An infinite-order two-component relativistic Hamiltonian by a simple one-step transformation

The authors report the implementation of a simple one-step method for obtaining an infinite-order two-component (IOTC) relativistic Hamiltonian using matrix algebra. They apply the IOTC Hamiltonian to calculations of excitation and ionization energies as well as electric and magnetic properties of the radon atom. The results are compared to corresponding calculations using identical basis sets and based on the four-component Dirac-Coulomb Hamiltonian as well as Douglas-Kroll-Hess and zeroth-order regular approximation Hamiltonians, all implemented in the DIRAC program package, thus allowing a comprehensive comparison of relativistic Hamiltonians within the finite basis approximation.     

Polymer complexes stabilized through hydrogen bonds: A semiquantitative theoretical model

Many studies have been devoted to the formation and behavior of polymer complexes. Unfortunately, the complexity of such systems do not allow a rigorous theoretical approach presently. In this paper we develop a semiquantitative theoretical model for cooperative association between macromolecules. The model is especially adapted for reversible polymer complexes stabilized through weak interactions, e.g., through hydrogen bonds. Theoretical predictions are compared with potentiometric and viscometric experimental results of poly(acrylic acid)/polybase system and a good agreement is established. The influence of parameters such as degree of neutralization of the polyacid, concentration, and molecular weight of polymers is also conveniently predicted.     

Carbon nanotube-based extraction and electrochemical detection of heavy metals

In this mini review, recent trends and challenges in developing carbon nanotube-based extraction and electrochemical detection of heavy metals in water are reviewed. Carbon nanotubes (CNT) have electrical, mechanical, chemical, and structural properties superior to those of conventional materials, for example graphite and activated carbon. CNT-based procedures are also more efficient than traditional techniques and methods, for example liquid?Cliquid extraction, atomic-absorption spectroscopy, flame photometry, and inductively coupled plasma, because they can enable rapid, sensitive, simple, and low-cost on-site detection. Different forms of CNT, including as-grown, oxidised, and functionalised CNT, can be well suited to metal adsorption. The measurement procedure relies on adsorbing the metal on the CNT surface after reasonable contact time, either by applying an electrical potential or under open-circuit conditions, and subsequent quantification. Different types of CNT-based electrode, including composite, paste, and binder-free, can be fabricated and used for metal detection. Application of CNT and their novel properties to the adsorption and detection of heavy metals is discussed in detail.     

Applying change of variable to calculus problems

This article describes the technique of introducing a new variable in some calculus problems to help students master the skills of integration and evaluation of limits. This technique is algorithmic and easy to apply.     

Percentage problems in bridging courses

Research on teaching high school mathematics shows that the topic of percentages often causes learning difficulties. This article describes a method of teaching percentages that the authors used in university bridging courses. In this method, the information from a word problem about percentages is presented in a two-way table. Such a table gives a logical structure to the problem and provides an algorithm for finding a simple equation for the unknown value of interest. The use of this procedure is illustrated by several examples of different levels of difficulty. The method can be applied to many types of percentage problems, so it is quite universal.     

The role of the isothermal bulk modulus in the molecular dynamics of super-cooled liquids

Elastic models imply that the energy expended for a flow event in ultra-viscous matter coincides with the elastic work required for deforming and re-arranging the environment of the moving entity. This is quite promising for explaining the strong non-Arrhenius behavior of dynamic quantities of fragile super-cooled liquids. We argue that the activation volume obtained from dielectric relaxation and light-scattering experiments for super-cooled liquids should scale with the Gibbs free energy of activation, with a proportionality constant determined by the isothermal bulk modulus and its pressure derivative, as described by an earlier thermodynamic elastic model. For certain super-cooled liquids the bulk compression transpiring in the local environment, as governed by the isothermal bulk modulus, play a significant role in the reorientational dynamics, with far-field density fluctuations and volume changes avoided by shear deformation.     

Electrical characterization of polymer matrix — TiO2 filler composites through isothermal polarization / depolarization currents and I–V tests

Specimens of polymer matrix — ceramic TiO₂ filler composites were prepared. The contribution of the filler content on the electrical conductivity and energy storage properties of the samples was examined. I–V and Isothermal Polarization/Depolarization Current (IPC/IDC) measurements were conducted. Dc conductivity values directly calculated from the I–V curves exhibited excellent agreement with corresponding values derived from the IPC/IDC recordings. Standard models were employed for fitting the IPC/IDC data. In specific, the short and the very long depolarization times were fitted by use of power laws of different slopes, while the intermediate depolarization times were fitted as a sum of three exponential decays. The present study reveals a strong dependence of the depolarization and polarization processes, as well as of the dc conductivity, on the filler concentration.     

Theoretical investigation of the binding energies of the iodide ion and xenon atom with decaborane

The interaction of decaborane (B(10)H(14)) with the I(-) ion and the (isoelectronic) Xe atom is investigated using a number of theoretical methods: MP2, CCSD(T), CCSD, spin-orbit CISD, and DFT using the B3LYP, B3PW91, PW91PW91, and PBE0 methods. All non-DFT and some DFT methods agree that B(10)H(14)I(-) is bound by charge-dipole electrostatic forces, charge- and dipole-induced-dipole forces, and dispersion forces, while B(10)H(14)Xe is bound by dipole-induced-dipole forces and dispersion forces. Counterpoise corrections are necessary to obtain reliable results. Relativistic effective core potentials were used for the I, Xe, and B atoms. Basis sets for use with these potentials are discussed as is the question of basis set balance in molecules. We find B(10)H(14)I(-) to be bound by 19.8 kcal/mol and B(10)H(14)Xe by 1.1 kcal/mol, indicating that the charge and polarizability of I(-) play the major role in the interaction energy.     

A Generalization of a Levitin and Parnovski Universal Inequality for Eigenvalues

In this paper, we derive “universal” inequalities for the sums of eigenvalues of the Hodge de Rham Laplacian on Euclidean closed submanifolds and of eigenvalues of the Kohn Laplacian on the Heisenberg group. These inequalities generalize the Levitin–Parnovski inequality obtained for the sums of eigenvalues of the Dirichlet Laplacian of a bounded Euclidean domain.