On the discrepancy between two Zagreb indices

We examine the quantity

$S\left(G\right)=\sum _{uv\in E\left(G\right)}min(degu,degv)$

over sets of graphs with a fixed number of edges. The main result shows the maximum possible value of $S\left(G\right)$ is achieved by three different classes of constructions, depending on the distance between the number of edges and the nearest triangular number. Furthermore we determine the maximum possible value when the set of graphs is restricted to be bipartite, a forest, or to be planar given sufficiently many edges. The quantity $S\left(G\right)$ corresponds to the difference between two well studied indices, the irregularity of a graph and the sum of the squares of the degrees in a graph. These are known as the first and third Zagreb indices in the area of mathematical chemistry.     

Synthesis and structure determination of 3β-hydroxyandrost-5-en-17-one (C19H28O2·CH3OH)

3-Hydroxyandrost-5-en-17-one (C₁₉H₂₈O₂.CH₃OH) has been prepared for undertaking its crystallographic analysis and to investigate the role of intra- and intermolecular interactions in steroids. The title compound crystallizes in the orthorhombic space group C222₁ with unit cell parameters a = 6.7892(17), b = 12.624(2), and c = 41.136(5) Å; V = 3525.7(12) ų and Z = 8. The three-dimensional structure has been solved by direct methods. The final reliability index for the computed structure is 0.050 for 1088 observed reflections. Ring A exist in chair conformation, Ring B in half-chair conformation, and the Ring C assumes a distorted chair conformation. The five-membered Ring D adopts half-chair conformation. The A/B ring junction is quasi-trans while as B/C and C/D are trans-fused. The oxygen atom of the solvent molecule (CH₃OH) is involved in O–H···O intermolecular interaction.     

Airline crew scheduling from planning to operations

Crew scheduling problems at the planning level are typically solved in two steps: first, creating working patterns, and then assigning these to individual crew. The first step is solved with a set covering model, and the second with a set-partitioning model. At the operational level, the (re) planning period is considerably smaller than during the strategic planning phase. We integrate both models to solve time critical crew recovery problems arising on the day of operations. We describe how pairing construction and pairing assignment are done in a single step, and provide solution techniques based on simple tree search and more sophisticated column generation and shortest-path algorithms.     

Mössbauer study of back co-ordination in some iron complexes of 1-(2-pyridylazo)-2-naphthol and 1-(2-pyridylazo)-2-phenanthrol

Mössbauer studies have been made on low-spin octahedral complexes of iron(II) and iron(III) formed with two terdentate ligands, viz., 1-(2-pyridylazo)-2-naphthol and 1-(2-pyridylazo)-2-phenanthrol. The data are suggestive of π-back bonding in the two iron(II) complexes.     

Synthesis and structure analysis of 2-(2′-propanonylthio)-3-(o-methyl phenyl) quinazol-4(3H)-one

The three-dimensional molecular and crystal structure of 2-(2'-propanonylthio)3-(o-methyl phenyl)quinazol-4(3H)-one has been determined by X-ray crystallographic methods. This compound crystallizes in the orthorhombic space group P_bca with unit cell parameters: a=9.649(5), b=30.102(10), c=11.403(9)Å. It has been solved by direct methods and refined to a residual index of 0.054. The magnitude of torsion along C16— C11— N3— C4 bond is 93.5(4)°. The dihedral angle between the plane comprising all the ring atoms of quinazoline moiety and the atoms of the methyl substituted phenyl ring is 94.12(1)°. The crystal structure is stabilized by one intramolecular C— HsO interaction and three intermolecular C— HsN contacts.     

Reinforcement learning for joint pricing,lead-time and scheduling decisions in make-to-order systems

The paper investigates a problem faced by a make-to-order (MTO) firm that has the ability to reject or accept orders, and set prices and lead-times to influence demands. Inventory holding costs for early completed orders, tardiness costs for late delivery orders, order rejection costs, manufacturing variable costs, and fixed costs are considered. In order to maximize the expected profits in an infinite planning horizon with stochastic demands, the firm needs to make decisions from the following aspects: which orders to accept or reject, the trade-off between price and lead-time, and the potential for increased demand against capacity constraints. We model the problem as a Semi-Markov Decision Problem (SMDP) and develop a reinforcement learning (RL) based Q-learning algorithm (QLA) for the problem. In addition, we build a discrete-event simulation model to validate the performance of the QLA, and compare the experimental results with two benchmark policies, the First-Come-First-Serve (FCFS) policy and a threshold heuristic policy. It is shown that the QLA outperforms the existing policies.     

Studies on Copolymerization of Acrylamide and N-Vinylpyrrolidone

Abstract

Copolymers of acrylamide and N-vinylpyrrolidone were prepared using different techniques, viz., solution, precipitation, and inverse emulsion. Xylene was used as a continuous medium and sorbitane monooleate as a surfactant for the inverse emulsion technique. Acetone was used as a solvent in the precipitation technique. The initiator used in all the reactions was 2,2-azobis(2-amidinopropane)dihydrochloride. C, H, and N elemental analysis was used to determine the compositions of the copolymers formed. Reactivity ratios as determined by the Fineman and Ross method were found to be 0.61 and 0.05 for acrylamide and n-vinylpyrrolidone, respectively. Intrinsic viscosity measurements were made at temperatures ranging from 16 to 75°C.     

Effect of gold electrode crystallographic orientations on charge transport through aromatic molecular junctions

ABSTRACT

We examined the electrical conduction through single-molecular junctions comprising of anthracenedithiol molecule coupled to two gold electrodes having ?1,0,1?, ?1,1,0? and ?1,1,1? crystallographic orientations. Owing to this jellium model, we evaluated the values of current and conductance using non-equilibrium Green's functions combined with extended Huckel theory. This data was further interpreted in terms of transmission spectra, density of states and their molecular orbital analysis for zero bias. We evinced the oscillating conductance in all three cases, due to the oscillation of orbital energy relative to Fermi level. Our detailed analysis suggested that electrode orientation can tune the molecule–electrode coupling and hence conduction. Anthracene molecular junction with ?1,1,0? orientation displayed favourable conduction, when compared to the other two orientations, thus can provide us an insight while designing futuristic molecular electronic devices.