Consistent empirical physical formulas for potential energy curves of 38–66Ti isotopes by using neural networks

Nuclear shape transition has been actively studied in the past decade. In particular, the understanding of this phenomenon from a microscopic point of view is of great importance. Because of this reason, many works have been employed to investigate shape phase transition in nuclei within the relativistic and nonrelativistic mean field models by examining potential energy curves (PECs). In this paper, by using layered feed-forward neural networks (LFNNs), we have constructed consistent empirical physical formulas (EPFs) for the PECs of ^38–66Ti calculated by the Hartree-Fock-Bogoliubov (HFB) method with SLy4 Skyrme forces. It has been seen that the PECs obtained by neural network method are compatible with those of HFB calculations.     

Optimisation of a solid-phase microextraction method for the analysis of nicotine in hair

A headspace solid-phase microextraction method (HS-SPME) followed by gas chromatography with mass spectrometric detection (GC/MS) has been developed for the determination of low concentrations of nicotine in hair. Parameters affecting the SPME procedure including type of fiber coating, extraction mode, extraction temperature and time, desorption time, stirring, and salt addition have been evaluated and optimised. The method provided good linearity (r(2)≥0.9980) over the concentration range tested (0.2-20 ng/mg) and low detection limit (0.02 ng/mg). Precision expressed as relative standard deviation was <10%. The average accuracy was 95%. The proposed method was used to determine hair nicotine levels in 100 children in order to assess exposure to environmental tobacco smoke (ETS). The described HS-SPME procedure is fast, simple, sensitive, and solvent-free and is therefore suitable for studies involving ETS exposure assessment.     

Incremental polynomial time dualization of quadratic functions and a subclass of degree-<Emphasis Type="Italic">k</Emphasis> functions

We consider the problem of dualizing a Boolean function f represented by a DNF. In its most general form, this problem is commonly believed not to be solvable by a quasi-polynomial total time algorithm. We show that if the input DNF is quadratic or is a special degree-k DNF, then dualization turns out to be equivalent to hypergraph dualization in hypergraphs of bounded degree and hence it can be achieved in incremental polynomial time.     

The crossover from collective motion to periphery diffusion for two-dimensional adatom-islands on Cu(111)

The diffusion of two-dimensional adatom-islands (up to 100 atoms) on Cu(111) has been studied, using the self-learning kinetic Monte Carlo method (Trushin et?al 2005 Phys. Rev. B 72 115401). A variety of multiple-?and single-atom processes are revealed in the simulations, and the size dependences of the diffusion coefficients and effective diffusion barriers are calculated for each. From the tabulated frequencies of events found in the simulation, we show a crossover from diffusion due to the collective motion of the island to a regime in which the island diffuses through periphery-dominated mass transport. This crossover occurs for island sizes between 13 and 19 atoms. For islands containing 19-100 atoms the scaling exponent is 1.5, which is in good agreement with previous work. The diffusion of islands containing 2-13 atoms can be explained primarily on the basis of a linear increase of the barrier for the collective motion with the size of the island.     

Towards multimodal HPLC separations on humic acid-bonded aminopropyl silica: RPLC and LEC behavior

In the present study, metal binding property of humic acid (HA) was successfully adapted to the ligand-exchange concept, and metal-loaded immobilized humic acid was used as a ligand exchanger stationary phase for separation of some nucleosides. Humic-acid bonded aminopropyl silica (EC-HA-APS) was turned into ligand exchanger forms by loading aqueous solutions of Cu²⁺, and Co²⁺ to the column (4.6 × 150; as mm) packed with EC-HA-APS. Metal ion solutions were loaded to the column in a stepwise manner where the concentration of metal ion solution being loaded to the column was increased gradually between 5 and 100 mM. The progress of metal loading process was monitored via the breakthrough curves propagated stepwise. Ligand-exchange chromatography (LEC) studies were performed on an HPLC system, and chromatographic behaviors of the studied nucleosides (i.e. uridine, Urd; thymidine, Tyd; cytidine, Cyd; adenosine, Ado; and guanosine, Guo) were investigated on Cu²⁺ and Co²⁺ loaded forms of the EC-HA-APS (Cu-EC-HA-APS and Co-EC-HA-APS). Effect of mobile phase composition, temperature, and the type of metal ion loaded to the column on the retentive behaviors of the compounds was studied, in detail. The studied solutes exhibited mixed-mode RPLC/LEC behavior on the stationary phase. Metal-loaded column (M-EC-HA-APS) was easily regenerated into its original form, EC-HA-APS, with 98 ± 2% metal recoveries, by using aqueous mixture of EDTA + NH₃ at pH = 7.5. Thus, the stationary phase exhibited a high flexibility between RPLC and LEC modes. This property, also, made it possible to convert the stationary phase into various ligand exchanger forms by loading different metal ions. Hence, capacity and selectivity of the stationary phase towards the studied species was manipulated easily by loading different metal ions to the stationary phase. Baseline separation for the studied species was achieved on Cu-EC-HA-APS and Co-EC-HA-APS and some differentiations were observed in capacity and selectivity, depending on the type of metal loaded. Thus, being as the first endeavor on usability of immobilized HA as a ligand exchanger stationary phase, the present study is believed to be useful to understand multifunctional character of HA-based solid/stationary phases.     

