The topological dynamics of semigroup actions

In these notes we explore the fine structure of recurrence for semigroup actions, using the algebraic structure of compactifications of the acting semigroup.

     

Experimental and numerical studies of intestinal frictions for propulsive force optimisation of a vibro-impact capsule system

This paper studies the intestinal frictions acting on a millimetre-scale self-propelled capsule (26 mm in length and 11 mm in diameter) for small bowel endoscopy by considering different capsule–intestine contact conditions under a wide range of capsule’s progression speeds. According to the experimental results, intestinal frictions vary from 7 mN to 4.5 N providing us with a guidance for designing the propelling mechanism of the controllable capsule endoscope. Our calculations show that the proposed vibro-impact mechanism can perform as a force magnifier generating a much larger propulsive force on the capsule than its original driving force. Therefore, the self-propelled capsule is capable of moving in the small intestine under a wide range of friction variation.

     

(5S)‐3‐Oxo‐4‐oxa‐endo‐tri­cyclo[5.2.1.02,6]­dec‐8‐en‐5‐yl acetate

The molecular structure of C₁₁H₁₂O₄, based on a norbornene core, was established to confirm the configuration of an acetoxy side‐chain group in addition to the formation of the endo product. The acetoxy side chain lies in an axial position relative to the five‐membered fused ring. Bond distances and angles show no unusual features, with all geometric parameters lying within their expected ranges. The overall stereochemistry of the mol­ecule was ascertained from the chiral furan­one starting material.     

Zwitterionic pyrrolidine‐2,2‐diylbis(phosphonic acid) at 100, 150 and 293 K

The title compound, C₄H₁₁NO₆P₂, reveals a two‐dimensional network of P—O—H?O=P and N—H?O=P hydrogen‐bond interactions, forming molecular slabs parallel with the (010) plane. One O—H?O interaction is distinct within these sets: whilst forming the shortest intermolecular hydrogen bond, it possesses a short P—O(H) bond of 1.5291 (10) Å. Weak C—H?O contacts link individual stacks to produce a three‐dimensional array. The compound is zwitterionic: one H atom from a P—O—H group has transferred to the pyrrolidine ring N atom.     

Large Deviation Principles and Complete Equivalence and Nonequivalence Results for Pure and Mixed Ensembles

We consider a general class of statistical mechanical models of coherent structures in turbulence, which includes models of two-dimensional fluid motion, quasi-geostrophic flows, and dispersive waves. First, large deviation principles are proved for the canonical ensemble and the microcanonical ensemble. For each ensemble the set of equilibrium macrostates is defined as the set on which the corresponding rate function attains its minimum of 0. We then present complete equivalence and nonequivalence results at the level of equilibrium macrostates for the two ensembles. Microcanonical equilibrium macrostates are characterized as the solutions of a certain constrained minimization problem, while canonical equilibrium macrostates are characterized as the solutions of an unconstrained minimization problem in which the constraint in the first problem is replaced by a Lagrange multiplier. The analysis of equivalence and nonequivalence of ensembles reduces to the following question in global optimization. What are the relationships between the set of solutions of the constrained minimization problem that characterizes microcanonical equilibrium macrostates and the set of solutions of the unconstrained minimization problem that characterizes canonical equilibrium macrostates? In general terms, our main result is that a necessary and sufficient condition for equivalence of ensembles to hold at the level of equilibrium macrostates is that it holds at the level of thermodynamic functions, which is the case if and only if the microcanonical entropy is concave. The necessity of this condition is new and has the following striking formulation. If the microcanonical entropy is not concave at some value of its argument, then the ensembles are nonequivalent in the sense that the corresponding set of microcanonical equilibrium macrostates is disjoint from any set of canonical equilibrium macrostates. We point out a number of models of physical interest in which nonconcave microcanonical entropies arise. We also introduce a new class of ensembles called mixed ensembles, obtained by treating a subset of the dynamical invariants canonically and the complementary set microcanonically. Such ensembles arise naturally in applications where there are several independent dynamical invariants, including models of dispersive waves for the nonlinear Schrödinger equation. Complete equivalence and nonequivalence results are presented at the level of equilibrium macrostates for the pure canonical, the pure microcanonical, and the mixed ensembles.     

High-energy QCD as a topological field theory

We propose an identification of the conformal field theory underlying Lipatov's spin-chain model of high-energy scattering in perturbative QCD. It is a twisted N = 2 supersymmetric topological field theory, which arises as the limiting case of the SL(2,R)/U(1) non-linear model that also plays a role in describing the Quantum Hall effect and black holes in string theory. The doubly-infinite set of non-trivial integrals of motion of the high-energy spin-chain model displayed by Faddeev and Korchemsky are identified as the Cartan subalgebra of a bosonic sub-symmetry possessed by this topological theory. The renormalization group and an analysis of instanton perturbations yield some understanding why this particular topological spin-chain model emerges in the high-energy limit, and provide a new estimate of the asymptotic behaviour of multi-Reggeized-gluon exchange. Received: 31 August 1998 / Published online: 11 March 1999     

Use of a surfactant in the determination of arsenic by flow injection hydride generation atomic absorption spectrometry

The possible benefits of the addition of an anionic surfactant, didodecyldimethylammonium bromide, in the determination of arsenic, by flow injection hydride generation atomic absorption spectrometry using a flame-heated quartz tube atomizer, were studied in the light of previous reports concerning the effects of surfactants on chemical vapor generation procedures. Concentrations of arsenic between 5 and 30 μg l⁻¹ were used. Calibrations in the presence and absence of the surfactant in the sample solution were not significantly different, either for the case where vesicles were formed in the presence of the analyte or where they were preformed in the surfactant solution and then added to the analyte. The surfactant had no effect on recoveries in the presence of copper, nickel or bismuth. The addition of the surfactant to the acid carrier and/or borohydride streams had no effect. It is proposed that there may be a greater role for surfactants in the improvement of the processes by which the hydride is transferred to the bulk gas phase than has been attributed in previous reports on this subject.     

