The Bott obstruction to the existence of nice polarizations

In this note, we prove and discuss the following theorem: if the symplectic or almost symplectic manifoldM admits a nice polarizationF with dim , we must have Chern ^q M=0 and Pont ^q M=0, forq>2n–k, and, in particular, the Euler class ofM vanishes.     

Electrochemical behavior of nickeladithiolene S,S'-dialkyl adducts: evidence for the formation of a metalladithiolene radical by electrochemical redox reactions

The electrochemical behavior of nickeladithiolene S,S'-dialkyl adducts (alkyl = benzyl, methyl, tert-butyl) was investigated by using cyclic voltammetry (CV), visible, near-IR, and ESR spectroscopies and bulk electrolyses. The redox potentials of the S,S'-dialkyl adducts were influenced by the electron-donating effect of the functional group on the sulfur atoms. The nickeladithiolene S,S'-dibenzyl adduct [Ni[S(SCH(2)Ph)C(2)Ph(2)](2)] (2) eliminated one benzyl radical by one-electron reduction, and then the monobenzyl adduct anion [Ni(S(2)C(2)Ph(2))[S(2)(CH(2)Ph)C(2)Ph(2)]](-) (3(-)) was formed. Anion 3(-) was also formed by the reaction of nickeladithiolene dianion [Ni(S(2)C(2)Ph(2))(2)](2)(-) (1(2-)) with 1 equiv of benzyl cation. When anion 3(-) was oxidized, the long-lived nickeladithiolene radical [Ni(S(2)C(2)Ph(2))[S(2)(CH(2)Ph)C(2)Ph(2)]] (3) was formed. The visible, near-IR, and ESR spectra of radical 3 could be measured and assigned. When radical 3 was further oxidized, the oxidant 3(+) eliminated one benzyl cation, and then free nickeladithiolene (1) was generated.     

Geometric quantization on presymplectic manifolds

In this paper, we discuss the possibilities of adapting geometric quantization to presymplectic manifolds, i.e., differentiable manifoldsM ^2n+k (k>0) endowed with a closed 2-form ω of rank2n. We show that such an adaptation is possible in various manners, and that, as a general idea, it reduces the quantization onM to quantization on the symplectic quotientM/V, whereV is the foliation defined by the annihilator of ω.     

Copolymerization with depropagation. III. Composition and sequence distribution from probability considerations

Elementary probability considerations have been used to derive completely general equations which describe both the sequence distributions and compositions to be expected for copolymerizations which follow kinetic models having complete reversibility for all propagation steps. It is shown that previously derived composition equations for both reversible and irreversible systems are special cases of the general equations derived herein.     

Syntheses and electrochemical behaviour of novel dmit or dmio (dithiolato) cobalt(iii) complexes with a η5-cyclopentadienyl or η5-pentamethylcyclopentadienyl ring

Four novel cobalt(III) complexes with a cyclopentadienyl or pentamethylcyclopentadienyl ring and dmit or dmio ligands were synthesized, and their electrochemical behaviour was investigated. All these complexes exhibited three one-electron transfer steps: one reduction and two oxidation steps. In addition, a novel organosulphur compound was afforded by electrochemical oxidation of dmit cobalt complex. Thus, these complexes may have considerable synthetic potential as precursors for electron reservoirs and organosulphur compounds.     

Effects of astigmatic axis orientation on postural stabilization with stationary equilibrium

We evaluated 15 healthy participants by assessing their maintenance of postural control while standing on a platform stabilometer for 1 min under the following conditions: eyes open; eyes open with + 3.00 D on both eyes on same directions (45, 90, 135, 180 degree axis); right eye on 45 degree axis and left eye on 135 degree axis (inverted V-pattern), and right eye on 135 degree axis and left eye on axis 45 degree axis (V-pattern). The differences in the linear length, area and maximum velocity of center of pressure during postural control before and after the six types of positive cylinder-oriented axes were analyzed. Comparing the antero-posterior lengths and antero-posterior maximum velocities, there were significant differences between the V-pattern condition and the six other conditions. Astigmatic defocus in the antagonistic axes conditions, particularly the V-pattern condition, affects postural control of antero-posterior sway (143/150).