In the case of an optimal separation, different peaks or patterns on the chromatogram correspond to different components of the separated mixture.

For the case of power-of-two, Papadimitriou ( 1979 ) argued that the number of complex-number additions achieved by Cooley – Tukey algorithms is optimal under certain assumptions on the graph of the algorithm ( his assumptions imply, among other things, that no additive identities in the roots of unity are exploited ).

Different amplitudes of bias field are optimal for different types of tape, so most recorders offer a bias setting switch on the control panel, or, in the case of the compact audio cassette, may switch automatically according to cutouts on the cassette shell.

In the special case that distances between cities are all either one or two ( and thus the triangle inequality is necessarily satisfied ), there is a polynomial-time approximation algorithm that finds a tour of length at most 8 / 7 times the optimal tour length.

In the case of bounded metrics it is known that there is no polynomial time algorithm that constructs a tour of length at most 321 / 320 times the optimal tour's length, unless P = NP.

In the latter case, one species measures all six orthogonal components of polarization, and is believed to have optimal polarization vision.

In the worst case, the algorithm results in a tour that is much longer than the optimal tour.

A rod is usually also classified by the optimal weight of fishing line or in the case of fly rods, fly line the rod should handle.

In this case, the market equilibrium in the steel industry will not be optimal.

Also, in economics and Game theory there is the notion of an Epsilon equilibrium, which is a generalization of the standard Nash equilibrium in which each player is within ε of his or her optimal payoff ( the standard Nash-equilibrium being the special case where ε = 0 ).

If a subsystem is only 50 % reliable, one can concentrate on improving the reliability of that subsystem, design in multiple subsystems in parallel ( 5 in this case would achieve approximately 97 % reliability of that subsystem ), purchase and store spare subsystems for rapid change out, establish repair capability that would get a failed subsystem back in operation in the required amount of time, and / or choose any combination of those approaches to achieve the optimal cost vs. reliability solution.

The deadline-monotonic scheduling algorithm is also optimal with equal periods and deadlines, in fact in this case the algorithms are identical ; in addition, deadline monotonic scheduling is optimal when deadlines are less than periods.

He has been shown to be able to teleport distances of up to two miles ( 3 km ) under optimal conditions, although this is usually his extreme limit, and he can become severely fatigued if he tries to teleport that distance ( in one case, however, he teleports somewhere over ).

They emphasize yet for these classical modalities that any optimal categorization depends very much on the application domain and use case.

The optimal tapping point ( or ratio of coil inductances ) depends on the amplifying device used, which may be a bipolar junction transistor, FET, triode, or amplifier of almost any type ( non-inverting in this case, although variations of the circuit with an earthed centre-point and feedback from an inverting amplifier or the collector / drain of a transistor are also common ), but a Junction FET ( shown ) or triode is often employed as a good degree of amplitude stability ( and thus distortion reduction ) can be achieved with a simple grid leak resistor-capacitor combination in series with the gate or grid ( see the Scott circuit below ) thanks to diode conduction on signal peaks building up enough negative bias to limit amplification.

However, when to archive, and what may be the optimal length for a talk page, are subjective decisions that should be adapted to each case.

Thus, it is most often the case that any solution to the optimal control problem is locally minimizing.

A special case of the general nonlinear optimal control problem given in the previous section is the linear quadratic ( LQ ) optimal control problem.

This is increasingly the case as new courses are more likely to be sited on less optimal land.

For them, the only evolutionary stable strategy is when the host accepts all signs of the parasite with optimal intensity, which must be below the threshold, if this is not the case, the host can use these signals to identify the parasite

If suppose only the case of a good say, good X < sup > 1 </ sup > is taken, then the optimal choice at each set of prices and income or in other words, the demand function for good X < sup > 1 </ sup > can be written as:

In Canny's original paper, the derivation of the optimal filter led to a Finite Impulse Response filter, which can be slow to compute in the spatial domain if the amount of smoothing required is important ( the filter will have a large spatial support in that case ).

