Minkowski diagram Minkowski diagram with resting frame (x,t), moving frame (x′,t′), light cone, and hyperbolas marking out time and space with respect to the origin. The Minkowski diagram, also known as a spacetime diagram, was developed in 1908 by Hermann Minkowski and provides an illustration of the properties of space and time in the special theory of relativity. It allows a quantitative understanding of the corresponding phenomena like time dilation and length contraction without mathematical equations. The term Minkowski diagram is used in both a generic and particular sense. In general, a Minkowski diagram is a graphic depiction of a portion of Minkowski space, often where space has been curtailed to a single dimension. These two-dimensional diagrams portray worldlines as curves in a plane that correspond to motion along the spatial axis. Basics[edit] A photon moving right at the origin corresponds to the yellow track of events, a straight line with a slope of 45°. Different scales on the axes. History
MIT researchers measure your pulse, detect heart abnormalities with smartphone camera Last year, a group of researchers from MIT’s Computer Science and Artificial Intelligence Lab (CSAIL) showed us just how easy it is to “see” a human heartbeat in ordinary video footage. With a little filtering, a little averaging, and a touch of turn-of-the-century (1900) mathematical analysis, the telltale color changes in the skin associated with the peak pressure pulse of the heart can be seen by anyone. The CSAIL researchers have now rejigged their algorithms to optimize instead for detection of the head motion artifact associated with each beat. Remote detection of the heartbeat is a tremendous convenience that could potentially spot heart abnormalities in those who would otherwise never look twice — if it is accurate enough. The release from MIT on this work mentions that the heart rate variability (HRV) — the moment-to-moment deviations from constancy — can be used to diagnose potential heart issues.
Hilbert space The state of a vibrating string can be modeled as a point in a Hilbert space. The decomposition of a vibrating string into its vibrations in distinct overtones is given by the projection of the point onto the coordinate axes in the space. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as infinite-dimensional function spaces. The earliest Hilbert spaces were studied from this point of view in the first decade of the 20th century by David Hilbert, Erhard Schmidt, and Frigyes Riesz. They are indispensable tools in the theories of partial differential equations, quantum mechanics, Fourier analysis (which includes applications to signal processing and heat transfer)—and ergodic theory, which forms the mathematical underpinning of thermodynamics. John von Neumann coined the term Hilbert space for the abstract concept that underlies many of these diverse applications. Definition and illustration[edit] Motivating example: Euclidean space[edit] Definition[edit]
Gravitation Gravitation, or gravity, is a natural phenomenon by which all physical bodies attract each other. It is most commonly recognized and experienced as the agent that gives weight to physical objects, and causes physical objects to fall toward the ground when dropped from a height. During the grand unification epoch, gravity separated from the electronuclear force. History of gravitational theory Scientific revolution Modern work on gravitational theory began with the work of Galileo Galilei in the late 16th and early 17th centuries. Newton's theory of gravitation In 1687, English mathematician Sir Isaac Newton published Principia, which hypothesizes the inverse-square law of universal gravitation. Newton's theory enjoyed its greatest success when it was used to predict the existence of Neptune based on motions of Uranus that could not be accounted for by the actions of the other planets. Equivalence principle Formulations of the equivalence principle include: General relativity Specifics
Metric (mathematics) In differential geometry, the word "metric" may refer to a bilinear form that may be defined from the tangent vectors of a differentiable manifold onto a scalar, allowing distances along curves to be determined through integration. It is more properly termed a metric tensor. d : X × X → R (where R is the set of real numbers). For all x, y, z in X, this function is required to satisfy the following conditions: d(x, y) ≥ 0 (non-negativity, or separation axiom)d(x, y) = 0 if and only if x = y (identity of indiscernibles, or coincidence axiom)d(x, y) = d(y, x) (symmetry)d(x, z) ≤ d(x, y) + d(y, z) (subadditivity / triangle inequality). Conditions 1 and 2 together produce positive definiteness. A metric is called an ultrametric if it satisfies the following stronger version of the triangle inequality where points can never fall 'between' other points: For all x, y, z in X, d(x, z) ≤ max(d(x, y), d(y, z)) d(x, y) = d(x + a, y + a) for all x, y and a in X. If a modification of the triangle inequality
Modele d'analyse d'une image fixe Modèle d'analyse d’une image et application... Stéphanie Dansereau, professeure, Éducation à l'image et aux médias, UQAMdansereau-trahan.stephanie@uqam.ca Exemple choisie par l'étudiante Livia Avram dans le cadre du cours : Éducation aux médias, 28 janvier 2002. Identifier - Explorer - Analyser - Contextualiser - Conclure Références L'Image qui a choqué le monde Photo des quelques uns des 158 prisonniers du camp de détention américain X-Ray, implanté sur la base militaire de Guantanamo Bay, à Cuba. Identifier l’œuvre:image d'art, photo de presse, publicité... Légende complémentaire sous la photo de presseL'image de ces détenus agenouillés pieds et poings liés, portant bâillons, casques antibruit et masques aveuglant, dans l'attente de leur transfert vers les cellules, a soulevé une vague d'indignation à travers le monde. Analyse proprement dite A. A. Contexte historique: voir plus haut Contexte artistique Contexte biographique (auteur si connu ou origine du diffuseur) B. Références et notes
Quelle hiérarchie de valeurs vous motive et guide votre jugement? FAITES LE TEST Mise à jour : Une révision de ce test, le Questionnaire des valeurs par portraits - révisé évalue 19 valeurs fondamentales plutôt que 10. Ce nouveau modèle est beaucoup plus précis et prédit mieux les attitudes et les comportements, soulignent les auteurs. Ce test, le Questionnaire des valeurs par portraits, publié par le chercheur en psychologie sociale Shalom H. Schwartz et ses collègues (1), évalue 10 valeurs fondamentales qui, selon le modèle de ces chercheurs, seraient universelles , c'est-à-dire se retrouveraient dans toutes les cultures. Les valeurs sont des croyances liées aux affects qui, à travers une diversité de contextes, motivent l'action et guident l'évaluation des actions des autres, des politiques, des personnes et des événements. Par exemple, les personnes pour qui l’indépendance est une valeur importante sont alertées si leur indépendance est menacée, malheureuses quand elles ne parviennent pas à la préserver, et heureuses quand elles peuvent l’exercer.
Hayashi track Stellar evolution tracks (blue lines) for the pre-main-sequence. The nearly-vertical curves are Hayashi tracks. Low-mass stars have nearly vertical evolution tracks until they arrive on the main sequence. For more massive stars, the Hayashi track bends lefts into the Henyey track. Even more massive stars are born directly onto the Henyey track. The end (leftmost point) of every track is labeled with the star's mass in solar masses, and represents its position on the main sequence. years old lie along the curve labeled , and similarly for the other 3 isochrones. The Hayashi track is a luminosity–temperature relationship obeyed by infant stars of less than 3 solar masses in the pre-main-sequence phase of stellar evolution. At an end of a low- or intermediate-mass star's life, the star follows an analogue of the Hayashi track, but in reverse—it increases in luminosity, expands, and stays at roughly the same temperature, eventually becoming a red giant. History[edit] where . Derivation[edit] .