Free, Isometric Circle Actions on Compact Symmetric Spaces

Let S=G/K be a strongly irreducible, simply connected, compact symmetric space and let be its group of isometries. We classify the symmetric spaces among these that admit free, isometric circle actions. The existence of such actions is important in constructing examples of manifolds with positive sectional curvature.     

Understanding deadlock and livelock behaviors in Hybrid Control Systems

This paper introduces a formal definition and a categorization of Deadlock and Livelock behaviors for a general class of deterministic Hybrid Control Systems (HCS), thus extending the classical notion known for (uncontrolled) discrete transition systems. This characterization hinges on three important aspects: (1) the concept of composition (or interconnection) of HCSs; (2) the notion of control-dependent specification, and that of composition of specifications; (3) the dynamical structure of an HCS and its related behaviors. The first notion is introduced in a novel manner, by including aspects from the literature of discrete transition systems, as well as accounting for classical concepts such as that of feedback interconnection of dynamical systems. The second point allows us to formally express general properties that are of interest from a systems and control theory perspective. The third part discriminates between the different and possibly pathological behaviors that are characteristic to HCSs. After commenting on the issues of Deadlock and Livelock prevention and verification, the article concludes with two case studies.     

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.     

An Efficient N‐Arylation of Heterocycles with Aryl‐, Heteroaryl‐, and Vinylboronic Acids Catalyzed by Copper Fluorapatite

N‐Arylation of N‐containing heterocycles, such as pyrazoles, imidazoles, and benzimidazoles with aryl‐, heteroaryl‐, and vinylboronic acids was efficiently carried out by copper fluorapatite (CuFAP) catalyst in MeOH at room temperature under base‐free conditions. The N‐arylated heterocycles were isolated in good‐to‐excellent yields.     

AlCl3-induced (hetero)arylation of thienopyrimidine ring: a new synthesis of 4-substituted thieno[2,3-d]pyrimidines

AlCl₃ facilitated C-C bond forming reaction between 4-chloro-thieno[2,3-d]pyrimidines and (hetero)arenes affording a direct and single-step method for the synthesis of 4-(hetero)aryl substituted thieno[2,3-d]pyrimidines. A number of novel thienopyrimidines were prepared in good to excellent yields using this methodology. The molecular structure of a representative compound was established unambiguously by single crystal X-ray diffraction.     

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.