On a first-passage problem for a cumulative process with exponential decay

A first-passage problem for a cumulative process is investigated. The cumulative process is assumed to be generated by a Poisson process, and the amplitude generated by an event is assumed to decay exponentially. An integral equation for the probability density of the first-passage time until the total amplitude exceeds a pre-specified threshold level is derived. The Laplace transform of the probability density of the first-passage time is obtained explicity when each amplitude generated by an event is distributed exponentially. The mean first-passage times are given in a closed form and plotted versus the threshold level.     

Purely periodic -expansions with Pisot unit base

Let 1$"> be a Pisot unit. A family of sets defined by a -numeration system has been extensively studied as an atomic surface or Rauzy fractal. For the purpose of constructing a Markov partition, a domain constructed by an atomic surface has appeared in several papers. In this paper we show that the domain completely characterizes the set of purely periodic -expansions.

     

General description of mechanical anisotropy of semicrystalline polymers in relation to orientation of structural units composed of crystalline and noncrystalline materials

A mathematical representation of the transformation of an orientation function between two sets of Cartesian coordinates is discussed in terms of a series expansion of the distribution function in generalized spherical harmonics. A general procedure for calculating the mechanical anisotropy of a single-phase system (a polycrystalline material) from the orientation of its structural units and the intrinsic mechanical anisotropy of the structural unit is discussed in relation to the transformation of the orientation distribution function, i.e., mutual conversion of the coefficients in the expansion of the distribution function between the two sets of Cartesian coordinates. The procedure is extended to a two-phase systems (semicrystalline polymers) containing structural units composed of crystalline and noncrystalline materials in three different geometrical arrangements.     

Electron-boson coupling and oxygen-isotope effect in the optical conductivity of high-Tc superconductors

We have investigated electron-boson coupling in the optical conductivity of high-T_c superconductors through the optical self-energy. The real part of the self-energy (ReΣ^op(ω)) of YBa₂Cu₃O_y (YBCO) shows a characteristic doping dependence. In the optimally doped YBCO, ReΣ^op(ω) has a single peak around 65 meV, which corresponds to the kink structure of the band dispersion. On the other hand, in the under-doped YBCO, the peak structure of ReΣ^op(ω) splits into two parts. To evaluate contribution from the phonons in electron-boson coupling, we have measured oxygen-isotope effects by substituting ¹⁶O→¹⁸O for the optimally doped and under-doped YBCO.     

Synthesis and photophysical properties of azuleno[1′,2′:4,5]pyrrolo[2,1-b]quinazoline-6,14-diones: Azulene analogs of tryptanthrin

Azulene analog of tryptanthrin, azuleno[1′,2′:4,5]pyrrolo[2,1-b]quinazoline-6,14-dione, was successfully prepared by the condensation reaction of azuleno[2,1-b]pyrrole-2,3-dione with isatoic anhydride in the presence of sodium hydride or diisopropylethylamine (DIPEA). Its 2-halo derivatives were also obtained in high yields by the condensation reaction with 5-haloisatoic anhydrides in the presence of DIPEA. Reactivity toward electrophilic reagents was revealed by halogenation with N-bromosuccinimide (NBS) or N-iodosuccinimide (NIS) to afford 12-halo derivatives in high yields. Among the halo derivatives, 2-iodo and 12-iodo derivatives were reactive enough to afford phenylethynyl derivatives under Pd-catalyzed Sonogashira cross-coupling conditions. Within the phenylethynyl derivatives, only 12-phenylethynyl derivative was transformed into its 1,1,4,4-tetracyanobutadiene (TCBD) derivative by the reaction with TCNE. Amphoteric redox properties of the novel azulene analogs of tryptanthrin were characterized by spectroscopic and voltammetric analyses.     

UPLC-MS/MS detection of disaccharides derived from glycosaminoglycans as biomarkers of mucopolysaccharidoses

Mucopolysaccharidoses (MPSs) are a group of disorders resulting from primary defects in lysosomal enzymes involved in the degradation of glycosaminoglycans (GAGs). Depending on the specific enzyme defect, the catabolism of one or more GAGs is blocked leading to accumulation in tissues and biological fluids. GAG measurements are important for high-risk screening, diagnosis, monitoring treatment efficacy, and patient follow up. The dimethylmethylene blue (DMB) spectrophotometric method commonly used in most biochemical genetics laboratories relies on a non-specific total GAG analysis which has led to false positive results, and even false negative results (mainly for MPS III and IV patients). The main objective of our project was to devise and validate a reliable tandem mass spectrometry multiplex analysis for the urine quantitation of four GAGs (dermatan sulfate (DS), heparan sulfate (HS), keratan sulfate (KS), and chondroitin sulfate (CS)) for an eventual technological transfer to the clinic. The developed methodology is rapid (7 min) and our results showed good intraday and interday precision (RSDs ≤ 8.7%) and accuracy (Biases range: −12.0%–18.4%). Linearity was good (r² > 0.995) for DS, HS, CS, and KS calibration curves. In comparison with the DMB spectrophotometric method, this multiplex tandem mass spectrometry method allows GAG fractionation, thus a differentiation of MPS types, except for MPS I and II which are characterized by the same GAG profile. The devised method is a useful and reliable tool for diagnosis of MPS patients, as well as their monitoring and follow up, as shown by longitudinal studies.     

Analytical method for determination of disaccharides derived from keratan sulfates in human serum and plasma by high-performance liquid chromatography/turbo-ionspray ionization tandem mass spectrometry

We established a highly sensitive LC/MS/MS method for the analysis of the disaccharides produced from keratan sulfates (KS). It was revealed that the disaccharides produced by keratanase II enzymatic digestion of KS could be determined with high sensitivity by negative ion mode of multiple reaction monitoring. Furthermore, monosulfated and disulfated disaccharides can be separated using a Hypercarb (2.0 mm i.d. x 150 mm, 5 microm) with a gradient elution of acetonitrile-0.01 m ammonium bicarbonate (pH 10). This method was applied to the determination of KS in serum and plasma of control subjects. The intra-day precision expressed as %CV was within 6.8% for five replicate analyses with three different control serum. The inter-day (overall, n = 15) precision was within 7.3% for three days. This method is sensitive, reproducible and would be useful for clinical analysis.     

Myrmekiosides a and b, novel mono-o-alkyl-diglycosylglycerols reversing tumor cell morphology of ras-transformed cells from a marine sponge of myrmekioderma sp

Novel mono-O-alkyl-diglycosylglycerols named myrmekiosides A (1) and B (2) were isolated from a marine sponge of Myrmekioderma sp. and their absolute stereostructures were elucidated on the basis of chemical and physicochemical evidence. Myrmekiosides A (1) and B (2) reversed the phenotype of melanoma H-ras transformed NIH3T3 cells at 5 μg/ml.     

Preferential orientation of crystallites spatially confined in lamellar microdomains of polyethylene‐block‐[atactic poly(propylene)]

Synchrotron small angle X‐ray scattering (SAXS), wide angle X‐ray scattering (WAXS), and transmission electron microscopy were carried out for an oriented polyethylene‐block‐[atactic poly(propylene)] with a molecular weight of 1.13×10⁵ and a volume fraction of polyethylene of 0.5. Isothermal crystallization at 93°C did not destroy the pre‐formed microdomain, however, with a higher crystallization temperature, the microdomain was more heavily deformed and more crystalline lamella grew. In WAXS profiles, preferential orientation of (020) reflection peak was observed, indicating that the crystalline lamella grew in parallel with the micro domain interface.