Extremal types for certainL p minimization problems and associated large scale nonlinear programs

Extremals for constrained minimization problems, min F, are classified according to the growth properties of the linear functionalF() restricted to . Various singular and nonsingular extremal types are investigated in detail for the special case where = {measurableu(·): [0, 1] U},U = a bounded polyhedral convex set in ^m , andF is understood in Fréchet's sense relative to anL ^p norm withp [1, ). The analysis yields newL ^p minimization corollaries of recently developed general convergence rate theories for conditional and projected gradient methods, and a Newton method for constrained minimization. These results help to explain trends in the behavior of computational procedures for certain large scale structured nonlinear programs in ^k ask increases to , with particular application to a large class of optimal control problems with linearly constrained inputs; control problems with bang-bang solutions are considered at some length.Investigation supported by NSF Research Grants ECS-8005958 and ENG 78-03385.     

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.     

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.     

Screening an In-House Isoquinoline Alkaloids Library for New Blockers of Voltage-Gated Na+ Channels Using Voltage Sensor Fluorescent Probes: Hits and Biases

Voltage-gated Na⁺ (Na_V) channels are significant therapeutic targets for the treatment of cardiac and neurological disorders, thus promoting the search for novel Na_V channel ligands. With the objective of discovering new blockers of Na_V channel ligands, we screened an In-House vegetal alkaloid library using fluorescence cell-based assays. We screened 62 isoquinoline alkaloids (IA) for their ability to decrease the FRET signal of voltage sensor probes (VSP), which were induced by the activation of Na_V channels with batrachotoxin (BTX) in GH3b6 cells. This led to the selection of five IA: liriodenine, oxostephanine, thalmiculine, protopine, and bebeerine, inhibiting the BTX-induced VSP signal with micromolar IC₅₀. These five alkaloids were then assayed using the Na⁺ fluorescent probe ANG-2 and the patch-clamp technique. Only oxostephanine and liriodenine were able to inhibit the BTX-induced ANG-2 signal in HEK293-hNa_V1.3 cells. Indeed, liriodenine and oxostephanine decreased the effects of BTX on Na⁺ currents elicited by the hNa_V1.3 channel, suggesting that conformation change induced by BTX binding could induce a bias in fluorescent assays. However, among the five IA selected in the VSP assay, only bebeerine exhibited strong inhibitory effects against Na⁺ currents elicited by the hNav1.2 and hNav1.6 channels, with IC₅₀ values below 10 µM. So far, bebeerine is the first BBIQ to have been reported to block Na_V channels, with promising therapeutical applications.