New telechelic polymers and sequential copolymers by polyfunctional initiator-transfer agents (inifers). LIII. Lithiation of 2,4,4-trimethyl-1-pentene and isopropylidene-capped polyisobutylenes by butyllithiums in the presence of complexing agents

Lithiated isopropylidene-telechelic polyisobutylenes (i.e., PIBs capped with end groups) are most interesting novel intermediates for further transformations, e.g., functionalization, polymerization. This report concerns model lithiation experiments of 2,4,4-trimethyl-1-pentene (TM1P) that guided us toward the subsequent quantitative lithiation of isopropylidene-telechelic PIBs. Thus, lithiation of TM1P with, n-, s-, and t-butyllithium, in the presence of various complexing agents (i.e., TMEDA, t-BuOK, 1,2-DPE, CH₃OCH₂CH₂OCH₃, THF, and 12-crown-4) followed by silylation with Me₃SiCl (for the purpose of quantitation) gave three products: 2(trimethylsilylmethyl)-4,4-dimethyl-1-pentene (TM1P-Si), 2(trimethylsilylmethyl)-4,4-dimethyl-2-pentene (TM2P-Si₂). The relative product composition strongly depends on the BuLi/complexing agent ratio and temperature. Among the different butyllithiums and complexing agents the best overall results were obtained with the s-BuLi/TMEDA combination. Complete lithiation of TM1P with minimum dilithiation was obtained using the molar ratio [s-BuLi]: [TMEDA]: [TM1P] = 2 : 2 : 1. The apparent activation energy of lithiation by s-BuLi/TMEDA was found to be 6.7 ± 0.8 kcal/mol. Guided by TM1P model experiments, quantitative monolithiation of isopropylidene-capped polyisobutylene (including ca. 4% chain and isomerization) was achieved using the molar ratio [s-BuLi] : [TMEDA] : [C? C] = 5 : 4 : 1.     

Model-Theoretic Investigations into Consequence Operation (Cn) in Quantum Logics: An Algebraic Approach

In this paper, we present the fundamentals of the so-called algebraic approach to propositional quantum logics. We define the set of formulae describing quantum reality as a free algebra freely generated by the set of quantum proportional variables. We define the general notion of logic as a structural consequence operation. Next, we introduce the concept of logical matrices understood as a model of quantum logics. We give the definitions of two quantum consequence operations defined in these models.     

Quantum Algorithm for Approximating Maximum Independent Sets

We present a quantum algorithm for approximating maximum independent sets of a graph based on quantum non-Abelian adiabatic mixing in the sub-Hilbert space of degenerate ground states,which generates quantum annealing in a secondary Hamiltonian.For both sparse and dense random graphs G,numerical simulation suggests that our algorithm on average finds an independent set of size close to the maximum size α(G) in low polynomial time.The best classical algorithms,by contrast,produce independent sets of size about half of α(G)in polynomial time.     

Diquarks and exotic spectroscopy

We propose that the recently discovered Theta(+) baryon is a bound state of four quarks and an antiquark, containing two highly correlated ud pairs. If so, the theta(+) has positive parity, and it lies in an near-ideally mixed SU(3)(f) 10;(f) plus sign in circle 8(f). The Roper resonance and the P11(1710) fit naturally into this classification. We predict an isospin 3/2 multiplet of Xi's (S=-2) with J(Pi)=1 / 2(+) around 1750 MeV. A search for manifestly exotic Xi(+) and Xi(--) in this mass range could provide a sharp test of our proposal. We predict that charm and bottom analogs of the Theta(+) may be stable against strong decays.