#( the cycle property of minimum spanning trees ): For any cycle C in the graph, if the weight of an edge e of C is larger than the weights of other edges of C, then this edge cannot belong to a MST.

#( Going up ) If B is an integral extension of A, then the extension satisfies the going-up property ( and hence the lying over property ), and the incomparability property.

#( Going down ) If B is an integral extension of A, and B is a domain, and A is integrally closed in its field of fractions, then the extension ( in addition to going-up, lying-over and incomparability ) satisfies the going-down property.

#( Coro ): " Ach Gott, wie manches Herzeleid " for choir, oboe d ' amore I / II and trombone col Basso, violin I / II, viola, and continuo.

#( 1197 / 1200 ): Anna, a relative of Emperor Isaac II Angelos

#( Betti numbers ) If X is a ( good ) " reduction mod p " of a non-singular projective variety Y defined over a number field embedded in the field of complex numbers, then the degree of P < sub > i </ sub > is the i < sup > th </ sup > Betti number of the space of complex points of Y.

#( Affine axiom of parallelism ) Given a point A and a line r, not through A, there is at most one line through A which does not meet r.

The diagonal lemma also requires that there be a systematic way of assigning to every formula θ a natural number #( θ ) called its Gödel number.

#( TR 3 ) Given a map between two morphisms, there is a morphism between their mapping cones ( which exist by axiom ( TR 1 )), that makes everything commute.

#( Crypto -) CatharAccording to this thesis, troubadour poetry is a reflection of Cathar religious doctrine.

#( Desargues ) Given seven distinct points A, A ', B, B ', C, C ', O, such that AA ', BB ', and CC ' are distinct lines through O and AB is parallel to A ' B ' and BC is parallel to B ' C ', then AC is parallel to A ' C '.

#( Rationality ) ζ ( X, s ) is a rational function of T = q < sup >− s </ sup >.

#( Functional equation and Poincaré duality ) The zeta function satisfies < dl >< dd ></ dl > or equivalently < dl >< dd ></ dl > where E is the Euler characteristic of X.

#( All ) y is a B

#( All ) y is a Z

#( TR 4 ) This is called the octahedral axiom.

Later came Rockford #( 3or7 ) with Spender / Megabucks site as well as Dale's site ( God ).

#( rock ) Star Hustler ( with Magicyclops )

#( a ) When necessary, the Convener and the Vice Convener shall be elected by the Business Committee from among its elected members at the first meeting following the second statutory half-yearly meeting of the General Council serving until their ordinary membership term expires.

#( TR 1 ) Every triangulated category contains the following triangles:

#( 30 seconds of the crowd chanting, no song )

at > ^ D #( press Control-D while at the beginning of a line )

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#( probably ) Theodoric I of Wettin, d. 976

#( Senior ) Project Manager: Has overall responsibility for design, implementation, and management of research projects.

#( Riemann hypothesis ) | α < sub > i, j </ sub >| = q < sup > i / 2 </ sup > for all and all j.

#( Later ) Jin and Korea will not violate each other's territory.

#( Polonaise ) in D minor, BWV Anh.

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#( 1954-hame. n dil me. n basaa bhi lo ).

#( For men only ) Doing istibra ' before ghusl janabat.

#( TR 2 ) The rotations of any distinguished triangle are distinguished.

#( porn ) Star Hustler ( feat.

#( 2 ). 50 caliber sniper rifles

#( probably ) Dietrich I, Count of Wettin, d. 976

#( a ) Minimal usage not an issue here.

* Predication ( property and relation attribution ): " It hurts to be blue.

Cohen ( 1955 ): working class teenagers joined gangs due to frustration of inability to achieve status and goals of the middle class ; Cloward and Ohlin ( 1960 ): blocked opportunity, but unequal distribution of opportunities lead to creating different types of gangs ( that is, some focused on robbery and property theft, some on fighting and conflict and some were retreatists focusing on drug taking ); Spergel ( 1966 ) was one of the first criminologists to focus on evidence-based practice rather than intuition into gang life and culture.

