From the pure mathematical point of view, why might your approach be preferable?
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A handful of research papers have come out in the past couple of years that tackle the question of fairness from a statistical and mathematical point-of-view.
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"At least from a mathematical point of view and from our analysis, there is nothing one can learn from the 11th green that can be applied to the 12th hole," Mittal said in a telephone interview.
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So, if you were a robot, and you ovulated at the exact same mathematical point in time each month, then you could assume that the days right after your period, but before your fertile window begins would be your "least-likely-to-conceive" days.
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From a mathematical point of view, the kernel K(x,y) here only depends of the difference between x and y.
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That is to say, Yang–Mills connections are precisely those that minimize their curvature. In this sense they are the natural choice of connection on a principal or vector bundle over a manifold from a mathematical point of view.
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In mathematics, a point source is a singularity from which flux or flow is emanating. Although singularities such as this do not exist in the observable universe, mathematical point sources are often used as approximations to reality in physics and other fields.
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Using complexification, rewrote the formula (1) into : where CS(S^3\backslash K) is called the Chern–Simons invariant. They showed that there is a clear relation between the complexified colored Jones polynomial and Chern–Simons theory from a mathematical point of view.
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However, Newton states in his Principia that he considers forces from a mathematical point of view, not a physical, thereby taking an instrumentalist view.I. Newton, Principia, p. 408 in the translation of I.B. Cohen and A. Whitman Moreover, he does not assign a cause to gravity.I. Newton, Principia, p.
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From a pure formal mathematical point of view, the BIR is straightforward. From a practical point of view, however, several further problems should be solved that relate to algorithms and data structures, such as, for example, the choice of terms (manual or automatic selection or both), stemming, hash tables, inverted file structure, and so on.
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The mathematics of gambling are a collection of probability applications encountered in games of chance and can be included in game theory. From a mathematical point of view, the games of chance are experiments generating various types of aleatory events, the probability of which can be calculated by using the properties of probability on a finite space of events.
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Scalar potential of a point charge shortly after exiting a dipole magnet, moving left to right. A point charge is an idealized model of a particle which has an electric charge. A point charge is an electric charge at a mathematical point with no dimensions. The fundamental equation of electrostatics is Coulomb's law, which describes the electric force between two point charges.
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Institut des Risques Industriels, Assurantiels et Financiers (in English : Institute of Industrial, Insurantial and Financial Risk), or IRIAF, is a component of University of Poitiers. It is situated in Niort, France. The institute is composed of two faculties: Risk Management and Statistics for Health and Insurance. The two departments comply each other to provide a different approaches of risk management, from technical and mathematical point of views.
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A point source is a single identifiable localised source of something. A point source has negligible extent, distinguishing it from other source geometries. Sources are called point sources because in mathematical modeling, these sources can usually be approximated as a mathematical point to simplify analysis. The actual source need not be physically small, if its size is negligible relative to other length scales in the problem.
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Namely, in a mathematical point of view, if an electric field is applied to a superlattice the relevant Hamiltonian exhibits an additional scalar potential. If an eigenstate exists, then the states corresponding to wave functions are eigenstates of the Hamiltonian as well. These states are equally spaced both in energy and real space and form the so-called Wannier-Stark ladder. Stimulated emission of phonons.
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He finally settled on R. Buckminster Fuller. Fuller spent much of his youth on Bear Island, in Penobscot Bay off the coast of Maine. He attended Froebelian Kindergarten. He disagreed with the way geometry was taught in school, being unable to experience for himself that a chalk dot on the blackboard represented an "empty" mathematical point, or that a line could stretch off to infinity.
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From the mathematical point of view the Lippmann–Schwinger equation in coordinate representation is an integral equation of Fredholm type. It can be solved by discretization. Since it is equivalent to the differential time-independent Schrödinger equation with appropriate boundary conditions, it can also be solved by numerical methods for differential equations. In the case of the spherically symmetric potential V it is usually solved by partial wave analysis.
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Case fatality ratio is the comparison between two different case fatality rates, expressed as ratio. It is used to compare different diseases or to assess the impact of interventions. From a mathematical point of view, CFRs, which take values between 0 and 1 (or 0% and 100%, i.e., nothing and unity), are actually a measure of risk (case fatality risk)— that is, they are a proportion of incidence, although they don't reflect a disease's incidence.
