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.     

Combined Entropic Regularization and Path-Following Method for Solving Finite Convex Min-max Problems Subject to Infinitely Many Linear Constraints

In this paper, we study the minimization of the max function of q smooth convex functions on a domain specified by infinitely many linear constraints. The difficulty of such problems arises from the kinks of the max function and it is often suggested that, by imposing certain regularization functions, nondifferentiability will be overcome. We find that the entropic regularization introduced by Li and Fang is closely related to recently developed path-following interior-point methods. Based on their results, we create an interior trajectory in the feasible domain and propose a path-following algorithm with a convergence proof. Our intention here is to show a nice combination of minmax problems, semi-infinite programming, and interior-point methods. Hopefully, this will lead to new applications.     

Assembly of Three 2D Metal‐Organic Frameworks (MOFs) Derived from Flexible Ligands, 1,4‐bis(3‐pyridyl)‐2,3‐diaza‐1,3‐butadiene (3‐bpd) and/or 1,2‐bis(4‐pyridyl)ethane (dpe)

Three coordination polymers, {[Cd(3‐bpd)₂(NCS)₂]×C₂H₅OH}_n ( 1 ), {[Cd(3‐bpd)(dpe)(NO₃)₂]×(3‐bpd)}₂ ( 2 ), {[Cd(dpe)₂(NCS)₂]×3‐bpd×2H₂O}_n ( 3 ) (3‐bpd = 1,4‐bis(3‐pyridyl)‐2,3‐diaza‐1,3‐butadiene; dpe = 1,2‐bis(4‐pyridyl)ethane), were prepared and structurally characterized by a single‐crystal X‐ray diffraction method. In compound 1 , each Cd(II) ion is six‐coordinate bonded to six nitrogen atoms from four 3‐bpd and two NCS^? ligands. The 3‐bpd acts as a bridging ligand connecting the Cd(II) ion to generate a 2D layered metal‐organic framework (MOF) by using a rhomboidal‐grid as the basic building units with the 4⁴ topology. In compound 2 , the Cd(II) ion is also six‐coordinate bonded to four nitrogen atoms of two 3‐bpd, two dpe and two oxygen atoms of two NO₃^? ligands. The 3‐bpd and dpe ligands both adopt bis‐monodentate coordination mode connecting the Cd(II) ions to generate a 2D layered MOF by using a rectangle‐grid as the basic building units with the 4⁴ topology. In compound 3 , two crystallographically independent Cd(II) ions are both coordinated by four nitrogen atoms of dpe ligands in the basal plane and two nitrogen atom of NCS^? in the axial sites. The dpe acts as a bridging ligand to connect the Cd(II) ions forming a 2D interpenetrating MOFs by using a square‐grid as the basic unit with the 4⁴ topology. All of their 2D layered MOFs in compounds 1 ‐ 3 are then arranged in a parallel non‐interpenetrating ABAB—packing manner in 1 and 2 , and mutually interpenetrating manner in 3 , respectively, to extend their 3D supramolecular architectures with their 1D pores intercalated with solvent (ethanol in 1 or H₂O in 3 ) or free 3‐bpd molecules in 2 and 3 , respectively. The photoluminescence measurements of 1 ‐ 3 reveal that the emission is tentatively assigned to originate from π‐π* transition for 1 and 2 and probably due to ligand‐center luminescence for compounds 3 , respectively.     

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.     

Synthesis, structure and oxygen-sensing properties of iridium(III)-containing coordination polymers with different cations

Four iridium(III)-containing coordination polymers 1-4 using Ir(ppy)(2)(H(2)dcbpy)PF(6) (L-H(2), ppy = 2-phenylpyridine, H(2)dcbpy = 4,4'-dicarboxy-2,2'-bipyridine) as the bridging ligand, [ZnL(2)]·3DMF·5H(2)O (1), [CdL(2)(H(2)O)(2)]·3DMF·6H(2)O (2), [CoL(2)(H(2)O)(2)]·2DMF·8H(2)O (3) and [NiL(2)(H(2)O)(2)]·3DMF·6H(2)O (4), have been synthesized and structurally characterized. The emissions from 1-4 are ascribed to a metal-to-ligand charge transfer transition (MLCT). The absolute emission quantum yields for 1-4 in single crystals were measured in air to be 0.274, 0.193, 0.001 and 0.002, respectively. The noteworthy oxygen-sensing properties of 1-4 as well as L-H(2) in a single crystal were also evaluated. The Stern-Volmer quenching constant, K(SV) values, of 1-4 and L-H(2) can be deduced to be 0.834, 2.820, 1.328, 1.111 and 2.476, respectively. The results show promising K(SV) values (e.g.2) that are competitive or even larger than those of many known Ir-complexes. Moreover, the short response time (e.g. compound 2) and recovery times toward oxygen of 1-4 have been measured in their single crystal forms. The reversibility experiments for 1-4 were carried out for seven repeated cycles. As a result, >75% recovery of intensity for 1 and 2 on each cycle demonstrates a high degree of reproducibility during the sensing process. It should be noted that iridium(III)-containing coordination polymers with high emission intensity and notable oxygen sensing properties are obscure, especially in the single crystal form. This, in combination with its fine reversibility, leads to success in single crystal oxygen recognition based on photoluminescence imaging. The detection limit could be 0.50% for gaseous oxygen. Moreover, the temperature effect of compound 2 in a single crystal upon application as an oxygen sensor was expected.