Our understanding of the solar system has taught us to replace our former elaborate rituals with the appropriate action which, in this case, amounts to doing nothing.

The arguments advanced by those individuals and groups who oppose the system in force and who would drastically curtail or do away entirely with hospital care for the non-service-connected case, seem to be coldly impractical and out-of-step with the wishes of the general public.

Westinghouse has a similar system, with two classifications representing various levels of competence on the strictly technical side: consulting engineer or scientist, as the case may be, and advisory engineer or scientist.

For the case of a purely inertial autonavigator consisting of three restrained gyros, a coordinate system is used where the sensitive axis of the X accelerometer is parallel to the east-west direction at the base point, and the Y accelerometer sensitive axis is parallel to the north-south direction at the base point.

And there was the case of Tom Hepker, a machinist, who was referred by a friend to a health machine quack who treated him with a so-called diagnostic machine for what Doctor Fraud said was a system full of arsenic and strychnine.

The case histories provide some interesting illustrations of ideological diffusion, embodied in the unwed mother's inability to identify independently a given value system or behavior pattern,, and her subsequent disinclination to assume any individual responsibility for her sexual behavior.

In most jurisdictions, the court system is divided into at least three levels: the trial court, which initially hears cases and reviews evidence and testimony to determine the facts of the case ; at least one intermediate appellate court ; and a supreme court ( or court of last resort ) which primarily reviews the decisions of the intermediate courts.

For example a two dimensional array with three rows and four columns might provide access to the element at the 2nd row and 4th column by the expression: ( in a row major language ) and ( in a column major language ) in the case of a zero-based indexing system.

However, although Apollonius came close to developing analytic geometry, he did not manage to do so since he did not take into account negative magnitudes and in every case the coordinate system was superimposed upon a given curve a posteriori instead of a priori.

In English, which has mostly lost the case system, the definite article and noun – " the car " – remain in the same form regardless of the grammatical role played by the words.

The adversarial system ( or adversary system ) is a legal system where two advocates represent their parties ' positions before an impartial person or group of people, usually a jury or judge, who attempt to determine the truth of the case.

As opposed to that, the inquisitorial system has a judge ( or a group of judges who work together ) whose task is to investigate the case.

As the election to maintain an accused person's right to silence prevents any examination or cross-examination of that person's position, it follows that the decision of counsel as to what evidence will be called is a crucial tactic in any case in the adversarial system and hence it might be said that it is a lawyer's manipulation of the truth.

In an adversarial system, there is no more controversy and the case proceeds to sentencing ; though in many jurisdictions the defendant must have allocution of her or his crime, a false confession will not be accepted even in common law courts.

By contrast, in an inquisitiorial system, the fact that the defendant has confessed is merely one more fact that is entered into evidence, and a confession by the defendant does not remove the requirement that the prosecution present a full case.

In the case of an observer on Earth, the direction of a star's velocity varies during the year as Earth revolves around the Sun ( or strictly speaking, the barycenter of the solar system ), and this in turn causes the apparent position of the star to vary.

Normally, the arteries in the vascular system carry oxygen-rich blood, except in the case of the pulmonary artery.

Each individual test, known as a case, exercises a particular operating condition of the user's environment or feature of the system, and will result in a pass or fail, or boolean, outcome.

The term " black-letter law " is also used commonly in the American legal system to mean well-established case law.

Chiefs and other leaders preside over customary, traditional courts, though all persons have the right to request that their case be considered under the formal British-based legal system.

Bulgarian, along with the closely related Macedonian language ( collectively forming the East South Slavic languages ), has several characteristics that set it apart from all other Slavic languages: changes include the elimination of case declension, the development of a suffixed definite article ( see Balkan language area ) and the lack of a verb infinitive ; but it retains and has further developed the Proto-Slavic verb system.

During the Middle Bulgarian period, the language underwent dramatic changes, losing the Slavonic case system, but preserving the rich verb system ( while the development was exactly the opposite in other Slavic languages ) and developing a definite article.