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In 1870, he wrote a critical paper in the Nature journal entitled The Theory of Natural selection from a Mathematical Point of View. He argued that small random variations could not accumulate in any single direction as the incipient steps of a modification of an organ would be useless to the individual.Ellegård, Alvar. (1990). Darwin and the General Reader: The Reception of Darwin's Theory of Evolution in the British Periodical Press, 1859-1872.
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Light is fundamental to plant development as well as photosynthesis. Light, absorbed by phytochrome, cryptochrome, photopsin, and other photoreceptor pigments, acts as a signal for the germination of many seeds and spores, for the development of seedlings, and for the initiation of flowering. Light-mediated development is known as photomorphogenesis. The current model of light in terms of a mathematical point-like photon or an infinite plane wave is not helpful in understanding how light influences plant development.
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241 It has many implications in various areas of network studies. For instance, in social network, one can ruminate how fast a rumor (or a contagious disease) is spread in a community. From a mathematical point of view, since path lengths in networks are typically scale as log n (where n = number of network vertices), it is only logical it remains a small number even with large complex networks. :Another idea comes along with the small-world effect is called funneling.
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However, fluid dynamics literature often refers to the full set – including the energy equation – of the more general compressible equations together as "the Euler equations". From the mathematical point of view, Euler equations are notably hyperbolic conservation equations in the case without external field (i.e., in the limit of high Froude number). In fact, like any Cauchy equation, the Euler equations originally formulated in convective form (also called "Lagrangian form") can also be put in the "conservation form" (also called "Eulerian form").
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Thus, repeated addition extends to the whole numbers (0, 1, 2, 3, 4, ...). The first challenge to the belief that multiplication is repeated addition appears when students start working with fractions. From the mathematical point of view, multiplication as repeated addition can be extended into fractions. For example, : 7/4 \times 5/6 literally calls for “one and three-fourths of the five-sixths.” This is later significant because students are taught that, in word problems, the word “of” usually indicates a multiplication.
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A midpoint is a mathematical point halfway between two stellar bodies that tells an interpretative picture for the individual. There are two types of midpoints: direct and indirect. A direct midpoint occurs when a stellar body makes an aspect to the midpoint of two other stellar bodies with an actual physical body at the halfway point. In other words, a direct midpoint means that there is actually a stellar body in the natal chart lying in the midpoint of two other stellar bodies.
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Emmy Noether (1882-1935) was an influential mathematician known for her groundbreaking contributions to abstract algebra and theoretical physics. The conservation of energy is a common feature in many physical theories. From a mathematical point of view it is understood as a consequence of Noether's theorem, developed by Emmy Noether in 1915 and first published in 1918. The theorem states every continuous symmetry of a physical theory has an associated conserved quantity; if the theory's symmetry is time invariance then the conserved quantity is called "energy".
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Emmy Noether (1882-1935) was an influential mathematician known for her groundbreaking contributions to abstract algebra and theoretical physics. The conservation of momentum is a common feature in many physical theories. From a mathematical point of view it is understood as a consequence of Noether's theorem, developed by Emmy Noether in 1915 and first published in 1918. The theorem states every continuous symmetry of a physical theory has an associated conserved quantity; if the theory's symmetry is space invariance then the conserved quantity is called "momentum".
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Consider that at the beginning all the particles are in one of the containers. It is expected that over time the number of particles in this container will approach N/2 and stabilize near that state (containers will have approximately the same number of particles). However from mathematical point of view, going back to the initial state is possible (even almost sure). From mean recurrence theorem follows that even the expected time to going back to the initial state is finite, and it is 2^N.
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The Dirac delta function was boldly defined by Paul Dirac (an aspect of his scientific formalism); this was to treat measures, thought of as densities (such as charge density) like genuine functions. Sergei Sobolev, working in partial differential equation theory, defined the first adequate theory of generalized functions, from the mathematical point of view, in order to work with weak solutions of partial differential equations.Kolmogorov, A. N., Fomin, S. V., & Fomin, S. V. (1999). Elements of the theory of functions and functional analysis (Vol. 1).
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Yau and Nadis 2010, p. 168 In physics, mirror symmetry is justified on physical grounds.Hori and Vafa 2000 However, mathematicians generally require rigorous proofs that do not require an appeal to physical intuition. From a mathematical point of view, the version of mirror symmetry described above is still only a conjecture, but there is another version of mirror symmetry in the context of topological string theory, a simplified version of string theory introduced by Edward Witten,Witten 1990 which has been rigorously proven by mathematicians.
