While the definition via velocities of curves is quite straightforward given the above intuition, it is also the most cumbersome to work with.

It is actually a more comprehensible proof than the above ( probably because it does not involve Zorn's Lemma, which is quite opaque to most mathematicians as far as intuition is concerned !).

The equation above can be rewritten in a more compact geometric form that helps our intuition:

One of the most significant breakthroughs, in the development of the waterjet, was to change the design so it expelled the jetstream above the water line, contrary to many people's intuition.

The intellectual intuition of Schelling, as above consciousness, the pure being of Hegel, as an empty abstraction, unvindicated, illegitimately assumed, and arbitrarily ' developed, are equally useless as bases of metaphysics.

The intuition for transforming the using the logit function ( the natural log of the odds ) was explained above.

* In line with the above intuition of " locally free = projective " is the following theorem due to Kaplansky: over a local ring, R, every projective module is free.

The intuition mentioned above ( that constructions that can be carried out in D can be " lifted " to D < sup > C </ sup >) can be made precise in several ways ; the most succinct formulation uses the language of adjoint functors.

This is the intuition behind the definition given above of a subgame.

To get some intuition for the definition above,

However, the underlying intuition is quite straightforward when keeping in mind the basic examples discussed above.

The functional areas are domains and subjects that have evolved in order to provide proper answers and solutions to the functional requirements above.

Such higher arity relationships provide information on all of the underlying domains at the same time, with none of them being privileged above the others.

The 2006 APA recommendations also include supervised clinical experience intended to integrate the above seven knowledge domains and assess competencies in skills and applied knowledge.

Note that we require the domains of G < sub > 2 </ sub >, G < sub > 3 </ sub > to be broad enough to make the above properties meaningful.

The three-domain system adds a level of classification ( the domains ) " above " the kingdoms present in the five-or-six-kingdom systems.

* mixed domains, involving two or more of the above

Basically, a variety is a scheme whose structure sheaf is a sheaf of k-algebras with the property that the rings R that occur above are all integral domains and are all finitely generated k-algebras, i. e., quotients of polynomial algebras by prime ideals.

As mentioned above, the domains of computation are always partially ordered.

Several < tt > int </ tt > domains were granted prior to the application of the strict guidelines described above.

While the order of the extension group is a general invariant, the other two invariants above do not seem to have interesting analogues outside the realm of fraction fields of one-dimensional domains and their completions.

( This is equivalent to the above condition " every element of k is a pth power " for integral domains.

One way of defining the exponential function for domains larger than the domain of real numbers is to first define it for the domain of real numbers using one of the above characterizations and then extend it to larger domains in a way which would work for any analytic function.

The above property for uniformly continuous function on convex domains admits a sort of converse at least in the case of real-valued functions: that is, every special uniformly continuous real-valued function defined on a subset of a normed space admits extensions over that preserves any subadditive modulus of.

MILS addresses the isolation underlying MLS without addressing the controlled interaction between the domains addressed by the above models.

Trusted security-compliant channels mentioned above can link MILS domains to support more MLS functionality.

"[...] the party leadership has uncovered the anti-party line which Alexandru Drăghici, encouraged by servile, uncultured, and decaying elements, has introduced to the bodies ' activities, attempting to remove them from party control and to erect them into supreme bodies standing above party and state leadership, thus causing serious harm to activity in various domains, including that of scientific research.

First published in 1950, ZAMP covers the fields of fluid mechanics, solid mechanics, differential equations / applied mathematics, and neighbouring domains of the above.

Plant immune systems also encode resistance proteins that resemble NOD-like receptors ( see above ), that feature NBS and LRR domains and can also carry other conserved interaction domains such as the TIR cytoplasmic domain found in Toll and Interleukin Receptors.

The lumen-side segment of cyt f includes two structural domains: a small one above a larger one that, in turn, is on top of the attachment to the membrane domain.

Numbers above the bars refer to the amino acid residues that separate the domains starting from the N-terminus ( left ) to C-terminus ( right ).

