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 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 constructions can convey shape, size, motion, location, movement, stative-descriptive, and / or handling information.

These arguments, and a discussion of the distinctions between absolute and relative time, space, place and motion, appear in a Scholium at the very beginning of Newton's work, The Mathematical Principles of Natural Philosophy ( 1687 ), which established the foundations of classical mechanics and introduced his law of universal gravitation, which yielded the first quantitatively adequate dynamical explanation of planetary motion.

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 results agree with those above for nonuniform circular motion.

These changes then automatically accounted for the constancy of the speed of light and all electromagnetic radiation, from the viewpoints of all observers — even those in relative motion.

These measurements can be considered as secondary realizations ( in a metrological sense ) of the primary definition of ET in terms of the solar motion, after a calibration of the mean motion of the Moon with respect to the mean motion of the Sun.

These were the key discoveries that made all non-live or non live-on-videotape narrative motion pictures and television possible — that shots ( in this case whole scenes since each shot is a complete scene ) can be photographed at widely different locations over a period of time ( hours, days or even months ) and combined into a narrative whole.

These first engines were used to power pumps and produced only reciprocating motion to move the pump rods at the bottom of the shaft.

These are like standard mazes except they use rules other than " don't cross the lines " to restrict motion.

These laws describe the relationship between the forces acting on a body and the motion of that body.

These machines are also used to lessen repetitive motion stress injuries to a dealer.

These verbs of motion or phrases can be taken as Plautine stage directions since no overt stage directions are apparent.

These deviations can then be computed based on the classical motion.

These springs keep the water moving in a constant circular motion, giving it little chance to freeze over.

These included a stock ticker, a mechanical vote recorder, a battery for an electric car, electrical power, recorded music and motion pictures.

The first studies of the electrophysiological properties of neurons in MT showed that a large portion of the cells were tuned to the speed and direction of moving visual stimuli These results suggested that MT played a significant role in the processing of visual motion.

These three white dwarfs, the first discovered, are the so-called classical white dwarfs .< sup >, p. 2 </ sup > Eventually, many faint white stars were found which had high proper motion, indicating that they could be suspected to be low-luminosity stars close to the Earth, and hence white dwarfs.

; Loop optimizations: These act on the statements which make up a loop, such as a for loop ( e. g., loop-invariant code motion ).

These are just another couple of characters to roll.

These men are not callous.

These things are important to almost all Persians and perhaps most important to the most ordinary.

These are traversed by another line of vaults, and thus rooms, arched on all four sides, are formed.

These songs ( practically all Persian music, for that matter ) are limited to a range of two octaves.

These are not, however, differences in federal structure.

These my grandmother left in their places ( they are still there, more persistent and longer-lived than the generations of man ) and planted others like them, that flourished without careful tending.

These are like the initial ways in which the world forces itself upon the self and thrusts the self into decision and choice.

These are suggestive of Selma Lagerlof.

These assumptions lead to an organization with one man at the top, six directly under him, six under each of these, and so on until there are six levels of personnel.

These ways are absolutely irreconcilable because they offer two different recipes for man's redemption from chaos.

These responses are explicable in terms of characteristics inherent in the crisis.

These discoveries are of present interest chiefly to the scientific community ; ;

These are personality factors ; ;

These are, if the research is done with subtlety and skill, researchable topics, but the research is missing.

These moments are historical events in the lives of individual authors with which the student of comparative literature must be frequently concerned.

These lives are in themselves outside of the moral order and are unburdened with moral responsibility.

These conceptions and the manner in which they were transposed into poetry or engendered by poetic form are intrinsic to western life from the time of Aeschylus to that of Shakespeare.

These biographical analogies are obvious, and far too much time has been spent speculating on their possible implications.

These women whose organization grew out of the old suffrage movement are dedicated to Thomas Jefferson's dictum that one must cherish the people's spirit but `` Keep alive their attention ''.

These are, of course, the same people whose support he has only now rejected to seek the independent vote.

These are New York, Pennsylvania, Michigan, Maryland, Missouri, New Jersey, Illinois and Minnesota.

These men are spenders.