Experimental and Theoretical Studies on the Rearrangement of 2‐Oxoazepane α,α‐Amino Acids into 2′‐Oxopiperidine β2,3,3‐Amino Acids: An Example of Intramolecular Catalysis

Enantiopure β‐amino acids represent interesting scaffolds for peptidomimetics, foldamers and bioactive compounds. However, the synthesis of highly substituted analogues is still a major challenge. Herein, we describe the spontaneous rearrangement of 4‐carboxy‐2‐oxoazepane α,α‐amino acids to lead to 2′‐oxopiperidine‐containing β^2,3,3‐amino acids, upon basic or acid hydrolysis of the 2‐oxoazepane α,α‐amino acid ester. Under acidic conditions, a totally stereoselective synthetic route has been developed. The reordering process involved the spontaneous breakdown of an amide bond, which typically requires strong conditions, and the formation of a new bond leading to the six‐membered heterocycle. A quantum mechanical study was carried out to obtain insight into the remarkable ease of this rearrangement, which occurs at room temperature, either in solution or upon storage of the 4‐carboxylic acid substituted 2‐oxoazepane derivatives. This theoretical study suggests that the rearrangement process occurs through a concerted mechanism, in which the energy of the transition states can be lowered by the participation of a catalytic water molecule. Interestingly, it also suggested a role for the carboxylic acid at position 4 of the 2‐oxoazepane ring, which facilitates this rearrangement, participating directly in the intramolecular catalysis.     

Synthesis,characterization, and some electrocatalytic properties of heteromultinuclear FeI/RuII Clusters

A series of new heteromultinuclear Fe^I/Ru^II clusters are described. The complexes (η⁶-arene)RuFe₂S₂(CO)₆ (arene = p-cymene 1 , C₆Me₆ 2 ) and Fe₂[μ-S (Cp*Ru)(CO)₂]₂(CO)₆ (Cp* = η⁵-C₅Me₅) ( 3 ) were prepared by the reduction reactions of (μ-S)₂Fe₂(CO)₆ with 2 equiv of LiHBEt₃, followed by treatment (μ-SLi)₂Fe₂(CO)₆ with ruthenium-arene complexes Ru₂(μ-Cl)₂Cl₂(η⁶-arene)₂ or Cp*Ru (CO)₂Cl in 22–33% yields. Further reactions of 1 and 2 with 1 equiv of triphenylphosphine in the presence of the decarbonylating agent Me₃NO·2H₂O, afforded the corresponding monophosphine-substituted Fe^I/Ru^II complexes (η⁶-arene)RuFe₂S₂(CO)₅(Ph₃P) (arene = p-cymene 4 , C₆Me₆ 5 ) in 75% and 78% yields. While treatment of parent complex 1 or 2 with 1 equiv of diphosphine Ph₂PCH₂PPh₂ (dppm) in xylene at reflux temperature resulted in the formation of the diphosphine-bridged RuFe₂S₂(CO)₉ derivate RuFe₂S₂(CO)₇(dppm) ( 6 ). The possible pathway for the formation was proposed. Two isomers of novel macrocyclic complexes involve the (η⁶-arene) Ru-bridged quadruple-butterfly Fe/S clusters [{μ-S (CH₂)₃S-μ}{(μ-CS₂)Fe₂(CO)₆}₂]₂[(η⁶-arene)Ru]₂ (arene = p-cymene 7a and 7b , C₆Me₆ 8a and 8b ) were isolated by reactions of two μ-CS₂-containing dianion [{μ-S (CH₂)₃S-μ}{(μ-S=CS)Fe₂(CO)₆}₂]²⁻ with [Ru₂(μ-Cl)₂Cl₂(η⁶-arene)₂], in which the propylene groups are attached to two S atoms by ee and ea types of bonds respectively. All the new complexes 1 – 8 have been characterized by elemental analysis, spectroscopy, and particularly for 1 – 6 , 7b and 8a by X-ray crystallography. In addition, the electrochemical properties of representative complexes 1 – 4 and 6 have been investigated.     

Optimal strategy of vaccination and treatment in an SIRS model with Markovian switching

Medical treatment and vaccination decisions are often sequential and uncertain. Markov decision process is an appropriate means to model and handle such stochastic dynamic decisions. This paper studies the near‐optimality of a stochastic SIRS epidemic model that incorporates vaccination and saturated treatment with regime switching. The stochastic model takes white noises and color noise into account. We first prove some priori estimates of the susceptible, infected, and recovered populations. Moreover, we establish some sufficient and necessary conditions of the near‐optimality by Pontryagin stochastic maximum principle. Our results show that the two kinds of environmental noises have great impacts on the infectious diseases. Finally, we illustrate our conclusions through numerical simulations.     

Stabilization in three-dimensional chemotaxis-growth model with indirect attractant production

This paper deals with the chemotaxis-growth system: $u_t=\mathrm{\Delta }u?\mathrm{?}?(u\mathrm{?}v)+\mu u(1?u)$, $v_t=\mathrm{\Delta }v?v+w$, $\tau w_t+\delta w=u$ in a smooth bounded domain $\mathrm{\Omega }?{\mathbb{R}}^3$ with zero-flux boundary conditions, where μ, δ, and τ are given positive parameters. It is shown that the solution $(u,v,w)$ exponentially stabilizes to the constant stationary solution $(1,\frac{1}{\delta },\frac{1}{\delta })$ in the norm of $L^{\infty }(\mathrm{\Omega })$ as $t\to \infty$ provided that $\mu >0$ and any given nonnegative and suitably smooth initial data $(u_0,v_0,w_0)$ fulfills $u_0?0$, which extends the condition $\mu >\frac{1}{8{\delta }^2}$ in [8].     

Performance guarantees of local search for minsum scheduling problems

Mathematical Programming - We study the worst-case performance guarantee of locally optimal solutions for the problem of minimizing the total weighted and unweighted completion time on parallel...     

Toolkit for simultaneously improving production and environmental efficiencies

Central European Journal of Operations Research - Environmental efficiency should not be treated independently of production efficiency. Several studies have demonstrated that lean management can...