Symplectic curvature tensors

In the paper, one establishes the decomposition of the space of tensors which have the symmetries of the curvature of a torsionless symplectic connection into Sp (n)-irreducible components. This leads to three interesting classes of symplectic connections: flat, Ricci flat, and similar to the Levi-Civita connections of Kähler manifolds with constant holomorphic sectional curvature (we call them connections with reducible curvature). A symplectic manifold with two transversal polarizations has a canonical symplectic connection, and we study properties that are encountered if this canonical connection belongs to the classes mentioned above. For instance, in the reducible case we can compute the Pontrjagin classes, and these will be zero if the polarizations are real, etc. If the polarizations are real and there exist points where they are either singular or nontransversal, one has residues in the sense ofLehmann [L], which should be expected to play an interesting role in symplectic geometry.     

Synthesis of polyamides by the polyaddition of bisimidazoline with dicarboxylic acids

N,N′-Dipropionylethylenediamine was synthesized by the ring-opening addition reaction of 2-ethyl-2-imidazoline with propionic acid at 220°C. By applying this reaction to polymerization, polyamides were synthesized by the ring-opening polyaddition reaction at 220°C. of 1,4-bis(imidazoline-2-yl)butane with adipic acid, succinic acid, sebacic acid, and terephthalic acid. The reaction product of 1,4-bis(imidazoline-2-yl)butane with adipic acid, which was proposed to be nylon 26, was compared with an authentic sample of nylon 26 and shown to possess a very similar infrared spectrum and melting point.     

Foliate partial holomorphic structures on principal bundles

Thefoliate partial holomorphic (f.p.h.) pseudogroup is the pseudogroup of the local diffeomorphisms of ^m which preserve a distribution of the form span , wherey ^a are real coordinates,z are complex coordinates, and ^m may have also some other real coordinates. The f.p.h. structures on manifolds are described geometrically by the Nirenberg-Frobenius theorem [N], and occur in many interesting situations [R], [FW], [DK1], [V3], etc. The present paper discusses f.p.h. structures on principal bundles, and associates with such structures adapted connections, and forms with values in an associated bundle of Lie algebras.     

Stir bar sorptive extraction with in situ derivatization and thermal desorption-gas chromatography-mass spectrometry for determination of chlorophenols in water and body fluid samples

A new method, stir bar sorptive extraction (SBSE) with in situ derivatization and thermal desorption (TD)-gas chromatography-mass spectrometry (GC-MS), which is used for the determination of trace amounts of chlorophenols, such as 2,4-dichlorophenol (2,4-DCP), 2,4,6-trichlorophenol (2,4,6-TrCP), 2,3,4,6-tetrachlorophenol (2,3,4,6-TeCP) and pentachlorophenol (PCP), in tap water, river water and human urine samples, is described. The derivatization conditions with acetic acid anhydride and the SBSE conditions such as extraction time are investigated. Then, the stir bar is subjected to TD followed by GC-MS. The detection limits of the chlorophenols in tap water, river water and human urine samples are 1-2, 1-2, and 10-20 pg ml⁻¹ (ppt), respectively. The calibration curves for the chlorophenols are linear and have correlation coefficients higher than 0.99. The average recoveries of the chlorophenols in all the samples are higher than 95% (R.S.D. < 10%) with correction using added surrogate standards, 2,4-dichlorophenol-d₅, 2,4,6-trichlorophenol-¹³C₆, 2,3,4,6-tetrachlorophenol-¹³C₆ and pentachlorophenol-¹³C₆. This simple, accurate, sensitive and selective analytical method may be applicable to the determination of trace amounts of chlorophenols in liquid samples.     