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2 for a non-anomalous point and Fig. 3 for a point that's more likely to be an anomaly. It is apparent from the pictures how anomalies require fewer random partitions to be isolated, compared to normal points. From a mathematical point of view, recursive partitioning can be represented by a tree structure named Isolation Tree, while the number of partitions required to isolate a point can be interpreted as the length of the path, within the tree, to reach a terminating node starting from the root.
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For the second- order type II APLL the conjecture is valid,. From a mathematical point of view, that means that the loss of global stability in type II APLL is caused by the birth of self-excited oscillations and not hidden oscillations (i.e., the boundary of global stability and the pull-in range in the space of parameters is trivial). A similar statement for the second-order APLL with lead-lag filter is known as Kapranov's conjecture on the pull-in range of type I APLL.
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The Dickinson System was a mathematical point formula that awarded national championships in college football. Devised by University of Illinois economics professor Frank G. Dickinson, the system crowned national champions from 1926 to 1940, and included predated rankings for 1924 and 1925. The system was originally designed to rank teams in the Big Nine (later the Big Ten) conference. Chicago clothing manufacturer Jack Rissman then persuaded Dickinson to rank the nation's teams under the system, and awarded the Rissman Trophy to the winning university.
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From a mathematical point of view, the phases are merely regions in which the solutions of the underlying PDE are continuous and differentiable up to the order of the PDE. In physical problems such solutions represent properties of the medium for each phase. The moving boundaries (or interfaces) are infinitesimally thin surfaces that separate adjacent phases; therefore, the solutions of the underlying PDE and its derivatives may suffer discontinuities across interfaces. The underlying PDEs are not valid at the phase change interfaces; therefore, an additional condition—the Stefan condition—is needed to obtain closure.
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From the mathematical point of view, the object corresponds to a function and the problem posed is to reconstruct this function from its integrals or sums over subsets of its domain. In general, the tomographic inversion problem may be continuous or discrete. In continuous tomography both the domain and the range of the function are continuous and line integrals are used. In discrete tomography the domain of the function may be either discrete or continuous, and the range of the function is a finite set of real, usually nonnegative numbers.
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The model layer is used to monitor a system and to evaluate if the actions are correct, while the control layer determines the actions and brings the system into a goal state. Typical techniques to implement a model are declarative programming languages like Prolog and Golog. From a mathematical point of view, a declarative model has much in common with the situation calculus as a logical formalization for describing a system. From a more practical perspective, a declarative model means, that the system is simulated with a game engine.
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However, Eörs Szathmáry and Irina Gladkih showed that an unconditional coexistence can be obtained even in the case of a non-enzymatic template replication that leads to a subexponential or a parabolic growth. This could be observed during the stages preceding a catalytic replication that are necessary for the formation of hypercycles. The coexistence of various non- enzymatically replicating sequences could help to maintain a sufficient diversity of RNA modules used later to build molecules with catalytic functions. From the mathematical point of view, it is possible to find conditions required for cooperation of several hypercycles.
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The formal definition of proper time involves describing the path through spacetime that represents a clock, observer, or test particle, and the metric structure of that spacetime. Proper time is the pseudo-Riemannian arc length of world lines in four- dimensional spacetime. From the mathematical point of view, coordinate time is assumed to be predefined and we require an expression for proper time as a function of coordinate time. From the experimental point of view, proper time is what is measured experimentally and then coordinate time is calculated from the proper time of some inertial clocks.
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The physical paradox was mathematically resolved in the 1990s by David E. Stewart. The Painlevé paradox has not only been solved by D. E. Stewart from the mathematical point of view (i.e. Stewart has shown the existence of solutions for the classical Painlevé example that consists of a rod sliding on a rough plane in 2-dimension), but it has been explained from a more mechanical point of view by Franck Génot and Bernard Brogliato. Génot and Brogliato have studied in great detail the rod dynamics in the neighborhood of a singular point of the phase space, when the rod is sliding.
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Beside the above-mentioned views on computer vision, many of the related research topics can also be studied from a purely mathematical point of view. For example, many methods in computer vision are based on statistics, optimization or geometry. Finally, a significant part of the field is devoted to the implementation aspect of computer vision; how existing methods can be realized in various combinations of software and hardware, or how these methods can be modified in order to gain processing speed without losing too much performance. Computer vision is also used in fashion ecommerce, inventory management, patent search, furniture, and the beauty industry.
