Estimates for transition probabilities on a compact manifold

The purpose of this note is to describe a procedure for transferring familiar estimates for transition probabilities on RN to transition probabilities on compact manifolds.     

Synthesis of New Plant Growth Regulators,Isomeric 1-(Dimethyloctyl)- and 1-Alkylpiperidinium and -morpholinium Halides by Telomerization of Isoprene with Secondary Amines

The known plant growth regulator, Al'den [1-(3,7-dimethyloctyl)-1-allylpiperidinium bromide], and also 1-(3,7-dimethyloctyl)-1-methylpiperidinium iodide were synthesized by treatment with allyl bromide and methyl iodide, respectively, of exhaustively hydrogenated 1-nerylpiperidine which was obtained by anionic telomerization of isoprene with piperidine. Various quaternary ammonium salts having a terpene sub- stituent with unnatural dimethyloctane skeleton, which effectively stimulate florification of Aster Chinensis L., were prepared by the action of alkyl halides on telomerization products derived from isoprene and piperidine or morpholine in the presence of palladium complexes.     

Dynamic mechanical thermal analysis transitions of partially and fully substituted cellulose fatty esters

The main transitions of cellulose fatty esters with different degrees of substitution (DSs) were investigated with dynamic mechanical thermal analysis. Two distinct main relaxations were observed in partially substituted cellulose esters (PSCEs). They were attributed to the glass‐transition temperature and to the chain local motion of the aliphatic substituents. The temperatures of both transitions decreased when DS or the number of carbon atoms (n) of the acyl substituent increased. Conversely, all the transitions of fully substituted cellulose esters occurred within a narrow temperature range, and they did not vary significantly with n. This phenomenon was explained by the formation of a crystalline phase of the fatty substituents. The presence of few residual OH groups in PSCEs was responsible for a large increase in the storage bending modulus, and it eliminated the effect of n on damping. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 281–288, 2003     

Projective varieties with projectively equivalent singular 0-dimensional sections

Fix integers m, n such that 1 ≤ m ≤ n ? 3. Let X ? Pⁿ be an integral non-degenerate m-dimensional variety. Assume either char(K) = 0 or char(K) > deg(X). Here we prove that all general 0-dimensional sections of X containing a tangent vector to a smooth point of X are protectively equivalent if and only if n ? m + 1 ≤ deg(X) ≤ n ? m + 2.     

Decrease in the group velocity of a light pulse in the Bose-Einstein condensate of a dilute gas

A semiclassical theory of electromagnetically induced transparency in a Bose-Einstein condensate is considered. A nonlinear Schrödinger equation that describes the interaction of the Bose-Einstein condensate with an electromagnetic field is derived. An analysis of the obtained solutions to this equation demonstrates a decrease in the group velocity of the light pulse.