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Precisely and for
Precisely at the moment when it has lost its vision the mind of the community turns out from itself in a search for the ontological standard whereby it can measure itself.
Precisely when early humans started to use tools is difficult to determine, because the more primitive these tools are ( for example, sharp-edged stones ) the more difficult it is to decide whether they are natural objects or human artifacts.
Precisely where and when nationalism emerged is difficult to determine, but its development is closely related to that of the modern state and the push for popular sovereignty that surfaced with the French Revolution and the American Revolution in the late 18th century and culminated with the ethnic / national revolutions of Europe, for instance the Greek War of Independence.
Precisely because some members of the government also held such views, the PNDC secretary for finance and economic planning, Kwesi Botchwey, felt the need to justify World Bank ( see Glossary ) assistance to Ghana in 1983:
Precisely, for any consistent first-order theory it gives an " explicit construction " of a model described by the theory ; and this model will be countable if the language of the theory is countable.
Precisely because the designation is for the process rather than the product, it is regarded as an " intangible " property and is the only stoneware pottery-making process so designated in Japan.
Precisely for that reason, Ecuadorians with marital troubles will often ask their godparents for advice.
Precisely the attributes which make Hrafnkels saga so accessible have served to make it an attractive target for different theories on the origins of the Icelandic sagas.
Precisely because these simple paradigms do not require linguistic strategies for solution, they are especially useful for working with patients whose language skills are compromised, or whose cognitive skills may be minimal.
* Precisely because natural resources were for a long time either non-reproducible or freely available goods ( i. e. not reproducible commodities ) the whole tendency in the market economy was for those resources to be plundered for private gain, rather than economized appropriately.

Precisely and by
Precisely, we can systematically define a model of any consistent effective first-order theory T in PA by interpreting each symbol of T by an arithmetical formula whose free variables are the arguments of the symbol.
Adams concludes that “ right action, by act-utilitarian standards, and right motivation, by motive-utilitarian standards, are incompatible in some cases .” The necessity of this conclusion is rejected by Fred Feldman who argues that “ the conflict in question results from an inadequate formulation of the utilitarian doctrines ; motives play no essential role in it …( and that )… Precisely the same sort of conflict arises even when MU is left out of consideration and AU is applied by itself .” Instead, Feldman proposes a variant of act utilitarianism that results in there being no conflict between it and motive utilitarianism.
Precisely what the Bar / Bat Mitzvah should lead during the service varies in Judaism's different denominations and from one congregation to another and is not fixed by Jewish law.
Precisely because he had submitted to Brian's authority, the King of Leinster was overthrown in 998 and replaced by Máel Morda mac Murchada.
Precisely two years later, the monument was inaugurated by Nicholas.
They are primarily influenced by Russian and Korean pop music and songs have titles like " Our Life Is Precisely a Song ", " We Shall Hold Bayonets More Firmly ", " The Joy of Bumper Harvest Overflows Amidst the Song of Mechanisation " and " The Dear General Uses Distance-Shrinking Magic < nowiki >.
Precisely, let T be a triangulation of an n-manifold M. Let S be a simplex of T. We denote the dual cell ( to be defined precisely ) corresponding to S by DS.
* April 18 – Precisely one year after the Doolittle Raid, Admiral Isoroku Yamamoto, Commander-in-Chief of the Imperial Japanese Navys Combined Fleet, is killed when the Mitsubishi G4M ( Allied reporting name " Betty ") in which he is riding as a passenger, T1-323, is ambushed and shot down by U. S. Army Air Forces P-38 Lightning fighters over Bougainville in Operation Vengeance.
: Precisely by inculcating a critical attitude, the " canon " served to demythologize the conventional pieties of the American bourgeoisie and provided the student with a perspective from which to critically analyze American culture and institutions.
Precisely in this year, they started the Cargo 92 project, embarking from the city of Nantes in the cargo ship Melquiades with the theater company Royal de Luxe, in order to start a boat trip to South America, subsidized by the French government.

Precisely and above
Precisely, the formal derivative of the formal Laurent series f above is

Precisely and be
Precisely which species of felid are able to purr is a matter of debate, but the sound has been recorded in most of the smaller species, as well as the cheetah and cougar, and may also be found in the big cats.
Precisely because such a comparison or reference may sometimes be appropriate, Godwin has argued that overuse of Nazi and Hitler comparisons should be avoided, because it robs the valid comparisons of their impact.
Precisely, let be a classical valuation defined on every atomic sentence of the language, and let be the number of distinct atomic sentences in.
Precisely which Bosnian Serb units were involved in the Kravica executions cannot be stated with any certainty.
Precisely why the two races hate each other so much is unknown, but what is known that the presence of an aquatic elf community within several miles of a sahuagin community occasionally causes some sahuagin to be born as malenti ; mutants who resemble aquatic elves.
Moreover, the speed of convergence in terms of the Lipschitz constants of the approximations is strictly related to the modulus of continuity of Precisely, let be the minimal concave modulus of continuity of which is
Precisely, the impulse response of the ideal matched filter, assuming white ( uncorrelated ) noise should be a time-reversed complex-conjugated scaled version of the signal that we are seeking.
Precisely which body parts must be covered varies between different schools of Islamic thought.
Precisely defined technical terms must be placed into the relevant subcategories of the: Category: Computing.
Precisely the question .” Near Dodge City, Kansas, Henry and his dilapidated dog Solstice ( whom he declined to put down, “ lacking the kindness to be so cruel ”) together

