Higgs boson The Higgs boson is named after Peter Higgs, one of six physicists who, in 1964, proposed the mechanism that suggested the existence of such a particle. Although Higgs's name has come to be associated with this theory, several researchers between about 1960 and 1972 each independently developed different parts of it. In mainstream media the Higgs boson has often been called the "God particle", from a 1993 book on the topic; the nickname is strongly disliked by many physicists, including Higgs, who regard it as inappropriate sensationalism.[17][18] In 2013 two of the original researchers, Peter Higgs and François Englert, were awarded the Nobel Prize in Physics for their work and prediction[19] (Englert's co-researcher Robert Brout had died in 2011). A non-technical summary[edit] "Higgs" terminology[edit] Overview[edit] If this field did exist, this would be a monumental discovery for science and human knowledge, and is expected to open doorways to new knowledge in many fields. History[edit]
Complex logarithm In complex analysis, a complex logarithm function is an "inverse" of the complex exponential function, just as the real natural logarithm ln x is the inverse of the real exponential function ex. Thus, a logarithm of a complex number z is a complex number w such that ew = z.[1] The notation for such a w is ln z or log z. Since every nonzero complex number z has infinitely many logarithms,[1] care is required to give such notation an unambiguous meaning. If z = reiθ with r > 0 (polar form), then w = ln r + iθ is one logarithm of z; adding integer multiples of 2πi gives all the others.[1] Problems with inverting the complex exponential function[edit] For a function to have an inverse, it must map distinct values to distinct values, i.e., be injective. forming a sequence of equally spaced points along a vertical line, are all mapped to the same number by the exponential function. There are two solutions to this problem. Definition of principal value[edit] For example, Log(-3i) = ln 3 − πi/2. .
Hans Thirring Hans Thirring (March 23, 1888 – March 22, 1976) was an Austrian theoretical physicist, professor, and father of the physicist Walter Thirring. He won the Haitinger Prize of the Austrian Academy of Sciences in 1920.[1] Together with the mathematician Josef Lense, he is known for the prediction of the Lense–Thirring frame dragging effect of general relativity in 1918.[2][3][4] He received a deferment during World War I because he had broken one of his feet while skiing. References[edit] ^ Dazinger, Walter (27 January 2014). External links[edit] Hans Thirring at the Mathematics Genealogy Project
Chaos theory A double rod pendulum animation showing chaotic behavior. Starting the pendulum from a slightly different initial condition would result in a completely different trajectory. The double rod pendulum is one of the simplest dynamical systems that has chaotic solutions. Chaos: When the present determines the future, but the approximate present does not approximately determine the future. Chaotic behavior can be observed in many natural systems, such as weather and climate.[6][7] This behavior can be studied through analysis of a chaotic mathematical model, or through analytical techniques such as recurrence plots and Poincaré maps. Introduction[edit] Chaos theory concerns deterministic systems whose behavior can in principle be predicted. Chaotic dynamics[edit] The map defined by x → 4 x (1 – x) and y → x + y mod 1 displays sensitivity to initial conditions. In common usage, "chaos" means "a state of disorder".[9] However, in chaos theory, the term is defined more precisely. where , and , is: .
Standard Model The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, as well as classifying all the subatomic particles known. It was developed throughout the latter half of the 20th century, as a collaborative effort of scientists around the world.[1] The current formulation was finalized in the mid-1970s upon experimental confirmation of the existence of quarks. Since then, discoveries of the top quark (1995), the tau neutrino (2000), and more recently the Higgs boson (2013), have given further credence to the Standard Model. Because of its success in explaining a wide variety of experimental results, the Standard Model is sometimes regarded as a "theory of almost everything". Historical background[edit] The Higgs mechanism is believed to give rise to the masses of all the elementary particles in the Standard Model. Overview[edit] Particle content[edit] Fermions[edit] Gauge bosons[edit] Higgs boson[edit] Main article: Higgs boson E.S.
Abstract algebra The permutations of Rubik's Cube have a group structure; the group is a fundamental concept within abstract algebra. History[edit] As in other parts of mathematics, concrete problems and examples have played important roles in the development of abstract algebra. Through the end of the nineteenth century, many -- perhaps most -- of these problems were in some way related to the theory of algebraic equations. Numerous textbooks in abstract algebra start with axiomatic definitions of various algebraic structures and then proceed to establish their properties. Early group theory[edit] There were several threads in the early development of group theory, in modern language loosely corresponding to number theory, theory of equations, and geometry. Leonhard Euler considered algebraic operations on numbers modulo an integer, modular arithmetic, in his generalization of Fermat's little theorem. Kronecker claimed in 1888 that the study of modern algebra began with this first paper of Vandermonde.
