New phosphonic analogs of aspartic and glutamic acid by aminoalkylation of trivalent phosphorus chlorides with ethyl acetyloacetate or ethyl levulinate and benzyl carbamate

Preparation of the phosphonic analogs of -methylaspartic (4 a–d), glutamic (7 a–b) and -methylpyroglutamic (5 a–b) acids by aminoalkylation of trivalent phosphorus chlorides with ethyl esters of oxoalkyloacids and benzyl carbamate is described. The phosphonic analogs of pyroglutamic acid (8 a–b) was obtained by the cyclization of the corresponding esters (9 a–b). The stability of the phosphonic analogs of pyroglutamic acid in acidic and alkaline media was also studied.

---

Die Herstellung von neuen Phosphonanalogen der Asparagin- und Glutaminsäure in der Reaktion von trivalenten Phosphorchloriden mit Ethyl-acetyloacetat oder Ethyl-lävulinat bzw. Benzylcarbaminat

Zusammenfassung Es wurde die Darstellung der Phosphonanalogen der -Methylasparaginsäure (4 a–d), Glutamin- (7 a–b) und -Methylpyroglutaminsäure (5 a–b) in der Reaktion der trivalenten Phosphorchloride und der Oxoalkansäureethylester sowie des Benzylcarbaminats beschrieben. In der Ringschlußreaktion der Ester (9 a–b) erhält man Phosphonanaloge der Pyroglutaminsäure. Die Stabilität der Analogen der Pyroglutaminsäure wurde in sauren und alkalischen Medien geprüft.

     

Electrochemical study of 18-crown-6-Tl+ complexes in binary solvent mixtures

Summary The formation constants,K _S, of the 18-crown-6 complex with thallium(I) ion were studied by polarographic measurements in binary mixtures of acetonitrile, acetone, tetrahydrofuran, and dimethylsulfoxide with water, as a function of the solvent mole fraction. In all the cases, the variation of the stability constant can be described by the empirical relation logK _S=a[(–1)/(2+1)]+b where stands for relative permittivity of a given mixture anda andb mark the regression coefficients. The values ofa calculated for four series of binary mixtures showed correlation with the Gutmann donor numbers of the neat organic solvents which form the mixture.On leave from the Department of Chemistry, Jingzhou Teacher's College, Jingzhou, Hubei, China     

Efficient Collocation Schemes for Singular Boundary Value Problems

We discuss an error estimation procedure for the global error of collocation schemes applied to solve singular boundary value problems with a singularity of the first kind. This a posteriori estimate of the global error was proposed by Stetter in 1978 and is based on the idea of Defect Correction, originally due to Zadunaisky. Here, we present a new, carefully designed modification of this error estimate which not only results in less computational work but also appears to perform satisfactorily for singular problems. We give a full analytical justification for the asymptotical correctness of the error estimate when it is applied to a general nonlinear regular problem. For the singular case, we are presently only able to provide computational evidence for the full convergence order, the related analysis is still work in progress. This global estimate is the basis for a grid selection routine in which the grid is modified with the aim to equidistribute the global error. This procedure yields meshes suitable for an efficient numerical solution. Most importantly, we observe that the grid is refined in a way reflecting only the behavior of the solution and remains unaffected by the unsmooth direction field close to the singular point.     

A simulation-based genetic algorithm approach for reducing emissions from import container pick-up operation at container terminal

Emissions from idle truck engines are a main source of pollution at container terminals. In this study, we focus on reducing such emission from waiting trucks as well as the related crane operations with a new truck arrival control method that gives individual truck limited time slots for entry. We develop a method to optimize the time slot assignment for individual trucks, aiming at minimizing total emissions from trucks and cranes at import yards. The method applies discrete event simulation to estimate total truck waiting times and crane moving distance, and then applies a genetic algorithm to minimize the generated emissions from these trucks and cranes. The experiment result shows that the truck arrivals should be controlled based on the stacking of import containers, and that such control is necessary for reducing truck idling emissions at a congested container terminal.     

Unique factorization of compositive hereditary graph properties

A graph property is any class of graphs that is closed under isomorphisms. A graph property P is hereditary if it is closed under taking subgraphs; it is compositive if for any graphs G1, G2 ∈ P there exists a graph G ∈ P containing both G1 and G2 as subgraphs. Let H be any given graph on vertices v1, . . . , vn, n ≥ 2. A graph property P is H-factorizable over the class of graph properties P if there exist P 1 , . . . , P n ∈ P such that P consists of all graphs whose vertex sets can be partitioned into n parts, possibly empty, satisfying: 1. for each i, the graph induced by the i-th non-empty partition part is in P i , and 2. for each i and j with i = j, there is no edge between the i-th and j-th parts if vi and vj are non-adjacent vertices in H. If a graph property P is H-factorizable over P and we know the graph properties P 1 , . . . , P n , then we write P = H [ P 1 , . . . , P n ]. In such a case, the presentation H[ P 1 , . . . , P n ] is called a factorization of P over P. This concept generalizes graph homomorphisms and (P 1 , . . . , P n )-colorings. In this paper, we investigate all H-factorizations of a graph property P over the class of all hered- itary compositive graph properties for finite graphs H. It is shown that in many cases there is exactly one such factorization.     

A sufficient condition of viability for fractional differential equations with the Caputo derivative

In this paper viability results for nonlinear fractional differential equations with the Caputo derivative are proved. We give the sufficient condition that guarantees fractional viability of a locally closed set with respect to nonlinear function. As an example we discuss positivity of solutions, particularly in linear case.     

A Mountain Pass-type Theorem for Vector-valued Functions

The mountain pass theorem for scalar functionals is a fundamental result of the minimax methods in variational analysis. In this work we extend this theorem to the class of \(\mathcal{C}^{1}\) functions \(f:\mathbb{R}^{n}\rightarrow\mathbb{R}^{m}\), where the image space is ordered by the nonnegative orthant \(\mathbb{R}_{+}^{m}\). Under suitable geometrical assumptions, we prove the existence of a critical point of f and we localize this point as a solution of a minimax problem. We remark that the considered minimax problem consists of an inner vector maximization problem and of an outer set-valued minimization problem. To deal with the outer set-valued problem we use an ordering relation among subsets of \(\mathbb{R}^{m}\) introduced by Kuroiwa. In order to prove our result, we develop an Ekeland-type principle for set-valued maps and we extensively use the notion of vector pseudogradient.     

Diels-alder reaction of 2-chloro-2-nitrosopropane with 1,3-cyclohexadiene

3-(2-Chloropropyl)-2-oxa-3-azabicyclo[2.2.2]oct-5-ene and 2-oxa-3-azabicyclo[2.2.2]oct-5-ene hydrochloride have been prepared by cycloaddition of 2-chloro-2-nitrosopropane to 1,3-cyclohexadiene and their structure determined by nmr, using a ¹H nmr shift reagent.