Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Paul Guldin (original name Habakkuk Guldin) (June 12, 1577 – November 3, 1643) was a Swiss Jesuit mathematician and astronomer. He discovered the Guldinus theorem to determine the surface and the volume of a solid of revolution. This theorem is also known as Pappus–Guldinus theorem and Pappus's centroid theorem, attributed to Pappus of Alexandria. He was noted for his association with the German mathematician and astronomer Johannes Kepler. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд...

ISBN: 978-6-1347-6105-5
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Paul Epstein (Frankfurt, July 24, 1871 – Dornbusch, August 11, 1939) was a German mathematician. He is known for his contributions to number theory, in particular the Epstein zeta function.Epstein was raised in Frankfurt where his father was a professor. He received his PhD in 1895 from the University of Strasbourg. From 1895 to 1918 he was a Privatdozent at the University in Strasbourg, which at that time was part of the German Empire. At the end of World War I the city of Strasbourg reverted to France, and Epstein, being German, had to return to Frankfurt. Данное издание не является...

ISBN: 978-6-1347-1829-5
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Paul Althaus Smith (1900 — 13 June 1980) was an American mathematician. His name occurs in two significant conjectures in geometric topology: the Smith conjecture, which is now a theorem, and the Hilbert-Smith conjecture, still open as of 2010[update]. Smith theory is a theory about homeomorphisms of finite order of manifolds, particularly spheres. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1346-6758-6
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Paul Flondor (born 1946) is a professor of algebra at the Polytechnic University of Bucharest, known for many studies and books in mathematical analysis.The professor of the Department of Mathematics II of Polytechnic University of Bucharest is well known in Romania and abroad due to his professional successes. Flondor has had fruitful collaborations with Italian mathematicians, being invited to the University of Rome and the University of Perugia. Together with Vasile Brinzanescu, he received the award of the Romanian Academy in 1986. Данное издание не является оригинальным....

ISBN: 978-6-1347-3619-0
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Paul-Andre Meyer (21 August 1934 – 30 January 2003) was a French mathematician, who played a major role in the development of the 'general theory of stochastic processes'. He worked at the Institut de Recherche Mathematique (IRMA) in Strasbourg.He is best known for his continuous-time analog of Doob's decomposition of a submartingale, known as the Doob–Meyer decomposition.Some of his main areas of research in probability theory were the general theory of stochastic processes, Markov processes, stochastic integration, stochastic differential geometry and quantum probability. His most cited book is...

ISBN: 978-6-1346-5385-5
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High Quality Content by WIKIPEDIA articles! The Pauli Equation, also known as the Schrodinger–Pauli equation, is the formulation of the Schrodinger equation for spin-1?2 particles which takes into account the interaction of the particle's spin with the electromagnetic field. It is the non-relativistic limit of the Dirac equation and can be used where particles are slow enough that relativistic effects can be neglected. It was formulated by Wolfgang Pauli in 1927. Note that because of the properties of the Pauli matrices, if the magnetic vector potential bold{A} is equal to zero, then the equation reduces to the familiar Schrodinger equation for a particle in a purely electric potential ?, except that it operates on a two component...

ISBN: 978-6-1311-2897-4
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High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! In physics, the Pauli matrices are a set of 2 x 2 complex Hermitian and unitary matrices (See also ref.[1]). Usually indicated by the Greek letter 'sigma' (?), they are occasionally denoted with a 'tau' (?) when used in connection with isospin symmetries. They are: sigma_1 = sigma_x = begin{pmatrix} 0 Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1303-3583-0
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High Quality Content by WIKIPEDIA articles! The Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang Pauli in 1925. It states that no two identical fermions may occupy the same quantum state simultaneously. A more rigorous statement of this principle is that, for two identical fermions, the total wave function is anti-symmetric. For electrons in a single atom, it states that no two electrons can have the same four quantum numbers, that is, if n, l, and ml are the same, ms must be different such that the electrons have opposite spins. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после...

ISBN: 978-6-1304-0056-9
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High Quality Content by WIKIPEDIA articles! Un pavage (ou dallage) est une partition d’un espace (generalement un espace euclidien comme le plan ou l’espace tridimensionnel) par un ensemble fini d’elements appeles tuiles (plus precisement, ce sont des compacts d’interieur non vide). Generalement, on considere des pavages par translations, c’est-a-dire que deux memes tuiles du pavage sont toujours deductibles l’une de l’autre par une translation (a l’exclusion des rotations ou symetries). Il existe aussi des pavages d’espaces non euclidien, les plus celebres etant sans doute les nombreux pavages de M.C. Escher (pavages d’espaces hyperboliques). Данное издание не является...