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From a mathematical point of view, a function of n arguments can always be considered as a function of one single argument which is an element of some product space. However, it may be convenient for notation to consider n-ary functions, as for example multilinear maps (which are not linear maps on the product space, if ). The same is true for programming languages, where functions taking several arguments could always be defined as functions taking a single argument of some composite type such as a tuple, or in languages with higher-order functions, by currying.
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These extrema are found by moving the probe back and forth along the line and the level at that point can then be measured on the meter.Gupta, pages 113–114 The extrema are not of any great interest in themselves, but are used in the calculation of several more useful parameters. Some of these parameters require the measurement of the exact position of the extremum. Either maxima or minima can equally be used, from a mathematical point of view, but minima are preferred because they are always much sharper than maxima, especially for large reflections, as shown in figure 4.
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As a main-sequence star increases in size during its evolution, it may at some point exceed its Roche lobe, meaning that some of its matter ventures into a region where the gravitational pull of its companion star is larger than its own. The result is that matter will transfer from one star to another through a process known as Roche lobe overflow (RLOF), either being absorbed by direct impact or through an accretion disc. The mathematical point through which this transfer happens is called the first Lagrangian point."Contact Binary Star Envelopes" by Jeff Bryant, Wolfram Demonstrations Project.
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M. Kruskal introduced the special term asymptotology, defined above, and called for a formalization of the accumulated experience to convert the art of asymptotology to a science. A general term is capable of possessing significant heuristic value. In his essay "The Future of Mathematics",The Future of Mathematics H. Poincaré wrote the following. In addition, “the success of ‘cybernetics’, ‘attractors’ and ‘catastrophe theory’ illustrates the fruitfulness of word creation as scientific research”.Arnol’d, V.I. (1994), "Basic concepts", Dynamical Systems V (editor--Arnol’d, V.I.), Springer, 207-215 Almost every physical theory, formulated in the most general manner, is rather difficult from a mathematical point of view.
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From mathematical point of view ligand docking represents a search for global minimum on the multidimensional surface describing the free energy of protein-ligand binding. With ligands having up to 15-20 degrees of freedom (freely rotatable bonds) and complex nature of energy surface, global optimum search represents generally unsolved scientific task. To tackle this computationally challenging problem Lead-Finder applies unique approach combining genetic algorithm search, local optimization procedures, and a smart exploitation of the knowledge generated during the search run. Rational combination of different optimization strategies makes Lead Finder efficient in terms of coarse sampling of ligand's phase space and refinement of promising solutions.
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His reasoning followed from the fact that a node is not a mathematical point but a physical point. If a violin string is stopped below halfway, the frequency of the bowed fraction is more than twice the frequency of its base note. Carrillo later extended his work on musical physics (the node law and harmonic law) in Dos leyes de física musical (Two laws of musical physics, Mexico City, 1956)In 1949, the first metamorphoser piano was made for third-tones and Carrillo brought it to the Paris Musical Conservatory the next year. In France, he met Jean-Étienne Marie, who spread Carrillo's theories in Europe.
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Like Poincaré, Einstein concluded in 1906 that the inertia of electromagnetic energy is a necessary condition for the center-of-mass theorem to hold. On this occasion, Einstein referred to Poincaré's 1900 paper and wrote: In Einstein's more physical, as opposed to formal or mathematical, point of view, there was no need for fictitious masses. He could avoid the perpetuum mobile problem because, on the basis of the mass–energy equivalence, he could show that the transport of inertia that accompanies the emission and absorption of radiation solves the problem. Poincaré's rejection of the principle of action–reaction can be avoided through Einstein's , because mass conservation appears as a special case of the energy conservation law.
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When developing quantum electrodynamics in the 1940s, Shin'ichiro Tomonaga, Julian Schwinger, Richard Feynman, and Freeman Dyson discovered that, in perturbative calculations, problems with divergent integrals abounded. The divergences appeared in calculations involving Feynman diagrams with closed loops of virtual particles. It is an important observation that in perturbative quantum field theory, time-ordered products of distributions arise in a natural way and may lead to ultraviolet divergences in the corresponding calculations. From the mathematical point of view, the problem of divergences is rooted in the fact that the theory of distributions is a purely linear theory, in the sense that the product of two distributions cannot consistently be defined (in general), as was proved by Laurent Schwartz in the 1950s.
