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Calabi–Yau manifold

Calabi–Yau manifold
A 2D slice of the 6D Calabi-Yau quintic manifold. Calabi–Yau manifolds are complex manifolds that are higher-dimensional analogues of K3 surfaces. They are sometimes defined as compact Kähler manifolds whose canonical bundle is trivial, though many other similar but inequivalent definitions are sometimes used. They were named "Calabi–Yau spaces" by Candelas et al. (1985) after E. Calabi (1954, 1957) who first studied them, and S. T. Definitions[edit] There are many different inequivalent definitions of a Calabi–Yau manifold used by different authors. A Calabi–Yau n-fold or Calabi–Yau manifold of (complex) dimension n is sometimes defined as a compact n-dimensional Kähler manifold M satisfying one of the following equivalent conditions: These conditions imply that the first integral Chern class c1(M) of M vanishes, but the converse is not true. In particular if a compact Kähler manifold is simply connected then the weak definition above is equivalent to the stronger definition. G2 manifold Related:  wikipediaPhysics

Leonard Susskind On His Black Hole War with Stephen Hawking Leonard Susskind [Photo by Anne Elizabeth Warren] CLR INTERVIEW: Leonard Susskind is the Felix Bloch Professor of theoretical physics at Stanford University. His new book, The Black Hole Wars, details his battles with Stephen Hawking over the true nature of black holes. The resulting theory postulates that every object in our world is actually a hologram being projected from the farthest edges of space. The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics by Leonard Susskind Little, Brown and Company, 480 pp. Would you give us an overview of what a black hole is? A black hole is what you get if you compress so much mass into a region of space that it collapses, under its own weight, to an infinitely small, dense, point called the “singularity.” There is a certain radius—a particular distance from the dangerous singularity—that I like to call “the point-of-no-return.” Passing the horizon seems very innocent while it is happening.

Sign (semiotics) There are two major theories about the way in which signs acquire the ability to transfer information; both theories understand the defining property of the sign as being a relation between a number of elements. In the tradition of semiotics developed by Ferdinand de Saussure the sign relation is dyadic, consisting only of a form of the sign (the signifier) and its meaning (the signified). Saussure saw this relation as being essentially arbitrary motivated only by social convention. According to Saussure (1857–1913), a sign is composed of the signifier[2] (signifiant), and the signified (signifié). A famous thesis by Saussure states that the relationship between a sign and the real-world thing it denotes is an arbitrary one. Charles Sanders Peirce (1839–1914) proposed a different theory. A sign is something which depends on an object in a way that enables (and, in a sense, determines) an interpretation, an interpretant, to depend on the object as the sign depends on the object.

Symmetric group Although symmetric groups can be defined on infinite sets as well, this article discusses only the finite symmetric groups: their applications, their elements, their conjugacy classes, a finite presentation, their subgroups, their automorphism groups, and their representation theory. For the remainder of this article, "symmetric group" will mean a symmetric group on a finite set. The symmetric group is important to diverse areas of mathematics such as Galois theory, invariant theory, the representation theory of Lie groups, and combinatorics. Definition and first properties[edit] The symmetric group on a finite set X is the group whose elements are all bijective functions from X to X and whose group operation is that of function composition.[1] For finite sets, "permutations" and "bijective functions" refer to the same operation, namely rearrangement. Applications[edit] Elements[edit] The elements of the symmetric group on a set X are the permutations of X. Multiplication[edit] Cycles[edit]

Cotton–Mouton effect In physical optics, the Cotton–Mouton effect refers to birefringence in a liquid in the presence of a constant transverse magnetic field. It is a similar but stronger effect than the Voigt effect (in which the medium is a gas instead of a liquid). The electric analog is the Kerr effect. It was discovered in 1907 by Aimé Cotton and Henri Mouton, working in collaboration. When a linearly polarized wave propagates perpendicular to magnetic field (e.g. in a magnetized plasma), it can become elliptized. Cotton effect

Membrane (M-theory) In string theory and related theories, D-branes are an important class of branes that arise when one considers open strings. As an open string propagates through spacetime, its endpoints are required to lie on a D-brane. The letter "D" in D-brane refers to the fact that we impose a certain mathematical condition on the system known as the Dirichlet boundary condition. See also[edit] References[edit] Jump up ^ Moore, Gregory (2005). El Camino de Wudang Andragogía La drago logia(del griego ἀνήρ "hombre" y ἀγωγή "guía" o "conducción") es el conjunto de las técnicas de enseñanza orientadas a educar personas adultas, en contraposición de la pedagogía, que es la enseñanza orientada a los niños. Actualmente se considera que la educación no es sólo cuestión de niños y adolescentes. El hecho educativo es un proceso que actúa sobre el hombre a lo largo de toda su vida, siendo que la naturaleza del hombre permite que pueda continuar aprendiendo durante toda su vida sin importar su edad cronológica. El andragogo[editar] Manuel Castro Pereira en su obra Conformación de un modelo de desarrollo curricular experimental para el postgrado de la universidad nacional abierta con base en los principios andragógicos (1990), al referirse al adulto que facilita el aprendizaje de otros adultos, escribe: ≪El andragogo es un educador que, conociendo al adulto que aprende, es capaz de crear ambientes educativos propicios para el aprendizaje. Orígenes[editar] Eduard C. 1. 2.

