Performance of group additivity methods for predicting the stability of uranyl complexes

Herein, we investigated the viability of two group additivity methods for predicting Gibbs energies of a set of uranyl complexes. In first place, we proved that both density functional theory (DFT)-based methods and Serezhkin's stereoatomic model provide equivalent answers in terms of stability. Moreover, we proposed a novel methodology based on Mayer's population analysis for estimating Serezhkin's empirical parameters theoretically. On the other hand, we showed that Cheong and Persson linear algebra methodology can be successfully applied to uranyl complexes, and analyzed its performance in connection with the chemical nature of the compounds employed in the model.     

Generating highly balanced sudoku problems as hard problems

Sudoku problems are some of the most known and enjoyed pastimes, with a never diminishing popularity, but, for the last few years those problems have gone from an entertainment to an interesting research area, a twofold interesting area, in fact. On the one side Sudoku problems, being a variant of Gerechte Designs and Latin Squares, are being actively used for experimental design, as in Bailey et al. (Am. Math. Mon. 115:383–404, 2008; J. Agron. Crop Sci. 165:121–130, 1990), Morgan (Latin squares and related experimental designs. Wiley, New York, 2008) and Vaughan (Electron. J. Comb. 16, 2009). On the other hand, Sudoku problems, as simple as they seem, are really hard structured combinatorial search problems, and thanks to their characteristics and behavior, they can be used as benchmark problems for refining and testing solving algorithms and approaches. Also, thanks to their high inner structure, their study can contribute more than studies of random problems to our goal of solving real-world problems and applications and understanding problem characteristics that make them hard to solve. In this work we use two techniques for solving and modeling Sudoku problems, namely, Constraint Satisfaction Problem (CSP) and Satisfiability Problem (SAT) approaches. To this effect we define the Generalized Sudoku Problem (GSP), where regions can be of rectangular shape, problems can be of any order, and solution existence is not guaranteed. With respect to the worst-case complexity, we prove that GSP with block regions of m rows and n columns with m≠n is NP-complete. For studying the empirical hardness of GSP, we define a series of instance generators, that differ in the balancing level they guarantee between the constraints of the problem, by finely controlling how the holes are distributed in the cells of the GSP. Experimentally, we show that the more balanced are the constraints, the higher the complexity of solving the GSP instances, and that GSP is harder than the Quasigroup Completion Problem (QCP), a problem generalized by GSP. Finally, we provide a study of the correlation between backbone variables—variables with the same value in all the solutions of an instance—and hardness of GSP.     

Rationalizing the Mechanism of Peroxyformate Decomposition: Computational Insights To Understand Solvent Influence

The heterolytic decomposition of tert-butyl peroxyformate to tert-butanol and carbon dioxide, catalyzed by pyridine, is a long-known example of a reaction whose kinetics are strongly affected by solvent polarity. From DFT and ab initio methods together with the SMD implicit solvation model, an extension on the formerly accepted mechanism is proposed. This novel proposal involves the formation of a carbonic acid ester intermediate and its further decomposition, through an unreported pyridine-mediated stepwise route. Computed barriers for this mechanism at DLPNO/CCSD(T)-def2-TZVP are in excellent agreement with experimental kinetic data across different solvents. Furthermore, the strong relationships between activation energies, geometric parameters in the transition state and the characteristics of the different solvents are also analyzed in depth.     

GRASP and Path Relinking for the Clustered Prize-collecting Arc Routing Problem

The Clustered Prize-collecting Arc Routing Problem is an arc routing problem where each demand edge is associated with a profit which is collected once if the edge is serviced, independently of the number of times it is traversed. It is further required that if a demand edge is serviced, then all the demand edges of its component are also serviced. This paper presents GRASP and Path Relinking heuristics for the Clustered Prize-collecting Arc Routing Problem. For the constructive phase of the GRASP two different strategies are considered. One of them follows a bottom-up style whereas the other one is a top-down procedure. The best solutions obtained with both strategies are used as elite solutions for the Path Relinking. The results of extensive computational experiments are presented and analyzed.     

The growth strategies in the hospitality industry from the perspective of the forgotten effects

This paper, using fuzzy incidence matrix, determines the causes why of major hotel chains in the world by number of rooms have used certain growth strategies for implement their international expansion. Both direct cause and second generation causes have been identified. In fact, determining the second generation effects (or forgotten effects) is one of the main contributions of this study as it shows that those causes that are usually not foreseen, at least in the first instance, affect notably in the expansion strategies of hotel chains in the medium and long term.     

On the optimization of bipartite secret sharing schemes

Optimizing the ratio between the maximum length of the shares and the length of the secret value in secret sharing schemes for general access structures is an extremely difficult and long-standing open problem. In this paper, we study it for bipartite access structures, in which the set of participants is divided in two parts, and all participants in each part play an equivalent role. We focus on the search of lower bounds by using a special class of polymatroids that is introduced here, the tripartite ones. We present a method based on linear programming to compute, for every given bipartite access structure, the best lower bound that can be obtained by this combinatorial method. In addition, we obtain some general lower bounds that improve the previously known ones, and we construct optimal secret sharing schemes for a family of bipartite access structures.     

Effect of Islands in Diffusive Properties of the Standard Map for Large Parameter Values

Foundations of Computational Mathematics - In this paper we review, based on massive, long-term, numerical simulations, the effect of islands on the statistical properties of the standard map for...     

Geometric Optics and Instability for Semi-Classical Schrödinger Equations

We prove some instability phenomena for semi-classical (linear or) nonlinear Schrödinger equations. For some perturbations of the data, we show that for very small times, we can neglect the Laplacian, and the mechanism is the same as for the corresponding ordinary differential equation. Our approach allows smaller perturbations of the data, where the instability occurs for times such that the problem cannot be reduced to the study of an ordinary differential equation.     

Synthetic and DFT Studies Towards a Unified Approach to Phlegmarine Alkaloids: Aza‐Michael Intramolecular Processes Leading to 5‐Oxodecahydroquinolines

A diastereoselective synthesis of cis‐5‐oxodecahydroquinolines is described in which three stereocenters are generated in a one‐pot reaction. The reaction involves a lithium hydroxide‐promoted Robinson annulation/intramolecular aza‐Michael domino process from an achiral acyclic tosylamine‐tethered β‐keto ester. The development and scope of this reaction was facilitated through the use of DFT‐based mechanistic studies, which enabled the observed diastereodivergent course of the azacyclization to be rationalized. The varying stereochemistry and stability of the resulting decahydroquinolines was found to depend on whether a β‐keto ester or ketone were embedded in the substrates undergoing aminocyclization. This synthetic approach gave access not only to both diastereomeric cis‐decahydroquinolines from the same precursor, but also to the corresponding trans isomers, through an epimerization processes of the corresponding N‐unsubstituted cis‐5‐oxodecahydroquinolines. The described methodology provides advanced building‐blocks with the three relative stereochemistries required for the total synthesis of phlegmarine alkaloids.