Correction: New stiff matter solutions are really not stiff

Four new solutions in general relativity have recently been derived as representing static spherically symmetric stiff matter,=p. It is pointed out that the equation of state is, in fact,+p=0. It is further shown that two of the solutions are physically reasonable, turning out to represent the vacuum, one of them with a term.     

Beta-delayed two-proton decay of39Ti

The beta-delayed two-proton decay of theT _z =–5/2 nuclide³⁹Ti has been observed. The³⁹Sc isobaric analog state has been calculated to lie at 8.82 MeV using the measured two-proton sum energy of 4750±40 keV for its decay to the³⁷K ground state. Combining this excitation energy with a Coulomb displacement energy calculation has lowered the energy available for ground state two-proton emission of³⁹Ti from 760 to 530 keV.This work was supported by Director, Office of Energy Research, Division of Nuclear Physics of the Office of High Energy and Nuclear Physics of the U.S. Depeartment of Energy under Contracts DE-AC03-76SF00098 with Lawrence Berkeley Laboratory, DE-AC02-76CH00016 with Brookhaven National Laboratory and DE-AC06-76RL0 1830 with Pacific Northwest Laboratories.     

Incoherent inelastic neutron scattering studies of potassium bicarbonate and caesium hydrogen dinitrate

Inelastic neutron scattering spectra of KHCO₃ and CsH(NO₃)₂ have been obtained in the region 400 → 2400 and 400 → 2800 cm^?1 respectively. The in- and out-of-phase bending vibrations of the hydrogen bonds have been observed and assigned. For CsH(NO₃)₂ the two bending modes are closer in frequency than in KHCO₃ and they are not resolved from the antisymmetric stretch.     

Facile syntheses of unsolvated UI3 and tetramethylcyclopentadienyl uranium halides

In the course of comparing the reaction chemistry of (C5Me5)3U, 1, and its slightly less crowded analogue (C5Me4H)3U, 2, new syntheses of UI3, (C5Me4H)3U, (C5Me4H)3UCl, 3, and (C5Me5)3UCl, 4, have been developed. Additionally, (C5Me4H)3UI, 5, and (C5Me4H)2UCl2, 6, have been identified for the first time. A facile synthesis of unsolvated UI3 is reported that proceeds in high yield with inexpensive equipment from iodine and hot uranium turnings. Both UI3 and UI3(THF)4 react with KC5Me4H in toluene to make unsolvated (C5Me4H)3U in higher yield than in previous reports that involve reduction of tetravalent (C5Me4H)3UCl, 3. A more atom-efficient synthesis of complex 3 is also reported that proceeds from reduction of t-BuCl, PhCl, or HgCl2 by 2. Similarly, (C5Me4H)3U reacts with PhI or HgI2 to generate (C5Me4H)3UI. These studies also provided a basis to improve the synthesis of (C5Me5)3UCl from 1 by employing t-BuCl or HgCl2 as the halide source. Like (C5Me5)3UCl, the (C5Me4H)3UCl complex reacts with HgCl2 to form (C5Me4H)2 and (C5Me4H)2UCl2, 6, but unlike (C5Me5)3UX (X = Cl or I), the less substituted (C5Me4H)3UX complexes do not reduce t-BuCl or PhX. The synthesis of 6 from (C5Me4H)MgCl x THF and UCl4 is also included.     

Theory-enforced Re-investigation of the Origin of the Large Metal–Carbon Bond Strength in PdCH2I+ and its reactions with unsaturated hydrocarbons

State-of-the-art ab initio studies demonstrate that the reaction Pd⁺ + CH₃I → PdCH₂I⁺ + H^. is endothermic by ca. 20 kcal/mol, which translates into a bond dissociation energy (BDE) of ca. 83 kcal/mol for the Pd⁺? CH₂I bond. This figure is in agreement with an experimental bracket of 68 kcal/mol < BDE(Pd⁺? CH₂I) < 92 kcal/mol. Based on these findings, the previously studied Pd⁺/CH₃I system was re-investigated, and double-resonance experiments demonstrate that the formation of PdCH₂I⁺ occurs stepwise via PdCH as a reactive intermediate. Further, ion/molecule reactions of PdCH₂I⁺ with unsaturated hydrocarbons are studied, which reveal the formation of carbon–carbon bonds in the gas phase.     

