where here the probability is understood to range over the random choice of code as well as the selection of (r,s). (64) il i=l We find the expected value (over e and s) It follows that d(y,x(r))-+ c@ + 2p in probability and therefore Pr{E,} + 0 as n + co. We are left with the evaluation of Pr{E*}. We write Pr{E,} 5 Pr{d(x(r)& I n(aj + 6p + E), for some r # 1 Ix(l) transmitted} 5 2nRr* Pr{d(x(2...

This note deals with the structure of the class NPR introduced by L. Blum, M. Shub, and S. Smale (1989, Bull. Amer. Math. Soc. 21, 1 46). It is shown that, assuming NPR 3 PR poly, there exists a problem NPR"(PR poly) which is not NPR-complete (w.r.t PR poly reductions). It also clarifies the scope of a padding technique used in a former similar result by R. Ladner (1975, J. Assoc. Comput. Mach....

La capacitŽ des Žquations d'Žtat (EoS) cubiques pour corrŽler et prŽdire les Žquilibres de phases en conditions hyperbares est analysŽe. Les donnŽes PVT de corps purs ainsi que les donnŽes d'Žquilibres liquide-vapeur (VLE) et volumŽtriques pour des mŽlanges binaires, jusqu'ˆ 2000 bar sont utilisŽes. Les rŽsultats des corrŽlations et des prŽdictions sont prŽsentŽs pour l'Žquation de Peng-Robinso...

Pig m e n t M a nu f a c turin g B y-Pr o d uc t s G e t a S e co n d L o ok

Tetranitromethane bleaches Avena phytochrome. The phytochrome (far-red absorbing form; Pfr) chromophore of 124 kilodalton (kD) phytochrome is oxidized 8 times more rapidly than the red absorbing form (Pr). Proteolysis of the 124 kD molecule to the extensively studied mixture of 118 and 114 kD polypeptides increases the rate of oxidation of Pfr 5-fold without affecting the rate of Pr oxidation. ...

Progesterone receptors (PR) are the strongest predictors of response to hormone therapy in metastatic breast cancer, while PR and the DNA indices of cell ploidy and percentage of S phase are useful prognostic indicators in early stage breast cancer. We have developed a flow cytometry method to measure PR and DNA indices simultaneously using two aneuploid breast cancer cell lines—PR-positive T...

served in Japan. PR has been developed industrially in order to enhance the nutritional functions of its source material, brown rice (BR). PR is produced by soaking BR in water for slight germination. Amounts of some constituents including g-aminobutyric acid (GABA) are remarkably increased in PR. GABA is also known to potentiate the insulin secretion in pancreas. Thus PR is thought to ameliora...

A novel platinum-mediated process involving intermolecular activation of a C(aryl)-H bond of toluene, intramolecular activation of an imine C(aryl)-Cl bond and formation of a C-C bond is reported.

Generation of azomethine imine and its scope in regioselective 1,3-dipolar cycloaddition (DC) of imine with PhIO toward highly substituted Delta(2)-1,2,4-triazoline, 1,2,4-triazole, and their fused, chiral, and sugar-based analogues are demonstrated.

Example 1.1. For each integer m > 1, there is an m-cover of Z which is not the union of two covers of Z. To wit, we let p1, . . . , pr be distinct primes with r > 2m − 1, and set N = p1 · · · pr. Clearly A∗ = {∏s∈I ps(N)}I⊆{1,... ,r}, |I|>m does not cover any integer relatively prime to N . Let a1, . . . , an be the list of those integers in {0, 1, . . . , N − 1} not covered by A∗ with each occ...