ISBN: 978-6-1339-1458-2
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High Quality Content by WIKIPEDIA articles! The Pearson symbol, or Pearson notation, is used in crystallography as a means of describing a crystal structure, and was originated by W.B Pearson. The first two letters specify the Bravais lattice, the first lower case letter specifying the crystal class, and the second upper case letter the lattice type. The number suffix is the number of the atoms in the unit cell. IUPAC (2005) recommends that this symbol can be used to specify the structure of inorganic solids where there is possible ambiguity, and should be italicised. The Pearson symbol does not uniquely identify the space group of a crystal structure, for example both the NaCl structure, (space group Fm3m) and diamond (space group Fd3m)...

ISBN: 978-6-1303-7488-4
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High Quality Content by WIKIPEDIA articles! Penalty methods are a certain class of algorithms for solving constrained optimization problems. A penalty method replaces a constrained optimization problem by a series of unconstrained problems whose solutions ideally converge to the solution of the original constrained problem. The unconstrained problems are formed by adding a term to the objective function that consists of a penalty parameter and a measure of violation of the constraints. The measure of violation is nonzero when the constraints are violated and is zero in the region where constraints are not violated. Данное издание не является оригинальным. Книга печатается по...

ISBN: 978-6-1312-9959-9
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ISBN: 978-6-1303-0520-8
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Derivations from Pendulum (mathematics). To begin, we shall make three assumptions about the simple pendulum: The rod/string/cable on which the bob is swinging is massless, does not stretch, and always remains taut. The bob is a point mass. Motion occurs in a 2-dimensional plane, i.e. pendulum does not swing into and out of the page. Consider Figure 1, showing the forces acting on a simple pendulum. Note that the path of the pendulum sweeps out an arc of a circle. The angle is measured in radians, and this is crucial for this formula. The blue arrow is the gravitational force acting on the bob, and the violet...

ISBN: 978-6-1312-9995-7
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High Quality Content by WIKIPEDIA articles!Like the Penman equation, the Penman-Monteith equation requires daily mean temperature, wind speed, relative humidity, and solar radiation to predict net evapotranspiration. Other than radiation, these parameter are implicit in the derivation of ?, cp, and ?q, if not conductances below. The United Nations Food Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1311-5440-9
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High Quality Content by WIKIPEDIA articles! The Penman equation describes evaporation (E) from an open water surface, and was developed by Howard Penman in 1948. Penman's equation requires daily mean temperature, wind speed, relative humidity, and solar radiation to predict E. Simpler Hydrometeorological equations continue to be used where obtaining such data is impractical, to give comparable results within specific contexts, eg. humid vs arid climates.Numerous variations of the Penman equation are used to estimate evaporation from water, and land. Specifically the Penman-Monteith equation refines weather based potential evapotranspiration (PET) estimates of vegetated land areas. It is widely regarded as one of the most accurate models,...

ISBN: 978-6-1311-5439-3
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High Quality Content by WIKIPEDIA articles! Penney's game (named after its inventor Walter Penney) is a binary (head/tail) sequence generating game between two players. At the start of the game, the two players agree on the length of the sequences to be generated. This length is usually taken to be three, but can be any larger number. Player A then selects a sequence of heads and tails of the required length, and shows this sequence to player B. Player B then selects another sequence of heads and tails of the same length. Subsequently, a fair coin is tossed until either player A's or player B's sequence appears as a subsequence of the coin toss outcomes. The player whose sequence appears first wins. Данное издание не...

