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 regions are presented to the attacking animal and their secretions may be foul-tasting or cause various physical or neurological symptoms.

These antigens can sometimes be presented by tumor cells and never by the normal ones.

These interpretations have been denied by company officials, and no evidence linking the company to any occult organization has ever been presented.

These charges have typically been presented as limited time offers exclusively for billionaires.

These are basically a subset of those found in the second half of E, but are presented here in a radically different order.

These new principles were presented in the Tamworth Manifesto which is considered by historians to be the basic statement of the beliefs of the new Conservative Party.

These last writings presented the fruits of his professional life.

These rehearsal-room or workshop activities evolved into an independent art form which can be presented or performed before an audience.

These " peers of the accused " are responsible for listening to a dispute, evaluating the evidence presented, deciding on the facts, and making a decision in accordance with the rules of law and their jury instructions.

These interpreters presented different virtual machines for COBOL, Fortran, etc.

These actions gained it enormous popularity among the Polish youth, who joined the movement, seeing it an alternative to the opposition style presented by the Solidarity, which they viewed as more stiff and boring.

These improvements were called SECAM II and SECAM III with the later being presented at the 1965 CCIR General Assembly in Vienna.

** These benthic and limnetic species even display their mating preferences when presented with sticklebacks from Japanese lakes ; that is, a Canadian benthic prefers a Japanese benthic over its close limnetic cousin from its own lake.

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 are usually attributed to bilaterally symmetrical worms, but the hypothesis presented here views animals derived from placuloids, and thus close relatives of Trichoplax adhaerens, to be the producers of the traces.

These temples, though greatly inferior to their gigantic neighbor, were still larger than that at Segesta, and even exceed the great temple of Neptune at Paestum ; so that the three, when standing, must have presented a spectacle unrivaled in antiquity.

These can be presented separately or together: biophilia, love for humanity and nature, and independence and freedom.

These were generally presented by John Quincy Adams, who as a member of Congress identified himself particularly with the struggle against any Congressional abridgment of the right of petition.

These reforms presented British Guiana's parties with an opportunity to participate in national elections and form a government, but maintained power in the hands of the British-appointed chief executive.

These logs were not available before President Johnson ’ s resolution was presented to Congress.

A statuette presented in gratitude to The Spectator, of an Aberdare miner, still sits in the editor ’ s office, bearing the inscription: " From the Townsfolk of Aberdare in Grateful Recognition: ' The Greatest of These is Love '".

These are descendants of those who chose to remain French when the then-ruling French establishment presented the people of Pondicherry with an option to either remain French or become Indians at the time of Pondicherry's transfer to India in 1954.

These are then presented to the project's cinematographer who achieves the director's vision.

These genealogies do not match the genealogy presented in 1 Chronicles ; various explanations have been suggested.

These arguments, which are presented in written form, and can range in length from dozens to hundreds of pages, are ironically known as " briefs ".