piperidinyl]methyl]-2-piperazinecarboxylic acid) is a potent inhibitor of FXa (IC(50)=0.006 microM), with high selectivity for FXa over trypsin and thrombin. The activity of this compound is ten times more powerful than the lead compound.     

Asymmetric Total Synthesis of Indole Alkaloids Containing an Indoline Spiroaminal Framework

The total synthesis of the indole alkaloids, neoxaline, oxaline and meleagrin A, all containing a unique indoline spiroaminal framework, was accomplished through the stereoselective introduction of a reverse prenyl group to the congested benzylic carbon of furoindoline, a two‐pot transformation of indoline (containing three nitrogen atoms at appropriate positions) to the featured indoline spiroaminal framework, and elimination of carbonate assisted by the adjacent imidazole moiety to construct the (E)‐dehydrohistidine. The absolute stereochemistry of neoxaline was elucidated through our total synthesis. In addition, we evaluated the bioactivity, especially the anti‐infectious properties, of neoxaline and oxaline, and of some synthetic intermediates.     

Determination of mineral and trace element concentrations in pine needles by ICP-OES: evaluation of different sample pre-treatment methods

In the present study, the determination of mineral and trace elements (Al, B, Ca, Cu, Fe, K, Mg, Mn, Na, P and Zn) from pine needles using three sample pre-treatment methods followed by inductively coupled plasma optical emission spectrometry, was examined. Sample pre-treatment methods tested were microwave digestion, ultrasound-assisted digestion and dry ashing. The new ultrasound-assisted digestion method was optimised by the analysis of the standard reference material (SRM) 1575a (pine needles) sample. The speed of dry ashing method was significantly increased by ultrasound dissolution after ashing. All the ICP-OES measurements were performed in robust plasma conditions which were tested by measuring the Mg II 280.270 nm/Mg I 285.213 nm line intensity ratios. The microwave digestion resulted generally in slightly higher element concentrations than ultrasound-assisted digestion. B, Cu and Na resulted in such low concentrations that they could not be accurately determined by using the microwave digestion method. The t-tests found no significant differences between the certified and the determined element concentrations of the SRM 1575a using the dry ashing method followed with ultrasound dissolution.     

1,4‐Diiodobenzene with –COO–TEMPO (TEMPO = 2,2,6,6‐tetramethylpiperidine‐1‐oxyl‐4‐yl) substituents at 2,5‐positions: synthesis and use as a monomer for new π‐conjugated polymers having nitroxyl radicals in side chains

The reaction of 2,5‐diiodo‐1,4‐benzenedicarbonyl chloride, C₆H₂I₂(COCl)₂‐p, with 4‐hydroxy‐2,2,6,6‐tetramethyl‐1‐piperidinyloxy (TEMPO‐ol) gave I–Ph(COO–TEMPO)₂–I, Monomer‐1. Pd‐catalyzed polycondensation of Monomer‐1 with Me₃Sn‐Th‐SnMe₃ (2,5‐bis(trimethylstannyl)thiophene) and Bu₃Sn–CH = CH–SnBu₃ (1,2‐bis‐(tributylstannyl)ethylene) gave the corresponding π‐conjugated polymers, Polymer‐1 and Polymer‐2, respectively. Monomer‐1 was converted to a diethynyl compound, H–C ≡ C–Ph(COO–TEMPO)₂–C ≡ C–H (Monomer‐1'), and Pd‐catalyzed polycondensation between Monomer‐1 and Monomer‐1' gave a π‐conjugated poly(arylene ethynylene) type polymer, Polymer‐3. According to the expansion of the π‐conjugation system by the polymerization, the UV–vis peaks of Monomer‐1 (λ_max = 323 nm) and Monomer‐1' (327 nm) are shifted to longer wavelengths (λ_max = 365 nm, 385 nm, and 396 nm for Polymer‐1, Polymer‐2, and Polymer‐3, respectively). Polymer‐1–Polymer‐3 showed ESR signals at about g = 2.01 with reasonable intensities. They are electrochemically active and showed a peak current anodic (oxidation) peak at about 0.9 V versus Ag/AgCl, which is reasonable for TEMPO polymers. Copyright © 2013 John Wiley & Sons, Ltd.     

