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 were verified by experiment by Heinrich Hertz in 1887, and the wave theory became widely accepted.

These teeth show " primitive morphology and wear pattern " which demonstrate that A. kadabba is a distinct species from A. ramidus.

These organizations require a lawyer to demonstrate special training, experience and knowledge to ensure that the lawyer's recognition as a certified specialist is meaningful and reliable.

These glasses containing red dye demonstrate qualitative changes in concentration.

These experts demonstrate that education in the English language and a good command of it is vital to identify that doublespeak is employed.

These flutes demonstrate that a developed musical tradition existed from the earliest period of modern human presence in Europe.

These seemingly antithetical images combine to demonstrate the proximity of the known and the unknown worlds, the two worlds of Understanding and Imagination.

These concrete examples and others like them demonstrate the moral considerations that Israelis ... have been dealing with since the Palestinans proudly decided to use suicide murder as their primary weapon.

These publications demonstrate that oral history can contribute greatly to our understanding of many interesting fields in human lives and history itself, such as the motives behind the dissidents ' activities, the formation of opposition groups, communication between dissidents and state representatives and the emergence of ex-communist elites and their decision-making processes.

These results demonstrate that the presidential Ortega was the right which caused the change in the correlation of political forces in the country.

Recent research results also demonstrate that the small intestine and large intestine ( colon ) seem to be inefficient at absorbing vitamin K. These results are reinforced by human cohort studies, where a majority of the subjects showed inadequate vitamins K amounts in the body.

These cases demonstrate a paradox not in the sense that they demonstrate a logical contradiction, but in the sense that they demonstrate a counter-intuitive result that is provably true: the situations " there is a guest to every room " and " no more guests can be accommodated " are not equivalent when there are infinitely many rooms ( an analogous situation is presented in Cantor's diagonal proof ).

These experiments demonstrate that all objects fall at the same rate when friction ( including air resistance ) is negligible.

These early suburban villas, such as the one at Rome's Auditorium site or at Grottarossa in Rome, demonstrate the antiquity and heritage of the villa suburbana in Central Italy.

These regulated carriers, known as contract carriers, must demonstrate that they are " fit, willing and able " to provide service, according to standards enforced by the regulator.

These samplers were stitched more to demonstrate knowledge than to preserve skill.

These glosses demonstrate typical vocabulary differences between Classical Latin and Vulgar Latin in Gallo-Romance:

These missions were intended to demonstrate the claim of the Spanish Empire to what is now modern-day California.

These Acts sought to demonstrate that establishing royal jurisdiction over the Church would ensure progress in " religious reformation " where papal authority had been insufficient.

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 organizations continue to demonstrate and teach various ways of shaping stone tools.

These things, Perry said, demonstrate " just how much the world has changed, just how much our security has changed, just how much the Department of Defense has changed, and just how much my job has changed.

These devices would have been limited in their effectiveness and could only serve to demonstrate a principle.