Ab initio study of sodium intercalation into metal oxides

Using the full-potential linearized augmented plane wave (FP-LAPW) method, we have studied the effect of chemistry on the average intercalation voltage (AIV) caused by the Na ions intercalating into transition metal oxides. The effect of transition metal was systematically studied by varying M=Co, Ni and Mn in NaMO₂ and fixing the α-NaFeO₂ layered structure. The effect of the guest atoms into the host material is discussed in terms of the structural and electronic properties. Comparatively to Li intercalation, a significant electron transfer towards transition metal was found. This observation suggests that the transition metal contribute to the AIV determination and confirms the common assumption that intercalated electron reduces M⁴⁺ to M³⁺.     

Advection and dispersion in time and space

Previous work showed how moving particles that rest along their trajectory lead to time-nonlocal advection–dispersion equations. If the waiting times have infinite mean, the model equation contains a fractional time derivative of order between 0 and 1. In this article, we develop a new advection–dispersion equation with an additional fractional time derivative of order between 1 and 2. Solutions to the equation are obtained by subordination. The form of the time derivative is related to the probability distribution of particle waiting times and the subordinator is given as the first passage time density of the waiting time process which is computed explicitly.     

First-principles study of field emission properties of gas adsorption on the carbon nanotubes

Carbon-containing gases usually present when preparing carbon nanotubes, and can affect the field emission of carbon nanotubes. Water vapor is also an important kind of gas for field emission, concerned by both experimental and theoretical studies. Under strong electric field, the gas molecules may be decomposed to radicals. Using DMol3 code based on density-functional theory, we calculated the adsorption of the gas molecules CH₄, CO and H₂O and the CH₃ and OH radicals under emission conditions. We found that the H₂O and the methyl have advantages to field emission and the CH₄, CO and the hydroxyl have disadvantages. The results of H₂O and CO are consistent with experiments, and the enhancement of current by CH₄ in the experiment may be due to the methyl decomposed from the CH₄.     

First and Second Order Optimality Conditions Using Approximations for Nonsmooth Vector Optimization in Banach Spaces

We use the first and second order approximations of mappings to establish both necessary and sufficient optimality conditions for unconstrained and constrained nonsmooth vector optimization problems. Ideal solutions, efficient solutions, and weakly efficient solutions are considered. The data of the problems need not even be continuous. Some often imposed compactness assumptions are also relaxed. Examples are provided to compare our results and some known recent results.This work was partially supported by the National Basic Research Program in Natural Sciences of Vietnam.     

Generalized Solution of a Kind of Nonparametric Curvature Evolution with Boundary Condition

The existence and uniqueness of the generalized solution for a kind of nonparametric curvature flow problem are obtained. This kind of curvature flow problem describes the evolution of graphs with speed depending on the reciprocal of the Gauss curvature.     

Products of compact spaces and the axiom of choice II

This is a continuation of [2]. We study the Tychonoff Compactness Theorem for various definitions of compactness and for various types of spaces (first and second countable spaces, Hausdorff spaces, and subspaces of ?^K). We also study well ordered Tychonoff products and the effect that the multiple choice axiom has on such products.     

具有第二次多选择服务的M[X]/G/1排队系统

本文研究成批到达的具有第二次多选择服务的单服务员排队系统．顾客的到达形成一广义泊松过程，不同批的顾客按先到先服务的规则，而同一批的顾客按随机次序接受服务．两次服务的服务时间都是一般分布且相互独立．本文采用补充变量法，求得在瞬态和稳态情况下系统队长的概率母函数，然后又计算出顾客的平均队长和平均等待时间．     

Structural,electrical and optical properties of Lin@C20 (n = 1–6) nanoclusters

The current research was undertaken to investigate the structural, electrical, and optical properties of C₂₀ fullerene decorated with different numbers of lithium (Li) atoms on its surface. The stability of the structure increased as the number of lithium atoms increased. Increasing the number of lithium atoms around C₂₀ from one to four slightly increased the E_g (energy gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital). Increasing the number to five or six narrowed the E_g. The electrical properties such as ionization potential (I), electron affinity (A), chemical potential (μ), global hardness (η), global softness (γ), global electrophilicity (ω), and electronegativity (χ) were also calculated. The polarizability (α) and first hyperpolarizability (β₀), which correspond to the linear optical and nonlinear optical properties, respectively, were also calculated. An intense increase in β₀ was recorded as the effect of five Li atoms adsorbed onto the C₂₀ surface. The results of this study can be used to design and fabricate nanomaterials with adjustable electro-optical properties.     

Mathematical aspects of the LCAO MO first order density function (1): atomic partition, metric structure and practical applications

Partition of the first order density function within LCAO MO theory permits the definition of Mulliken and Minkowski metric spaces. The metric matrices obtained become useful to connect density atomic partition with quantum similarity measures, Mulliken populations, EHT, expectation values of Hermitian operators and the comparison of two density distributions.     

On integrability of the Szekeres system. I

The Szekeres system is a four-dimensional system of ?rst-order ordinary differential equations with nonlinear but polynomial (quadratic) right-hand side. It can be derived as a special case of the Einstein equations, related to inhomogeneous and nonsymmetrical evolving spacetime. The paper shows how to solve it and ?nd its three global independent ?rst integrals via Darboux polynomials and Jacobi’s last multiplier method. Thus the Szekeres system is completely integrable. Its two-dimensional subsystem is also investigated: we present its solutions explicitly and discuss its behaviour at in?nity.