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It follows readily from the definition of the spectrum of a ring, the space of prime ideals of equipped with the Zariski topology, that the Krull dimension of is precisely equal to the irreducible dimension of its spectrum.
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follows and readily
People readily make the modus ponens inference, that is, given if A then B, and given A, they conclude B, but only about half of participants in experiments make the modus tollens inference, that is, given if A then B, and given not-B, only about half of participants conclude not-A, the remainder say that nothing follows ( Evans et al., 1993 ).
The form of currency follows its function, which is to serve as a readily accepted medium of exchange of value.
The hypothetical motion that the body follows under the gravitational effect of one other body only is typically a conic section, and can be readily described with the methods of geometry.
Most political appointees can readily find jobs as lobbyists or elsewhere in the public sector, so no financial consequence really follows.
In the symphonic poems his gift for pictorial representation is most readily apparent ; music follows text almost in the manner of a film score.
follows and from
These publications may be secured as follows: The Annual Catalog from the Director of Admissions and other issues from the Publications Office.
In type 1 the pulmonary vein closely follows the course of the bronchus and the pulmonary artery from the periphery to the hilum.
The specificity of staining with Af was established as follows: Af specifically stained tumor sections but not sections of healthy sweet clover stems or of crown gall tumor tissue from sweet clover.
It was assumed that the shift in autonomic hypothalamic balance occurring spontaneously in neuropsychiatric patients from the application of certain therapeutic procedures follows the pattern known from the sleep-wakefulness cycle.
The fact that there can not be any limit points of the set except in closed intervals follows from the argument used in Lemma 1, namely, that near any tangent point in the C-plane the curves C and Af are analytic, and therefore the difference between them must be a monotone function in some neighborhood on either side of the tangent point.
Since the complex of singular lines is of order K and since there is no complex of invariant lines, it follows from the formula Af that the order of the involution is Af.
A final class of exceptional lines is identifiable from the following considerations: Since no two generators of Af can intersect, it follows that their image curves can have no free intersections.
This belief follows the theology of St. Paul: For it is by grace you have been saved, through faith — and this not from yourselves, it is the gift of God, not by works, so that no one can boast.
Although Dirac did not himself use the term antimatter, its use follows on naturally enough from antielectrons, antiprotons, etc.
For Hume, every effect only follows its cause arbitrarily — they are entirely distinct from one another.
Today, Methodism follows this ancient Alexandrian practice as bishops are elected from and by the order of the presbyterate: the Discipline of the Methodist Church, in ¶ 303, affirms that " ordination to this ministry is a gift from God to the Church.
This conservation law mathematically follows from continuous directional symmetry of space ( no direction in space is any different from any other direction ).
The debate might be framed starkly as follows: on the one hand, we can hypothesise a poem put together from various tales concerning the hero ( the Grendel episode, the Grendel's mother story, and the firedrake narrative ).
follows and definition
Here the first equality follows from the first part of Einstein's theory, the third equality follows from the definition of Boltzmann's constant as, and the fourth equality follows from Stokes ' formula for the mobility.
Using terms from formal language theory, the precise mathematical definition of this concept is as follows: Let S and T be two finite sets, called the source and target alphabets, respectively.
Rosser 1939 addresses the notion of " effective computability " as follows: " Clearly the existence of CC and RC ( Church's and Rosser's proofs ) presupposes a precise definition of " effective ".
St. Anselm's ontological argument, in its most succinct form, is as follows: " God, by definition, is that for which no greater can be conceived.
Since any Godlike object is necessarily existent, it follows that any Godlike object in one world is a Godlike object in all worlds, by the definition of necessary existence.
We can solve both problems using a more abstract definition of the exponential map that works for all Lie groups, as follows.
The European Union, in the principal statement of its Badinter Committee, follows the Montevideo Convention in its definition of a state: by having a territory, a population, and a political authority.
Turing machines can compute functions as follows: if f is a function that takes natural numbers to natural numbers, M < sup > A </ sup > is a Turing machine with oracle A, and whenever M < sup > A </ sup > is initialized with the work tape consisting of n + 1 consecutive 1's ( and blank elsewhere ) M < sup > A </ sup > eventually halts with f ( n ) 1's on the tape, then M < sup > A </ sup > is said to compute the function f. A similar definition can be made for functions of more than one variable, or partial functions.
But a critical logical analysis shows that this definition is too naive to be proper, and so it must be qualified as follows:
The above definition follows a classical approach to biochemistry, established at times when the distinction between a protein and a functional, proteinaceous unit was difficult to elucidate.
Durkheim's definition of religion, from Elementary Forms, is as follows: " A religion is a unified system of beliefs and practices relative to sacred things, that is to say, things set apart and forbidden – beliefs and practices which unite into one single moral community called a Church, all those who adhere to them.
A very useful special case, often given as the definition of torque in fields other than physics, is as follows:
* A corollary is a proposition that follows with little or no proof from one other theorem or definition.
What follows is a typical definition of " God ," which, perhaps with some adjustments, would be acceptable to many within the Jewish, Christian, and Muslim faiths:
Thus, by definition, one mole of pure < sup > 12 </ sup > C has a mass of exactly 12 g. It also follows from the definition that X moles of any substance will contain the same number of molecules as X moles of any other substance.
0.822 seconds.