Pick a point x in M. A derivation at x is a linear map D: C < sup >∞</ sup >( M ) → R which has the property that for all ƒ, g in C < sup >∞</ sup >( M ):

The same one-time fees apply when a person dies without a will or a trust ( dies Intestate ): State laws require that an intestate probate be opened at the local courthouse, that the decedent's closest relatives be identified, located and notified, and that the decedent's real and personal property be collected, accounted, and distributed to said relatives.

According to the National School Safety Center, since the 1992-1993 U. S. school year there has been a significant decline in school-associated violent deaths ( deaths on private or public school property for kindergarten through grade 12 and resulting from schools functions or activities ):

The DCT, and in particular the DCT-II, is often used in signal and image processing, especially for lossy data compression, because it has a strong " energy compaction " property ( Ahmed, Natarajan and Rao, 1974 ; Rao and Yip, 1990 ): most of the signal information tends to be concentrated in a few low-frequency components of the DCT, approaching the Karhunen-Loève transform ( which is optimal in the decorrelation sense ) for signals based on certain limits of Markov processes.

This is why a neutron moderator ( a medium which slows down fast neutrons, thereby turning them into thermal neutrons capable of sustaining a chain reaction ) is a material full of atoms with light nuclei ( with the additional property that they do not easily absorb neutrons ): the lightest nuclei have about the same mass as a neutron.

* Additivity ( also called the superposition property ): f ( x + y ) = f ( x ) + f ( y ).

Gregory detested Chilperic, calling him " the Nero and Herod of his time " ( History of the Franks book VI. 46 ): he had provoked Gregory's wrath by wresting Tours from Austrasia, seizing ecclesiastical property, and appointing as bishops counts of the palace who were not clerics.

* 1460 ( Chōroku 3 ): Yoshimasa initiated planning for construction of a retirement villa and gardens as early as 1460 ; and after his death, this property would become a Buddhist temple called Jisho-ji ( also known as Ginkaku-ji or the " Silver Pavilion ").

In individual choice theory, the name " IIA " is sometimes used to refer to Chernoff's condition or Sen's property α ( alpha ):

An important property of the exponential map is the following lemma of Gauss ( yet another Gauss's lemma ): given any tangent vector v in the domain of definition of exp < sub > p </ sub >, and another vector w based at the tip of v ( hence w is actually in the double-tangent space T < sub > v </ sub >( T < sub > p </ sub > M )) and orthogonal to v, remains orthogonal to v when pushed forward via the exponential map.

In mathematical analysis, a function of bounded variation, also known as a BV function, is a real-valued function whose total variation is bounded ( finite ): the graph of a function having this property is well behaved in a precise sense.

* Federal Office for Buildings and Logistics ( FBL ): Responsible for property management, central procurement of non-durable goods, federal publications and the production of the Swiss passport.

* Bouygues Immobilier ( 100 % share ): residential, corporate, commercial and hotel real estate and urban development, property development

The Hartley transform has the convenient property of being its own inverse ( an involution ):

A function f on an interval I is uniformly continuous if its natural extension f * in I * has the following property ( see Keisler, Foundations of Infinitesimal Calculus (' 07 ), p. 45 ):

Toledo, approximately 75 kilometres south-east of Madrid, was strategically important to the Muslims, and there the Christians were able to arrange a compromise making Toledo somewhat different from the rest of Muslim Iberia ( the Al Andalus ): Christians were permitted to practice their religion and retain their property.

WFF consists of three separate parcels of real property totaling 6, 200 acres ( 25 km² ): the Main Base, the Mainland, and the Wallops Island Launch Site.

This actually involves the sending of two AppleEvents to the target application ( and the receipt of their corresponding replies ): first, a get-data event is sent to retrieve the background color property of the window identified by the name " Old Drawing "; then a set-data event is sent to apply the value returned as the background color property of the window named " New Drawing ".

* Identify the real estate ( property ): At least the address, but preferably the legal description must be on the contract.