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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 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 express
These things both express and, at the same time, continue contributing to, their identity diffusion in an area that could have become a source of developing dignity and self-certainty.
These three express in divine Science the threefold, essential nature of the infinite.
These nonce orders all express the " speaking architecture " ( architecture parlante ) that was taught in the Paris courses, most explicitly by Étienne-Louis Boullée, in which sculptural details of classical architecture could be enlisted to speak symbolically, the better to express the purpose of the structure and enrich its visual meaning with specific appropriateness.
These minutes correspond to the Latin diei scrupulis, and used to express periods of planetary motions.
These words express the deep and respectable knowledge that Palaestrio has of the Latin language.
These outcomes occur because giving some passengers full express services means bypassing often large numbers of passengers at intermediate stations along the corridors.
These are quantities that express the local state of the system, besides the usual local thermodynamic variables ; in a sense such variables might be seen as expressing the ' memory ' of the materials.
These words must be factual yet entertaining as the Count states, “ then, it is necessary to arrange what is to be said or written in its logical order, and after that to express it well in words that, if I am not mistaken, should be appropriate, carefully chosen, clear and well formed, but above all that are still in popular use " ( Courtier 77 ).
These myths also express some hope that the idyllic state of affairs they describe is not irretrievably and irrevocably lost to mankind, that it can be regained in some way or other.
These words and terms were used because of their familiarity, but more so because in most cases there were no equivalent terms in the vernacular which could express the Jewish concepts or describe the objects of cultural significance.
These complications mean that there are three common ways to express a polynomial as an integer: the first two, which are mirror images in binary, are the constants found in code ; the third is the number found in Koopman's papers.
The path loss for the first ten kilometers may be 150 -- 190 dB ( Note: These values are very approximate and are given here only as an illustration of the range in which the numbers used to express the path loss values can eventually be, these are not definitive or binding figures -- the path loss may be very different for the same distance along two different paths and it can be different even along the same path if measured at different times.
These few words succinctly express the missionary nature of the Church ".
These cells express a-smooth muscle actin ( a-SMA ).
" These symbols express a self-view of the Prieneians as a maritime democracy aligned with Athens but located in Asia.
These demonstrate his attempt to express the tension between the static stone and the dynamic desires of the figures represented emerging into solidity from it.
These included express coach ( Transport Act 1980 ), British Telecom ( completed in 1984 ), privatisation of London bus services ( 1984 ), local bus services ( Transport Act 1985 ) and the railways ( 1993 ).
These cells are also known as CD4 < sup >+</ sup > T cells because they express the CD4 protein on their surface.
These cells are also known as CD8 < sup >+</ sup > T cells since they express the CD8 glycoprotein at their surface.
These self-antigens are expressed by thymic cortical epithelial cells that express Activation-Induced ( Cytidine ) Deaminase on both MHC molecules on the surface of cortical cells.
These, along with the similar British Rail Class 86 | Class 86 formed the backbone of express passenger services on the WCML from the 1970s until the 2000s.
These vehicles remained the mainstay of the WCML's express services until the early 2000s.
" These phrases express the idea that the totem always accompanies, belongs to, and stands behind one as a guide and warner of dangers.

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