Synthesis and characterization of functional polysilanes [RMe2Si(CH2)x(Me)Si]n (R = 2‐Fu, 5‐Me‐2‐Fu, 2‐Th, 4‐Me‐2‐Th; x = 2, 3) with appended furyl/thienyl groups on the carbosilyl side chains and their application in the generation and stabilization of palladium nanoparticles

The polysilanes [RMe₂Si(CH₂)_x(Me)Si]_n [x = 2, 3; R = 2‐Fu ( 1, 2 ), 5‐Me‐2‐Fu ( 3, 4 )] bearing furyl‐substituted carbosilyl side chains have been synthesized by dehalocondensation reaction (Wurtz coupling) of the corresponding carbosilanes using sodium dispersion in refluxing toluene. On the other hand, analogous polysilanes with appended thienyl groups [x = 2, 3; R = 2‐Th ( 5, 6 ), 4‐Me‐2‐Th ( 7, 8 )] are only accessible by the reaction of the corresponding carbosilane precursors under mild Wurtz coupling conditions (THF, RT). These polysilanes reveal monomodal molecular weight distribution with M_w/PDI = 3.3–5.4 × 10⁴/1.22–1.47 ( 1–4 ) and 9.1–14.4 × 10⁴/1.45–1.61 ( 5–8 ) and are characterized by FT‐IR, multinuclear (¹H, ¹³C{¹H}, ²⁹Si{¹H}) NMR, and UV/PL spectral studies as well as thermogravimetric analysis (TGA). Preliminary studies on the reactivity of polysilane 2 with palladium acetate (toluene, RT) reveal the formation of spherical palladium nanoparticles of size 8.2 ± 0.6 nm, which remain stable in solution for several weeks. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 7816–7826, 2008     

Inclusive ∑±(1385) production inK − p interactions at 110 GeV/c

Results are presented on inclusive production of ∑⁺(1385) and ∑^?(1385) inK ^? p interactions at 110 GeV/c. The inclusive and topological cross sections have been estimated and compared with published results at lower energies. The inclusive cross section of ∑⁺(1385) seems to decrease with c.m. energy, while that of the ∑^?(1385) is nearly constant. The mean charged multiplicity associate to Σ(1385) increases with c.m. energy. The ∑⁺(1385) is produced both in the target fragmentation region and in the central region where ∑^?(1385) is predominantly produced in the central region. Approximately 16% of the Λ's stem from the decay of ∑^±(1385) and the kinematic distributions of these Λ's are not very different from the inclusive Λ's.     

Improved constants for some separator theorems

We describe a device for improving the constants involved in graph separator theorems, and sketch some applications.     

Hydroxyl group orientation affects hydrolysis rates of methyl α-septanosides

Hydrolysis rates for three related methyl α-septanosides were obtained. The septanosides were synthesized via mCPBA epoxidation and methanolysis of d-mannose, d-galactose, and d-glucose-based oxepines. The rate of hydrolysis correlates with the orientation of hydroxyl groups on the septanose ring in a manner analogous to pyranosides.     

The first examples of supramolecular discotic C3h tris(N-salicylideneamine)s featuring inter- and intra-molecular H-bonding: synthesis and characterization

Supramolecular liquid crystalline tris(N-salicylideneamine)s (TSANs) featuring both inter- and intra-molecular hydrogen bonding have been synthesized and characterized for the first time. These TSANs formed by condensing 3 equiv of 3,4,5-trialkoxybenzoylhydrazine with 1,3,5-triformylphloroglucinol exist as the single C_3h-symmetric keto-enamine product solely, unlike the previously reported TSANs. Their self-assembly into supramolecular fluid hexagonal columnar phase over a wide thermal range is evidenced with the aid of optical microscopic, calorimetric, and powder X-ray diffraction techniques.     

