Search results for "NUMB"
showing 10 items of 3956 documents
Arithmetic and geometry of a K3 surface emerging from virtual corrections to Drell–Yan scattering
2020
We study a K3 surface, which appears in the two-loop mixed electroweak-quantum chromodynamic virtual corrections to Drell--Yan scattering. A detailed analysis of the geometric Picard lattice is presented, computing its rank and discriminant in two independent ways: first using explicit divisors on the surface and then using an explicit elliptic fibration. We also study in detail the elliptic fibrations of the surface and use them to provide an explicit Shioda--Inose structure. Moreover, we point out the physical relevance of our results.
Inflection points and topology of surfaces in 4-space
2000
We consider asymptotic line fields on generic surfaces in 4-space and show that they are globally defined on locally convex surfaces, and their singularities are the inflection points of the surface. As a consequence of the generalized Poincare-Hopf formula, we obtain some relations between the number of inflection points in a generic surface and its Euler number. In particular, it follows that any 2-sphere, generically embedded as a locally convex surface in 4-space, has at least 4 inflection points.
Analogy Construction and Success in Mathematics and Science Problem-solving: a Study with Secondary Students // Construcción de analogías y éxito en …
2012
We conducted an empirical study to analyse the association between students’ perception of surface and structural analogies between problems, and their algebraic success. Different surface and structural relationships between one ‘source’ problem and ‘target’ problems were considered. We also considered high (daily life) and low (scientific) familiarity contexts. Algebraic success was measured by the equations selected to solve each problem. Similarities and differences between problems were explicitly asked to students. Results showed a significant correlation between detecting the correct structural relation between problems and selecting the correct equations to solve them. Low familiari…
Morphological Analysis of Binary Scene in APR Integrated Environment
2009
This paper describes principles of binary scene [1] morphological analysis in script based application - APR (Analysis, Processing and Recognition). The aim of the method is to find object on the scene and then to describe theirs basic features like edges, neighbors and surface [2]. The algorithm construction gives benefits in terms speed as well as to computation costs, at the same time being capable of presenting number of attributes values for scene and each of the objects. There are also some practical algorithm applications showed.
Quenched molecular dynamics studies on the extraction energy of aluminum atoms
2007
The extraction energy of an aluminum atom is calculated at 0 K as a function of coordination number and defect depth for three surface orientations [(100), (110) and (111)]. For each orientation, atoms are selected and extracted one by one. A linear relationship is obtained between the extraction energy of surface atoms and their coordination numbers (with slight variations due to the geometrical configuration of the atoms). However, the study of the influence of the defect depth on the extraction energy highlights the role played by intrinsic stress on the extraction energy. Copyright © 2008 John Wiley & Sons, Ltd.
Appendix: Diophantine Approximation on Hyperbolic Surfaces
2002
In this (independent) appendix, we study the Diophantine approximation properties for the particular case of the cusped hyperbolic surfaces, in the spirit of Sect. 2 (or [11]), and the many still open questions that arise for them. We refer to [9], [10]for fundamental results and further developments. We study in particular the distance to a cusp of closed geodesics on a hyperbolic surface.
Metal clusters on an inert surface: A simple model
1997
The shapes of metal clusters (with 2 to 14 valence electrons) on an inert surface are studied with a simple model based on the ultimate jellium model. It is shown that within certain approximations the surface-cluster interaction can be described with an external potential in the Kohn-Sham method. No restrictions for the cluster geometry are imposed. The results show that depending on the strength of the interaction and on the size of the cluster, the ground state is either planar or three-dimensional, but in many cases both geometries are stable and there is a marked energy barrier between them. The results agree qualitatively with ab initio calculations of Na clusters on a NaCl(100) surfa…
Study on Interfacial Surface in Modified Spray Tower
2019
This paper presents an analysis of the changes in interfacial surface and the size of droplets formed in a spray tower. The interfacial surface and the size of droplets formed are of fundamental importance to the performance of the equipment, both in terms of pressure drop and process efficiency. Liquid film and droplet sizes were measured using a microphotography technique. The confusors studied were classical, with profiled inside surface, and with double profiled inside surface. The liquids studied were water and aqueous solutions of high-molecular polyacrylamide (PAA) of power-law characteristics. The ranges of process Reynolds number studied were as follows: ReG &isin
Structural properties of core and surface of silica nanoparticles investigated by Raman spectroscopy
2013
We studied the experimental Raman spectra of various commercial silica nanoparticles of average diameter from 7 to 40 nm and specific surface from 50 to 380 m2/g. We found that the peculiarities of the particles Raman spectra systematically depend on their specific surface. In detail, the peak position of the R band at about 440 cm−1 shifts towards high wavenumbers following an almost linear dependence on the specific surface. Similarly, the amplitudes of the D1 and D2 bands, at about 495 and 605 cm−1, respectively, increase linearly with the same quantity. Our results are interpreted in the frame of the shell model for the nanoparticles clarifying that the network of the core of the nanopa…
Surface-directed spinodal decomposition: modelling and numerical simulations
1997
We critically review the modelling and simulations of surface-directed spinodal decomposition, namely, the dynamics of phase separation of a critical or near-critical binary mixture in the presence of a surface with a preferential attraction for one of the components of the mixture.