Search results for "Trigonometry"

Painlevé analysis and exact solutions for the coupled Burgers system

2006

We perform the Painleve test to a system of two coupled Burgers-type equations which fails to satisfy the Painleve test. In order to obtain a class of solutions, we use a slightly modified version of the test. These solutions are expressed in terms of the Airy functions. We also give the travelling wave solutions, expressed in terms of the trigonometric and hyperbolic functions.

A robust forward-displacement analysis of spherical parallel robots

2009

The forward-displacement analysis of spherical parallel robots (SPRs) is revisited. A robust approach, based on the input–output (I/O) equation of spherical four-bar linkages, is proposed. In this approach, the closed-loop kinematic chain of a SPR is partitioned into two four-bar spherical chains, whose I/O equations are at the core of the analysis reported here. These equations lead to a trigonometric equation in the joint angles, which is solved semigraphically to obtain the joint variables for the determination of the moving plate orientation. Examples are included to demonstrate the application of the method.

Relevansen av trigonometri : En studie i to deler på relevansen av trigonometri for elever på videregående skole

2017

Masteroppgave matematikkdidaktikk MA502 – Universitetet i Agder 2017 The topic of this master’s thesis is the relevance of mathematics, especially the relevance of trigonometry. Many students ask the question “why do I need to learn about this”. The aim of this study was to give the students an answer to this question. In the research literature, I found that this question has to do with relevance, and that relevance is a connection between people, an activity and future goals. In particular, one needs to question: relevance of what? relevance according to whom? relevance for whom? And relevance to what end? The empirical part of my research consisted of two studies. In Study 1 the purpose …

Atom-based Stochastic and non-Stochastic 3D-Chiral Bilinear Indices and their Applications to Central Chirality Codification

2006

Abstract Non-stochastic and stochastic 2D bilinear indices have been generalized to codify chemical structure information for chiral drugs, making use of a trigonometric 3D-chirality correction factor. In order to evaluate the effectiveness of this novel approach in drug design we have modeled the angiotensin-converting enzyme inhibitory activity of perindoprilate's σ-stereoisomers combinatorial library. Two linear discriminant analysis models, using non-stochastic and stochastic linear indices, were obtained. The models had shown an accuracy of 95.65% for the training set and 100% for the external prediction set. Next the prediction of the σ-receptor antagonists of chiral 3-(3-hydroxypheny…

Non Linear Fitting Methods for Machine Learning

2017

This manuscript presents an analysis of numerical fitting methods used for solving classification problems as discriminant functions in machine learning. Non linear polynomial, exponential, and trigonometric models are mathematically deduced and discussed. Analysis about their pros and cons, and their mathematical modelling are made on what method to chose for what type of highly non linear multi-dimension problems are more suitable to be solved. In this study only deterministic models with analytic solutions are involved, or parameters calculation by numeric methods, which the complete model can subsequently be treated as a theoretical model. Models deduction are summarised and presented a…

Applications of Bond-Based 3D-Chiral Quadratic Indices in QSAR Studies Related to Central Chirality Codification

2009

The concept of bond-based quadratic indices is generalized to codify chemical structure information for chiral drugs, making use of a trigonometric 3D-chirality correction factor. In order to evaluate the effectiveness of this novel approach in drug design, we have modeled several well-known data sets. In particularly, Cramer's steroid data set has become a benchmark for the assessment of novel QSAR methods. This data set has been used by several researchers using 3D-QSAR approaches. Therefore, it is selected by us for the shake of comparability. In addition, to evaluate the effectiveness of this novel approach in drug design, we model the angiotensin-converting enzyme inhibitory activity o…

Grover’s Search with Faults on Some Marked Elements

2016

Grover's algorithm is a quantum query algorithm solving the unstructured search problem of size N using $$O\sqrt{N}$$ queries. It provides a significant speed-up over any classical algorithm [2]. The running time of the algorithm, however, is very sensitive to errors in queries. Multiple authors have analysed the algorithm using different models of query errors and showed the loss of quantum speed-up [1, 4]. We study the behavior of Grover's algorithm in the model where the search space contains both faulty and non-faulty marked elements. We show that in this setting it is indeed possible to find one of marked elements in $$O\sqrt{N}$$ queries.

Erratum: Partition function of the trigonometric SOS model with reflecting end

2010

Partition function of the trigonometric SOS model with reflecting end

2010

We compute the partition function of the trigonometric SOS model with one reflecting end and domain wall type boundary conditions. We show that in this case, instead of a sum of determinants obtained by Rosengren for the SOS model on a square lattice without reflection, the partition function can be represented as a single Izergin determinant. This result is crucial for the study of the Bethe vectors of the spin chains with non-diagonal boundary terms.

Bond-based 3D-chiral linear indices: Theory and QSAR applications to central chirality codification

2008

The recently introduced non-stochastic and stochastic bond-based linear indices are been generalized to codify chemical structure information for chiral drugs, making use of a trigonometric 3D-chirality correction factor. These improved modified descriptors are applied to several well-known data sets to validate each one of them. Particularly, Cramer's steroid data set has become a benchmark for the assessment of novel quantitative structure activity relationship methods. This data set has been used by several researchers using 3D-QSAR approaches such as Comparative Molecular Field Analysis, Molecular Quantum Similarity Measures, Comparative Molecular Moment Analysis, E-state, Mapping Prope…