Furthermore, the pirate mechanics have also changed: the pirate moves through the middle of the map in a fixed path every turn, and attacks the owner of any nearby settlements.

Furthermore, Milowice was placed on a 1561 map.

Furthermore, because ontologies are topic maps themselves, they can also be merged thus allowing for the automated integration of information from diverse sources into a coherent new topic map.

Furthermore, the elements that are actually in P are precisely those whose reflection vanishes at P. So if we think of the map, associated to any element a of A:

Furthermore, every continuous map with codomain Y gives rise to a uniquely defined local homeomorphism with codomain Y in a natural way.

Furthermore, Möbius transformations map generalized circles to generalized circles since circle inversion has this property.

Furthermore, both of these functions can always be written as functions of η, even when η ( θ ) is not a one-to-one function, i. e. two or more different values of θ map to the same value of η ( θ ), and hence η ( θ ) cannot be inverted.

Furthermore, it is easy to check that f < sup > − 1 </ sup > ( like any inverse image map ) preserves finite intersections and arbitrary unions and therefore is a morphism of frames.

If f is flat and locally of finite presentation, then f is universally open .< ref > EGA IV < sub > 2 </ sub >, Théorème 2. 4. 6 .</ ref > However, if f is faithfully flat and quasi-compact, it is not in general true that f is open, even if X and Y are noetherian .< ref > EGA IV < sub > 2 </ sub >, Remarques 2. 4. 8 ( i ).</ ref > Furthermore, no converse to this statement holds: If f is the canonical map from the reduced scheme X < sub > red </ sub > to X, then f is a universal homeomorphism, but for X noetherian, f is never flat .< ref > EGA IV < sub > 2 </ sub >, Remarques 2. 4. 8 ( ii ).</ ref >

Furthermore, if two points on the 3-sphere map to the same point on the 2-sphere, i. e., if p ( z < sub > 0 </ sub >, z < sub > 1 </ sub >)

Furthermore, the map φ ↦ φ < sup > an </ sup > maps open immersions into open immersions.

Furthermore, Animagus disguises, Polyjuice Potion, and Invisibility Cloaks cannot fool the map, as shown in Goblet of Fire when Barty Crouch, Jr., using a Polyjuice Potion to disguise himself as Moody, and in Prisoner of Azkaban when Peter Pettigrew, who is supposed to be dead but as an Animagus has transformed into a rat, are both displayed on the map.

Furthermore, the people who helped to develop the map such as Choe Han-gi and Shin Hun was not convicted at all.

Furthermore, the surrounding wall of the city has shrunk since dating methods made it possible to show the precedence of the outer battlements compared to the inner battlements ( see the map ).

Furthermore, the approach is meant to allow the dynamic adjunction of a path in the map, i. e. adding a new strategy or a new section in the actual course of the process.

Furthermore he produced a large world map and a map of the Chinese empire and neighboring territories.

Furthermore, every positive map from to can be decomposed into a sum of completely positive and completely copositive maps, when and.

Furthermore, a Patterson map of N points will have N ( N − 1 ) peaks, excluding the central peak and any overlap.

Furthermore, because f is differentiable at g ( a ) by assumption, Q is continuous at g ( a ).

Furthermore, for mathematicians, according to this formula the gluon color field can be represented by a SU ( 3 )- Lie algebra-valued " curvature "- 2-form where is a " vector potential "- 1-form corresponding to G and is the ( antisymmetric ) " wedge product " of this algebra, producing the " structure constants " f < sup > abc </ sup >.

Furthermore, if the morphism f is a monomorphism, then so is the morphism ker a → ker b, and if g is an epimorphism, then so is coker b → coker c.

Furthermore, for each f for which f ( 1 ) ≠ 0 there exists a g such that f * g =

Furthermore, Marx seems to believe that the former ( and hence, of both ) is ' imminent ' ( c. f.