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Solving the geodesic problem for an ellipsoid of revolution is, from the mathematical point of view, relatively simple: because of symmetry, geodesics have a constant of motion, given by Clairaut's relation allowing the problem to be reduced to quadrature. By the early 19th century (with the work of Legendre, Oriani, Bessel, et al.), there was a complete understanding of the properties of geodesics on an ellipsoid of revolution. On the other hand, geodesics on a triaxial ellipsoid (with three unequal axes) have no obvious constant of the motion and thus represented a challenging unsolved problem in the first half of the 19th century. In a remarkable paper, discovered a constant of the motion allowing this problem to be reduced to quadrature also .
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Just as with Bresenham's line algorithm, this algorithm can be optimized for integer-based math. Because of symmetry, if an algorithm can be found that only computes the pixels for one octant, the pixels can be reflected to get the whole circle. We start by defining the radius error as the difference between the exact representation of the circle and the center point of each pixel (or any other arbitrary mathematical point on the pixel, so long as it's consistent across all pixels). For any pixel with a center at (x_i, y_i), the radius error is defined as: :RE(x_i,y_i) = \left\vert x_i^2 + y_i^2 - r^2 \right\vert For clarity, this formula for a circle is derived at the origin, but the algorithm can be modified for any location.
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By virtue of the linearity property of optical non-coherent imaging systems, i.e., : Image(Object1 \+ Object2) = Image(Object1) + Image(Object2) the image of an object in a microscope or telescope can be computed by expressing the object-plane field as a weighted sum over 2D impulse functions, and then expressing the image plane field as the weighted sum over the images of these impulse functions. This is known as the superposition principle, valid for linear systems. The images of the individual object-plane impulse functions are called point spread functions, reflecting the fact that a mathematical point of light in the object plane is spread out to form a finite area in the image plane (in some branches of mathematics and physics, these might be referred to as Green's functions or impulse response functions).
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Subtraction is a type of analysis called ordinal analysis > ...let space be now regarded as the field of progression which is to be > studied, and POINTS as states of that progression. ...I am led to regard the > word "Minus," or the mark −, in geometry, as the sign or characteristic of > analysis of one geometric position (in space), as compared with another > (such) position. The comparison of one mathematical point with another with > a view to the determination of what may be called their ordinal relation, or > their relative position in space... The first example of subtraction is to take the point A to represent the earth, and the point B to represent the sun, then an arrow drawn from A to B represents the act of moving or vection from A to B. ::B − A this represents the first example in Hamilton's lectures of a vector. In this case the act of traveling from the earth to the moon.
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In Hindu astrology, Varshaphala (annual horoscopes) or the Progressed Horoscopes are cast according to the Tajika System propounded by Kesava and Neelakantha, which enables the astrologer to forecast events of immediate importance. The Lagna or ascendant of an annual horoscope is cast for the moment the Sun, after making a full round of twelve rasis or zodiacal signs, returns to the same position it occupied at the time of one’s birth. Muntha, which is an imaginary mathematical point, has an important role in this method of prognostication. Muntha is the progressed ascendant that travels one Rasi or Sign per year beginning from the birth-ascendant at birth. It is found by adding the number (number denoting the particular sign) of the ascendant at the time of birth to the number of the years elapsed between birth and the year for which Progressed Annual Horoscope is cast, dividing the sum by 12 and rejecting the quotient.
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In physics, a front can be understood as an interface between two different possible states (either stable or unstable) in a physical system. For example, a weather front is the interface between two different density masses of air, in combustion where the flame is the interface between burned and unburned material or in population dynamics where the front is the interface between populated and unpopulated places. Fronts can be static or mobile depending on the conditions of the system, and the causes of the motion can be the variation of a free energy, where the most energetically favorable state invades the less favorable one, according to Pomeau or shape induced motion due to non-variation dynamics in the system, according to Alvarez-Socorro, Clerc, González-Cortés and Wilson. From a mathematical point of view, fronts are solutions of spatially extended systems connecting two steady states, and from dynamical systems point of view, a front corresponds to a heteroclinic orbit of the system in the co-mobile frame (or proper frame).
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