Search results for "Quadrat"

Quantum walk on the line through potential barriers

2015

Quantum walks are well-known for their ballistic dispersion, traveling $\Theta(t)$ away in $t$ steps, which is quadratically faster than a classical random walk's diffusive spreading. In physical implementations of the walk, however, the particle may need to tunnel through a potential barrier to hop, and a naive calculation suggests this could eliminate the ballistic transport. We show by explicit calculation, however, that such a loss does not occur. Rather, the $\Theta(t)$ dispersion is retained, with only the coefficient changing, which additionally gives a way to detect and quantify the hopping errors in experiments.

Reply to 'The super-quadratic growth of high-harmonic signal as a function of pressure'

2010

A Quasilinear Parabolic Equation with Quadratic Growth of the Gradient modeling Incomplete Financial Markets

2004

We consider a quasilinear parabolic equation with quadratic gradient terms. It arises in the modeling of an optimal portfolio which maximizes the expected utility from terminal wealth in incomplete markets consisting of risky assets and non-tradable state variables. The existence of solutions is shown by extending the monotonicity method of Frehse. Furthermore, we prove the uniqueness of weak solutions under a smallness condition on the derivatives of the covariance matrices with respect to the solution. The in influence of the non-tradable state variables on the optimal value function is illustrated by a numerical example.

Quadratically Tight Relations for Randomized Query Complexity

2020

In this work we investigate the problem of quadratically tightly approximating the randomized query complexity of Boolean functions R(f). The certificate complexity C(f) is such a complexity measure for the zero-error randomized query complexity R0(f): C(f) ≤R0(f) ≤C(f)2. In the first part of the paper we introduce a new complexity measure, expectational certificate complexity EC(f), which is also a quadratically tight bound on R0(f): EC(f) ≤R0(f) = O(EC(f)2). For R(f), we prove that EC2/3 ≤R(f). We then prove that EC(f) ≤C(f) ≤EC(f)2 and show that there is a quadratic separation between the two, thus EC(f) gives a tighter upper bound for R0(f). The measure is also related to the fractional…

Quasilinear elliptic equations with singular quadratic growth terms

2011

In this paper, we deal with positive solutions for singular quasilinear problems whose model is [Formula: see text] where Ω is a bounded open set of ℝN, g ≥ 0 is a function in some Lebesgue space, and γ > 0. We prove both existence and nonexistence of solutions depending on the value of γ and on the size of g.

Quadrature Formula Based on Interpolating Polynomials: Algorithmic and Computational Aspects

2007

The aim of this article is to obtain a quadrature formula for functions in several variables and to analyze the algorithmic and computational aspects of this formula. The known information about the integrand is {λi(f)}i=1n, where λi are linearly independent linear functionals. We find a form of the coefficients of the quadrature formula which can be easy used in numerical calculations. The main algorithm we use in order to obtain the coefficients and the remainder of the quadrature formula is based on the Gauss elimination by segments method. We obtain an expression for the exactness degree of the quadrature formula. Finally, we analyze some computational aspects of the algorithm in the pa…

Using Modelling and Tablets in the Classroom to Learn Quadratic Functions

2017

In this chapter, we present teaching material to work with a quadratic function and the meaning of its parameters through the mathematical modelling of a real-life phenomenon: the relation between the time and the height of a ball during a complete vertical rebound and fall. The teaching material uses electronic tablets to collect and process real data in the classroom. After analysing a year 11 implementation, we note that a qualitative analysis of the phenomenon and the families of functions and the students’ prior knowledge about these functions are key elements to manage and control the modelling process, especially, to choose the model and to interpret the results in terms of the pheno…

<strong>Machine Learning and Atom-Based Quadratic Indices for Proteasome Inhibition Prediction </strong>

2015

The atom-based quadratic indices are used in this work together with some machine learning techniques that includes: support vector machine, artificial neural network, random forest and k-nearest neighbor. This methodology is used for the development of two quantitative structure-activity relationship (QSAR) studies for the prediction of proteasome inhibition. A first set consisting of active and non-active classes was predicted with model performances above 85% and 80% in training and validation series, respectively. These results provided new approaches on proteasome inhibitor identification encouraged by virtual screenings procedures. .

Atom-based 3D-chiral quadratic indices. Part 2: prediction of the corticosteroid-binding globulinbinding affinity of the 31 benchmark steroids data s…

2005

A quantitative structure-activity relationship (QSAR) study to predict the relative affinities of the steroid 'benchmark' data set to the corticosteroid-binding globulin (CBG) is described. It is shown that the 3D-chiral quadratic indices closely correlate with the measured CBG affinity values for the 31 steroids. The calculated descriptors were correlated with biological data through multiple linear regressions. Two statistically significant models were obtained when non-stochastic (R = 0.924 and s = 0.46) as well as stochastic (R = 0.929 and s = 0.46) 3D-chiral quadratic indices were used. A leave-one-out (LOO) approach to model validation is used here; the best results obtained in the cr…

Atom-Based Quadratic Indices to Predict Aquatic Toxicity of Benzene Derivatives to <i>Tetrahymena pyriformis</i>

2009

The non-stochastic and stochastic atom-based quadratic indices are applied to develop quantitative structure-activity relationship (QSAR) models for the prediction of aquatic toxicity. The used dataset, consisting of 392 benzene derivatives for which toxicity data to the ciliate Tetrahymena pyriformis were available, is divided into training and test sets. The obtained multiple linear regression models are statistically significant (R2 = 0.787 and s = 0.347, R2 = 0.806 and s = 0.329, for non-stochastic and stochastic quadratic indices, respectively) and show rather good stability in a cross-validation experiment (q2 = 0.769 and scv = 0.357, q2 = 0.791 and scv = 0.337, correspondingly). In a…