Carbon dioxide fixation by an unprecedented hydroxo lead-chromium carbonyl complex: synthesis, reactivity, and theoretical calculations

The novel hydroxo-bridged dimeric lead-chromium carbonyl complex [Et4N]2[{PbCr2(CO)10}2(mu-OH)2] ([Et4N]2[1]) was synthesized from the reaction of PbCl2 and Cr(CO)6 followed by metathesis with [Et4N]Br in a KOH/MeOH solution. The X-ray crystallographic structure shows that dianion 1 consists of two Pb{Cr(CO)5}2 units bridged by two hydroxo fragments in which the Pb atoms are further coordinated with two Cr(CO)5 groups, resulting in a distorted tetrahedral geometry. A CO2 molecule can insert itself into dianion 1 to form two new carbonate complexes, [Et(4)N]2[{PbCr2(CO)10}(CO3)] ([Et4N]2[2]) and [Et4N]2[{PbCr2(CO)10}2(CO3)] ([Et4N]2[3]), depending on the reaction conditions. In addition, complex 2 can be transformed into 3 in CH2Cl2 solution at an elevated temperature. While the carbonate group in dianion 2 is bonded to one Pb atom, which is coordinated with two Cr(CO)5 fragments, the carbonate group in 3 bridges the two Pb centers in a mu-1kappa2OO':2kappa2OO' fashion in which each Pb atom is further bonded to two Cr(CO)5 moieties. Complexes 2 and 3 can be converted back the hydroxo complex 1 under appropriate conditions. All three unprecedented lead-chromium compounds, 1-3, were fully characterized by spectroscopic methods and single-crystal X-ray diffraction analyses. The nature and formation of complexes 1-3 were also examined by molecular orbital calculations using the B3LYP method of the density functional theory.     

Max-Plus Stochastic Control and Risk-Sensitivity

In the Maslov idempotent probability calculus, expectations of random variables are defined so as to be linear with respect to max-plus addition and scalar multiplication. This paper considers control problems in which the objective is to minimize the max-plus expectation of some max-plus additive running cost. Such problems arise naturally as limits of some types of risk sensitive stochastic control problems. The value function is a viscosity solution to a quasivariational inequality (QVI) of dynamic programming. Equivalence of this QVI to a nonlinear parabolic PDE with discontinuous Hamiltonian is used to prove a comparison theorem for viscosity sub- and super-solutions. An example from mathematical finance is given, and an application in nonlinear H-infinity control is sketched.     

Optimal age-replacement model with age-dependent type of failure and random lead time based on a cumulative repair-cost limit policy

In this paper, we consider an age-replacement model with minimal repair based on a cumulative repair cost limit and random lead time for replacement delivery. A cumulative repair cost limit policy uses information about a system’s entire repair cost history to decide whether the system is repaired or replaced; a random lead time models delay in delivery of a replacement once it is ordered. A general cost model is developed for the average cost per unit time based on the stochastic behavior of the assumed system, reflecting the costs of both storing a spare and of system downtime. The optimal age for preventive replacement minimizing that cost rate is derived, its existence and uniqueness is shown, and structural properties are presented. Various special cases are included, and a numerical example is given for illustration. Because the framework and analysis are general, the proposed model extends several existing results.     

A new finding of the existence of Feigenbaum’s constants in the fractional-order Chen–Lee system

This paper examines the universal quantitative properties of the fractional- and integer-order Chen?CLee systems. A?series of bifurcation diagrams of the system were generated in order to measure Feigenbaum??s constants. It was found that the measured values of the integer-order system were accurately approaching their universal constants, while the errors between measured values of the fractional-order system and the universal constants were not very large. The results showed that both the fractional- and integer-order Chen?CLee systems belonged to a quadratic map. To the authors?? knowledge, this is the first paper to measure Feigenbaum??s constants in fractional-order systems.     

Novel Polyhydroxysteroids from the Formosan Soft Coral Sarcophyton Glaucum

Two novel polyhydroxysteroids, (24S)‐24‐methylcholestane‐3β,5α,6β,25ξ;,26‐pentol 26‐n‐decanoate ( 1 ), (24S)‐24‐methylcholestane‐3β,5α,6β,25ξ;,26‐pentol 25,26‐diacetate ( 2 ), and three known sterols ( 3‐5 ), have been isolated from a Formosan soft coral Sarcophyton glaucum. The molecular structures of these compounds were determined by spectral methods. The cytotoxicity of these compounds toward various cancer cell lines has also been determined.     

Simultaneous determination of sweeteners and preservatives in preserved fruits by micellar electrokinetic capillary chromatography

A micellar electrokinetic capillary method for the simultaneous determination of the sweeteners dulcin, aspartame, saccharin, and acesulfame-K and the preservatives sorbic acid; benzoic acid; sodium dehydroacetate; and methyl-, ethyl-, propyl-, isopropyl-, butyl-, and isobutyl-p-hydroxybenzoate in preserved fruits is developed. These additives are ion-paired and extracted using sonication followed by solid-phase extraction from the sample. Separation is achieved using a 57-cm fused-silica capillary with a buffer comprised of 0.05 M sodium deoxycholate, 0.02 M borate-phosphate buffer (pH 8.6), and 5% acetonitrile, and the wavelength for detection is 214 nm. The average recovery rate for all sweeteners and preservatives is approximately 90% with good reproducibility, and the detection limits range from 10 to 25 microg/g. Fifty preserved fruit samples are analyzed for the content of sweeteners and preservatives. The sweeteners found in 28 samples was aspartame (0.17-11.59 g/kg) or saccharin (0.09-5.64 g/kg). Benzoic acid (0.02-1.72 g/kg) and sorbic acid (0.27-1.15 g/kg) were found as preservatives in 29 samples.     

The Regioselectivity of (Dimethylvinylidene)carbene Directed by Aromatic Ring upon the Addition into Aryl Alkenes in the Presence of Other Olefins

Regioselective cycloaddition of (dimethylvinylidene)carbene (1) into aryl alkenes in the presence of other olefins is reported. The reaction is presumably controlled by the phenyl group, which forms an aromatic π-complex with the carbene C-3 orbital, followed by the selective addition of 1 to the closest phenyl-substituted double bond. Also, this selectivity is assumed to be attributed to delocalization of aromatic π electrons which increases the electron density of the conjugated carbon-carbon double bond, thus leading to the facile addition of vinylidenecarbene.     

New Norcembranoids from the Soft Coral Sinularia Lochmodes

Two new C‐4 norcembranoids sinulochmodins D ( 1 ) and E ( 2 ), along with three known norditerpenoids ( 3–5 ), have been isolated from the organic extract of a Taiwanese soft coral Sinularia lochmodes (Kolonko). The structures of 1 and 2 were determined on the basis of extensive spectroscopic analyses and by comparison of their spectral data with those of related metabolites.     

Drying induced phase transformation of mesoporous silica

Solvent evaporation upon drying the precipitate was found to be the key factor for the phase transformation of cubic mesoporous silica SBA-1 to hexagonal SBA-3 studied by in-situ X-ray diffraction and 29Si solid state NMR on the precipitates formed various crystallisation conditions.