A <Emphasis Type="Italic">p</Emphasis>-adic RANSAC algorithm for stereo vision using Hensel lifting

A p-adic variation of the Ran(dom) Sa(mple) C(onsensus) method for solving the relative pose problem in stereo vision is developed. From two 2-adically encoded images a random sample of five pairs of corresponding points is taken, and the equations for the essential matrix are solved by lifting solutions modulo 2 to the 2-adic integers. A recently devised p-adic hierarchical classification algorithm imitiating the known LBG quantization method classifies the solutions for all the samples after having determined the number of clusters using the known intra-inter validity of clusterings. In the successful case, a cluster ranking will determine the cluster containing a 2-adic approximation to the “true” solution of the problem.     

From image processing to topological modelling with <Emphasis Type="Italic">p</Emphasis>-adic numbers

Encoding the hierarchical structure of images by p-adic numbers allows for image processing and computer vision methods motivated from arithmetic physics. The p-adic Polyakov action leads to the p-adic diffusion equation in low level vision. Hierarchical segmentation provides another way of p-adic encoding. Then a topology on that finite set of p-adic numbers yields a hierarchy of topological models underlying the image. In the case of chain complexes, the chain maps yield conditions for the existence of a hierarchy, and these can be expressed in terms of p-adic integrals. Such a chain complex hierarchy is a special case of a persistence complex from computational topology, where it is used for computing persistence barcodes for shapes. The approach is motivated by the observation that using p-adic numbers often leads to more efficient algorithms than their real or complex counterparts.     

Ferroelectric Liquid Crystals with New Chiral Building Blocks

Esterification of 4-nitrocinnamoyl chloride by new chiral alcohols((d) and (1) 2-butanol; (d) 2-heptanol), followed by reduction of the nitro group by a new reagent(SnC1₂), gives new chiral 4-aminocinnamates.Condensation of these amines with 4-alkyloxybenzaldehydes or terephthaldehyde gives Schiff bases showing in some cases chiral smectic C phases. A comparative study of the mesomorphism of both these compounds and the compounds of the DOBAMBC family is made, in order to evaluate the effect of the chiral building block structure on the liquid crystalline properties.During this study, a new compound has been prepared, which exhibits the smectic O phase: ((d) 1-methylhexyl)terephthalidene Bis 4-aminocinna-mate.     

Interstack Interactions in Potassium Bis(1,2-Cyclobutenedione 3,4-dithiolato) Palladate. Crystal Structure

Abstract

Potassium bis(1,2-cyclobutenedione 3,4-dithiolato) palladate (Pd(dithiosquarato)₂K₂) crystallizes in the monolinic system, space group P2₁/c, a = 8.046(2), b = 15.235(4), c = 6.289(1). The dithiosquarate entities are stacked in parallel columns separated by potassium cations and water molecules. π-interactions within a stack are evidenced by the short stacking distance (3.51 Å). Further interstack interactions involve close S…O or O…O interstack contacts. (～3.5 Å). As a result, the structural arrangement is nearly two-dimensional. Conductivity measurements carried out on pressed pellets show a semi-conductive behavior (σ = 2 × 10^?5 Ω^?1 cm¹).     

Potential applications of high pressures in pharmaceutical science and medicine

Abstract

High pressure (HP) technology appears to be of paramount interest for valuable applications in pharmacy and medicine, owing to academic studies and industrial developments of this technology for food processing. The main potential application of HP between 100 MPa and 1200 MPa (1 kbar to 12kbar) is the inactivation of biological agents (bacteria, moulds, yeasts, virus and even prions) which allows the sterilization (i.e, “pascalization”) of thermo-, chemo-, or radio-sensitive materials and chemicals. The immunogenicity of some pressure-killed bacteria or virus suggests also the potentiality of making new vaccines. Another interest of the HP technology is the possibility of storage at subzero temperatures without freezing of cells and animal tissues to be used for cells and organs for transplant. HP engineering may be used for enzyme-catalyzed synthesis of fine chemicals, production of modified proteins of medical or pharmaceutical interest, and organic synthesis of pharmaceuticals.     

Current Applications of Magnetic Nanomaterials for Extraction of Mycotoxins,Pesticides, and Pharmaceuticals in Food Commodities

Environmental pollutants, such as mycotoxins, pesticides, and pharmaceuticals, are a group of contaminates that occur naturally, while others are produced from anthropogenic sources. With increased research on the adverse ecological and human health effects of these pollutants, there is an increasing need to regularly monitor their levels in food and the environment in order to ensure food safety and public health. The application of magnetic nanomaterials in the analyses of these pollutants could be promising and offers numerous advantages relative to conventional techniques. Due to their ability for the selective adsorption, and ease of separation as a result of magnetic susceptibility, surface modification, stability, cost-effectiveness, availability, and biodegradability, these unique magnetic nanomaterials exhibit great achievement in the improvement of the extraction of different analytes in food. On the other hand, conventional methods involve longer extraction procedures and utilize large quantities of environmentally unfriendly organic solvents. This review centers its attention on current applications of magnetic nanomaterials and their modifications in the extraction of pollutants in food commodities.     

Estimates on the size of the cycle spectra of Hamiltonian graphs

Given a graph $G$, let $S\left(G\right)$ be the set of all cycle lengths contained in $G$ and let $s\left(G\right)=\left|S\left(G\right)\right|$. Let $?\left(G\right)=\{3,\dots ,n\}?S\left(G\right)$ and let $d$ be the greatest common divisor of $n?2$ and all the positive pairwise differences of elements in $?\left(G\right)$. We prove that if a Hamiltonian graph $G$ of order $n$ has at least $\frac{n(p+2)}{4}+1$ edges, where $p$ is an integer such that $1\le p\le n?2$, then $s\left(G\right)\ge p$ or $G$ is exceptional, by which we mean $d?(??2)$ for some $?\in ?\left(G\right)$. We also discuss cases where $G$ is not exceptional, for example when $n?2$ is prime. Moreover, we show that $s\left(G\right)\ge min\{p,\frac{n?3}{2}\}$, which if $G$ is bipartite implies that $s\left(G\right)\ge min\{?\frac{4(m?1)}{n}?2?,\frac{n?2}{2}\}$, where $m$ is the number of edges in $G$.     

Mathematics teacher training at the State Technical University in Chile

During the fifties and sixties in Chile many mathematics graduates of Pedagogical Institutes became university instructors rather than high school teachers as intended. In the late sixties Masters level programmes began giving more advanced training for university mathematics instructors. A ‘modern’ mathematics curriculum including computer science was introduced in the high schools. The first significant attempt to adapt the training of Chilean high school mathematics teachers to the new academic and social realities was begun in 1976 at the State Technical University with the cooperation of Teachers College, Columbia University, and the support of the Organization of American States.

The four‐year programme leads to Licenciatura (Bachelors) in Mathematics and Computer Education. All courses are taught by faculty members of the Department of Mathematics and Computer Science. The three basic areas of instruction are mathematics, computer science, and mathematics education. Funds provided by the O.A.S. have helped to make possible the development of curricular materials in Spanish, and the acquisition of computing and video tape equipment.