Distributions of Runs and Consecutive Systems on Directed Trees

In this paper we study exact distributions of runs on directed trees. On the assumption that the collection of random variables indexed by the vertices of a directed tree has a directed Markov distribution, the exact distribution theory of runs is extended from based on random sequences to based on directed trees. The distribution of the number of success runs of a specified length on a directed tree along the direction is derived. A consecutive-k-out-of-n:F system on a directed tree is introduced and investigated. By assuming that the lifetimes of the components are independent and identically distributed, we give the exact distribution of the lifetime of the consecutive system. The results are not only theoretical but also suitable for computation.     

Sooner and Later Waiting Time Problems for Runs in Markov Dependent Bivariate Trials

In this paper we study exact distributions of sooner and later waiting times for runs in Markov dependent bivariate trials. We give systems of linear equations with respect to conditional probability generating functions of the waiting times. By considering bivariate trials, we can treat very general and practical waiting time problems for runs of two events which are not necessarily mutually exclusive. Numerical examples are also given in order to illustrate the feasibility of our results.     

Synthesis and properties of new halogen‐substituted polyamides from 5‐halo‐m‐phenylenediamines and both aliphatic and aromatic dicarboxylic acids

New halogen‐substituted aromatic–aliphatic and wholly aromatic polyamides with high inherent viscosities were synthesized by the direct polycondensation of 5‐halo‐m‐phenylenediamines, where the halogens were Cl, Br, and I, with both aliphatic and aromatic dicarboxylic acids in N‐methyl‐2‐pyrrolidone with a mixture of triphenyl phosphite and pyridine as a condensing agent. The solubility of the halogen‐substituted polyamides was much higher than that of the parent polyamides derived from m‐phenylenediamine. The glass‐transition temperatures of the substituted aromatic–aliphatic polyamides increased in the order Cl < Br < I, whereas the temperatures of 10% weight loss in air decreased in the reverse order. The limiting oxygen index values, as an indication of flammability, increased for the substituted aromatic–aliphatic polyamides in the order Cl < Br < I. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 3911–3918, 2000     

Tocopheryl Phosphate Inhibits Rheumatoid Arthritis-Related Gene Expression In Vitro and Ameliorates Arthritic Symptoms in Mice

Anti-rheumatoid arthritis (RA) effects of α-tocopherol (α-T) have been shown in human patients in a double-blind trial. However, the effects of α-T and its derivatives on fibroblast-like synoviocytes (FLS) during the pathogenesis of RA remain unclear. In the present study, we compared the expression levels of genes related to RA progression in FLS treated with α-T, succinic ester of α-T (TS), and phosphate ester of α-T (TP), as determined via RT-PCR. The mRNA levels of interleukin (IL)-6, tumor necrosis factor-α (TNF-α), matrix metalloproteinase (MMP)-3, and MMP-13 were reduced by treatment with TP without cytotoxicity, while α-T and TS did not show such effects. Furthermore, intraperitoneal injection of TP ameliorated the edema of the foot and joint and improved the arthritis score in laminarin-induced RA model mice. Therefore, TP exerted anti-RA effects through by inhibiting RA-related gene expression.     

Short-step synthesis and structure-activity relationship of cortistatin A analogs

An improved method for synthesizing structurally simplified analogs of cortistatin A (1), a novel anti-angiogenic steroidal alkaloid from a marine sponge, was developed. In contrast to previous methods, step- and redox-economical synthesis was achieved using a known α-bromoketone as the starting material. The structure-activity relationship study revealed that the isoquinoline portion was strictly recognized by the target molecule. Surprisingly, the introduction of the acetamide moiety on the A-ring structure dramatically enhanced the selective antiproliferative activity against endothelial cells. This new method can be easily applied to gram-scale synthesis and enabled us to prepare various analogs, which were focused on the participation of the side chain and A-ring structure.     

