Correction to the Paper - Determination of a Domain in Complex Space by its Automorphism Group

The author offers some corrections to his article which appeared in Vol. 47, No. 3 of this journal.     

ON θ-PROXIMITIES AND RELATED f-PROXIMITIES

Abstract

We show that every θ-proximity as defined by V.V. Fedor?uk is an f-proximity which we call a k-proximity. Two related f-proximities are introduced, viz. t- and d-proximities. The smallest and largest members of M_f(X, c) for f=k, d and t are characterised where M_f(X, c) is the family of f-proximities compatible with a given closure space (X, c).     

ESSENTIALLY ALGEBRAIC CATEGORIES

Abstract

Various familiar concepts of algebraic categories (such as primitive and quasiprimitive categories of algebras as well as varietal, monadic, regular monadic, and regular categories) are contrasted with each other and with the new notion of essentially algebraic categories.

The new notion has pleasant features and covers several cases of an apparently algebraic nature, which are not covered by any of the older concepts.     

An improved edge detection algorithm for depth map inpainting

Three-dimensional (3D) measurement technology has been widely used in many scientific and engineering areas. The emergence of Kinect sensor makes 3D measurement much easier. However the depth map captured by Kinect sensor has some invalid regions, especially at object boundaries. These missing regions should be filled firstly. This paper proposes a depth-assisted edge detection algorithm and improves existing depth map inpainting algorithm using extracted edges. In the proposed algorithm, both color image and raw depth data are used to extract initial edges. Then the edges are optimized and are utilized to assist depth map inpainting. Comparative experiments demonstrate that the proposed edge detection algorithm can extract object boundaries and inhibit non-boundary edges caused by textures on object surfaces. The proposed depth inpainting algorithm can predict missing depth values successfully and has better performance than existing algorithm around object boundaries.     

Melham's Conjecture on Odd Power Sums of Fibonacci Numbers

Ozeki and Prodinger showed that the odd power sum of the first several consecutive Fibonacci numbers of even order is equal to a polynomial evaluated at a certain Fibonacci number of odd order. We prove that this polynomial and its derivative both vanish at 1, and will be an integer polynomial after multiplying it by a product of the first consecutive Lucas numbers of odd order. This presents an a?rmative answer to a conjecture of Melham.     

Organic field effect transistor composed by fullerene C60 and heterojunctions

We present a study of the complex electronic behavior of a fullerene (C₆₀) molecule attached to six leads (heterojunctions), which works as a three-dimension rectifier. In addition, we confirmed that the fullerene works not only as an electron donor, but also as barrier and transport channel to electrons through the molecule. Moreover, when the phenylpropanodinilla (PPP) lead is orthogonally subjected to bias voltage, the charge distribution and the current displays regions of saturation and resonance similar to semiconductor devices. In order to understand the electronic transport in the molecule, we applied non-equilibrium green function (NEGF) method and performed Fowler-Nordheim (FN) and Millikan-Lauritsen (ML) analyses. The ML curves proved to be sufficient to describe the FN characteristics. In this work, we report the theoretical design for electronic transport of a 3D device (6-terminal).     

Bifurcation diagrams and caustics of simple quasi border singularities

Quasi boundary and quasi corner singularities of functions are discussed. They correspond to the classifications of Lagrangian projections with a boundary or a corner. The geometry of bifurcation diagrams and caustics of simple quasi boundary and quasi corner singularities in R³ and R⁴ are described.     

A non-metric perfectly normal hereditarily indecomposable continuum

We construct an example of a non-metric perfectly normal hereditarily indecomposable continuum. The example is constructed as an inverse limit of non-metric analogues of solenoids. Theorems needed to insure perfect normality are stated and proven. It is shown that the example cannot be embedded in a countable product of Hausdorff arcs.     

General relationships for isovalent cation substitution into oxides with the rocksalt structure

Isovalent cation substitution into rocksalt oxides, MO, has been investigated using atomistic simulation. A strain related parameter, ε, is established that relates the size of a substitutional cation to the host lattice ion for which it has been substituted. This has allowed us to identify relationships between solution energy, defect volume and a strain parameter, which are general for any rocksalt oxide host lattice and as such are predictive for any combination of a divalent cation and rocksalt host lattice.