Development and validation of an LC-ESI-MS/MS method for simultaneous quantitation of olmesartan and pioglitazone in rat plasma and its pharmacokinetic application

A simple, high‐throughput and specific high‐performance liquid chromatography tandem mass spectrometry method has been developed and validated according to the FDA guidelines for simultaneous quantification of olmesartan and pioglitazone in rat plasma. The bioanalytical method consists of liquid–liquid extraction and quantitation by triple quadrupole mass spectrometry using electrospray ionization technique, operating in multiple reaction monitoring and positive ion modes. The compounds were eluted isocratically on a C₁₈ column with a mobile phase consisting of a mixture of methanol and water (containing 0.5% formic acid) in a ratio of 9:1. The response to olmesartan and pioglitazone was linear over the range 0.01–10 µg/mL. The validation results demonstrated that the method had satisfactory precision and accuracy across the calibration range. Intra‐ and inter‐day precisions ranged from 0.66 to 3.32 and from 0.94 to 2.93% (%CV), respectively. The accuracy determined at three quality control levels was within 91.27–107.28%. There was no evidence of instability of the analytes in rat plasma following the stability studies. The method proved highly reproducible and sensitive and was successfully applied in a pharmacokinetic study after single dose oral administration of olmesartan and pioglitazone to the rat. Copyright © 2010 John Wiley & Sons, Ltd.     

Loss reduction in silicon nanophotonic waveguide micro-bends through etch profile improvement

Single mode silicon photonic wire waveguides allow low-loss sharp micro-bends, which enables compact photonic devices and circuits. The circuit compactness is achieved at the cost of loss induced by micro-bends, which can seriously affect the device performance. The bend loss strongly depends on the bend radius, polarization, waveguide dimension and profile. In this paper, we present the effect of waveguide profile on the bend loss. We present waveguide profile improvement with optimized etch chemistry and the role of etch chemistry in adapting the etch profile of silicon is investigated. We experimentally demonstrate that by making the waveguide sidewalls vertical, the bend loss can be reduced up to 25% without affecting the propagation loss of the photonic wires. The bend loss of a 2 μm bend has been reduced from 0.039dB/90° bend to 0.028dB/90° bend by changing the sidewall angle from 81° to 90°, respectively. The propagation loss of 2.7 ± 0.1dB/cm and 3 ± 0.09dB/cm was observed for sloped and vertical photonic wires respectively was obtained.     

The augmented multiplicative coalescent,bounded size rules and critical dynamics of random graphs

Random graph models with limited choice have been studied extensively with the goal of understanding the mechanism of the emergence of the giant component. One of the standard models are the Achlioptas random graph processes on a fixed set of \(n\) vertices. Here at each step, one chooses two edges uniformly at random and then decides which one to add to the existing configuration according to some criterion. An important class of such rules are the bounded-size rules where for a fixed \(K\ge 1\) , all components of size greater than \(K\) are treated equally. While a great deal of work has gone into analyzing the subcritical and supercritical regimes, the nature of the critical scaling window, the size and complexity (deviation from trees) of the components in the critical regime and nature of the merging dynamics has not been well understood. In this work we study such questions for general bounded-size rules. Our first main contribution is the construction of an extension of Aldous’s standard multiplicative coalescent process which describes the asymptotic evolution of the vector of sizes and surplus of all components. We show that this process, referred to as the standard augmented multiplicative coalescent (AMC) is ‘nearly’ Feller with a suitable topology on the state space. Our second main result proves the convergence of suitably scaled component size and surplus vector, for any bounded-size rule, to the standard AMC. This result is new even for the classical Erd?s–Rényi setting. The key ingredients here are a precise analysis of the asymptotic behavior of various susceptibility functions near criticality and certain bounds from Bhamidi et al. (The barely subcritical regime. Arxiv preprint, 2012) on the size of the largest component in the barely subcritical regime.     

Axial eigenfunctions and inhomogeneous solutions for the three-dimensional Stokes system with an application to natural convection in a cylinder

This paper presents two contributions to the analysis of three-dimensional slow viscous flows in cylinders of circular section. First the vector axial eigenfunctions for this geometry, namely those that satisfy homogeneous boundary conditions on the flat end walls, are derived. Secondly a method is presented to find particular solutions to the inhomogeneous Stokes equations in this geometry. These new results, together with some results obtained earlier, are used to analyse slow natural convection in a vertical cylinder completely filled with a viscous liquid. The fluid motion is generated by the differential heating of the walls of the cylinder. The natural convection flow field is shown to be a superposition of an inhomogeneous field, the fields generated by the vector eigenfunctions and a Stokes flow field. A by-product of this work has been the identification of constraints on the boundary data that have to be satisfied in order for the eigenfunction expansions to work; this knowledge will be useful when attempts are made to prove the completeness of these Stokes flow eigenfunctions.