A nonlinear problem having a continuous locus of singular points and no multiple solutions

AbstractThe boundary-value problem ϵz″ = (z2 − t2)z′, ϵ > 0, z(− 1) = α, z(0) = β, t ϵ [−1, 0], has been shown to have a solution, and moreover, depending on the choice of α and β, multiple solutions to it exist. We consider the more general equation f(z, t)z″ = (zr − ts)z′ for a particular non-negative function f(z, t), and integrate the equation exactly. Depending on α and β, we find that either there are no solutions, or that only unique solutions exist. The conclusion is that the presence of a continuous locus of singular points, given by zr = ts, does not necessarily produce multiple solutions

Crystal structure of 4,4-dimethyl-2-(trifluoromethyl)-4,5-dihydro-1H-imidazole, C6H9F3N2

C6H9F3N2, monoclinic, P21/n (no. 14), a = 10.6224(9) Å, b = 11.8639(9) Å, c = 13.3139(11) Å, β = 105.903(3)°, V = 1613.6(2) Å3, Z = 8, Rgt(F) = 0.0618, wRref(F2) = 0.1629, T = 102(2) K [1–3]

Isolation and Identification of Pathogenic Bacteria That Cause External Ocular Infections in Sabha City Libya

The aim of this study was the isolation and identification of the specific bacterial pathogens causing ocular infections in patients attending Sabha Eye Clinics. A total of 120 samples were collected using a sterile cotton swab from patients with conjunctivitis (aged between 1 to more than 60 years) attending different Eye Clinics in Sabha city (under the supervision of ophthalmologists). All samples were examined by Gram stain, culture on blood agar, mannitol salt agar and MacConkey agar. Different biochemical tests were studied. Results revealed that the species of bacteria isolated were: Staphylococcus aureus (40%), Coagulase-negative Staphylococci (20%), Klebsiella pneumoniae species (10%), Pseudomonas aeruginosa (22%) and E. coli 8%

VoroCrust: Voronoi Meshing Without Clipping

Polyhedral meshes are increasingly becoming an attractive option with particular advantages over traditional meshes for certain applications. What has been missing is a robust polyhedral meshing algorithm that can handle broad classes of domains exhibiting arbitrarily curved boundaries and sharp features. In addition, the power of primal-dual mesh pairs, exemplified by Voronoi-Delaunay meshes, has been recognized as an important ingredient in numerous formulations. The VoroCrust algorithm is the first provably-correct algorithm for conforming polyhedral Voronoi meshing for non-convex and non-manifold domains with guarantees on the quality of both surface and volume elements. A robust refinement process estimates a suitable sizing field that enables the careful placement of Voronoi seeds across the surface circumventing the need for clipping and avoiding its many drawbacks. The algorithm has the flexibility of filling the interior by either structured or random samples, while preserving all sharp features in the output mesh. We demonstrate the capabilities of the algorithm on a variety of models and compare against state-of-the-art polyhedral meshing methods based on clipped Voronoi cells establishing the clear advantage of VoroCrust output.Comment: 18 pages (including appendix), 18 figures. Version without compressed images available on https://www.dropbox.com/s/qc6sot1gaujundy/VoroCrust.pdf. Supplemental materials available on https://www.dropbox.com/s/6p72h1e2ivw6kj3/VoroCrust_supplemental_materials.pd

Cherchell: an Algerian Mediterranean Historical City with a Rich Islamic Heritage Housing

Islamic residential architecture has some common architectural and architectonic elements issued from shared values such as privacy, simplicity and sobriety. Applied to residential architecture, these values led to some characteristic spaces and architectural elements such as patios or arcs. However, the Islamic civilisation is composed by different cultures spread on a great geographical area; this variety induced different interpretations of these elements by using different building shapes or materials. In this paper, we will present an example of this interpretation in the historical coastal city of Cherchell in northern Algeria. The city of Cherchell is a historic coastal city that witnessed the passage of several civilizations before the arrival of the Islamic one since its founding more than 2500 years ago. This specific situation as historical coastal city allowed the exchange with different civilizations around the Mediterranean Sea, giving rise in the Islamic period to a typical earth architecture characterised by a specific arch's typology. The objective of this article is to present an interpretation of Islamic heritage housing architecture in a Mediterranean historical coastal city (through two specific elements: building material and architectonic element). The long term aim of this study is the dissemination of traditional technics and know-how in order restore cultural heritage buildings and construct new projects with a strong Islamic identity

Island Size Selectivity during 2D Ag Island Coarsening on Ag (111)

We report on early stages of submonolayer Ag island coarsening on Ag(111) surface at room temperature ($300$ K) carried out using realistic kinetic Monte Carlo (KMC) simulations. We find that during early stages, coarsening proceeds as a sequence of selected island sizes creating peaks and valleys in the island size distribution. We find that island-size selectivity is due to formation of kinetically stable islands for certain sizes because of adatom detachment/attachment processes and large activation barrier for kink detachment. In addition, we find that the ratio of number of adatom attachment to detachment processes to be independent of parameters of initial configuration and also on the initial shapes of the islands confirming that island-size selectivity is independent of initial conditions.These simulations were carried out using a very large database of processes identified by their local environment and whose activation barriers were calculated using the embedded-atom method

Numerical analysis of bonded composite patch efficiency in the case of lateral U and V-notched aluminium panels

In this study, the finite element method is applied to investigate the mechanical behavior of aluminium notched structures reinforced by composite patch. In order to evaluate the efficiency of patches in the case of lateral semicircular and V-notches, it is very important to analyze the stress distribution at the notch tip and to take in consideration the influence of the geometrical and mechanical properties of the patch and the adhesive. Simple and double patch were used as reinforcement techniques. Results showed that the stress concentration factor is reduced at the notch tip by using a double patch reinforcement. This reduction becomes more noticeable when the patch thickness increases