Continuous location of an assembly station

Demand existing at client points in the plane for several products should be met. Products have to be assembled from different components obtainable at given prices at various sources with known production capacities. The optimal design of the resulting supply chain must be determined, including the location of a central assembly station in the plane, so as to minimize the total operational cost comprising buying and transport of components as well as transport of final products. This problem leads to a difficult nonlinear and non-convex optimization problem for which a locally convergent algorithm is proposed. Some computational results are presented.     

Weakly coupled bound states of Pauli operators

We consider the two-dimensional Pauli operator perturbed by a weakly coupled, attractive potential. We show that besides the eigenvalues arising from the Aharonov?CCasher zero modes there are two or one (depending on whether the flux of the magnetic field is integer or not) additional eigenvalues for arbitrarily small coupling and we calculate their asymptotics in the weak coupling limit.     

Improved laser-induced forward transfer of organic semiconductor thin films by reducing the environmental pressure and controlling the substrate–substrate gap width

Laser-induced forward transfer (LIFT) has been investigated for bilayer transfer material systems: silver/organic film (Alq₃ or PFO). The LIFT process uses an intermediate dynamic release layer of a triazene polymer. This study focuses on the effect of introducing a controlled donor–receiver substrate gap distance and the effect of doing the transfer at reduced air pressures, whilst varying the fluence up to ∼200 mJ/cm². The gap between ‘in-contact’ substrates has been measured to be a minimum of 2–3 μm. A linear variation in the gap width from ‘in contact’ to 40 μm has been achieved by adding a spacer at one side of the substrate–substrate sandwich. At atmospheric pressure, very little transfer is achieved for Alq₃, although PFO shows some signs of successful doughnut transfer (with a large hole in the middle) in a narrow fluence range, at gaps greater than 20 μm. For the transfer of Ag/PFO bilayers at atmospheric pressure, the addition of a PFO layer onto the receiver substrate improved the transfer enormously at smaller gaps and higher fluences. However, the best transfer results were obtained at reduced pressures where a 100% transfer success rate is obtained within a certain fluence window. The quality of the pixel morphology at less than 100 mbar is much higher than at atmospheric pressure, particularly when the gap width is less than 20 μm. These results show the promise of LIFT for industrial deposition processes where a gap between the substrates will improve the throughput.     

Evaluating the accuracy of theoretical one‐bond 13C─13C scalar couplings and their ability to predict structure in a natural product

This study explores the feasibility of using a combination of experimental and theoretical 1‐bond ¹³C─¹³C scalar couplings (¹J_CC) to establish structure in organic compounds, including unknowns. Historically, ⁿJ_CC and ⁿJ_CH studies have emphasized 2 and 3‐bond couplings, yet ¹J_CC couplings exhibit significantly larger variations. Moreover, recent improvements in experimental measurement and data processing methods have made ¹J_CC data more available. Herein, an approach is evaluated in which a collection of theoretical structures is created from a partial nuclear magnetic resonance structural characterization. Computed ¹J_CC values are compared to experimental data to identify candidates giving the best agreement. This process requires knowledge of the error in theoretical methods, thus the B3LYP, B3PW91, and PBE0 functionals are evaluated by comparing to 27 experimental values from INADEQUATE. Respective errors of ±1.2, ±3.8, and ±2.3 Hz are observed. An initial test of this methodology involves the natural product 5‐methylmellein. In this case, only a single candidate matches experimental data with high statistical confidence. This analysis establishes the intramolecular hydrogen‐bonding arrangement, ring heteroatom identity, and conformation at one position. This approach is then extended to hydroheptelidic acid, a natural product not fully characterized in prior studies. The experimental/theoretical approach proposed herein identifies a single best‐fit structure from among 26 candidates and establishes, for the first time, 1 configuration and 3 conformations to complete the characterization. These results suggest that accurate and complete structural characterizations of many moderately sized organic structures (<800 Da) may be possible using only ¹J_CC data.