A Class of Orthogonal Polynomials Suggested by a Trigonometric Hamiltonian: Symmetric States

A new subclass of the Jacobi polynomials arising in the exact analytical solution of the one-dimensional Schrödinger equation with a trigonometric potential has been introduced. The polynomials which consist of a free parameter are not ultraspherical polynomials and have been simply named the -polynomials since they are generated by a trigonometric Hamiltonian. In certain sense, it is shown that the -polynomials can be regarded as a generalisation of the airfoil polynomials or the Chebyshev polynomials of the third kind. This paper is intended to discuss the basic properties of the polynomials so defined.     

Experimental indications for the response of the spectators to the participant blast

Precise momentum distributions of identified projectile fragments, formed in the reactions 238U+Pb and 238U+Ti at 1A GeV, are measured with a high-resolution magnetic spectrometer. With increasing mass loss, the velocities first decrease as expected from previously established systematics, then level off, and finally increase again. Light fragments are on the average even faster than the projectiles. This finding is interpreted as the response of the spectators to the participant blast. The reacceleration of projectile spectators is sensitive to the nuclear mean field and provides a new tool for investigating the equation of state of nuclear matter.     

The hit problem for the Dickson algebra

Let the mod 2 Steenrod algebra, , and the general linear group, , act on with in the usual manner. We prove the conjecture of the first-named author in Spherical classes and the algebraic transfer, (Trans. Amer. Math Soc. 349 (1997), 3893-3910) stating that every element of positive degree in the Dickson algebra is -decomposable in for arbitrary 2$">. This conjecture was shown to be equivalent to a weak algebraic version of the classical conjecture on spherical classes, which states that the only spherical classes in are the elements of Hopf invariant one and those of Kervaire invariant one.

     

Quantum Monodromy and Bohr–Sommerfeld Rules

This article is based on a talk given in Dijon for the 2000 summer school Topological and Geometrical Methods: Applications to Dynamical Systems. The standard definitions of the monodromy invariant for completely integrable classical systems are reviewed, and the link to the quantum monodromy observed in the joint spectrum of commuting operators is explained. The mathematical treatment relies on a modern and attractive version of the Bohr–Sommerfeld quantisation rules.     

Structure of 231Ac: Measurements of level half-lives

There is lack of knowledge of the structure of the ²³¹Ac nucleus located in the upper border of the island of octupole deformation centered around A = 225. We have populated the excited states in ²³¹Ac by beta-decay from the parent ²³¹Ra produced at ISOLDE, CERN. The low-energy structure of ²³¹Ac has been investigated by means of γ, conversion electrons, γ-γ and γ-e^- spectroscopy. We report here in the precise determination in ²³¹Ac of the half-life of the most intensively populated states by the Advanced Time Delayed ββγ(t) technique.     

Structural studies of the chemical constituents of Tithonia tagetiflora Desv. (Asteraceae)

Tithonia tagetiflora Desv. (Asteraceae) is a widespread plant in Vietnam, and the species of Tithonia are known as plants containing many biologically active compounds. However, T. tagetiflora's chemical composition remains mostly unknown. Therefore, we now report the structural elucidation of two new sesquiterpene lactones, 8‐angeloyloxy‐2,14‐epoxygermacra‐4,10(1),11(13)‐trien‐6,12‐olide (1) and 6‐angeloyloxy‐1‐hydroxy‐3,4‐epoxygermacra‐9,11(13)‐dien‐8,12‐olide (2), together with three known compounds, including two norisoprenoids, (6S,9S)‐vomifoliol or (6R,9R)‐vomifoliol (3) and (6S,9S)‐roseoside (4), and one glutinane type triterpene, epi‐glutinol (5), from the leaves of T. tagetiflora. Their structures are established by 1D and 2D NMR spectroscopy, as well as ESI‐MS analysis and comparison with literature data. Copyright © 2013 John Wiley & Sons, Ltd.     

Synthesis of polynorbornene‐poly(tert‐butyl acrylate) nanoparticles with original morphologies by tandem ROMP and ATRP in microemulsion

Composite latex particles based on homopolymers and graft‐copolymers composed of polynorbornene (PNB) and poly(tert‐butyl acrylate) (PtBA) were synthesized in microemulsion conditions by simultaneous combination of two distinct methods of polymerization: Ring‐opening metathesis polymerization (ROMP) and atom transfer radical polymerization (ATRP). Only one commercial compound (first generation Grubbs catalyst) was used to initiate the ROMP of norbornene (NB) and activate the ATRP of tert‐butyl acrylate (tBA). Well‐defined nanoparticles with hydrodynamic diameters smaller than 50 nm were prepared with original morphologies depending on the monomer compositions, the type of combination (polymer blend or graft‐copolymer), and the conditions of microemulsion polymerizations. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Poly(trialkylsilyl methacrylate)s: A family of hydrolysable polymers with tuneable erosion profiles

Polymers containing hydrolytically labile trialkylsilyl ester side groups were synthesised via a conventional and a controlled radical polymerization. The trialkylsilyl methacrylate monomer unit was chosen for its capacity to hydrolyse into basic, acid or sea water varying the hydrophilic character of the resulting polymer backbone with time. The hydrolysis or saponification reaction of the ester bond of the trialkylsilyl methacrylate was monitored through a ¹H NMR study showing the formation of siloxane side-products. Several copolymers and polymer blends were prepared as matrixes for controlled erodible systems. Their capacity to hydrolyse was demonstrated through SEM investigations with selective dissolution of free films containing hydrolysable copolymers and PMMA blends. Well-defined random and diblock copolymers with methyl methacrylate were investigated to show the effect of the microstructure on the erosion properties of the corresponding coatings. Poly(methyl methacrylate-b-tert-butyldimethylsilyl methacrylate) diblock copolymers synthesised through the RAFT process showed a better control of the erosion with a constant erosion rate over a long-time service in sea water at pH = 8.2. In addition, experiments showed that the erosion rate could be modulated by varying the molar proportion of hydrolysable side groups onto the copolymer backbone and the weight amount of copolymers mixed with PMMA in toluene solution.     

Bis‐benzimidazolium‐palladium system catalyzed Suzuki‐Miyaura coupling reaction of aryl bromides under mild conditions

Bis‐benzimidazolium salts were prepared successfully from commercially available and inexpensive o‐phenylenediamine through a series of simple reactions. The bis‐NHC‐Pd complexes prepared in situ can catalyze Suzuki‐Miyaura cross‐coupling reaction under very mild conditions in aqueous media with excellent yields. The efficiency of this reaction is demonstrated by its compatibility with a range of functional groups. Di‐ortho‐substituted biaryls could be accomplished in 89–99% yields. Moreover, the rigorous exclusion of air or moisture is not required in these transformations.     

Simple Method in Diagnosing Cancer Cells by a Novel Fluorescence Probe BMVC

Different cellular accumulations with distinct fluorescence properties of BMVC in cancer cells from normal cells allow us to establish a simple and economic method for the diagnosis of cancer cells. With using a light emitting diode to excite the BMVC molecule, microarray fluorescence analysis of a cell‐based glass chip provides an easy method towards the detection of a limited number of cancer cells.