Frame-dragging Effect of general relativity In 2015, new general-relativistic extensions of Newtonian rotation laws were formulated to describe geometric dragging of frames which incorporates a newly discovered antidragging effect.[4] Effects Rotational frame-dragging (the Lense–Thirring effect) appears in the general principle of relativity and similar theories in the vicinity of rotating massive objects. Under the Lense–Thirring effect, the frame of reference in which a clock ticks the fastest is one which is revolving around the object as viewed by a distant observer. Also, an inner region is dragged more than an outer region. Another interesting consequence is that, for an object constrained in an equatorial orbit, but not in freefall, it weighs more if orbiting anti-spinward, and less if orbiting spinward. Linear frame dragging is the similarly inevitable result of the general principle of relativity, applied to linear momentum. Experimental tests Astronomical evidence Mathematical derivation See also
Chaos game Animation of chaos game method The "chaos game" method plots points in random order all over the attractor. This is in contrast to other methods of drawing fractals, which test each pixel on the screen to see whether it belongs to the fractal. With the aid of the "chaos game" a new fractal can be made and while making the new fractal some parameters can be obtained. See also[edit] Chaos theory References[edit] Jump up ^ Barnsley, Michael (1993). External links[edit] IFS Fractal fern and Sierpinski triangle - JAVA applet Complex analysis Murray R. Spiegel described complex analysis as "one of the most beautiful as well as useful branches of Mathematics". Complex analysis is particularly concerned with the analytic functions of complex variables (or, more generally, meromorphic functions). Because the separate real and imaginary parts of any analytic function must satisfy Laplace's equation, complex analysis is widely applicable to two-dimensional problems in physics. History[edit] Complex analysis is one of the classical branches in mathematics with roots in the 19th century and just prior. Complex functions[edit] For any complex function, both the independent variable and the dependent variable may be separated into real and imaginary parts: and where are real-valued functions. In other words, the components of the function f(z), can be interpreted as real-valued functions of the two real variables, x and y. Holomorphic functions[edit] See also: analytic function, holomorphic sheaf and vector bundles. Major results[edit]
Full Report On 60+ Anticancer Herbs Please Share This Page: List Of 60+ Anti-Cancer Herbs image to repin / shareBackground pic © Jag_cz - Fotolia.com Introduction The subject of anticancer herbs is certainly a controversial one. Opinions are polarized - with some strongly opposed to orthodox cancer treatments, and some strongly opposed to herbal medicine. A very significant amount of scientific research has been done in the investigation of anticancer properties of various plants - however much work still needs to be done. The purpose of this page is neither to attempt to persuade, nor to debunk - but simply to present as much good information as possible on the subject, in order that the person interested in the possibility of anticancer herbs may be assisted in "doing their homework". Note - this page uses the term "anticancer" with a broad brush; and it is the most widely-used term - however please note that the National Cancer Institute considers that the term "anticancer herb" is not accurate enough. Aloe vera References
Lense–Thirring precession Precession of a gyroscope due to a nearby celestial body's rotation affecting spacetime In general relativity, Lense–Thirring precession or the Lense–Thirring effect (Austrian German: [ˈlɛnsə ˈtɪrɪŋ]; named after Josef Lense and Hans Thirring) is a relativistic correction to the precession of a gyroscope near a large rotating mass such as the Earth. It is a gravitomagnetic frame-dragging effect. It is a prediction of general relativity consisting of secular precessions of the longitude of the ascending node and the argument of pericenter of a test particle freely orbiting a central spinning mass endowed with angular momentum The difference between de Sitter precession and the Lense–Thirring effect is that the de Sitter effect is due simply to the presence of a central mass, whereas the Lense–Thirring effect is due to the rotation of the central mass. According to a 2007 historical analysis by Herbert Pfister,[1] the effect should be renamed the Einstein–Thirring–Lense effect. where , and .
Theory of everything A theory of everything (ToE) or final theory, ultimate theory, or master theory is a hypothetical single, all-encompassing, coherent theoretical framework of physics that fully explains and links together all physical aspects of the universe.[1]:6 Finding a ToE is one of the major unsolved problems in physics. Over the past few centuries, two theoretical frameworks have been developed that, as a whole, most closely resemble a ToE. The two theories upon which all modern physics rests are general relativity (GR) and quantum field theory (QFT). GR is a theoretical framework that only focuses on the force of gravity for understanding the universe in regions of both large-scale and high-mass: stars, galaxies, clusters of galaxies, etc. On the other hand, QFT is a theoretical framework that only focuses on three non-gravitational forces for understanding the universe in regions of both small scale and low mass: sub-atomic particles, atoms, molecules, etc. Historical antecedents[edit] [edit]