Besides the domains mentioned above, self-determination theory research has been widely applied to the field of sports.

We are above being jealous.

( Divide the amount being allotted by the result obtained in item 9 above.

Thus, in the example cited above Fromm rests his whole case on the premise that the workers are being deprived unconsciously, unknowingly, of fulfillment, and then supports this with survey data reporting conscious, experienced frustrations.

Scores above 0 are " ranked ", with the highest score being ranked 1st, the next-highest 2nd, and so on.

This agrees with the reference to the Ainu being a merger of Okhotsk and Satsumon referenced above.

The Acropolis of Athens ( Greek: Ακρόπολη Αθηνών ) is an ancient citadel located on a high rocky outcrop above the city of Athens and containing the remains of several ancient buildings of great architectural and historic significance, the most famous being the Parthenon.

St. Thomas called them ( perhaps not originally ) the transcendentia, " transcendentals ", because they " climb above " the categories, just as being climbs above substance.

The terrain is low-lying and sandy: a coral island surrounded by a narrow fringing reef with a depressed central area devoid of a lagoon with its highest point being above sea level.

Contrary to the above, the Expositor's Bible Commentary ( Zondervan, 1990 ) says that the language of Daniel, in comparison with the Hebrew and Aramaic texts of the Hellenistic period, " prove quite conclusively to any scholar that the second-century date and Palestinian provenance of the Book of Daniel cannot be upheld any longer without violence being done to the science of linguistics.

One of the major themes of the book is Yahweh's sovereignty and the importance of being loyal to Him and His laws above all other gods and sovereigns.

It combines the symbol for " writing tool " or " pen " ( a line inclined, as a pen being used ) with the symbol for " world ", which in its turn combines " ground " or " earth " ( a horizontal line below ) and its counterpart derivate " sky " ( a horizontal line above ).

If the first theory is correct ( see above ), then the absence of cavalry removed the main Athenian tactical disadvantage, and the threat of being outflanked made it imperative to attack.

Taken together with an increased emphasis on discipline in the RIC, this helped to curb the random atrocities the Black and Tans committed since March 1920 for the remainder of the war, if only because reprisals were now directed from above rather than being the result of a spontaneous desire for revenge.

Contemporary Christian theologians have provided explanations for " born from above " being a more accurate translation of the original Greek word transliterated anōthen.

Another well known town is Fonni, being the highest town in Sardinia, More than 1000 meters above sea level.

The Global Competitiveness Report for 2009-2010 ranks Chile as being the 30th most competitive country in the world and the first in Latin America, well above from Brazil ( 56th ), Mexico ( 60th ) and Argentina which ranks 85th.

So in the second case cited above, it is likely that two different versions are being conflated: one version with an embassy of three people, another with just two people.

Most denominations ( a notable exception being the Seventh Day Adventists ) would affirm the statement from the Catechism of the Catholic Church ( above ), with the exception of the parenthetical phrase, " through a purification or immediately.

Astronomers did not observe large amounts of water following the collisions, and later impact studies found that fragmentation and destruction of the cometary fragments in an ' airburst ' probably occurred at much higher altitudes than previously expected, with even the largest fragments being destroyed when the pressure reached, well above the expected depth of the water layer.

In early medieval Riez in upper Provence, alluvial silt from two small rivers raised the riverbeds and widened the floodplain, which slowly buried the Roman settlement in alluvium and gradually moved new construction to higher ground ; concurrently the headwater valleys above Riez were being opened to pasturage.

Although his administrative abilities had been noticed, on the eve of the U. S. entry into World War II he had never held an active command above a battalion and was far from being considered by many as a potential commander of major operations.

The above three-level database architecture also relates to and being motivated by the concept of data independence which has been described for long time as a desired database property and was one of the major initial driving forces of the Relational model.

In the context of the above architecture it means that changes made at a certain level do not affect definitions and software developed with higher level interfaces, and are being incorporated at the higher level automatically.