Sooner and later waiting time problems in a two-state Markov chain

LetX ₁,X ₂,... be a time-homogeneous {0, 1}-valued Markov chain. LetF ₀ be the event thatl runs of 0 of lengthr occur and letF ₁ be the event thatm runs of 1 of lengthk occur in the sequenceX ₁,X ₂, ... We obtained the recurrence relations of the probability generating functions of the distributions of the waiting time for the sooner and later occurring events betweenF ₀ andF ₁ by the non-overlapping way of counting and overlapping way of counting. We also obtained the recurrence relations of the probability generating functions of the distributions of the sooner and later waiting time by the non-overlapping way of counting of 0-runs of lengthr or more and 1-runs of lengthk or more.     

Electrochemical fluorination of acetamide and formamide in molten KH2F3

The electrofluorination of acetamide (CH₃CONH₂) and formamide (HCONH₂) on the anode was studied in molten KH₂F₃ at 120°C. Amorphous carbon was used as the anode and Pt-rod as the reference electrode. Anodic products were analyzed by both gas chromatography and infrared spectroscopy.In the cases of both CH₃CONH₂ and HCONH₂, the anode effect occurred often in electrolysis at the current density range of 3～20 mA·cm^?2 and the anode gas was then composed 5of N₂(+O₂), NF₃, CF₄, C₂F₆, N₂O, CO₂(+COF₂) and so on. The addition of 1.0 wt% LiF into the electrolyte decreased the yield of NF₃.From these results, it is suggested that CH₃CONH₂ and HCONH₂ would react chemically with atomic fluorine produced on the (C_xF)n [x > 2] film by the discharge of fluoride ion. The mechanism of electrofluorination of CH₃CONH₂ or HCONH₂ in this melt is as follows;

     

Preparation and Characterization of Titania Thin Films from Aqueous Solutions

Dip- or spin-coating and characterization of titania (TiO₂) thin films from various aqueous solutions have been studied. The aqueous titanium solutions mainly used in this study were halogen- and chelate-free solutions with the concentrations up to 1.4 M derived from titanium isopropoxide (TIP) with tetramethylammonium hydroxide (TMAOH) or some alkylamines, while aqueous and alcoholic solutions containing titanium atoms stabilized chelating ligands were examined for comparison. The TiO₂ films prepared from the TIP-TMAOH solution were already crystallized at 350°C to anatase form and those formed at 600°C had high transparency and refractive indices of 2.40. No carbon residue in the film prepared at 400°C was detected by XPS. The pure anatase form was sustained up to 850°C. Interestingly, it was found that the (004) preferentially oriented anatase films were obtained from TIP-lactic acid (LA) system until 700°C. The solutions containing citric acid (CA) or alkanolamines yielded anatase and rutile form fired at the temperatures equal to or higher than 600°C. Carbon residue was detected in the film fired at 400°C. The film thickness monotonically decreased from the upper to the bottom ends of the substrate. However, it was found that the thickness uniformity was drastically improved by an addition of sucrose to the aqueous solutions. The effects of the solution composition and polyhydroxy compounds on the crystal modifications of formed films and the film uniformity are discussed.     

Intercalation of α,ω-Alkanediamines in Layered Aluminium Dihydrogen Triphosphate Dihydrate

Intercalation of ,-alkanediamines, NH₂(CH₂) _n NH₂ (n = 3–10), into layered aluminium dihydrogen triphosphate dihydrate, AlH₂(P₃(O₁₀... 2H₂O, was investigated by XRD, DTA-TG, elemental analysis, and solid-state ³¹P, ¹³C and ²⁷Al NMR. ,-Alkanediamines are intercalated to form a monomolecular layer in the interlayer region, in which the alkanediamines incline at 57 ± 5° to the phosphate layers, whereas n-alkylamines form a bilayer structure with the same inclination angle. Two amino groups in an ,-alkanediamine molecule bridge the layered sheets of phosphates.