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.     

Direct observation of broken time-reversal symmetry on the surface of a magnetically doped topological insulator

We study interference patterns of a magnetically doped topological insulator Bi(2-x)Fe(x)Te(3+d) by using Fourier transform scanning tunneling spectroscopy and observe several new scattering channels. A comparison with angle-resolved photoemission spectroscopy allows us to unambiguously ascertain the momentum-space origin of distinct dispersing channels along high-symmetry directions and identify those originating from time-reversal symmetry breaking. Our analysis also reveals that the surface state survives far above the energy where angle-resolved photoemission spectroscopy finds the onset of continuum bulk bands.     

Experimental studies of the jamming behaviour of triblock copolymer solutions and triblock copolymer-anionic surfactant mixtures

Photon correlation spectroscopy and rheological measurements are performed to investigate the microscopic dynamics and mechanical responses of aqueous solutions of triblock copolymers and aqueous mixtures of triblock copolymers and anionic surfactants. Increasing the concentration of triblock copolymers results in a sharp increase in the magnitude of the complex moduli characterising the samples. This is understood in terms of the changes in the aggregation and packing behaviours of the copolymers and the constraints imposed upon their dynamics due to increased close packing. The addition of suitable quantities of an anionic surfactant to a strongly elastic copolymer solution results in a decrease in the complex moduli of the samples by several decades. It is argued that the shape anisotropy and size polydispersity of the micelles comprising mixtures cause dramatic changes in the packing behaviour, resulting in sample unjamming and the observed decrease in complex moduli. Finally, a phase diagram is constructed in the temperature-surfactant concentration plane to summarise the jamming-unjamming behaviour of aggregates constituting triblock copolymer-anionic surfactant mixtures.     

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.     

Bifurcation analysis of the Zhukovskii-Volterra system via bi-Hamiltonian approach

The main goal of this paper consists of bifurcation analysis of classical integrable Zhukovskii-Volterra system. We use the fact that the ZV system is bi-Hamiltonian and apply new techniques [1] for analysis of singularities of bi-Hamiltonian systems, which can be formulated as follows: the structure of singularities of a bi-Hamiltonian system is determined by that of the corresponding compatible Poisson brackets.