Solving this differential equation yields an infinite set of functions, of which the Gaussian beam is the lowest-order solution or mode.

Defocus is the lowest-order true optical aberration.

For the case of Bragg reflection only the lowest-order reflection is allowed if the light is incident along the helical axis, whereas for oblique incidence higher-order reflections become permitted.

Since the lowest-order term observed in magnetic sources is the dipolar term, it dominates at large distances.

If the lowest-order non-zero derivative is of even order, the point is not a point of inflection.

The mass quadrupole, however, can change in time, and is the lowest-order contribution to gravitational radiation.

is obviously zero, the lowest-order MP correlation energy appears in second order.

It nevertheless is worthwhile to formalize the procedure because it yields the lowest-order approximation for scaling and essential input for the renormalization group.

In this technique, the square cells are not subdivided diagonally ; only the lowest-order digit is written in each cell, while any higher-order digit must be remembered or recorded elsewhere and then " carried ” to be added to the next cell.

Post-Newtonian formalism is a calculational tool that expresses Einstein's ( nonlinear ) equations of gravity in terms of the lowest-order deviations from Newton's law of universal gravitation.

For small the lowest-order approximation may be found by inserting the ansatz

:< ref > The lowest-order term in the energy can be written in more than one way because, by definition, .</ ref >

For both families, the lowest-order solution describes a Gaussian beam, while higher-order solutions describe higher-order transverse modes in an optical resonator.

Willcocks in 1946 and has 24 squares ; however, it was not until 1982 that Duijvestijn, Pasquale Joseph Federico and P. Leeuw mathematically proved it to be the lowest-order example.

Because there is no protection or privilege limitation in real mode, even if a segment could be defined to be smaller than 64 KiB, it would still be entirely up to the programs to coordinate and keep within the bounds of their segments, as any program can always access any memory ( since it can arbitrarily set segment selectors to change segment addresses with absolutely no supervision ).

But there is reason in all things, and in this country the heathenish cult of the motor-car is exceeding all bounds in its demands.

But by comparison with the railroad, the motor car is a relatively new object of popular worship, so it is too much to hope that it may be brought within the bounds of civilized usage quickly and easily.

insufficient and that reporting confidence bounds is preferred.

This is usually defined as a decision outside the bounds of reasonableness.

He called this new policy novæ institutiones in his deeds, and he declared that " Nothing can set bounds to generosity of the Royal Majesty, and the best measure of grants, for a monarch, is immeasurableness ".

A key point which is often overlooked is that published lower bounds for problems are often given for a model of computation that is more restricted than the set of operations that you could use in practice and therefore there are algorithms that are faster than what would naively be thought possible.

Because of this, each of the infinitely many antiderivatives of a given function f is sometimes called the " general integral " or " indefinite integral " of f and is written using the integral symbol with no bounds:

Similarly if the jack is knocked into the ditch it is still alive unless it is out of bounds to the side resulting in a " dead " end which is replayed, though according to international rules the jack is " respotted " to the centre of the rink and the end is continued.

A succinct data structure is one which takes the absolute minimum possible space, as established by information theoretical lower bounds.

The next occurrence of the Bodmin Hurl will be following the next beating of the bounds, which is unlikely to take place until 2015.

Historically, allegations of cannibalism were used by the colonial powers to justify the enslavement of what were seen as primitive peoples ; cannibalism has been said to test the bounds of cultural relativism as it challenges anthropologists " to define what is or is not beyond the pale of acceptable human behavior ".

If a fumbled ball goes out of bounds, the team whose player last touched it is awarded possession at the spot where it went out of bounds.

Most courses define these areas as out of bounds or in bounds on tee signs at each hole, however, there is no universal standard for these.

However, George Macartney wrote in 1773, in the wake of the territorial expansion that followed Britain's victory in the Seven Years ' War, of " this vast empire on which the sun never sets, and whose bounds nature has not yet ascertained.

`` So that the man should not have thoughts of grandeur, and become lifted up, as if he had no lord, because of the dominion that had been given to him, and the freedom, fall into sin against God his Creator, overstepping his bounds, and take up an attitude of self-conceited arrogance towards God, a law was given him by God, that he might know that he had for lord the lord of all.

In summer, the inhabitants lose touch with the sea altogether: " for all its nearness, the sea was out of bounds ; young limbs had no longer the run of its delights.

The legal bounds of a badminton court during various stages of a rally for singles and doubles games.

Theoretically, exponential lower bounds have been proved for the DPLL family of algorithms.

Religious, historical and socio-cultural factors have helped define the bounds of endogamy for Muslims in some parts of Pakistan.

It did not catch on as did Dewey's system because Cutter died before it was completely finished, making no provision for the kind of development necessary as the bounds of knowledge expanded and scholarly emphases changed throughout the 20th century.

The rules do not permit a player to have a supporting point touching out of bounds on release so this is the reason for the relief.

If a player lands within a meter of the out of bounds and is in bounds, they are still granted this relief for the same reasoning.

Many of the high court officials construed Emperor Yōzei's actions as exceeding the bounds of acceptable behavior, and as justifiable cause for the emperor to be forcibly deposed.

In terms of content, enforcement of the Production Code ensured that no film character could literally get away with murder or be seen sharing a bed with anyone but a spouse ; within those bounds, however, many films now identified as noir feature plot elements and dialogue that were very risqué for the time.

Also for several decades alternatives to the scrimmage for playing the ball from across the sideline after it had gone out of bounds -- a throw-in or " fair ", and " bounding in " -- existed.

Therefore, as widely recognized, existing low-energy bounds cannot be applied to high-energy phenomena ; however, many searches for Lorentz violation at high energies have been carried out using the Standard-Model Extension.

In fact, the root mean square ( rms ) errors are much better than these upper bounds, being only O ( ε √ log N ) for Cooley – Tukey and O ( ε √ N ) for the naïve DFT ( Schatzman, 1996 ).

His esteem for Maimonides knew no bounds: he placed him next to the Prophets, and he exhibited little patience with Maimonides ' critics and detractors.

Since the beginning of modern philosophy during the seventeenth century, problems that were not originally considered within the bounds of metaphysics have been added to its purview, while other problems considered metaphysical for centuries are now typically subjects of their own separate regions in philosophy, such as philosophy of religion, philosophy of mind, philosophy of perception, philosophy of language, and philosophy of science.

Burger noted that, " current standards for the ethical treatment of participants clearly place Milgram ’ s studies out of bounds.

One of Mage's highlights is its system for describing magic, based on spheres, a relatively open-ended ' toolkit ' approach to using game mechanics to define the bounds of a given character's magical ability.