Minimal comparability completions of arbitrary graphs

A transitive orientation of an undirected graph is an assignment of directions to its edges so that these directed edges represent a transitive relation between the vertices of the graph. Not every graph has a transitive orientation, but every graph can be turned into a graph that has a transitive orientation, by adding edges. We study the problem of adding an inclusion minimal set of edges to an arbitrary graph so that the resulting graph is transitively orientable. We show that this problem can be solved in polynomial time, and we give a surprisingly simple algorithm for it. We use a vertex incremental approach in this algorithm, and we also give a more general result that describes graph classes Π for which Π completion of arbitrary graphs can be achieved through such a vertex incremental approach.     

l1 solution of linear inequalities

The numerical solution of a possible inconsistent system oflinear inequalities in the l₁ sense is considered. The non-differentiablel₁ norm minimization problem is approximated by a piecewisequadratic Huber smooth function. A continuation algorithm isdesigned to find an l₁ solution of the inequality system. Inthe case where the linear inequality system is consistent, asolution is obtained by solving any smoothed problem. Otherwise,the algorithm is shown to terminate in a finite number of iterations.We also consider an alternative smoothing scheme which sharessimilar properties with the first one, but results in an improvedcomputational performance of the continuation algorithm on inconsistentsystems. Numerical experiments are conducted to test the efficiencyof the algorithm.     

Simulations of grazing-incidence pumped Ni-like Sn X-ray laser at 11.9 nm

Grazing-incidence pumped Ni-like Sn X-ray laser media at 11.9 nm (4d-4p, J = 0-1) is modelled using code EHYBRID and a post-processor code. The required atomic data are obtained using the Cowan code. In this study the pre-formed plasma is pumped on longitudinal direction with a grazing angle. Detailed simulations were performed to optimize the driving laser configurations. Relatively high gain is produced for the Ni-like Sn X-ray laser at 11.9 nm with long pre-pulse and short main pulse drive energy of only 100 mJ on 4 mm slab targets. Using low intensity pre-pulse prior to long pulse decreases the electron density gradient. X-ray resonance lines between 13 and 25 Å emitted from tin plasma have been simulated using post-processor coupled with EHYBRID. The ratio of these resonance lines can be used to measure electron temperature of the laser produced Sn plasma.     

Supramolecular self-assembly of new thiourea derivatives directed by intermolecular hydrogen bonds and weak interactions: crystal structures and Hirshfeld surface analysis

Research on Chemical Intermediates - We synthesized and characterized a series of four closely related thiourea derivatives (1–4) obtained by reaction of 4-R-benzoyl chloride (R: H, Cl, CH3,...     

Simultaneous determination of chlorophyll a and chlorophyll b by derivative spectrophotometry

Chlorophyll a (Chl a) and chlorophyll b (Chl b) plant pigments, which are important in the food industry and are beneficial as environmental pollution indicators, have been extracted with a novel solvent mixture (1:1 v/v acetone–propanol) not containing chloroform and simultaneously determined by first-derivative spectrophotometry. The results were statistically compared to those obtained by the ordinary absorption spectrophotometric reference utilizing the principle of additivity of absorbances. The testing of the developed method in synthetic mixtures of Chl a and Chl b and in real plant material samples (grass, spinach, chard, purslane, black cabbage, crisp lettuce, rocket, dill and seaweed) proved successful in that the developed extractive derivative spectrophotometric method was both rapid and precise, and was not dependent on the Chl a/b ratio in contrast to the reference method which was adversely affected by the latter parameter.     

Polar permutation graphs are polynomial-time recognisable

Polar graphs generalise bipartite graphs, cobipartite graphs, and split graphs, and they constitute a special type of matrix partitions. A graph is polar if its vertex set can be partitioned into two, such that one part induces a complete multipartite graph and the other part induces a disjoint union of complete graphs. Deciding whether a given arbitrary graph is polar, is an NP$\text{NP}$-complete problem. Here, we show that for permutation graphs this problem can be solved in polynomial time. The result is surprising, as related problems like achromatic number and cochromatic number are NP$\text{NP}$-complete on permutation graphs. We give a polynomial-time algorithm for recognising graphs that are both permutation and polar. Prior to our result, polarity has been resolved only for chordal graphs and cographs.     

Scheduling and lot sizing models for the single-vendor multi-buyer problem under consignment stock partnership

We consider a centralized supply chain composed of a single vendor serving multiple buyers and operating under consignment stock arrangement. Solving the general problem is hard as it requires finding optimal delivery schedule to the buyers and optimal production lot sizes. We first provide a nonlinear mixed integer programming formulation for the general scheduling and lot sizing problem. We show that the problem is NP-hard in general. We reformulate the problem under the assumption of ‘zero-switch rule’. We also provide a simple sequence independent lower bound to the solution of the general model. We then propose a heuristic procedure to generate a near-optimal delivery schedule. We assess the cost performance of that heuristic by conducting sensitivity analysis on the key model parameters. The results show that the proposed heuristic promises substantial supply-chain cost savings that increase as the number of buyers increases.     

SAMPL7 blind challenge: quantum–mechanical prediction of partition coefficients and acid dissociation constants for small drug-like molecules

The physicochemical properties of a drug molecule determine the therapeutic effectiveness of the drug. Thus, the development of fast and accurate theoretical approaches for the prediction of such properties is inevitable. The participation to the SAMPL7 challenge is based on the estimation of logP coefficients and pK_a values of small drug-like sulfonamide derivatives. Thereby, quantum mechanical calculations were carried out in order to calculate the free energy of solvation and the transfer energy of 22 drug-like compounds in different environments (water and n-octanol) by employing the SMD solvation model. For logP calculations, we studied eleven different methodologies to calculate the transfer free energies, the lowest RMSE value was obtained for the M06L/def2-TZVP//M06L/def2-SVP level of theory. On the other hand, we employed an isodesmic reaction scheme within the macro pK_a framework; this was based on selecting reference molecules similar to the SAMPL7 challenge molecules. Consequently, highly well correlated pK_a values were obtained with the M062X/6–311+G(2df,2p)//M052X/6–31+G(d,p) level of theory.

     

A neutral state green polymer with a superior transmissive light blue oxidized state

This report highlights the synthesis of only the second green polymer in the literature, which possesses superior properties over the first: a highly transmissive light blue color in the oxidized state with high optical contrast and excellent switching properties.