Riemannian manifolds with a parallel field of complex planes

The purpose of this paper is to discuss Riemannian manifolds which admit a parallel field of complex planes, consisting of vectors of the form , where a,b are real orthogonal vectors of equal length. Using the Nirenberg Frobenius Theorem [12], it follows that these are reducible Riemannian manifolds, whose metric is locally a sum of a Kähler and of a Riemann metric, and we are calling thempartially Kähler manifolds.After a general presentation of these manifolds (including a general presentation of the complex integrable plane fields) we are discussing harmonic forms, Betti numbers, and Dolbeault cohomology. This discussion is based on a theorem of Chern [4], and it provides generalizations of the results of Goldberg [9], as well as some other new results.To Prof. R. Artzy on his 70th Birthday     

On locally conformal almost Kähler manifolds

In the first section of this note, we discuss locally conformal symplectic manifolds, which are differentiable manifoldsV ²ⁿ endowed with a nondegenerate 2-form Ω such thatdΩ=θ ∧ Ω for some closed form θ. Examples and several geometric properties are obtained, especially for the case whendΩ ≠ 0 at every point. In the second section, we discuss the case when Ω above is the fundamental form of an (almost) Hermitian manifold, i.e. the case of the locally conformal (almost) Kähler manifolds. Characterizations of such manifolds are given. Particularly, the locally conformal Kähler manifolds are almost Hermitian manifolds for which some canonically associated connection (called the Weyl connection) is almost complex. Examples of locally conformal (almost) Kähler manifolds which are not globally conformal (almost) Kähler are given. One such example is provided by the well-known Hopf manifolds.     

Exotic characteristic classes of quaternionic bundles

For aC ^∞ quaternionic vector bundle, the odd-dimensional real Chern classes vanish, and this allows for a construction of secondary (exotic) characteristic classes associated with a pair of quaternionic structures of a given complex vector bundle. This construction is then applied to obtain exotic characteristic classes associated with an automorphismβ of the holomorphic tangent bundle of a Kähler manifold. These results are the complex analoga of those given for the higher order Maslov classes in [V2].     

Capillary and slit-die flow of two liquid-crystalline polymers. The effect of pressure on viscosity

Viscosity measurements on two commercial thermotropic liquid crystalline polymers (LCPs) (a copolyester and a polyesteramide) were performed using both capillary and slit die methods. The results are in agreement with those presented in the literature for the same LCPs, when the measurements are carried out with a L/D = 30 die; these results are affected more by Bagley corrections for the polyesteramide than for the copolyester. For both LCPs, viscosities measured in the slit die are lower than those obtained by capillary rheometry. Nevertheless, the difference is much bigger in the case of the polyesteramide, for which a reduction by a factor of 3 is observed. This is not due to the preshear or thermal history, since the same piston-barrel system and thermal treatment were applied in both types of measurements. Depending on the polymer sample and temperature, concave and convex curvatures were observed in the pressure profiles during the slit flow. From these curvatures, the pressure coefficient α of viscosity was evaluated. However, in the case of the polyesteramide the convex curvature leads to a negative coefficient (the viscosity decreases with pressure, instead of increasing). This result may be explained by envisaging a change in the structure of the melt along the slit length. © 1993 John Wiley & Sons, Inc.     

Stir bar sorptive extraction and thermal desorption-gas chromatography-mass spectrometry for trace analysis of triclosan in water sample

A simple and highly sensitive method called stir bar sorptive extraction (SBSE) and thermal desorption (TD)-gas chromatography-mass spectrometry (GC-MS), which is used for the determination of trace amounts of 5-chloro-2-(2,4-dichlorophenoxy)phenol (triclosan) in river water samples, is described. A stir bar coated with polydimethylsiloxane (PDMS) is added to a 10mL water sample and stirring is carried out for 120min at room temperature (25 degrees C) in a vial. Then, the PDMS stir bar is subjected to TD-GC-MS. The detection limit of triclosan is 5ngL(-1) (ppt). The method shows linearity over the calibration range (0.02-20mugL(-1)) and the correlation coefficient is higher than 0.997 for triclosan standard solution. The recovery of triclosan in river water samples ranges from 91.9 to 108.3% (RSD: 4.0-7.0%). This simple, accurate, sensitive, and selective analytical method may be used in the determination of trace amounts of triclosan in river water samples.