On Waiting Time for Reversed Patterns in Random Sequences

By using a combinatorial method it is shown that for every finite pattern, the distribution of the waiting time for the reversed pattern coincides with that of the waiting time for the original pattern in a multi-state dependent sequence with a certain type of exchangeability. The number of the typical sequences until the occurrence of a given pattern and that of the typical sequences until the occurrence of the reversed pattern are shown to be equal. Further, the corresponding results for the waiting time for the r-th occurrence of the pattern, and for the number of occurrences of a specified pattern in n trials are also studied. Illustrative examples based on urn models are also given.     

Newly developed chemical probes and nano-devices for cellular analysis.

A cellular analyzing system including a "real-time cellular imaging system" and a "comprehensive analyzing system for cellular responses" was developed. A "real-time cellular imaging system" is a system used to measure real-time imaging of multiple phenomena of a single cell with high special and temporal resolutions for the purpose to understand the pathology and physiology in a single cell and realize to single cell level diagnosis. A "real-time cellular imaging system" includes multi-probe imaging with AFM (atomic force microscopy), optical and SECM (scanning electrochemical microscopy) modes, which provides us with topological information and biochemical reactions at the local area of the interior and exterior of a cell. Scanning electrochemical/optical microscopy was applied to image PC12 cells. On the other hand, cells respond to their specific substances via their ligands. Therefore, the comprehensive analysis of protein-protein interaction is the important issue to determine the functions of cells. For this purpose, a "comprehensive analysis system for cellular responses" was developed. This system is based on SPR (surface plasmon resonance) and MS (mass spectrometry) using a nano-fabricated substrate. The interaction between IL-1 beta and anti-IL-1 beta antibodies was detected.     

Improving carbon dioxide solubility in ionic liquids

Previously we showed that CO2 could be used to extract organic molecules from ionic liquids without contamination of the ionic liquid. Consequently a number of other groups demonstrated that ionic liquid/CO2 biphasic systems could be used for homogeneously catalyzed reactions. Large differences in the solubility of various gases in ionic liquids present the possibility of using them for gas separations. More recently we and others have shown that the presence of CO2 increases the solubility of other gases that are poorly soluble in the ionic liquid phase. Therefore, a knowledge and understanding of the phase behavior of these ionic liquid/CO2 systems is important. With the aim of finding ionic liquids that improve CO2 solubility and gaining more information to help us understand how to design CO2-philic ionic liquids, we present the low- and high-pressure measurements of CO2 solubility in a range of ionic liquids possessing structures likely to increase the solubility of CO2. We examined the CO2 solubility in a number of ionic liquids with systematic increases in fluorination. We also studied nonfluorinated ionic liquids that have structural features known to improve CO2 solubility in other compounds such as polymers, for example, carbonyl groups and long alkyl chains with branching or ether linkages. Results show that ionic liquids containing increased fluoroalkyl chains on either the cation or anion do improve CO2 solubility when compared to less fluorinated ionic liquids previously studied. It was also found that it was possible to obtain similar, high levels of CO2 solubility in nonfluorous ionic liquids. In agreement with our previous results, we found that the anion frequently plays a key role in determining CO2 solubility in ionic liquids.     

Bivariate Fibonacci polynomials of order <Emphasis Type="Italic">k</Emphasis> with statistical applications

In the present article, we investigate the properties of bivariate Fibonacci polynomials of order k in terms of the generating functions. For k and ℓ (1 ≤ ℓ ≤ k − 1), the relationship between the bivariate Fibonacci polynomials of order k and the bivariate Fibonacci polynomials of order ℓ is elucidated. Lucas polynomials of order k are considered. We also reveal the relationship between Lucas polynomials of order k and Lucas polynomials of order ℓ. The present work extends several properties of Fibonacci and Lucas polynomials of order k, which will lead us a new type of geneses of these polynomials. We point out that Fibonacci and Lucas polynomials of order k are closely related to distributions of order k and show that the distributions possess properties analogous to the bivariate Fibonacci and Lucas polynomials of order k.