Precisely and simply
Precisely what the Ferengi Alliance consisted of was never revealed ; it may simply encompass Ferenginar and any uninhabited planets that the Ferengi have colonized, since there was little indication that the Ferengi government exercised authority over any species other than its own.

s-cobordism and theorem
Then a finer statement of the s-cobordism theorem is that the isomorphism classes of this category ( up to Cat-isomorphism of h-cobordisms ) are torsors for the respective < ref > Note that identifying the Whitehead groups of the various manifolds requires that one choose base points and a path in W connecting them .</ ref > Whitehead groups Wh ( π ), where
While an h-cobordism W between simply-connected closed connected manifolds M and N of dimension n > 4 is isomorphic to a cylinder ( the corresponding homotopy equivalence can be taken to be a diffeomorphism, PL-isomorphism, or homeomorphism, respectively ), the s-cobordism theorem states that if the manifolds are not simply-connected, an h-cobordism is a cylinder if and only if the Whitehead torsion of the inclusion vanishes.
The expression is non-unique: the manipulation of handlebody decompositions is an essential ingredient of the proof of the Smale h-cobordism theorem, and its generalization to the s-cobordism theorem.

theorem and s
* s < sub > mn </ sub > theorem
A sufficient condition for recovering s ( t ) ( and therefore S ( ƒ )) from just these samples is that the non-zero portion of s ( t ) be confined to a known interval of duration P, which is the frequency domain dual of the Nyquist – Shannon sampling theorem.
It ’ s easy to see the Coase theorem at work in examples like this.
* Charles McCreery ’ s tutorials on chi-square, probability and Bayes ’ theorem for Oxford University psychology students
In the case that y < sub > i </ sub > are independent observations from a normal distribution, Cochran's theorem shows that s < sup > 2 </ sup > follows a scaled chi-squared distribution:
* If instead the sampling frequency is known, the theorem gives us an upper bound for frequency components, B < f < sub > s </ sub >/ 2, of the signal to allow for perfect reconstruction.
The usefulness of the theorem is that the distribution of approaches normality regardless of the shape of the distribution of the individual X < sub > i </ sub >’ s.
# Kevin S. Van Horn, " Constructing a logic of plausible inference: a guide to Cox ’ s theorem ", International Journal of Approximate Reasoning, Volume 34, Issue 1, September 2003, Pages 3 – 24.
The technique of pi – theorems usage (`` the method of dimensions ’’) became widely known due to the works of Rayleigh ( the first application of the pi – theorem in the general case to the dependence of pressure drop in a pipe upon governing parameters probably dates back to 1892, a heuristic proof with the use of series expansion, to 1894 ).
Bell ’ s theorem states that the concept of local realism, favoured by Einstein, yields predictions that disagree with those of quantum mechanical theory.
Shortly after publishing this paper de Moivre also generalized Newton ’ s famous Binomial Theorem into the Multinomial theorem.
The mathematician Paul Erdős was known for describing proofs he found particularly elegant as coming from " The Book ", a hypothetical tome containing the most beautiful method ( s ) of proving each theorem.
In social choice theory, Arrow ’ s impossibility theorem, the General Possibility Theorem, or Arrow ’ s paradox, states that, when voters have three or more distinct alternatives ( options ), no rank order voting system can convert the ranked preferences of individuals into a community-wide ( complete and transitive ) ranking while also meeting a specific set of criteria.
According to Allen Weiss, in Mirrors of Infinity, this optical effect is a result of the use of the tenth theorem of Euclid ’ s Optics which asserts that “ the most distant parts of planes situated below the eye appear to be the most elevated .” In Fouquet ’ s time, interested parties could cross the canal in a boat, but walking around the canal provides a view of the woods that mark what is no longer the garden and shows the distortion of the grottos previously seen as sculptural.
In 1678, he published a now famous theorem on synthetic geometry in a triangle called Ceva ’ s Theorem.
Also in the case of the right triangle, the sides c, h, s of the three above-mentioned squares are related to each other by the symphonic theorem, which states that
Counterexamples in which the theorem fails are known in spacetime dimensions higher than four ; in the presence of non-abelian Yang-Mills fields, non-abelian Proca fields, some non-minimally coupled scalar fields, or skyrmions ; or in some theories of gravity other than Einstein ’ s general relativity.
For two colours, Ramsey's theorem states that for any pair of positive integers ( r, s ), there exists a least positive integer R ( r, s ) such that for any complete graph on R ( r, s ) vertices, whose edges are coloured red or blue, there exists either a complete subgraph on r vertices which is entirely blue, or a complete subgraph on s vertices which is entirely red.

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