ISBN: 978-6-1313-0013-4
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High Quality Content by WIKIPEDIA articles! A Penrose tiling is a nonperiodic tiling generated by an aperiodic set of prototiles named after Sir Roger Penrose, who investigated these sets in the 1970s. Because all tilings obtained with the Penrose tiles are non-periodic, Penrose tilings are considered aperiodic tilings. A Penrose tiling may be constructed so as to exhibit both reflection symmetry and fivefold rotational symmetry, as in the diagram at the right. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1303-1543-6
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High Quality Content by WIKIPEDIA articles! In mathematics and physics, Penrose graphical notation or tensor diagram notation is a (usually handwritten) visual depiction of multilinear functions or tensors proposed by Roger Penrose. A diagram in the notation consists of several shapes linked together by lines, much like tinker toys. The notation has been studied extensively by Predrag Cvitanovi?, who used it to classify the classical Lie groups. It has also been generalized using representation theory to spin networks in physics, and with the presence of matrix groups to trace diagrams in linear algebra. Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1313-0068-4
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High Quality Content by WIKIPEDIA articles! In geometry, a pentagon is any five-sided polygon. A pentagon may be simple or self-intersecting. The internal angles in a simple pentagon total 540°. A pentagram is an example of a self-intersecting pentagon. The term pentagonal is commonly used to mean a regular convex pentagon, where all sides are equal and all interior angles are equal (to 108°). Its Schlafli symbol is {5}. The chords of this pentagon are in golden ratio to its sides. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1303-2311-0
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High Quality Content by WIKIPEDIA articles! In mathematics, the pentagonal number theorem, originally due to Euler, relates the product and series representations of the Euler function. It states that prod_{n=1}^infty (1-x^n)=sum_{k=-infty}^infty(-1)^kx^{k(3k-1)/2}. In other words, (1-x)(1-x^2)(1-x^3) cdots = 1 - x - x^2 + x^5 + x^7 - x^{12} - x^{15} + x^{22} + x^{26} + cdots. A striking feature of this expansion is the amount of cancellation in the product. The indices 1, 2, 5, 7, 12, ... appearing on the right hand side are called pentagonal numbers (or more accurately, generalized pentagonal numbers). Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1313-0119-3
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High Quality Content by WIKIPEDIA articles! In mathematics, the pentagram map is a kind of iteration on polygons. The pentagram map takes a given convex pentagon, finds the intersections of the diagonals of the pentagon and constructs a new pentagon from these intersections. Pentagram maps were studied by John Conway and Richard Schwartz among others. They possess a cross ratio and are an example of an integrable system and have applications in computer vision. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1313-0136-0
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High Quality Content by WIKIPEDIA articles! The pentad was a Pythagorean term for the number five. A pentagram, symbol of the pentad, was used by the Pythagoreans as a secret sign to recognize each other. It represents the number five, life, power and invulnerability. Nicomachus explored the mathematical characteristics of the pentad as related to the Pythagorean saying "Justice is five". The Nicomachean extracts reads: "The pentad is change of quality, because it changes that which is triply extended or which has length, breadth and depth into the sameness of a sphere" Pythagoreanism is a term used for the esoteric and metaphysical beliefs held by Pythagoras and his followers, the Pythagoreans, who were considerably influenced by...

ISBN: 978-6-1309-8450-2
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High Quality Content by WIKIPEDIA articles! A pentaprism is a five-sided reflecting prism used to deviate a beam of light by 90°. The beam reflects inside the prism twice, allowing the transmission of an image through a right angle without inverting it (that is, without changing the image's handedness) as an ordinary right-angle prism or mirror would. The reflections inside the prism are not caused by total internal reflection, since the beams are incident at an angle less than the critical angle, or minimum angle for total internal reflection. Instead, the two faces are coated to provide mirror surfaces. The two opposite transmitting faces are often coated with an antireflection coating to reduce spurious reflections. The fifth face of...

ISBN: 978-6-1313-0194-0
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High Quality Content by WIKIPEDIA articles! In geometry, the pentagonal antiprism is the third in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps. It consists of two pentagons joined to each other by a ring of 10 triangles for a total of 12 faces. Hence, it is a non-regular dodecahedron.If the faces of the pentagonal antiprism are all regular, it is a semiregular polyhedron. It can also be considered as a parabidiminished icosahedron, a shape formed by removing two pentagonal pyramids from a regular icosahedron leaving two nonadjacent pentagonal faces; a related shape, the metabidiminished icosahedron (one of the Johnson solids), is likewise form from the icosahedron by...

ISBN: 978-6-1313-0082-0
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High Quality Content by WIKIPEDIA articles! Pentation is the operation of repeated tetration, just as tetration is the operation of repeated exponentation and is a hyperoperation. Like tetration, it has little real-world applications. It is non-commutative, and therefore has two inverse functions, which might be named the penta-root and the penta-logarithm (analogous to the two inverse functions for exponentiation: nth root function and logarithm). Pentation also bounds the elementary recursive functions.The word "Pentation" was coined by Reuben Goodstein from the roots penta- (five) and iteration). It is part of his general naming scheme for hyperoperations. Данное издание не является оригинальным....

ISBN: 978-6-1311-2276-7
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Дата выхода: июль 2011