MODIFIED DIRECT TWOS-COMPLEMENT PARALLEL ARRAY MULTIPLICATION ALGORITHM FOR COMPLEX MATRIX OPERATION

A direct twos-complement parallel array multiplication algorithm is introduced and modified for digital optical numerical computation. The modified version overcomes the problems encountered in the conventional optical twos-complement algorithm. In the array, all the summands are generated in parallel, and the relevant summands having the same weights are added simultaneously without carries, resulting in the product expressed in a mixed twos-complement system. In a two-stage array, complex multiplication is possible with using four real subarrays. Furthermore, with a three-stage array architecture, complex matrix operation is straightforwardly accomplished. In the experiment, parallel two-stage array complex multiplication with liquid-crystal panels is demonstrated.

Stereoselective polymerization of rac-lactide using a monoethylaluminum Schiff base complex

A monoethylaluminum Schiff base complex (2) with formula LA1Et (L = N,N'-(2,2-dimethylpropylene)bis(3,5-di-tei-t-butylsalicylideneimine) was synthesized and employed for the stercoselective ring-opening polymerization of rac-lactide (rac-LA). The complex 2 was characterized by nuclear magnetic resonance, crystal structure, and elemental analysis. It contains a five-coordinate aluminum atom with distorted trigonal bipyramidal geornetry in the solid state. In the presence of 2-propanol, 2 showed high stereoselectivity for the polymerization of rac-LA. The polymerization yielded crystalline poly(rac-LA) with a high melting temperature (193-201 degreesC). NMR, differential scanning calorimetry, and wide-angle X-ray diffraction indicated that the poly(rac-LA) was highly isotactic, and a stereocomplex was formed between poly-L- and poly-D-lactide block sequences. By the analysis of electrospray-ionization mass spectrometry and H-1 NMR, the polymer was demonstrated to be endcapped in both terminals with an isopropyl ester and a hydroxy group, respectively. The polymerization was of first order in rac-LA concentration. The relationship between the rac-LA conversion and molecular weights of the polymer was linear so that the polymerization could be well controlled.

ASSIGNMENT OF C-13 NMR-SPECTRA OF POLYMER WITH SEMIEMPIRICAL METHOD - SURVEY OF SPECTRUM OF SECONDARY CARBON OF 1,2-PBD

In chain molecules of 1, 2-PBD, there are two kinds of gauche arrangements, which is the cause of making the spectrum of the secondary carbon in main chain of the polymer split. In such a complex system, the gauche arrangements of the secondary carbon and the tertiary carbon occupy an important position. Hence, the contribution of the tertiary carbon to the chemical shifts of the secondary carbon has a decisive effect on the sequence structure distribution. In comparison the contribution of vinyl groups is ...