The Critical Values of a Polynomial

It has been known for a long time that any real sequence y ₁ , . . . ,y _n-1 is the sequence of critical values of some real polynomial. Here we show that any complex sequence w ₁ , . . . ,w _n-1 is the sequence of critical values of some complex polynomial.     

Extreme values of {zeta}'({rho})

Assuming the Riemann hypothesis, we exhibit large and smallvalues of the derivative of the zeta function evaluated at thenon-trivial zeros of the zeta function. These results are provedby applying Soundararajan's resonance method.     

二苯并噻吩在分散型钼催化剂和原位产生的氢存在下的加氢脱硫Ⅲ. 催化剂前身物、硫化氢、一氧化碳和水对反应的影响(英)

研究了水／ 甲苯乳化液中二苯并噻吩（ 硫芴） 在分散型钼酸、磷钼酸和四硫钼酸铵催化剂存在下的加氢脱硫反应． 反应在高压釜中于３４０ ℃及三种不同的气氛即Ｈ２ ，Ｈ２／Ｈ２ Ｏ和ＣＯ／Ｈ２Ｏ（ＣＯ 和Ｈ２Ｏ 经水煤气转换反应（ ＷＧＳＲ） 产生原位氢） 的存在下进行． 用ＧＣ和ＧＣＭＳ鉴定、分析了气体和液体产物的组成． 结果表明： 对硫芴的加氢脱硫反应，在分散型四硫钼酸铵催化剂存在下，原位产生的氢的效果仅比加入的氢气稍好，而在分散型钼酸和磷钼酸催化剂存在下，原位产生的氢远比加入的氢气有效． 实验结果还表明： 硫化氢能显著提高分散型钼酸和磷钼酸催化剂的加氢脱硫活性，但在分散型四硫钼酸铵催化剂存在下，硫化氢能促进加氢反应而抑制氢解反应． 一氧化碳和水均选择性地抑制氢解反应．     

Experimental and computational studies of the macrocyclic effect of an auxiliary ligand on electron and proton transfers within ternary copper(II)-Histidine complexes

The dissociation of [Cu^II(L)His]^•2+ complexes [L=diethylenetriamine (dien) or 1,4,7-triazacyclononane (9-aneN₃)] bears a strong resemblance to the previously reported behavior of [Cu^II(L)GGH]^•2+ complexes. We have used low-energy collision-induced dissociation experiments and density functional theory (DFT) calculations at the B3LYP/6-31+G(d) level to study the macrocyclic effect of the auxiliary ligands on the formation of His^•+ from prototypical [Cu^II(L)His]^•2+ systems. DFT revealed that the relative energy barriers of the same electron-transfer (ET) dissociation pathways of [Cu^II(9-aneN₃)His]^•2+ and [Cu^II(dien)His]^•2+ are very similar, with the ET reactions of [Cu^II(9-aneN₃)His]^•2+ leading to the generation of two distinct His^•+ species; in contrast, the proton transfer (PT) dissociation pathways of [Cu^II(9-aneN₃)His]^•2+ and [Cu^II(dien)His]^•2+ differ considerably. The PT reactions of [Cu^II(9-aneN₃)His]^•2+ are associated with substantially higher barriers (>13 kcal/mol) than those of [Cu^II(dien)His]^•2+. Thus, the sterically encumbered auxiliary 9-aneN₃ ligand facilitates ET reactions while moderating PT reactions, allowing the formation of hitherto nonobservable histidine radical cations.     

The synthesis and reactivity of polysilylacetylenes: Diels—Alder reactions to give bis (silyl) benzenes

Six bis(silyl)acetylenes (XMe²Si? C?C? SiMe₂X) with the following varied silicon substituents X were prepared: 1 (Me, Me); 2 (H, H); 3 (C1, H); 4 (CI, CI); 5 (MeO, H); 6 (MeO, MeO). While 1 and 2 may be prepared by the reaction of dilithio- or bis(bromomagnesium)-acetylide with the appropriate chlorosilane, similar reactions designed to give 3–6 yielded oligomers, XMe₂Si? (? C?C? SiMe₂)_n? X, 7, X=CI, MeO, as the major products, indicating that the acetylenic functionality on silicon activates the chlorosilane towards nucleophilic substitution. Compounds 3 and 4 were prepared by free radical chlorination of 2. Methanolysis of 3 and 4 gave quantitative yields of 5 and 6 respectively. Compounds 1–6 undergo a Diels–Alder reaction with α-pyrone to produce, after loss of carbon dioxide, bis(silyl)-substituted benzene derivatives. The order of reactivity has been determined to be: 4=6>3=5>1>2, indicating that chloro or alkoxy substituents favor the cycloaddition with 2- pyrone. The adducts formed by compounds 3–6 undergo an unusually facile hydrolysis or elimination to give 1,1,3,3-tetramethyl-1,3-disila-2-oxaindane.     

The role of substituents on the addition of muonium to aromatics: As seen through muonium-radicals in allyl benzene compared to styrene,and from hammett parameters in aqueous solution

Muonium-radicals resulting from insertion into the benzene ring are found to be much more prevalent in allyl benzene (C₆H₅CH₂CH=CH₂) than in styrene (C₆H₅CH=CH₂). The salient implication of this comparison is that intramolecular rearrangements preceeded the μSR observation for the case of styrene. In turn, this suggests that muonium-containing free radicals, as seen directly by kilogauss transverse field μSR, are not necessarily theprimary radicals. Therefore, the elucidation of mechanism (and identification of the precursor) of Mu-radical formation is further complicated by the fact that the observations may refer to thermodynamically more stable secondary radicals-those resulting from a variety of intra-or inter-molecular relaxations or exchanges. Primary kinetic selectivities of thermalized muonium atom addition reactions can be determined, however, through the substituent effect on the Hammett linear free energy parameter in dilute solution. Results have been obtained for substituted benzenes and benzoic acids. Muonium apparently has a mild nucleophilic character. And, most interestingly, this is opposite to that of its heavy isotope hydrogen.     

Model for the evolution of hot and compressed spherical nuclei

A hydrodynamical approach and the Thomas Fermi approximation have been used to study the evolution of hot and compressed nuclei. Spherical symmetry was assumed in the calculation. The dynamical equations have been transformed into “Schrödinger like” equations (using the Madelung transformation) and were solved numerically. Dissipation was simulated in the same way as in the Navier-Stokes equation by introducing shear and bulk viscosities. Global as well as local thermal equilibrium have been studied. The model has been applied to small amplitude oscillations (the breathing mode) and to the stability of hot and compressed nuclei. It was found that compression is more efficient to break nuclei than thermal excitation. The relaxation time for global equilibrium was estimated to be of the order of 10^?22 s. It was found that the results obtained in the case of global and local thermal equilibrium are very similar.