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Hyperbolic Growth
When a quantity grows towards a singularity under a finite variation (a "finite-time singularity") it is said to undergo hyperbolic growth. More precisely, the reciprocal function 1/x has a hyperbola as a graph, and has a singularity at 0, meaning that the limit as x \to 0 is infinite: any similar graph is said to exhibit hyperbolic growth. Description If the output of a function is inversely proportional to its input, or inversely proportional to the difference from a given value x_0, the function will exhibit hyperbolic growth, with a singularity at x_0. In the real world hyperbolic growth is created by certain non-linear positive feedback mechanisms. Comparisons with other growth Like exponential growth and logistic growth, hyperbolic growth is highly nonlinear, but differs in important respects. These functions can be confused, as exponential growth, hyperbolic growth, and the first half of logistic growth are convex functions; however their asymptotic behavior (behavior ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rectangular Hyperbola
In mathematics, a hyperbola (; pl. hyperbolas or hyperbolae ; adj. hyperbolic ) is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows. The hyperbola is one of the three kinds of conic section, formed by the intersection of a plane and a double cone. (The other conic sections are the parabola and the ellipse. A circle is a special case of an ellipse.) If the plane intersects both halves of the double cone but does not pass through the apex of the cones, then the conic is a hyperbola. Hyperbolas arise in many ways: * as the curve representing the reciprocal function y(x) = 1/x in the Cartesian plane, * as the path followed by the shadow of the tip of a sundial, * as the shape of an open orbit (as distinct from a closed elliptical orbit), such as the orbit of a spa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
World-system Theory
World-systems theory (also known as world-systems analysis or the world-systems perspective)Immanuel Wallerstein, (2004), "World-systems Analysis." In ''World System History'', ed. George Modelski, in ''Encyclopedia of Life Support Systems'' (EOLSS), Developed under the Auspices of the UNESCO, Eolss Publishers, Oxford, UK is a multidisciplinary approach to world history and social change which emphasizes the world-system (and not nation states) as the primary (but not exclusive) unit of social analysis. "World-system" refers to the inter-regional and transnational division of labor, which divides the world into core countries, semi-periphery countries, and the periphery countries. Core countries focus on higher-skill, capital-intensive production, and the rest of the world focuses on low-skill, labor-intensive production and extraction of raw materials. This constantly reinforces the dominance of the core countries. Nonetheless, the system has dynamic characteristics, in par ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rein Taagepera
Rein Taagepera (born 28 February 1933) is an Estonian political scientist and former politician. Education Born in Tartu, Estonia, Taagepera fled from occupied Estonia in 1944. Taagepera graduated from high school in Marrakech, Morocco and then studied physics in Canada and the United States. He received a B.A. Sc (Nuclear Engineering) in 1959 and a M.A. (Physics) in 1961 from the University of Toronto, and a Ph.D. from the University of Delaware in 1965. Working in industry until 1970, he received another M.A. in international relations in 1969 and switched to academe as a political scientist at the University of California, Irvine, where he stayed for his entire American career. Taagepera is professor emeritus at University of Tartu. Political career Taagepera served as president of the Association for the Advancement of Baltic Studies from 1986 until 1988. In 1991, he returned to Estonia as the founding dean of a new School of Social Sciences at the University of Tartu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael Kremer
Michael Robert Kremer (born November 12, 1964) is an American development economist who is University Professor in Economics And Public Policy at the University of Chicago. He is the founding director of the Development Innovation Lab at the Becker Friedman Institute for Economics. Kremer served as the Gates Professor of Developing Societies at Harvard University until 2020. In 2019, he was jointly awarded the Nobel Memorial Prize in Economics, together with Esther Duflo and Abhijit Banerjee, "for their experimental approach to alleviating global poverty." Early life and education Michael Robert Kremer was born in 1964 to Eugene and Sara Lillian (née Kimmel) Kremer in New York City. His father, Eugene Kremer was the son of Jewish immigrants to the US from Austria-Poland. His mother, Sara Lillian Kremer was a professor of English literature, who specialized in American Jewish and Holocaust literature. Her parents were Jewish immigrants to the US from Poland. He graduated f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Palaeoworld
''Palaeoworld'' is a peer-reviewed academic journal with a focus on palaeontology and stratigraphy research in and around China. It was founded in 1991 by the Nanjing Institute of Geology and Palaeontology at the Chinese Academy of Sciences (NIGPAS). The journal has been published quarterly since 2006; prior to 2006, it did not adhere to a fixed publication schedule. The journal publishes articles from several specialised fields pertaining to palaeobiology and earth science, such as: fossil taxonomy; biostratigraphy, chemostratigraphy, and chronostratigraphy; evolutionary biology; evolutionary ecology; palaeoecology; palaeoclimatology; and molecular palaeontology. Its editors-in-chief are Shuzhong Shen of the State Key Laboratory of Palaeobiology and Stratigraphy at NIGPAS, and Norman MacLeod of the Natural History Museum, London. See also * ''Paleontological Journal'' * List of fossil sites References External links * (Elsevier.com) * (ScienceDirect ScienceDirect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logistic Growth
A logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with equation f(x) = \frac, where For values of x in the domain of real numbers from -\infty to +\infty, the S-curve shown on the right is obtained, with the graph of f approaching L as x approaches +\infty and approaching zero as x approaches -\infty. The logistic function finds applications in a range of fields, including biology (especially ecology), biomathematics, chemistry, demography, economics, geoscience, mathematical psychology, probability, sociology, political science, linguistics, statistics, and artificial neural networks. A generalization of the logistic function is the hyperbolastic function of type I. The standard logistic function, where L=1,k=1,x_0=0, is sometimes simply called ''the sigmoid''. It is also sometimes called the ''expit'', being the inverse of the logit. History The logistic function was introduced in a series of three papers by Pierre François Verhuls ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential Growth
Exponential growth is a process that increases quantity over time. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself. Described as a function, a quantity undergoing exponential growth is an exponential function of time, that is, the variable representing time is the exponent (in contrast to other types of growth, such as quadratic growth). If the constant of proportionality is negative, then the quantity decreases over time, and is said to be undergoing exponential decay instead. In the case of a discrete domain of definition with equal intervals, it is also called geometric growth or geometric decay since the function values form a geometric progression. The formula for exponential growth of a variable at the growth rate , as time goes on in discrete intervals (that is, at integer times 0, 1, 2, 3, ...), is x_t = x_0(1+r)^t where is the value of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scale Factor
In affine geometry, uniform scaling (or isotropic scaling) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a '' scale factor'' that is the same in all directions. The result of uniform scaling is similar (in the geometric sense) to the original. A scale factor of 1 is normally allowed, so that congruent shapes are also classed as similar. Uniform scaling happens, for example, when enlarging or reducing a photograph, or when creating a scale model of a building, car, airplane, etc. More general is scaling with a separate scale factor for each axis direction. Non-uniform scaling (anisotropic scaling) is obtained when at least one of the scaling factors is different from the others; a special case is directional scaling or stretching (in one direction). Non-uniform scaling changes the shape of the object; e.g. a square may change into a rectangle, or into a parallelogram if the sides of the square are not parallel to the scaling axes (the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Enzyme Kinetics
Enzyme kinetics is the study of the rates of enzyme-catalysed chemical reactions. In enzyme kinetics, the reaction rate is measured and the effects of varying the conditions of the reaction are investigated. Studying an enzyme's kinetics in this way can reveal the catalytic mechanism of this enzyme, its role in metabolism, how its activity is controlled, and how a drug or a modifier (inhibitor or activator) might affect the rate. An enzyme (E) is typically a protein molecule that promotes a reaction of another molecule, its substrate (S). This binds to the active site of the enzyme to produce an enzyme-substrate complex ES, and is transformed into an enzyme-product complex EP and from there to product P, via a transition state ES*. The series of steps is known as the mechanism: : E + S ⇄ ES ⇄ ES* ⇄ EP ⇄ E + P This example assumes the simplest case of a reaction with one substrate and one product. Such cases exist: for example, a mutase such as phosphoglucomutase ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Substrate (biochemistry)
In chemistry, the term substrate is highly context-dependent. Broadly speaking, it can refer either to a chemical species being observed in a chemical reaction, or to a surface on which other chemical reactions or microscopy are performed. In the former sense, a reagent is added to the ''substrate'' to generate a product through a chemical reaction. The term is used in a similar sense in synthetic and organic chemistry, where the substrate is the chemical of interest that is being modified. In biochemistry, an enzyme substrate is the material upon which an enzyme acts. When referring to Le Chatelier's principle, the substrate is the reagent whose concentration is changed. ;Spontaneous reaction : :*Where S is substrate and P is product. ;Catalysed reaction : :*Where S is substrate, P is product and C is catalyst. In the latter sense, it may refer to a surface on which other chemical reactions are performed or play a supporting role in a variety of spectroscopic and microscop ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Enzyme
Enzymes () are proteins that act as biological catalysts by accelerating chemical reactions. The molecules upon which enzymes may act are called substrates, and the enzyme converts the substrates into different molecules known as products. Almost all metabolic processes in the cell need enzyme catalysis in order to occur at rates fast enough to sustain life. Metabolic pathways depend upon enzymes to catalyze individual steps. The study of enzymes is called ''enzymology'' and the field of pseudoenzyme analysis recognizes that during evolution, some enzymes have lost the ability to carry out biological catalysis, which is often reflected in their amino acid sequences and unusual 'pseudocatalytic' properties. Enzymes are known to catalyze more than 5,000 biochemical reaction types. Other biocatalysts are catalytic RNA molecules, called ribozymes. Enzymes' specificity comes from their unique three-dimensional structures. Like all catalysts, enzymes increase the reac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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