Generalized evaluation subgroups of product spaces relative to a factor

For any -complexes and , we show that . We use this fact to compute generalized evaluation subgroups of generalized tori relative to a sphere.

     

Non-linear parabolic problem associated with the penetration of a magnetic field into a substance

We study the following initial and boundary value problem: In section 1, with u₀ in L²(Ω), f continuous such that f(u) + ? non-decreasing for ? positive, we prove the existence of a unique solution on (0,T), for each T > 0. In section 2 it is proved that the unique soluition u belongs to L²(0, T; H ∩ H²) ∩ L^∞(0, T; H) if we assume u₀ in H and f in C¹(?,?). Numerical results are given for these two cases.     

Determination of sugar structures in solution from residual dipolar coupling constants: methodology and application to methyl beta-D-xylopyranoside

We have developed methodology for the determination of solution structures of small molecules from residual dipolar coupling constants measured in dilute liquid crystals. The power of the new technique is demonstrated by the determination of the structure of methyl beta-d-xylopyranoside (I) in solution. An oriented sample of I was prepared using a mixture of C(12)E(5) and hexanol in D(2)O. Thirty residual dipolar coupling constants, ranging from -6.44 to 4.99 Hz, were measured using intensity-based J-modulated NMR techniques. These include 15 D(HH), 4 (1)D(CH), and 11 (n)D(CH) coupling constants. The accuracy of the dipolar coupling constants is estimated to be < +/- 0.02 Hz. New constant-time HMBC NMR experiments were developed for the measurement of (n)D(CH) coupling constants, the use of which was crucial for the successful structure determination of I, as they allowed us to increase the number of fitted parameters. The structure of I was refined using a model in which the directly bonded interatom distances were fixed at their ab initio values, while 16 geometrical and 5 order parameters were optimized. These included 2 CCC and 6 CCH angles, and 2 CCCC and 6 CCCH dihedral angles. Vibrationally averaged dipolar coupling constants were used during the refinement. The refined solution structure of I is very similar to that obtained by ab initio calculations, with 11 bond and dihedral angles differing by 0.8 degrees or less and the remaining 5 parameters differing by up to 3.3 degrees . Comparison with the neutron diffraction structure showed larger differences attributable to crystal packing effects. Reducing the degree of order by using dilute liquid crystalline media in combination with precise measurement of small residual dipolar coupling constants, as shown here, is a way of overcoming the limitation of strongly orienting liquid crystals associated with the complexity of (1)H NMR spectra for molecules with more than 12 protons.     

α-松油烯-马来酸酐加成物的气相色谱分析

气相色谱法直接测定α－松油佛－马来酸酐加成物，不但免去了容量滴定法测定时必先分离共存马来酸酐的繁琐手续，而且方法简便、快速，能满足合成过程中跟踪分析的需要。