On the Hamming distances of repeated-root constacyclic codes of length 4ps

Let $p$ be an odd prime, $s$, $m$ be positive integers, $\gamma ,\lambda$ be nonzero elements of the finite field ${\mathbb{F}}_{p^m}$ such that ${\gamma }^{p^s}=\lambda$. In this paper, we show that, for any positive integer $\eta$, the Hamming distances of all repeated-root $\lambda$-constacyclic codes of length $\eta p^s$ can be determined by those of certain simple-root $\gamma$-constacyclic codes of length $\eta$. Using this result, Hamming distances of all constacyclic codes of length $4p^s$ are obtained. As an application, we identify all MDS $\lambda$-constacyclic codes of length $4p^s$.     

Maximal Elements Under Reference-Dependent Preferences with Applications to Behavioral Traps and Games

We study reference-dependent preference relations defined by a real-valued bivariate function and prove an existence criterion for maximal elements. Then we formulate a generalized version of the well-known Brondsted maximum principle and apply it to behavioral traps and Nash equilibrium in games with preference relations that are not necessarily partial orders.     

Estimation of radon and thoron caused dose at exraction and processing sites of mineral sand mining area in Vietnam (HA TINH province)

Mineral sands are mined in several countries to supply to the titanium and zircon producing industries. Coastal black mineral sands usually contain, besides ilmenite (FeTiO₃) and rutile (TiO₂), radioactive minerals such as zircon (ZrSiO₄) and monazite (RePO₄). Radon and thoron activity concentration originated from natural radioactive contents of the black mineral sand was monitored at the extraction and processing for black minerals in the coastal areas of Ha Tinh Province, one of the around 40 coastal mineral sand deposits in Vietnam. The survey was carried out with the Raduet chambers made by Radosys Ltd—Hungary. The obtained results for 25 investigated points show that the measured values are not high in the residential houses and in case of the sand extraction site as well. At the titanium processing plant the measured values were higher than outside the facility (Radon: 18–55 Bq/m³ with average of 34 Bq/³ and Thoron 33–118 Bq/m³ with average of 58 Bq/m³) but still comparable to the average concentration of the world published by UNSCEAR. The typical outdoor levels of radon and thoron gas are each of the order of 10 Bq/m³. Although the radon concentrations were low in the zircon and titanium processing plants, the thoron concentrations in the houses for separating rutile and zircon were very high. At zircon processing factory, the thoron concentration could reach 2,931 Bq/m³ and the estimated annual effective dose would be 21.4 mSv/a. Intervention has to be taken in order to reduce the thoron level in this factory since the level of thoron and its progenies corresponding to an annual occupational effective dose is beyond the action level of 6 mSv/a.     

Efficient solutions and optimality conditions for vector equilibrium problems

Necessary optimality conditions for efficient solutions of unconstrained and vector equilibrium problems with equality and inequality constraints are derived. Under assumptions on generalized convexity, necessary optimality conditions for efficient solutions become sufficient optimality conditions. Note that it is not required here that the ordering cone in the objective space has a nonempty interior.     

Isolated and Proper Efficiencies in Semi-Infinite Vector Optimization Problems

This paper deals with a nonsmooth semi-infinite multiobjective/vector optimization problem (SIMOP, for short). We first establish necessary and sufficient conditions for (local) strongly isolated solutions and (local) positively properly efficient solutions of an SIMOP. Then, we propose a dual problem to the SIMOP under consideration and examine weak and strong duality relations between them.     

Simulation of Atomic Force Microscopy for investigating BaTiO3 and LiMn2O4 nanostructures based on Phase Field Approach

Atomic Force Microscopy (AFM) probes the surface features of specimens using an extremely sharp tip scanning the sample surface while the force is applied. AFM is also widely used for investigating the electrically non-conductive materials by applying an electric potential on the tip. Piezoresponse Force Microscopy (PFM) and Electrochemical Strain Microscopy (ESM) are variants of AFM for different materials. Both PFM and ESM signals are obtained by observing the displacement of the tip when applying electric fields during the scanning process. The PFM technique is based on converse piezoelectric effect of ferroelectrics and the ESM technique is based on electrochemical coupling in solid ionic conductors. In this work, two continuum-mechanical formulations for simulation of PFM and ESM are discussed. In the first model, for PFM simulation, a phase field approach based on the Allen-Cahn equation for non-conserved order parameters is employed for ferroelectrics. Here, the polarization vector is chosen as order parameter. Since ferroelectrics have highly anisotropic properties, this model accounts for transversely isotropic symmetry using an invariant formulation. The polarization switching behavior under the electric field will be discussed with some numerical examples. In the simulation of ESM, we employ a constitutive model based on the work of Bohn et al. [8] for the modeling of lithium manganese dioxide LiMn₂O₄ (LMO). It simulates the deformation of the LMO particle according to an applied voltage and the evolution of lithium concentration after removing a DC pulse. The modeling results are compared to experimental data. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Toward efficient catalysts for electrochemical CO2 conversion to C2 products

With impressive progress in carbon capture and renewable energy, carbon dioxide (CO₂) conversion into useful chemicals has become a potential tool against climate change. Electrochemical CO₂ conversion into C₂ products (ethylene and ethanol) is an especially economically promising approach and an active research area. Nonetheless, catalyst layer design for CO₂ conversion is challenging because of the complex CO₂-to-C₂ reaction pathways. In this review, we highlight key ideas in catalyst layer design for CO₂ conversion to C₂ in the past few years. We identify three fundamental principles to control catalyst selectivity—local CO₂ and CO concentration, local pH, and intermediate–catalyst interaction. To achieve these goals, we introduce design strategies for both catalytic materials and overall catalyst layer morphology.