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sufficient and set
" The Federal Public Defender recommends that defendants speak in terms of how a lenient sentence will be sufficient, but not greater than necessary, to comply with the statutory directives set forth in.
This is one of many possible assignments, with for instance, any set of assignments including x < sub > 1 </ sub > = TRUE being sufficient.
An intensional definition, also called a coactive definition, specifies the necessary and sufficient conditions for a thing being a member of a specific set.
The same night, Lee breaks into the underground base, avoiding a booby-trap set for him, and gathers sufficient evidence to warrant Han's arrest, but sets off an alarm while using the radio transmitter to contact Braithwaite.
Given a complete set of axioms ( see below for one such set ), modus ponens is sufficient to prove all other argument forms in propositional logic, and so we may think of them as derivative.
After this the doses are titrated until they reach either a clinically sufficient level that prevents withdrawal, cravings and possible continued use of illicit opioids, or until they reach a maximum dose set by clinic policy.
Because, through the dithering process, the printer builds a single image pixel out of several printer dots to increase color depth, the printer's DPI setting must be set far higher than the desired PPI to ensure sufficient color depth without sacrificing image resolution.
The Supreme Court held in United States v. Carll, that “ in an indictment ... it is not sufficient to set forth the offense in the words of the statute, unless those words of themselves fully, directly, and expressly, without any uncertainty or ambiguity, set forth all the elements necessary to constitute the offense intended to be punished .” Vague wording, even if taken directly from a statute, does not suffice.
An organic chemical compound ( or related set of compounds ) is called a vitamin when it cannot be synthesized in sufficient quantities by an organism, and must be obtained from the diet.
Therefore, to obtain a full set of Fourier transform data, it is necessary to rotate the crystal through slightly more than 180 °, or sometimes less if sufficient symmetry is present.
Stephens shows a set of necessary and jointly sufficient conditions “… for an instance of reciprocal altruism:
In cases where the measure is not complete, it is sufficient that the set is contained within a set of measure zero.
To smoke test a venue the venue is filled to the full capacity with smoke to see if there are any smoke detectors still live, or if there are any leaks of smoke from the venue sufficient to set off detectors in other parts of the venue being tested.
* Cuny – A set of conditions that occurs when large numbers of people in a region cannot obtain sufficient food, resulting in widespread, acute malnutrition.
Zorn's lemma is equivalent to the well-ordering theorem and the axiom of choice, in the sense that any one of them, together with the Zermelo – Fraenkel axioms of set theory, is sufficient to prove the others.
* In quantum mechanics, a complete set of commuting operators ( or CSCO ) is one whose eigenvalues are sufficient to specify the physical state of a system.
Given a base for a topology, in order to prove convergence of a net or sequence it is sufficient to prove that it is eventually in every set in the base which contains the putative limit.
Five-bit codes are needed to give sufficient combinations to encompass this set of 27 values.
If the diet is changed from a highly glycemic diet to a diet that does not provide sufficient carbohydrate to replenish glycogen stores, the body goes through a set of stages to enter ketosis.
Benjamin Jowett held that their light car class was suffering from engines either from cyclecars with sufficient power but subject to rapid deterioration because of inadequate bearing surfaces, or engines from larger cars too heavy for the rest of the car's structure leading to a different set of troubles.
In 1848, he attempted to set up the Bumgay Navigation Tontine Co., which would buy the rights to levy tolls and trade on the river, using a tontine, but the scheme failed to attract sufficient investors to become viable.
Any set of headphones that provide good right and left channel isolation are sufficient to hear the immersive effects of the recording, and anyone who has even a cheap set of headphones can enjoy the recordings.