A new strategy for the construction of the imidazo[1,5-a]quinoxalin-4-one ring system and its application to the efficient synthesis of BMS-238497, a novel and potent Lck inhibitor

A new efficient strategy was developed for the construction of the imidazo[1,5-a]quinoxalin-4-one ring system. The new method involves condensation of o-nitroaniline with glyoxylate in methanol followed by treatment of the resulting alpha-(o-nitroanilino)-alpha-methoxy acetate with tosylmethyl isocyanide (TosMIC) reagent to give 1-(o-nitrophenyl)imidazole-5-carboxylate. Reductive cyclization of the nitro imidazole carboxylate afforded imidazo[1,5-a]quinoxalin-4-one in three steps and 60% overall yield. The new method was successfully applied to the synthesis of BMS-238497, a novel and potent Lck inhibitor.     

An investigation into causes and effects of high cyanide levels in the palladium-catalyzed cyanation reaction

[reaction: see text] The palladium-catalyzed cyanation reaction is known to be sensitive to dissolved cyanide. Investigation into some causes of high levels of dissolved cyanide is presented here, along with a robust solution to this problem.     

Intrinsically homogeneous sets,splitting times,and the big shift

Summary Let X be a strong Markov process. Let M be an optional set with the property that _1MoT (S)=1 _M (s+T) whenever s>0 and T is an optional time with [T]M. If L=sup{t>0 tM}M, we show that L is a splitting time of X: the pre-L events and the post-L events are conditionally independent given X _L . To prove this, we extend work of Sharpe's to show that the big shift operators _T and commute with optional projection and dual optional projection, respectively, whenever T is an optional time. Examples are given which are not contained within previous work of Millar and Getoor.     

Catalysts for Suzuki-Miyaura coupling processes: scope and studies of the effect of ligand structure

Suzuki-Miyaura coupling reactions of aryl and heteroaryl halides with aryl-, heteroaryl- and vinylboronic acids proceed in very good to excellent yield with the use of 2-(2',6'-dimethoxybiphenyl)dicyclohexylphosphine, SPhos (1). This ligand confers unprecedented activity for these processes, allowing reactions to be performed at low catalyst levels, to prepare extremely hindered biaryls and to be carried out, in general, for reactions of aryl chlorides at room temperature. Additionally, structural studies of various 1.Pd complexes are presented along with computational data that help elucidate the efficacy that 1 imparts on Suzuki-Miyaura coupling processes. Moreover, a comparison of the reactions with 1 and with 2-(2',4',6'-triisopropylbiphenyl)diphenylphosphine (2) is presented that is informative in determining the relative importance of ligand bulk and electron-donating ability in the high activity of catalysts derived from ligands of this type. Further, when the aryl bromide becomes too hindered, an interesting C-H bond functionalization-cross-coupling sequence intervenes to provide product in high yield.     

Some limit results for longest common subsequences

The length l_n of a longest common subsequence before time n sequences (B₁₁, B₁₂, …) (B₂₁, B₂₂, …) is the cardinality of the largest increasing set of pairs of integers {(j_1α, j_2α)}

$\text{l?}\text{j}{}_{11}\text{<}\text{j}{}_{12}\text{<·<}\text{j}{}_{11}{}_{\mathrm{n}}\text{?}\text{n}\text{l?}\text{j}{}_{21}\text{<}\text{j}{}_{22}\text{<·<}\text{j}{}_{21}{}_{\mathrm{n}}\text{?}\text{n}$

such that ?1?α?l_n, (B_1j1α=B_2j2α). If B₁ and B₂ are independent random sequences with co-ordinates i.i.d. uniform on {1, 2, …, k}, it follows from Kingman's subadditive ergodic theorem that the ratio l_n/n converges to a constant c_k a.s. A method of deriving lower bounds for the constants c_k is given, the bounds obtained improving known lower bounds, for k>2. The rate of decrease of c_k with k is shown to be no faster than 1/√k, contrasting with P{B_1i?B_2i}=1/k. Finally, an alternative method of deriving lower bounds is given and used to improve the lower bound for c₂.