Search results for "algebra"
showing 10 items of 4129 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.
Modeling of surface structure formation after laser irradiation
2011
The Stefan problem in a semi-infinite media under laser irradiation is considered. It is related to the melting and solidification processes, resulting in certain surface structure after the solidification. A simple model, as well as a more sophisticated one is proposed to describe this process. The latter model allows us to calculate the surface profile by solving a system of two nonlinear differential equations, if the shape of the solid-liquid interface is known. It has to be found as a solution of two-phases Stefan problem. The results of example calculations by the fourth-order Runge-Kutta method are presented, assuming that the solid-liquid interface has a parabolic shape. The calcula…
Efficient Analysis of Arbitrarily Shaped Inductive Obstacles in Rectangular Waveguides Using a Surface Integral Equation Formulation
2007
In this paper we propose to use the Surface Integral Equation technique for the analysis of arbitrarily shaped Hplane obstacles in rectangular waveguides, which can contain both metallic and/or dielectric objects. The Green functions are formulated using both spectral and spatial images series, whose convergence behavior has been improved through several acceleration techniques. Proceeding in this way, the convergence of the series is not attached to the employment of any particular basis or test function, thus consequently increasing the flexibility of the implemented technique. In order to test the accuracy and numerical efficiency of the proposed method, results for practical microwave c…
Digit replacement: A generic map for nonlinear dynamical systems
2016
A simple discontinuous map is proposed as a generic model for nonlinear dynamical systems. The orbit of the map admits exact solutions for wide regions in parameter space and the method employed (digit manipulation) allows the mathematical design of useful signals, such as regular or aperiodic oscillations with specific waveforms, the construction of complex attractors with nontrivial properties as well as the coexistence of different basins of attraction in phase space with different qualitative properties. A detailed analysis of the dynamical behavior of the map suggests how the latter can be used in the modeling of complex nonlinear dynamics including, e.g., aperiodic nonchaotic attracto…
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…
Numerical-Experimental Study Regarding the Single Point Incremental Forming Process
2021
The present paper proposes a numerical-experimental comparative study on the single point incremental forming process. A DC04 steel sheet with a thickness of 0.6 mm was used for both the numerical simulation using the finite element method and the experimental research. The type of trajectory used was a spiral trajectory and the finished part obtained was a truncated cone-shaped part. The analysis program used for simulation was Ls-Dyna. The simulations were performed in several variants: with a fixed mesh and with an adaptive mesh, using two different element formulations: 25 (Belytschko-Tsay formulation with thickness stretch) and -16 (fully integrated shell element modified for higher ac…
Topological classification of 4-dimensional complete intersections
1996
Let X,,(d) C C P "+r denote a complete intersection, the transversal intersection of r hypersurfaces in C P ~+r defined by r homogeneous polynomials of degrees (d l , . . . ,dr) =: d, with dld2...d,. =: d the total degree. It is well-known that the diffeomorphism type of X,,(d) is determined by n and d. In [7] and [8], Libgober and Wood showed that in dimension n -~ 2, there exist k distinct multidegrees ibr any integer k 6 N such that the corresponding complete intersections are all diffeomorphic. For n = 1,3, the diffeomorphism classification of Xn(d) is well-known by surface theory and the classification of 1-connected six-manifolds [12] respectively. For 7z = 2, at least the topological…
Vassiliev invariants for braids on surfaces
2000
We show that Vassiliev invariants separate braids on a closed oriented surface, and we exhibit an universal Vassiliev invariant for these braids in terms of chord diagrams labeled by elements of the fundamental group of the considered surface.
Automorphisms of $mathbb{A}^{1}$-fibered affine surfaces
2011
We develop technics of birational geometry to study automorphisms of affine surfaces admitting many distinct rational fibrations, with a particular focus on the interactions between automorphisms and these fibrations. In particular, we associate to each surface S of this type a graph encoding equivalence classes of rational fibrations from which it is possible to decide for instance if the automorphism group of S is generated by automorphisms preserving these fibrations.
Luminescence of the surface nonbridging oxygen hole center in silica: Spectral and decay properties
2008
We investigated the red luminescence in a porous film of silica nanoparticles, originating from surface nonbridging oxygen hole centers. The excitation spectrum was measured from 1.8 to 8.0 eV by a tunable laser system and a synchrotron radiation source; this spectrum evidences a peak at 2.0 eV, nearly overlapping with the emission, and an ultraviolet broadband with peaks at 4.8 and 6.0 eV. The emission is characterized by a spectrum with two subbands split by 0.07 eV, its decay occurs with lifetime longer than 30 microsec and undergoes a thermal quenching by a factor aboout 2 with increasing temperature from 10 to 290 K. The optical characteristics of surface and bulk centers are discussed…