Supramolecular Aggregation in the 1:1 Co-crystal Formed Between Merocyanine Dye and 3-Nitrophenol,Characterized as a Hydrate

Abstract  The title organic salt comprises a (E)-4-[2-(4-hydroxyphenyl)vinyl]-1-methylpyridinium cation, a 3-nitro-phenoxide anion and a solvent water molecule of crystallisation. The anions and water molecules aggregate to form supramolecular chains facilitated by charge-assisted O–H···O hydrogen bonds and these form layers which are interspersed by layers of cations. Interactions between layers include O–H···O hydrogen bonding, as well as C–H···O and C–H···π contacts; π···π and C–H···O contacts are found within layers of cations. The compound crystallizes in the monoclinic space group P2₁/n with a = 15.018(7) ?, b = 7.328(2) ?, c = 17.571(7) ?, β = 112.342(15)°, and Z = 4. Index Abstract  A layer structure comprising alternating anions/water molecules and cations associated via charge-assisted O–H···O hydrogen bonding as well as C–H···O, C–H···π and π···π contacts is found in (II) .     

Dendrimer Conjugation Enables Multiphoton Chemical Neurophysiology Studies with an Extended π‐Electron Caging Chromophore

We have developed a caged neurotransmitter using an extended π‐electron chromophore for efficient multiphoton uncaging on living neurons. Widely studied in a chemical context, such chromophores are inherently bioincompatible due to their highly lipophilic character. Attachment of two polycarboxylate dendrimers, a method we call “cloaking”, to a bisstyrylthiophene (or BIST) core effectively transformed the chromophore into a water‐soluble optical probe, whilst maintaining the high two‐photon absorption of over 500 GM. Importantly, the cloaked caged compound was biologically inert at the high concentrations required for multiphoton chemical physiology. Thus, in contrast to non‐cloaked BIST compounds, the BIST‐caged neurotransmitter can be safely delivered onto neurons in acutely isolated brain slices, thereby enabling high‐resolution two‐photon uncaging without any side effects. We expect that our cloaking method will enable the development of new classes of cell‐compatible photolabile probes using a wide variety of extended π‐electron caging chromophores.     

Niobium isocyanide complexes,Nb(CNAr)6, with Ar = 2,6‐dimethylphenyl (Xyl), a diamagnetic dimer containing four reductively coupled isocyanides,and Ar = 2,6‐diisopropylphenyl (Dipp), a paramagnetic monomer analogous to the highly unstable hexacarbonylniobium(0)

Treatment of bis(mesitylene)niobium(0) with 6–7 equivalents of 2,6‐dimethylphenyl isocyanide (CNXyl) affords two products with the empirical formula Nb(CNXyl)_n (n = 7 or 6), which have been shown to be the diamagnetic dimers bis[μ‐N,N′,N′′,N′′′‐tetrakis(2,6‐dimethylphenyl)squaramidinato(2?)]bis[pentakis(2,6‐dimethylphenyl isocyanide)niobium(I)], [Nb₂(C₉H₉N)₁₀(C₃₆H₃₆N₄)] or [Nb(CNXyl)₅]₂[μ‐C₄(NXyl)₄]·xSolvent, 1 , and bis[μ‐N,N′,N′′,N′′′‐tetrakis(2,6‐dimethylphenyl)squaramidinato(2?)]bis[tetrakis(2,6‐dimethylphenyl isocyanide)niobium(I)] tetrahydrofuran trisolvate, [Nb₂(C₉H₉N)₈(C₃₆H₃₆N₄)]·3C₄H₈O or [Nb(CNXyl)₄]₂[μ‐C₄(NXyl)₄]·3THF (THF = tetrahydrofuran), 2 . Each contains Nb^I bound to either five or four terminal isocyanides, respectively, and to an unprecedented bridging tetraarylsquaramidinate(2?) unit, coordinated as a bidentate ligand to each niobium center, symmetrically due to the crystallographic inversion center that coincides with the centroid of the central C₄ unit. Thus, in the presence of CNXyl, the bis(mesitylene)niobium(0) is oxidized to niobium(I), resulting in the facile loss of both mesitylene groups and the reductive coupling of two CNXyl groups per niobium to provide the first examples of tetraarylsquaramidinate(2?) ligands, [cyclo‐C₄N₄Ar₄]^2?, coordinated to metals. In contrast, bis(mesitylene)niobium(0) reacts with the more crowded 2,6‐diisopropylphenyl isocyanide (CNDipp) to afford the paramagnetic monomer hexakis(2,6‐diisopropylphenyl isocyanide)niobium(0), [Nb(C₁₃H₁₇N)₆] or Nb(CNDipp)₆, 3 , the first zero‐valent niobium isocyanide analog of the highly unstable Nb(CO)₆, which is presently only known to exist in an argon matrix at 4.2 K.