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 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 recommendations vary by the type of device, and specify tests for safety and efficacy.

These spurious dogs floated about the astronomical literature until Hevelius decided to specify their presence in the sky by making them a separate constellation in 1687.

( See Browser wars ) These included extensions to control stylistic aspects of documents, contrary to the " belief the academic engineering community that such things as text color, background texture, font size and font face were definitely outside the scope of a language when their only intent was to specify how a document would be organized.

These procedures specify how an IFR pilot should respond, even in the event of a complete radio failure, and loss of communications with ATC, including the expected aircraft course and altitude.

These rules specify that kilts are to be worn ( except that in the national dances, the female competitors will be wearing the Aboyne dress ).

These standards specify the familiar formats for text email headers and body and rules pertaining to commonly used header fields such as " To :", " Subject :", " From :", and " Date :".

These are roughly comparable to IP addresses used in the Internet Protocol ; they can specify a piece of equipment connected to an Asynchronous Transfer Mode ( ATM ) network.

These included Muslim sailors being " paid a fixed wage " in advance " with an understanding that they would owe money in the event of desertion or malfeasance, in keeping with Islamic conventions " in which contracts should specify " a known fee for a known duration ", in contrast to Roman and Byzantine sailors who were " stakeholders in a maritime venture, in as much as captain and crew, with few exceptions, were paid proportional divisions of a sea venture's profit, with shares allotted by rank, only after a voyage's successful conclusion.

These included Muslim sailors being paid a fixed wage " in advance " with an understanding that they would owe money in the event of desertion or malfeasance, in keeping with Islamic conventions in which contracts should specify " a known fee for a known duration.

These actions are determined by programmed routines that specify the direction, acceleration, velocity, deceleration, and distance of a series of coordinated motions.

These passages do not specify tying particular types or numbers of knots in the fringes.

These types of misunderstandings and unrealistic expectations are usually avoided through the use of detailed critical path schedules, which specify the work, and timetable to be used, but most importantly, the logical sequence of events which must occur for a project to be completed.

These jurisdictions also usually specify that only pharmacists may supply scheduled pharmaceuticals to the public, and that pharmacists cannot form business partnerships with physicians or give them " kickback " payments.

These may be compounded with other verbs that further specify the direction, such as 上去 ( shàng qù, to ascend ), 过来 ( gùo lái, to come over ), which may then be themselves affixed to a verb ( such as 走过去, zǒu gùo qù, to walk over ).

These scientific requirements are then transformed into mission concepts that start to specify the kind of spacecraft and scientific instruments need to be developed for these scientific questions to be answered.

These observations serve to characterize eruptive behavior, identify the nature of precursory activity leading to eruption, define the processes by which different types of deposits are emplaced, and specify the hazards that could be unleashed by each kind of eruption.

These datatypes can be used to describe interfaces to existing libraries without having to specify the language ( such as Fortran or C ).

These editing programs allow artists to have instant feedback on how a particle system will look with properties and constraints that they specify.

These Bilateral Air Transport Agreements similar to the Bermuda I and Bermuda II agreements specify rights awardable only to locally registered airlines, forcing some governments to jump-start airlines to avoid being disadvantaged in the face of foreign competition.

These orders usually specify a period of time for the recipient of the order to request a hearing.

These specify the complete and unique quantum state of a single electron in an atom, and make up its wavefunction or orbital.

These options specify parameters such as the resolution of the scan, the scan area, colour model, etc.

These allow the format to specify a string of text in a separate window that can be selected by the user.

These two lengths completely specify the shape of the ellipsoid but in practice geodesy publications classify reference ellipsoids by giving the semi-major axis and the inverse flattening, 1 / f, The flattening, f, is simply a measure of how much the symmetry axis is compressed relative to the equatorial radius: