* Every continuous functor on a small-complete category which satisfies the appropriate solution set condition has a left-adjoint ( the Freyd adjoint functor theorem ).

In analytic geometry, any equation involving the coordinates specifies a subset of the plane, namely the solution set for the equation.

A standard solution to this problem is found in Zermelo's set theory, which does not allow the unrestricted formation of sets from arbitrary properties.

Formally, one has an implication, not an equivalence, so the solution set may get larger.

The solution set can then be expressed parametrically ( that is, in terms of the free variables, so that if values for the free variables are chosen, a solution will be generated ).

In mathematics a hyperbola is a curve, specifically a smooth curve that lies in a plane, which can be defined either by its geometric properties or by the kinds of equations for which it is the solution set.

When this is the case, and x < sub > 0 </ sub > is one solution of ( 1 ), then the set of all solutions is given by

However, these prices set by cartels only provided a short-term solution because cartel members would cheat on each other by setting a lower price than the price set by the cartel.

The most viable solution to this problem was for firms to merge, through horizontal integration, with other top firms in the market in order to control a large market share and thus successfully set a higher price.

Similarly, the set of all solutions to Einstein's field equations is simpler than a specific solution.

One possible solution is that God could know every possible life one might live, but allows for free will according to laws set in place that cannot be contradicted.

As it is constant, its value can be set to one by defining the standard state as being the solution containing the background electrolyte.

In the solution, c < sub > 1 </ sub > and c < sub > 2 </ sub > are two constants determined by the initial conditions, and the origin is set to be the equilibrium position.

* In mathematics, a system of equations or a set of simultaneous equations share variables ; a solution is a set of variable values for which all these equations are satisfied together.

His solution is to introduce an order into the set of predicates.

Krasnikov proposed that, if tachyonic matter cannot be found or used, then a solution might be to arrange for masses along the path of the vessel to be set in motion in such a way that the required field was produced.

where is a set of Lagrange multipliers which come out of the solution alongside.

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

One solution to the problem is when some authors set their stories in an indefinite future, often in a society where the current calendar has been disrupted due to a societal collapse or undergone some form of distortion due to the impact of technology.

It is common for students and those new to working with glassware to set hotplates to a high value initially to rapidly warm a solution or solid.

He states: " And yet, even the elementary form that Russell < sup > 9 </ sup > gave to the set-theoretic antinomies could have persuaded them König, Jourdain, F. Bernstein that the solution of these difficulties is not to be sought in the surrender of well-ordering but only in a suitable restriction of the notion of set ".

We can escape from such a difficulty by ruling out the animal as not constituting a trial, but such a solution is not always satisfactory.

Roleplaying was offered as a solution -- and the procedure worked as follows: all candidates were invited to a hotel conference room, where the president explained the difficulty he had, and how unnecessary it seemed to him to hire people who just did not work out.

When Governor Al Smith offered New York National Guard planes to fly the mail in and out of the state, it seemed a likely temporary solution, easing Burlington's bottleneck and that at Montpelier too.

Party leaders came out of the final meeting apparently satisfied and stated that complete agreement had been reached on a solution to the crisis created by the elections which left no party with enough strength to form a government on its own.

Let her out, let her out -- that would be the solution, wouldn't it??

When this happens the carbon atoms will no longer be soluble with the iron, and will be forced to precipitate out of solution, nucleating into the spaces between the crystals.

The solution, stationer, is an anagram of into tears, the letters of which have burst out of their original arrangement to form the name of a type of businessman.

Internally the positively charged cations are flowing away from the anode ( even though it is negative and therefore would be expected to attract them, this is due to electrode potential relative to the electrolyte solution being different for the anode and cathode metal / electrolyte systems ); but, external to the cell in the circuit, electrons are being pushed out through the negative contact and thus through the circuit by the voltage potential as would be expected.

Further separation was carried out in the presence of a citric acid / ammonium buffer solution in a weakly acidic medium ( pH ≈ 3. 5 ), using ion exchange at elevated temperature.

The company simply collects the ions out of the solution after the bacteria have finished.

It is also useful for determining the tertiary structure and quaternary structure of purified proteins, especially since it can be carried out under native solution conditions.

* Gas evolution reaction, the process of a gas bubbling out ( or evolving ) from a solution

* Deposition ( chemistry ), molecules settling out of a solution

Since the water near the bottom is saturated, the salt precipitates out of solution onto the sea floor.

Larger amounts of radioactive material were later isolated from coral debris of the atoll, which were delivered to the U. S. The separation of suspected new elements was carried out in the presence of a citric acid / ammonium buffer solution in a weakly acidic medium ( pH ≈ 3. 5 ), using ion exchange at elevated temperatures ; fewer than 200 atoms of einsteinium were recovered in the end.

Although Abel had already proved the impossibility of a " quintic formula " by radicals in 1824 and Ruffini had published a solution in 1799 that turned out to be flawed, Galois ' methods led to deeper research in what is now called Galois theory.

Rail fins evolved into being and surged into popularity as riders ( Simon Anderson, most famously ) sought a solution to two major performance issues of a central " single " fin-both related to engagement of the foil: For one, a centrally-mounted fin is tilted up out of the water as the board is leaned over, and thus it loses more and more of its lift as the lean angle increases-if the lean angle is acute enough, the fin's tip can be the only area left in the water ; the tip may then rapidly stall and, having lost its lift, become disengaged from the water, leaving the board's bottom as the only control surface still operating.

Gold ions in solution are readily reduced and precipitated out as gold metal by adding any other metal as the reducing agent.

For these developments, it was essential that the solution of the Dirac equation for the hydrogen atom could be worked out exactly, such that any experimentally observed deviation had to be taken seriously as a signal of failure of the theory.

Remaining plant materials are filtered out of the solution and sent to the compost.

Instead of figuring out which ship, if either, is the " same ", and then declaring that it should be returned, the pragmatic solution is to figure out which ship should be returned, and then declare that it is the " same ".

Such molecules have minimum solubility in water or salt solutions at the pH that corresponds to their pI and often precipitate out of solution.