1-Boryl-3,4-dimethylphosphole trimer: Synthesis, crystal structure and quantum chemical calculations

A novel cycloadduct of 1-boryl-3,4-dimethylphosphole was prepared by reaction of 3,4-dimethylphospholyl anion with monobromoborane-methylsulfide complex (CH₃)₂S · BH₂Br at −60 °C. It was characterized as a six-membered trimer by spectroscopic means, and its structure confirmed by an X-ray crystal analysis and quantum chemical calculations. Density functional theory calculations (B3LYP) showed that the cyclic trimer is by far more stable than the monomer, dimers or open-chain forms. Various molecular and spectroscopic properties of the borylphosphole monomer and trimer were evaluated. In particular, the changes of the ³¹P NMR chemical shifts upon oligomerization were examined. The six-membered ring was demonstrated to exist preferentially in a chair-like conformation. Computed NMR chemical shifts (¹H, ¹³C and a lesser extent ³¹P) appear to be a highly sensitive analytical tool for distinguishing ring conformations having only small energy differences.     

Travel time estimation and order batching in a 2-block warehouse

Order batching problem (OBP) is the problem of determining the number of orders to be picked together in one picking tour. Although various objectives may arise in practice, minimizing the average throughput time of a random order is a common concern. In this paper, we consider the OBP for a 2-block rectangular warehouse with the assumptions that orders arrive according to a Poisson process and the method used for routing the order-pickers is the well-known S-shape heuristic. We first elaborate on the first and second moment of the order-picker’s travel time. Then we use these moments to estimate the average throughput time of a random order. This enables us to estimate the optimal picking batch size. Results from simulation show that the method provides a high accuracy level. Furthermore, the method is rather simple and can be easily applied in practice.     

Radical Formation in the Gas‐Phase Ozonolysis of Deprotonated Cysteine

Although the deleterious effects of ozone on the human respiratory system are well‐known, many of the precise chemical mechanisms that both cause damage and afford protection in the pulmonary epithelial lining fluid are poorly understood. As a key first step to elucidating the intrinsic reactivity of ozone with proteins, its reactions with deprotonated cysteine [Cys?H]^? are examined in the gas phase. Reaction proceeds at near the collision limit to give a rich set of products including 1) sequential oxygen atom abstraction reactions to yield cysteine sulfenate, sulfinate and sulfonate anions, and significantly 2) sulfenate radical anions formed by ejection of a hydroperoxy radical. The free‐radical pathway occurs only when both thiol and carboxylate moieties are available, implicating electron‐transfer as a key step in this reaction. This novel and facile reaction is also observed in small cys‐containing peptides indicating a possible role for this chemistry in protein ozonolysis.     

3D Study of the Morphology and Dynamics of Zeolite Nucleation

The principle aspects and constraints of the dynamics and kinetics of zeolite nucleation in hydrogel systems are analyzed on the basis of a model Na‐rich aluminosilicate system. A detailed time‐series EMT‐type zeolite crystallization study in the model hydrogel system was performed to elucidate the topological and temporal aspects of zeolite nucleation. A comprehensive set of analytical tools and methods was employed to analyze the gel evolution and complement the primary methods of transmission electron microscopy (TEM) and nuclear magnetic resonance (NMR) spectroscopy. TEM tomography reveals that the initial gel particles exhibit a core–shell structure. Zeolite nucleation is topologically limited to this shell structure and the kinetics of nucleation is controlled by the shell integrity. The induction period extends to the moment when the shell is consumed and the bulk solution can react with the core of the gel particles. These new findings, in particular the importance of the gel particle shell in zeolite nucleation, can be used to control the growth process and properties of zeolites formed in hydrogels.     

Value sharing problems for differential and difference polynomials of meromorphic functions in a non-Archimedean field

In this paper we discuss the uniqueness problem for differential and difference polynomials of the form (f ^nm (z)f ^nd (qz + c))^(k) for meromorphic functions in a non-Archimedean field.     

Splitting extragradient-like algorithms for strongly pseudomonotone equilibrium problems

In this paper, two splitting extragradient-like algorithms for solving strongly pseudomonotone equilibrium problems given by a sum of two bifunctions are proposed. The convergence of the proposed methods is analyzed and the R-linear rate of convergence under suitable assumptions on bifunctions is established. Moreover, a noisy data case, when a part of the bifunction is contaminated by errors, is studied. Finally, some numerical experiments are given to demonstrate the efficiency of our algorithms.     

On functional equations for meromorphic functions and applications

Donovan’s conjecture states that there exist only finitely many Morita equivalence classes of p-blocks with a given defect. This conjecture was shown by Radha Kessar to be equivalent to two other conjectures, one of which is that the basic algebras of p-blocks with a given defect can all be defined over a single finite field. We shall show that this latter conjecture is equivalent to the seemingly stronger statement that all p-blocks with a given defect can be defined over a single finite field.     

On exponential stability of nonlinear Volterra difference equations in phase spaces

Using a novel approach, we present some new explicit criteria for global exponential stability of the zero solution of general nonlinear Volterra difference equations in phase spaces. In particular, this gives a solution to an open problem posed very recently by E. Braverman and I. M. Karabash in Journal of Difference Equations and Applications 18 , 909–939 (2012). As an application, we apply the obtained results to study asymptotic behavior of equilibriums of discrete time neural networks.