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Concept

Sine and cosine

In mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that of the hypotenuse. For an angle \theta, the sine and cosine functions are denoted simply as \sin \theta and \cos \theta. More generally, the definitions of sine and cosine can be extended to any real value in terms of the lengths of certain line segments in a unit circle. More modern definitions express the sine and cosine as infinite series, or as the solutions of certain differential equations, allowing their extension to arbitrary positive and negative values and even to complex numbers. The sine and cosine functions are commonly used to model period

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Boosting contact sliding and wear protection via atomic intermixing and tailoring of nanoscale interfaces

Reuben Yeo Jueyuan

Friction and wear cause energy wastage and system failure. Usually, thicker overcoats serve to combat such tribological concerns, but in many contact sliding systems, their large thickness hinders active components of the systems, degrades functionality, and constitutes a major barrier for technological developments. While sub-10-nm overcoats are of key interest, traditional overcoats suffer from rapid wear and degradation at this thickness regime. Using an enhanced atomic intermixing approach, we develop a similar to 7- to 8-nm-thick carbon/silicon nitride (C/SiNx) multilayer overcoat demonstrating extremely high wear resistance and low friction at all tribological length scales, yielding similar to 2 to 10 times better macroscale wear durability than previously reported thicker (similar to 20 to 100 nm) overcoats on tape drive heads. We report the discovery of many fundamental parameters that govern contact sliding and reveal how tuning atomic intermixing at interfaces and varying carbon and SiNx thicknesses strongly affect friction and wear, which are crucial for advancing numerous technologies.

American Association for the Advancement of Science (AAAS)2019

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Investigation of kNN Classifier on Posterior Features Towards Application in Automatic Speech Recognition

Afsaneh Asaei, Hervé Bourlard, Benjamin Picart

Class posterior distributions can be used to classify or as intermediate features, which can be further exploited in different classifiers (e.g., Gaussian Mixture Models, GMM) towards improving speech recognition performance. In this paper we examine the possibility to use kNN classifier to perform local phonetic classification of class posterior distribution extracted from acoustic vectors. In that framework, we also propose and evaluate a new kNN metric based on the relative angle between feature vectors to define the nearest neighbors. This idea is inspired by the orthogonality characteristic of the posterior features. To fully exploit this attribute, kNN is used in two main steps: (1) the distance is computed as the cosine function of the relative angle between the test vector and the training vector and (2) the nearest neighbors are defined as the samples within a specific relative angle to the test data and the test samples which do not have enough labels in such a hyper-cone are considered as uncertainties and left undecided. This approach is evaluated on TIMIT database and compared to other metrics already used in literature for measuring the similarity between posterior probabilities. Based on our experiments, the proposed approach yield 78.48% frame level accuracy while specifying 15.17% uncertainties in the feature space.

Idiap2010

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Optimization of front SiNx/ITO stacks for high-efficiency two-side contacted c-Si solar cells with co-annealed front and rear passivating contacts

Christophe Ballif, Franz-Josef Haug, Andrea Ingenito, Frank Meyer, Sylvain Nicolay, Xavier Niquille

In this contribution, we present an electron selective passivating contact metallised with a low temperature process to target front side applications in crystalline silicon (c-Si) solar cells. In addition to an interfacial silicon oxide (SiOx) and an in-situ phosphorous doped micro-crystalline silicon (μc-Si(n)) layer, it comprises an ultra-thin indium tin oxide (ITO) layer of 15 nm for lateral conductivity and a hydrogen rich silicon nitride (SiNx:H) layer which serves as hydrogen (H) reservoir and as anti-reflection coating. We use one single thermal treatment for 30 min at 350 °C to sinter the screen-printed paste, to recover sputtering damage induced during ITO deposition, and to diffuse hydrogen from the SiNx:H layer towards the c-Si/SiOx interface where it passivates interfacial defects. Applied to symmetrically processed textured samples, we find implied open-circuit voltage (iVOC) > 728 mV for optimal ITO thickness of 15 nm and annealing temperatures of 350 °C. The developed stack was applied on the front textured side of co-annealed (800 °C) p-type c-Si solar cells in combination with a tunnel oxide hole selective passivating contact on the rear side. We demonstrate solar cells with fill factor (FF) up to 81.9% and an open-circuit voltage (VOC) up to 719 mV. With a short-circuit current density (JSC) of 38.6 mA/cm2, we obtain a final cell efficiency to 22.8%. We find that the annealing of the SiNx:H/ITO stack strongly increases the ITO free carrier density penalizing the solar cell spectral response at high wavelengths.

2020

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Fonction trigonométrique

thumb|upright=1.35|Toutes les valeurs des fonctions trigonométriques d'un angle θ peuvent être représentées géométriquement. En mathématiques, les fonctions trigonométriques permettent de relier les

Trigonométrie

vignette|droite|Un triangle rectangle sur lequel est indiqué un angle Â, le côté adjacent à cet angle, le côté opposé à celui-ci, l'hypoténuse du triangle, et son angle droit. vignette|Cercle trigonom

Nombre complexe

En mathématiques, l'ensemble des nombres complexes est actuellement défini comme une extension de l'ensemble des nombres réels, contenant en particulier un nombre imaginaire noté i tel que i = −1. L

MATH-325: Dynamics and bifurcation

Introduction to local and global behavior of nonlinear dynamical systems arising from maps and ordinary differential equations. Theoretical and computational aspects studied.

PHYS-216: Mathematical methods for physicists

This course complements the Analysis and Linear Algebra courses by providing further mathematical background and practice required for 3rd year physics courses, in particular electrodynamics and quantum mechanics.

MATH-106(a): Analysis II

Étudier les concepts fondamentaux d'analyse, et le calcul différentiel et intégral des fonctions réelles de plusieurs variables.