M-theory M-theory is a theory in physics that unifies all consistent versions of superstring theory. The existence of such a theory was first conjectured by Edward Witten at the string theory conference at the University of Southern California in the summer of 1995. Witten's announcement initiated a flurry of research activity known as the second superstring revolution. Background[edit] Quantum gravity and strings[edit] One of the deepest problems in modern physics is the problem of quantum gravity. Number of dimensions[edit] In everyday life, there are three familiar dimensions of space (up/down, left/right, and forward/backward), and there is one dimension of time (later/earlier). Despite the obvious relevance of four-dimensional spacetime for describing the physical world, there are several reasons why physicists often consider theories in other dimensions. Dualities[edit] Main articles: S-duality and T-duality A diagram of string theory dualities. and winding number in the dual description. .

Birefringence A calcite crystal laid upon a graph paper with blue lines showing the double refraction Doubly refracted image as seen through a calcite crystal, seen through a rotating polarizing filter illustrating the opposite polarization states of the two images. Explanation[edit] The simplest (and most common) type of birefringence is that of materials with uniaxial anisotropy. That is, the structure of the material is such that it has an axis of symmetry with all perpendicular directions optically equivalent. What's more, the extraordinary ray is an inhomogeneous wave whose power flow (given by the Poynting vector) is not exactly parallel to the wave vector. When the light propagates either along or orthogonal to the optic axis, such a lateral shift does not occur. Sources of optical birefringence[edit] While birefringence is usually obtained using an anisotropic crystal, it can result from an optically isotropic material in a few ways: Examples of uniaxial birefringent materials[edit] . and

Cyclic model A cyclic model (or oscillating model) is any of several cosmological models in which the universe follows infinite, or indefinite, self-sustaining cycles. For example, the oscillating universe theory briefly considered by Albert Einstein in 1930 theorized a universe following an eternal series of oscillations, each beginning with a big bang and ending with a big crunch; in the interim, the universe would expand for a period of time before the gravitational attraction of matter causes it to collapse back in and undergo a bounce. Overview[edit] In the 1920s, theoretical physicists, most notably Albert Einstein, considered the possibility of a cyclic model for the universe as an (everlasting) alternative to the model of an expanding universe. One new cyclic model is a brane cosmology model of the creation of the universe, derived from the earlier ekpyrotic model. Other cyclic models include Conformal cyclic cosmology and Loop quantum cosmology. The Steinhardt–Turok model[edit] See also[edit]

On Truth & Reality: Philosophy Physics Metaphysics of Space, Wave Structure of Matter. Famous Science Art Quotes. Kakapo The Kakapo is critically endangered; as of March 2014, with an additional six[4] from the first hatchings since 2011, the total known population is only 130[5] living individuals, as reported by the Kakapo Recovery program, most of which have been given names.[6] Because of Polynesian and European colonisation and the introduction of predators such as cats, rats, ferrets, and stoats, the Kakapo was almost wiped out. Conservation efforts began in the 1890s, but they were not very successful until the implementation of the Kakapo Recovery Plan in the 1980s. As of April 2012, surviving Kakapo are kept on three predator-free islands, Codfish (Whenua Hou), Anchor and Little Barrier islands, where they are closely monitored.[7][8] Two large Fiordland islands, Resolution and Secretary, have been the subject of large-scale ecological restoration activities to prepare self-sustaining ecosystems with suitable habitat for the Kakapo. Taxonomy, systematics and naming[edit] Description[edit]

CP violation It plays an important role both in the attempts of cosmology to explain the dominance of matter over antimatter in the present Universe, and in the study of weak interactions in particle physics. CP-symmetry[edit] The idea behind parity symmetry is that the equations of particle physics are invariant under mirror inversion. Overall, the symmetry of a quantum mechanical system can be restored if another symmetry S can be found such that the combined symmetry PS remains unbroken. Simply speaking, charge conjugation is a simple symmetry between particles and antiparticles, and so CP-symmetry was proposed in 1957 by Lev Landau as the true symmetry between matter and antimatter. CP violation in the Standard Model[edit] "Direct" CP violation is allowed in the Standard Model if a complex phase appears in the CKM matrix describing quark mixing, or the PMNS matrix describing neutrino mixing. and , and their antiparticles . and the corresponding antiparticle process , and denote their amplitudes . . .

Doughnut theory of the universe Bloom Toroidal Model of the Universe The doughnut theory of the universe is an informal description of the theory that the shape of the universe is a three-dimensional torus. The name comes from the shape of a doughnut, whose surface has the topology of a two-dimensional torus. The foundation for the doughnut theory started with Bell Lab’s discovery of cosmic microwave background (CMB). With the information provided from the study of CMB, Dr. Supporting evidence[edit] Dr. Cosmic Background Explorer (COBE)[edit] The Cosmic Background Explorer was an explorer satellite launched in 1989 by NASA that used a Far Infrared Absolute Spectrometer (FIRAS) to measure the radiation of the universe.[2] Led by researchers John C. Wilkinson Microwave Anisotropy Probe (WMAP)[edit] WMAP cosmic microwave background map The Wilkinson Microwave Anisotropy Probe (WMAP) was launched in 2001 as NASA’s second explorer satellite intended to map the precise distribution of CMB across the universe. Notes References

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