Reasons for the exclusive formation of heterodimeric capsules between tetra-tolyl and tetra-tosylurea calix[4]arenes

The selective heterodimerization of tetra-tolyl () and tetra-tosylurea () calixarenes, serendipitously found by Rebek et al. (R. K. Castellano, B. H. Kim and J. Rebek, Jr., J. Am. Chem. Soc., 1997, 119, 12671-12672), has been used for the construction of highly sophisticated macrocycles and well-defined supramolecular assemblies. Regrettably, hitherto, neither the exact structure of these heterodimers nor the reason for their exclusive formation is known. We present molecular dynamics simulations using the AMBER force field in explicit chloroform solvent for the two homodimers, the heterodimer and the two uncomplexed tetra-urea calixarenes. The rigid rotation about the C-S-N-C bond of the tosylurea group has been calculated for a model compound (N-mesylformamide) at the RHF/6-31G* level of theory. The calculations suggest that the heterodimer . is energetically favored over the homodimers by a sterically relaxed conformation of the tosylurea hemisphere in ., by a moderate degree of reorganization of the hemispheres from the uncomplexed to the complexed state and by favorable interactions between the hemispheres. The tosylurea S=O groups are involved in the hydrogen bonding system which results in different sizes of the three capsules in increasing order . < . < .. To prove the computational predictions, 1H NMR experiments have been carried out with solvents/guests differing in shape and size. The largest capsule . prefers the larger guests toluene and p-xylene while the latter is not encapsulated in the smallest capsule ..     

Fast 3D coronary artery contrast-enhanced magnetic resonance angiography with magnetization transfer contrast, fat suppression and parallel imaging as applied on an anthropomorphic moving heart phantom

A magnetic resonance sequence for high-resolution imaging of coronary arteries in a very short acquisition time is presented. The technique is based on fast low-angle shot and uses fat saturation and magnetization transfer contrast prepulses to improve image contrast. GeneRalized Autocalibrating Partially Parallel Acquisitions (GRAPPA) is implemented to shorten acquisition time. The sequence was tested on a moving anthropomorphic silicone heart phantom where the coronary arteries were filled with a gadolinium contrast agent solution, and imaging was performed at varying heart rates using GRAPPA. The clinical relevance of the phantom was validated by comparing the myocardial relaxation times of the phantom's homogeneous silicone cardiac wall to those of humans. Signal-to-noise ratio and contrast-to-noise ratio were higher when parallel imaging was used, possibly benefiting from the acquisition of one partition per heartbeat. Another advantage of parallel imaging for visualizing the coronary arteries is that the entire heart can be imaged within a few breath-holds.     

Fatou Components of Attracting Skew-Products

We investigate the existence of wandering Fatou components for polynomial skew-products in two complex variables. In 2004, the non-existence of wandering domains near a super-attracting invariant fiber was shown in Lilov (Fatou theory in two dimensions, PhD thesis, University of Michigan, 2004). In 2014, it was shown in Astorg et al. (Ann Math, arXiv:1411.1188 [math.DS], 2014) that wandering domains can exist near a parabolic invariant fiber. In Peters and Vivas (Math Z, arXiv:1408.0498, 2014), the geometrically attracting case was studied, and we continue this study here. We prove the non-existence of wandering domains for subhyperbolic attracting skew-products; this class contains the maps studied in Peters and Vivas (Math Z, arXiv:1408.0498, 2014). Using expansion properties on the Julia set in the invariant fiber, we prove bounds on the rate of escape of critical orbits in almost all fibers. Our main tool in describing these critical orbits is a possibly singular linearization map of unstable manifolds.     

Normal form theory for reversible equivariant vector fields

We give a method to obtain formal normal forms of reversible equivariant vector fields. The procedurewe present is based on the classical method of normal forms combined with tools from invariant theory. Normal forms of two classes of resonant cases are presented, both with linearization having a 2-dimensional nilpotent part and a semisimple part with purely imaginary eigenvalues.     

Operators associated with the Jacobi semigroup

The aim of this paper is to introduce some operators induced by the Jacobi differential operator and associated with the Jacobi semigroup, where the Jacobi measure is considered in the multidimensional case.In this context, we introduce potential operators, fractional integrals, fractional derivates, Bessel potentials and give a version of Carleson measures.We establish a version of Meyer’s multiplier theorem and by means of this theorem, we study fractional integrals and fractional derivates.Potential spaces related to Jacobi expansions are introduced and using fractional derivates, we give a characterization of these spaces. A version of Calderon’s Reproduction Formula and a version of Fefferman’s theorem are given.Finally, we present a definition of Triebel–Lizorkin spaces and Besov spaces in the Jacobi setting.     

Solving a bi-objective Transportation Location Routing Problem by metaheuristic algorithms

In this work we consider a Transportation Location Routing Problem (TLRP) that can be seen as an extension of the two stage Location Routing Problem, in which the first stage corresponds to a transportation problem with truck capacity. Two objectives are considered in this research, reduction of distribution cost and balance of workloads for drivers in the routing stage. Here, we present a mathematical formulation for the bi-objective TLRP and propose a new representation for the TLRP based on priorities. This representation lets us manage the problem easily and reduces the computational effort, plus, it is suitable to be used with both local search based and evolutionary approaches. In order to demonstrate its efficiency, it was implemented in two metaheuristic solution algorithms based on the Scatter Tabu Search Procedure for Non-Linear Multiobjective Optimization (SSPMO) and on the Non-dominated Sorting Genetic Algorithm II (NSGA-II) strategies. Computational experiments showed efficient results in solution quality and computing time.     

Optimising a general repair kit problem with a service constraint

Field services are a particular type of after-sales service performed at the customer’s location where technicians repair malfunctioning machines. The inventory decisions about which spare part types to take to the repair site and in what quantities is called the repair kit problem. This problem is characterized by an order-based performance measure since a customer is only satisfied when all required spare parts are available to fix the machine. As a result, the service level in the decision making process is defined as a job fill rate. In this paper we derive a closed-form expression for the expected service level and total costs for the repair kit problem in a general setting, where multiple units of each part type can be used in a multi-period problem. Such an all-or-nothing strategy is a new characteristic to investigate, but commonly used in practice. Namely, items are only taken from the inventory when all items to perform the repair are available in the right quantity. We develop a new algorithm to determine the contents of the repair kit both for a service and cost model while incorporating this new expression for the job fill rate. We show that the algorithm finds solutions which differ on average 0.2% from optimal costs. We perform a case study to test the performance of the algorithm in practice. Our approach results in service level improvements of more than 30% against similar holding costs.