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These equations arise from applying Newton's second law to fluid motion, together with the assumption that the fluid stress is the sum of a diffusing viscous term ( proportional to the gradient of velocity ) and a pressure term.
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These and equations
These assumptions and the resulting forms of the momentum equations are outlined below.
These range from simplified forms of the first-principles equations that are easier or faster to solve, to approximations limiting the size of the system ( for example, periodic boundary conditions ), to fundamental approximations to the underlying equations that are required to achieve any solution to them at all.
These two equations can be differentiated and combined in various ways to produce the following data:
These equations of state were also previously published by the Soviet physicist Yakov Frenkel in 1928, together with some other remarks on the physics of degenerate matter.
These equations can be used as the starting point in the analysis of a flexible chain acting under any external force.
These equations express mathematically that, in the case of an object that moves along a circular path with a changing speed, the acceleration of the body may be decomposed into a perpendicular component that changes the direction of motion ( the centripetal acceleration ), and a parallel, or tangential component, that changes the speed.
These equations are usually combined into a single equation
These texts deal with solving algebraic equations, many of which are now lost.
These interactions are described by Maxwell's equations and the Lorentz force law.
These equations are derived from Maxwell's equations.
These equations specify how the geometry of space and time is influenced by whatever matter is present, and form the core of Einstein's general theory of relativity.
These equations are often referred to as the " equations of the straight line.
These equations are notoriously difficult to solve, but in many instances approximations suffice for a good description of lifting airfoils.
These equations are valid for all types of ( one-dimensional ) linear prediction.
These types of integrals seem first to have attracted Laplace's attention in 1782 where he was following in the spirit of Euler in using the integrals themselves as solutions of equations.
These same interpolation formulas nevertheless continue to be used as part of the software algorithms for solving differential equations.
These equations explain quantitatively how quarks can bind together into protons and neutrons ( and all the other hadrons ).
These may be combined into so-called coupled equations, of which the strain-charge form is:
These equations of motion are then supplemented by commutation relations derived from the canonical quantization procedure described below, thereby incorporating quantum mechanical effects into the behavior of the field.
These observations corroborated Alexander Friedman's 1922 work, in which he derived the famous Friedmann equations.
These equations demonstrate that the simple harmonic motion is isochronous ( the period and frequency are independent of the amplitude and the initial phase of the motion ).
These equations were verified by experiment by Heinrich Hertz in 1887, and the wave theory became widely accepted.
These and arise
These problems frequently arise where a firm is making items for the Government not directly along the lines of its normal civilian business or where the Government specifications require operations that the firm did not understand when it undertook the contract.
These are very closely related to intrinsic pathway, and tumors arise more frequently through intrinsic pathway than the extrinsic pathway because of sensitivity.
These two invasions caused English to become " mixed " to some degree ( though it was never a truly mixed language in the strictest sense of the word ; mixed languages arise from the cohabitation of speakers of different languages, who develop a hybrid tongue for basic communication ).
These numbers also arise in combinatorics, where gives the number of different combinations of b elements that can be chosen from an n-element set.
These " extras " to the basic systematic search have been empirically shown to be essential for handling the large SAT instances that arise in electronic design automation ( EDA ).
These forces arise from the presence of the body in force fields, e. g. gravitational field ( gravitational forces ) or electromagnetic field ( electromagnetic forces ), or from inertial forces when bodies are in motion.
These are supported by small bundles of microtubules that arise near a point on the nuclear membrane.
These seizures arise from the frontal lobes and consist of complex motor movements, such as hand clenching, arm raising / lowering, and knee bending.
These arise from a basal body or kinetosome, with microtubule roots that are an important part of the cell's brain.
These tasks arise from the forthcoming final struggle of two opposing political systems.
These traits arise from the interaction of its genotype with the environment.
These islands arise from volcanoes where the subduction of one plate under another is occurring.
These can arise via incomplete splicing, V ( D ) J recombination in the adaptive immune system, mutations in DNA, transcription errors, leaky scanning by the ribosome causing a frame shift, and other causes.
These blue stragglers are also observed in globular clusters, and in the very dense cores of globulars they are believed to arise when stars collide, forming a much hotter, more massive star.
These ambiguities can arise from the intentional use and abuse of homophonic, homographic, metonymic, or metaphorical language.
These preferences may arise when an arbitrary female preference for some aspect of male morphology — initially, perhaps, a result of genetic drift — creates, in due course, selection for males with the appropriate ornament.
* Inconsistency: These are logical contradictions which will inevitably arise during the development of large ontologies, and when ontologies from separate sources are combined.
These usually arise as a result of some sort of special relationship between the parties.
These so-called " hotspots ", for example Hawaii, are postulated to arise from upwelling diapirs with magma from the core – mantle boundary, 3, 000 km deep in the Earth.
These secondary peaks, not to be confused with high energy satellites which are discussed later, arise from the presence of the same element in multiple different chemical states on a surface ( i. e. Adsorbate layers ) or from relaxation transitions involving valence band electrons of the substrate.
These problems do not arise if the bubble velocity is kept subluminal, but it is still necessary to provide exotic matter for the drive to work.
These questions arise: ( a ) How federal and non-federal countries are different with respect to ' fiscal federalism ' or ' fiscal decentralization ' and ( b ): How fiscal federalism and fiscal decentralization are related ( similar or different )?
These other types of patterns that may arise are reflected in the different types of stochastic convergence that have been studied.
# Occupation: These could arise from both official positions, as in the case of Sima ( 司马 / 司馬 ), originally akin to " Minister of War ".
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