In order theory, the famous Suslin problem asks whether every linear continuum satisfying the countable chain condition that has no maximum or minimum element is necessarily order-isomorphic to.

For example, from elementary calculus, we know that a necessary condition for a local minimum or a maximum of a differentiable function is a vanishing first derivative ( that is, the first derivative is becoming zero ).

One implication is that the condition number is 1 ( which is the minimum ), so errors are not magnified when multiplying with an orthogonal matrix.

The SoS includes the definition of a minimum condition grade, which is established by considering the consequences of a failure of the infrastructure asset.

** Establishment of a minimum condition grade

It is possible to determine a minimum energy condition which is the minimum energy density that a region with a given emissivity can have, but for many years there was no particular reason to believe that the true energies were anywhere near the minimum energies.

At the end of his term as Governor, having now met the condition on a minimum of ten years between elections as consul, the Senate ordered he resign command of his army.

* A deficiency in construction, an item, or condition that is considered sub-standard, or below minimum expectations

In April 2010 a judge released Castillo from probation " on the condition that he leave the United States and not return for a minimum of three years.

The optimal control can be derived using Pontryagin's maximum principle ( a necessary condition also known as Pontryagin's minimum principle or simply Pontryagin's Principle ), or by solving the Hamilton-Jacobi-Bellman equation ( a sufficient condition ).

A sufficient condition for a local minimum is that all of these minors have the sign of (– 1 )< sup > m </ sup >.

This condition cannot be effectively corrected through diet and exercise alone, as the panniculus consists of adipocytes and other supporting cell types shrunken to their minimum volume and diameter.

Unless interrupted by weather, Craftsman Truck Series races had to end under green flag conditions, and the rule mandated that all races must end with a minimum of two consecutive laps in green flag condition, often referred to as a " green-white-checkered " finish.

The relation between the two is by a Legendre transform, and the condition that determines the classical equations is that the Action is a minimum.

At the " throat ", where the cross sectional area is a minimum, the gas velocity locally becomes sonic ( Mach number = 1. 0 ), a condition called choked flow.

It may be shown that the Legendre transformation changes the maximum condition of the entropy ( valid at equilibrium ) in a minimum condition of the extended Massieu function for stationary states, no matter whether at equilibrium or not.

The definition of Artinian rings may be restated by interchanging the descending chain condition with an equivalent notion: the minimum condition.

The condition number for the problem of finding the eigenspace of a normal matrix corresponding to an eigenvalue has been shown to be inversely proportional to the minimum distance between and the other distinct eigenvalues of.

After that, it requires several minutes of concentrated work, including six separate and deliberate actions by a minimum of three men sitting at three separate stations in a bomber, each with another man beside him to help, for an armed bomb to be released.

It includes a raise in the county minimum wage, creation of several new jobs at the executive level, financing of beefed-up industrial development efforts, and increased expenditures for essential services such as health and welfare, fire protection, sanitation and road maintenance.

Then Goodbody will hand over a minimum of $15.5 million for developing the spacious Graves Tract to house the center.

The Act further provides for a `` floor '' or minimum allotment, set at the 1954 level, which is called the `` base '' allotment, and a `` ceiling '' or maximum allotment, for each State.

( Each State's unadjusted allotment for any fiscal year, which exceeds its minimum allotment described in item 13 below by a percentage greater than one and one-half times the percentage by which the sum being allotted exceeds $23,000,000, must be reduced by the amount of the excess.

For the States which maintain two separate agencies -- one for the vocational rehabilitation of the blind, and one for the rehabilitation of persons other than the blind -- the Act specifies that their minimum ( base ) allotment shall be divided between the two agencies in the same proportion as it was divided in fiscal year 1954.

Prior to 1960, in order to provide matching for the minimum ( base ) allotment, State funds had to equal 1954 State funds.

Beginning in 1960, the matching requirements for the base allotment are being adjusted ( upward or downward, as required ) 25% a year, so that by 1963 the entire support allotment will be matched on the basis of a 40% pivot State share, with maximum and minimum State shares of 50% and 30%, respectively.

Wall panels and structural timbers are standard as are windows and doors, making for a minimum of cutting.

Fortunately, it is the FHA which has arrived at this conclusion, for it means that cooling equipment of all kinds may now be included in a mortgage, and thus acquired with a minimum of financial stress.

The minimum cost for an average one-story, 7-room house with basement, is likely to run $1500 above the cost of the heating alone.

Acreage in excess of the minimum is good practice as recreation areas are never too large for the future and it is often more economical to operate one large area than several small ones.

Advances in equipment and fabrication techniques give the sign or display manufacturer an extremely wide choice of production techniques, ranging from injection molding for intricate, smaller-size, mass-production signs ( generally 5000 units is the minimum ) to vacuum and pressure forming for larger signs of limited runs.

This is interesting for it combines both the thermodynamic concept of a minimum Gibbs function for equilibrium and minimum mechanical potential energy for equilibrium.

When we look at countries like Iran, Iraq, Pakistan, and Burma, where substantial progress has been made in creating a minimum supply of modern men and of social overhead capital, and where institutions of centralized government exist, we find a second category of countries with a different set of problems and hence different priorities for policy.

Even if we strip their respective claims to the barest minimum, the `` odds '' still favor them both, for the trend in effect is always more likely to continue than to reverse.

These minimum costs may come to $1 per month, more or less, for residential and small commercial customers, although they are substantially higher for large industrial users, who require more costly connections and metering devices.

In seed plants, the gametophyte is even more reduced ( at the minimum to only three cells ), gaining all its nutrition from the sporophyte.

He led the 1901 strike in that mining camp to a successful conclusion, gaining a standard minimum wage for the miners.

The qualification which is minimum for gaining chartership in engineering is the Master of Engineering ( MEng ) in addition to 4 – 6 years peer reviewed professional practice.

After reaching the 1, 200 hour regulatory flight time minimum for pilot in command on Instrument Flight Rules, flying for cargo airlines operating smaller aircraft under Part 135 is a common means of gaining experience in line operations, weather flying, etc., leading to passenger airline jobs.

This included gaining a minimum of a blackbelt in judo in addition to training in aikido, karate and Katori Shinto Ryu.

The domestic competition was planned to be based in Athens consisted of four teams, as that is the minimum requirement in gaining associate membership into the Rugby League European Federation.