Search results for "Linear"
showing 10 items of 7165 documents
Periodic Classification of Local Anaesthetics (Procaine Analogues)
2006
Algorithms for classification are proposed based on criteria (information entropyand its production). The feasibility of replacing a given anaesthetic by similar ones in thecomposition of a complex drug is studied. Some local anaesthetics currently in use areclassified using characteristic chemical properties of different portions of their molecules.Many classification algorithms are based on information entropy. When applying theseprocedures to sets of moderate size, an excessive number of results appear compatible withdata, and this number suffers a combinatorial explosion. However, after the equipartitionconjecture, one has a selection criterion between different variants resulting fromc…
The Rank of Trifocal Grassmann Tensors
2019
Grassmann tensors arise from classical problems of scene reconstruction in computer vision. Trifocal Grassmann tensors, related to three projections from a projective space of dimension k onto view-spaces of varying dimensions are studied in this work. A canonical form for the combined projection matrices is obtained. When the centers of projections satisfy a natural generality assumption, such canonical form gives a closed formula for the rank of the trifocal Grassmann tensors. The same approach is also applied to the case of two projections, confirming a previous result obtained with different methods in [6]. The rank of sequences of tensors converging to tensors associated with degenerat…
Contextuality Analysis of the Double Slit Experiment (With a Glimpse Into Three Slits)
2018
The Contextuality-by-Default theory is illustrated on contextuality analysis of the idealized double-slit experiment. The experiment is described by a system of contextually labeled binary random variables each of which answers the question: has the particle hit the detector, having passed through a given slit (left or right) in a given state (open or closed)? This system of random variables is a cyclic system of rank 4, formally the same as the system describing the EPR/Bell paradigm with signaling. Unlike the latter, however, the system describing the double-slit experiment is always noncontextual, i.e., the context-dependence in it is entirely explainable in terms of direct influences of…
Rational Solutions to the KdV Equation in Terms of Particular Polynomials
2022
Here, we construct rational solutions to the KdV equation by particular polynomials. We get the solutions in terms of determinants of the order n for any positive integer n, and we call these solutions, solutions of the order n. Therefore, we obtain a very efficient method to get rational solutions to the KdV equation, and we can construct explicit solutions very easily. In the following, we present some solutions until order 10.
Study of periodic Dielectric Frequency-Selective Surfaces under 3D plane wave incidence
2016
A periodic Dielectric Frequency-Selective Surface (DFSS) is studied under 3D plane-wave incidence, whose unit cell in the periodic direction is composed of a dielectric grating and a homogeneous dielectric layer. The structure is excited by a linearly polarized plane-wave. The procedure for computing the Brillouin diagram of the structure under 2D plane-wave incidence with TE or TM polarization was already described by the authors, and the extension to the 3D incidence case has been performed in a similar way. Following the same formalism, it has been obtained the Generalized Scattering Matrix (GSM) of one period of the infinite periodic lattice. This requires the knowledge of the modal spe…
Systematic conformational search analysis of the SRR and RRR epimers of 7-hydroxymatairesinol
2009
An extensive and systematic conformational search was performed on the two epimers of the natural lignan 7-hydroxymatairesinol (HMR), by means of a home-made Systematic Conformational Search Analysis (SCSA) code, designed to select more and more stable conformers through sequential geometry optimization of trial structures at increasing levels of calculation theory. In the present case, the starting molecular structures were selected by the semi-empirical AM1 method and filtered – i.e. decreased in number by choosing the more stable species – on the basis of their energy calculated by the HF method and the 6-31G(d) basis set. The geometries obtained were further refined by performing densit…
A Lotka-type model for oscillations in surface reactions
1997
In this paper we introduce a reaction model on a lattice which leads to oscillations. The model consists of two monomolecular and one bimolecular reaction step and is related to the Lotka model. Despite the simple evolution rules, the model shows a complex behaviour (i.e. the appearance of oscillations). This offers us the opportunity to test different types of stochastic approximations and compare them with the results of a Monte Carlo simulation. The simulation is performed on a large lattice (L = 1024) in order to take long-range correlations into account. Comparing the results of this simulation with the stochastic approaches shows that only advanced numerical approximations are able to…
Missing Curious Fraction Problems
2018
In this paper we present a study of one of the best-known types of descriptive word fraction problems. These problems have disappeared from today’s textbooks but are hugely important for developing arithmetic thinking. The aim of this paper is to examine the historical solution methods for these problems and discuss the analytical readings suggested by the authors. On the basis of this analysis we have conducted a preliminary study of the performance of 35 Spanish students who are highly trained in mathematics. Our results show that these students have a preference for algebraic reasoning, are reluctant to use arithmetic methods, and have reading comprehension difficulties that are reflecte…
Comparison results for Monge - Ampère type equations with lower order terms
2003
In this paper we deal with Monge-Ampère type equations in two dimensions and, using the symmetrization with respect to the perimeter, we prove some comparison results for solutions of such equations involving the solutions of conveniently symmetrized problems.
Feature selection using ROC curves on classification problems
2010
Feature Selection (FS) is one of the key stages in classification problems. This paper proposes the use of the area under Receiver Operator Characteristic curves to measure the individual importance of every input as well as a method to discover the variables that yield a statistically significant improvement in the discrimination power of the classification model.