sufficient and relations
Demand and supply relations in a market can be statistically estimated from price, quantity, and other data with sufficient information in the model.
Since our concepts of good and evil as instilled in us by God are only intended to facilitate ethical behaviour in our relations with other humans, we should have no expectation that our concepts are accurate beyond what is needed to fulfil this function, and therefore cannot presume that they are sufficient to determine whether what we call evil really is evil.
Transvections satisfy the Steinberg relations, but these are not sufficient: the resulting group is the Steinberg group, which is not the special linear group, but rather the universal central extension of the commutator subgroup of GL.
Therefore, according to Barrett, the destruction of capitalist economic relations is necessary but not sufficient for the liberation of women.
According to the theory three dimensions of interpersonal relations were deemed to be necessary and sufficient to explain most human interaction: Inclusion, Control and Affection.
" The interest … is not in investigating a mathematically definable system which has some relation to language, as being a generalization or a subset of it, but in formulating as a mathematical system all the properties and relations necessary and sufficient for the whole of natural language.
For some knot polynomials, such as the Conway, Alexander, and Jones polynomials, the relevant skein relations are sufficient to calculate the polynomial recursively.
Bibliophilia is not to be confused with bibliomania, an obsessive-compulsive disorder involving the collecting of books to the point where social relations or health are damaged, and in which the mere fact that an object is a book is sufficient for it to be collected or loved.
There is no sufficient evidence for the allegations of the Whigs that Harcourt entered into treasonable relations with the Pretender.
In fact, the extent to which official histories are partisan varies considerably: some are indeed little more than exercises in public relations and promotion, whereas in other cases the authors will have retained sufficient independence to be able to express negative as well as positive judgements about their subjects.
When we have generated enough of these relations ( it's generally sufficient that the number of relations be a few more than the size of P ), we can use the methods of linear algebra ( for example, Gaussian elimination ) to multiply together these various relations in such a way that the exponents of the primes on the right-hand side are all even:
Reductionistic explanations claim that two or at most three term relations are sufficient to account for the system's behavior.
Non-state actors are categorized as entities that ( i ) participating or acting in the sphere of international relations ; organizations with sufficient power to influence and cause change in politics which are
No social order is ever destroyed before all the productive forces for which it is sufficient have been developed, and new superior relations of production never replace older ones before the material conditions for their existence have matured within the framework of the old society.
" No social order is ever destroyed before all the productive forces for which it is sufficient have been developed, and new superior relations of production never replace older ones before the material conditions for their existence have matured within the framework of the old society.
The English Government, however, expressed the view that " force had been exercised towards the natives without sufficient warranty "< sup > 4 </ sup > and urged the necessity of maintaining friendly relations with the Aborigines.
When we have generated enough of these relations ( it's generally sufficient that the number of relations be a few more than the size of P ), we can use the methods of linear algebra to multiply together these various relations in such a way that the exponents of the primes are all even.
The truth of the rule of transposition is dependent upon the relations of sufficient condition and necessary condition in logic.

sufficient and for
When I mentioned that for my first long voyage I did not even have the money for the return fare, but had trusted to luck that I would earn a sufficient amount, the young people looked at me doubtingly.
Others mentioned that I might have had to ask friends or even strangers for help and that to be stranded in a foreign country without sufficient funds did not contribute to international understanding.
Was it supposed, perchance, that A & M ( vocational training, that is ) was quite sufficient for the immigrant class which flooded that part of the New England world in the post-Civil War period, the immigrants having been brought in from Southern Europe, to work in the mills, to make up for the labor shortage caused by migration to the West??
Because of these involvements in the matter at stake, Boniface lacked the impartiality that is supposed to be an essential qualification for the position of arbiter, and in retrospect that would seem to be sufficient reason why the English embassies to the Curia proved so fruitless.
Stigmata quite sufficient for diagnosis are nevertheless there.
Without a great acceleration in the metropolitan area's economy, there will not be sufficient jobs for the growing numbers of youngsters, and St. Louis will slip into second-class status.
in interstellar gas, concentrations as low as Af molecules per Af may be sufficient, as compared to the Af hydrogen atom's Af required for detection of the 21-cm line.
The Peace Corps can either begin in very low gear, with only preparatory work undertaken between now and when Congress finally appropriates special funds for it -- or it can be launched now and in earnest by executive action, with sufficient funds and made available from existing Mutual Security appropriations to permit a number of substantial projects to start this summer.
After it has been seen, have the child start on a mat on hands and knees ( a thin, inexpensive mat is quite sufficient for anything that does not require falling ).
One or two practice runs should be sufficient for solo.
In theory, compulsive behavior is a way of diminishing anxiety, and one might expect a negative association except for the possibility that for many children the obsessive-compulsive defenses are not sufficient to quell the amount of anxiety they suffer.
Elaborate studies have been made in labor surplus areas in order to identify sufficient numbers of local job vacancies and future replacement needs for certain skills to justify training programs for those skills.
Editor Foss stated, `` Of their guilt there can be no doubt but they are entitled to sufficient time to prepare for trial, and a fair trial ''.
Verbal and adverbial elements too participated in each epic diction, but it is for the present sufficient to mark the large nominal and adjectival supply of semantic near-equivalents, and to designate the members of any system of equivalents as basic formulas of the poetic language.
In determining the extent to which any poem is formulaic it is idle, however, to inspect nothing besides lines repeated in their entirety, for a stock of line-fragments would be sufficient to permit the poet to extemporize with deftness if they provided for prosodic needs.
Washing is continued for 30 minutes or for a period of time sufficient to allow 100 nips or passes through the squeeze rolls.
To proceed from one stage to the next a sufficient number of feed states must be investigated to allow for interpolation ; ;
Religious faith can be considered a necessary condition of membership in a congregation, since the decision to join a worshiping group requires some motive force, but faith is not a sufficient condition for joining ; ;
But the Communists never gave sufficient provocation at any one time for the United States to want to risk a limited or an all-out war over Laos.

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