Precisely, let be a classical valuation defined on every atomic sentence of the language, and let be the number of distinct atomic sentences in.

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, 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.

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, 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 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.

Precisely, the s-cobordism theorem ( the s stands for simple-homotopy equivalence ), proved independently by Barry Mazur, John Stallings, and Dennis Barden, states ( assumptions as above but where M and N need not be simply connected ):

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 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 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 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 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 '', said Mr. Frans.

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.

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.

VLADIMIR: Precisely.

Precisely what " The Great and Abomninable Church " is, however, remains vague.

Precisely what was arranged is unknown.

Precisely the two processes, which he described have.

Precisely when it became common to include the name of a man's voting tribe as part of his full name is unknown.

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 it is the result of multiplying the chromosome number in an F1 hybrid.

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 because it carries on, as it has carried on ever since the middle of the eighteenth century, a war against that anachronistic survival, Pop Art is, whatever its overt politics, subversive: a threat to all hierarchies insofar as it is hostile to order and ordering in its own realm.

Ward included a passage from one of his anarchist forebears, Peter Kropotkin, who said of the empty and overgrown landscape of Surrey and Sussex at the end of the 19th century, ‘ in every direction I see abandoned cottages and orchards going to ruin, a whole population has disappeared .’ Ward himself went on to observe: ‘ Precisely a century after this account was written, the fields were empty again.

Precisely what happened to Pershore in the later 10th century is poorly documented, but some sources seem to hint that it went into decline during the succession crisis which emerged in the wake of King Edgar's death.

Precisely when the settlement became known as Jeffersonville is unclear, but it was probably around 1801, the year in which President Thomas Jefferson took office.

Precisely what brought Dr. Knapp to Louisiana is unclear.

Precisely how old the church is remains a mystery, and although at one time it belonged to the priory of Whithorn, Wigtown parish church was afterwards set up as a free rectory with the king as patron.

Precisely two years later, the monument was inaugurated by Nicholas.

* 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.

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, ODP of a given substance is defined as the ratio of global loss of ozone due to given substance over the global loss of ozone due to CFC-11 of the same mass.

: 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.

In the notation of the proof of Theorem 12, let us take a look at the special case in which the minimal polynomial for T is a product of first-degree polynomials, i.e., the case in which each Af is of the form Af.

Let M be a smooth manifold and let x be a point in M. Let T < sub > x </ sub > M be the tangent space at x.

First, let T = T ( s ) be the force of tension as a function of s. The chain is flexible so it can only exert a force parallel to itself.

Second, let G = G ( s ) be the external force per unit length acting on a small segment of a chain as a function of s. The forces acting on the segment of the chain between s and s + Δs are the force of tension T ( s + Δs ) at one end of the segment, the nearly opposite force − T ( s ) at the other end, and the external force acting on the segment which is

For the converse direction, let A be a partially ordered set and T a totally ordered subset of A.

Hulk Hogan wrote in his autobiography that Mr. T saved the main event of WrestleMania I between them and " Rowdy " Roddy Piper and " Mr. Wonderful " Paul Orndorff because when he arrived, security would not let his entourage into the building.

Then N < sub > x </ sub > is a directed set, where the direction is given by reverse inclusion, so that S ≥ T if and only if S is contained in T. For S in N < sub > x </ sub >, let x < sub > S </ sub > be a point in S. Then ( x < sub > S </ sub >) is a net.

Formally, let S and T be finite sets and let F =

For a red – black tree T, let B be the number of black nodes in property 5.

If the bias is small, we can let U − E ≈ φM in the expression for κ, where φM, the work function, gives the minimum energy needed to bring an electron from an occupied level, the highest of which is at the Fermi level ( for metals at T = 0 kelvins ), to vacuum level.

For a collection T of subsets of X ( that is, for any subset of the power set P ( X ) of X ), let

Let V and W be vector spaces ( or more generally modules ) and let T be a linear map from V to W. If 0 < sub > W </ sub > is the zero vector of W, then the kernel of T is the preimage of the zero subspace

A bijection g ( t ) from T to ( 0, 1 ) is defined by: If t is the n < sup > th </ sup > string in sequence b, let g ( t ) be the n < sup > th </ sup > number in sequence a ; otherwise, let g ( t ) = 0. t.

Let K be a closed subset of a compact set T in R < sup > n </ sup > and let C < sub > K </ sub > be an open cover of K. Then

Let the curve be a unit speed curve and let t = u × T so that T, u, t form an orthonormal basis: the Darboux frame.

In the months leading up to Nixon's 1969 speech, his vice-president Spiro T. Agnew said on May 9, " It is time for America's silent majority to stand up for its rights, and let us remember the American majority includes every minority.

To achieve this, let T be the initial theory and let κ be any cardinal number.