Analysis of chorismate mutase catalysis by QM/MM modelling of enzyme-catalysed and uncatalysed reactions

Chorismate mutase is at the centre of current controversy about fundamental features of biological catalysts. Some recent studies have proposed that catalysis in this enzyme does not involve transition state (TS) stabilization but instead is due largely to the formation of a reactive conformation of the substrate. To understand the origins of catalysis, it is necessary to compare equivalent reactions in different environments. The pericyclic conversion of chorismate to prephenate catalysed by chorismate mutase also occurs (much more slowly) in aqueous solution. In this study we analyse the origins of catalysis by comparison of multiple quantum mechanics/molecular mechanics (QM/MM) reaction pathways at a reliable, well tested level of theory (B3LYP/6-31G(d)/CHARMM27) for the reaction (i) in Bacillus subtilis chorismate mutase (BsCM) and (ii) in aqueous solvent. The average calculated reaction (potential energy) barriers are 11.3 kcal mol(-1) in the enzyme and 17.4 kcal mol(-1) in water, both of which are in good agreement with experiment. Comparison of the two sets of reaction pathways shows that the reaction follows a slightly different reaction pathway in the enzyme than in it does in solution, because of a destabilization, or strain, of the substrate in the enzyme. The substrate strain energy within the enzyme remains constant throughout the reaction. There is no unique reactive conformation of the substrate common to both environments, and the transition state structures are also different in the enzyme and in water. Analysis of the barrier heights in each environment shows a clear correlation between TS stabilization and the barrier height. The average differential TS stabilization is 7.3 kcal mol(-1) in the enzyme. This is significantly higher than the small amount of TS stabilization in water (on average only 1.0 kcal mol(-1) relative to the substrate). The TS is stabilized mainly by electrostatic interactions with active site residues in the enzyme, with Arg90, Arg7 and Glu78 generally the most important. Conformational effects (e.g. strain of the substrate in the enzyme) do not contribute significantly to the lower barrier observed in the enzyme. The results show that catalysis is mainly due to better TS stabilization by the enzyme.     

Macrocyclic Architecture: Tuning Cavity Size and Shape through Maleimide Photochemistry

Open wide: Irradiation of N-alkyl alkynyl maleimides yields imide-cyclobutene containing macrocycles with C(i) and C(2) symmetry. In the case of the C(i) isomers increasing the tether length leads to a one-dimensional increase in cavity size akin to a "letterbox" effect.     

Symmetry reduction,exact group-invariant solutions and conservation laws of the Benjamin–Bona–Mahoney equation

We show that the Benjamin–Bona–Mahoney (BBM) equation with power law nonlinearity can be transformed by a point transformation to the combined KdV–mKdV equation, that is also known as the Gardner equation. We then study the combined KdV–mKdV equation from the Lie group-theoretic point of view. The Lie point symmetry generators of the combined KdV–mKdV equation are derived. We obtain symmetry reduction and a number of exact group-invariant solutions for the underlying equation using the Lie point symmetries of the equation. The conserved densities are also calculated for the BBM equation with dual nonlinearity by using the multiplier approach. Finally, the conserved quantities are computed using the one-soliton solution.     

A note on interval estimation of the standard deviation of a gamma population with applications to statistical quality control

Traditional process control charts for a measurement standard deviation are based on the assumption of normality, which may not always be valid. Assuming that measurements follow a gamma distribution, we have obtained an approximate distribution of the sample variance, scaled appropriately. This approximate distribution, which happens to be another gamma model, is used to derive an interval estimate of the population standard deviation. Further, the above approximate gamma model for the sample variance can be used to develop a process control chart as demonstrated by a simulated data set.     

New integer linear programming formulation for the traveling salesman problem with time windows: minimizing tour duration with waiting times

The travelling salesman problem, being one of the most attractive and well-studied combinatorial optimization problems, has many variants, one of which is called ‘travelling salesman problem with Time Windows (TSPTW)’. In this problem, each city (nodes, customers) must be visited within a time window defined by the earliest and the latest time. In TSPTW, the traveller has to wait at a city if he/she arrives early; thus waiting times directly affect the duration of a tour. It would be useful to develop a new model solvable by any optimizer directly. In this paper, we propose a new integer linear programming formulation having O(n²) binary variables and O(n²) constraints, where (n) equals the number of nodes of the underlying graph. The objective function is stated to minimize the total travel time plus the total waiting time. A computational comparison is made on a suite of test problems with 20 and 40 nodes. The performances of the proposed and existing formulations are analysed with respect to linear programming relaxations and the CPU times. The new formulation considerably outperforms the existing one with respect to both the performance criteria. Adaptation of our formulation to the multi-traveller case and some additional restrictions for special situations are illustrated.