Furthermore, f is Lebesgue integrable on

Furthermore, if, and if the Frobenius endomorphism of F is an automorphism, g may be written as, and in particular, ; a contradiction of the irreducibility of f. Therefore, if F possesses an inseparable irreducible ( non-zero ) polynomial, then the Frobenius endomorphism of F cannot be an automorphism ( where F is assumed to have prime characteristic p ).

Furthermore, the polynomial f ( Y )= Y < sup > p </ sup >− X is inseparable.

Furthermore, let S be a subset of P that has a least upper bound s. Then f preserves the supremum of S if the set f ( S ) =

Furthermore, of the song Beauty Fiend, she stated: “ Beauty Fiend is meant to be a real ‘ f ** ck you ’ of a song ... I ’ m not here to be your sex symbol, I ’ m not here to be your pretty girl on the cover.

Furthermore, | f ( b < sub > k </ sub >)| should be less than or equal to | f ( a < sub > k </ sub >)|, so that b < sub > k </ sub > is a better guess for the unknown solution than a < sub > k </ sub >.

Furthermore, it may happen that all polynomial invariants f take the same value on a given pair of points u and v in V, yet these points are in different orbits of the G-action.

Furthermore, there are pure injective homomorphisms H → H **, natural in H. One can often simplify a problem by first applying the *- functor, since algebraically compact modules are easier to deal with.

Furthermore, I < sup > α </ sup > ƒ tends to ƒ in the L < sup > p </ sup > sense as α → 0 along the real axis.

Furthermore, there is a simplex category, denoted by whose objects are maps ( i. e. natural transformations ) Δ < sup > n </ sup > → X and whose morphisms are natural transformations Δ < sup > n </ sup > → Δ < sup > m </ sup > over X arising from maps n → m in Δ.

Furthermore, assorted pastas are rich in essential nutrients, such as iron and vitamin B.

Furthermore, maximal ideals can be generalized by defining a maximal sub-bimodule M of a bimodule B to be a proper sub-bimodule of M which is contained by no other proper sub-bimodule of M. So, the maximal ideals of R are exactly the maximal sub-bimodules of the bimodule < sub > R </ sub > R < sub > R </ sub >.

Furthermore, for every object A, the identity function on the underlying set of A must be a morphism from A to A, and the composition of a morphism from A to B followed by a morphism from B to C must be a morphism from A to C.

Furthermore the two are simultaneously diagonalizable, that is: both A and B are made diagonal by the same unitary matrix U. Both UAU < sup >*</ sup > and UBU < sup >*</ sup > are diagonal matrices.

Furthermore, Bahia were relegated to Série B in 2003 and relegated, for the first time ever, to Série C in 2005, spending two seasons at the bottom of the Brazilian League System.

Furthermore, both arguments, which can be reduced to “ If A, then B ; but not-A, therefore not-B ”, are logically flawed.

Furthermore, depletion of Emi1 in somatic cells leads to the lack of accumulation of cyclin B.

Furthermore, allocation of a drug in Category B does not necessarily imply greater safety than Category C.

Furthermore, in the video codec H. 264, the frame can be segmented into sequences of macroblocks called slices, and instead of using I, B and P-frame type selections, the encoder can choose the prediction style distinctly on each individual slice.

* Furthermore, every free module has a free resolution of length zero, so by the argument above, if F is a free R-module, then Tor ( F, B ) = 0 for all n ≥ 1.

Furthermore, the distance between the two images, 6 arcseconds, was too great to have been produced by the gravitational effect of the galaxy G1, a galaxy identified near quasar B.

Furthermore, we assume that we are given a SO ( p, q ) principal bundle B over M and a SO ( p, q )- vector bundle V associated to B by means of the natural n-dimensional representation of SO ( p, q ).

Furthermore, Federal Highway ( Bundesstraße ) B 455 also runs through the town.

Furthermore, it produced three popular singles, all charting at least in the top 50 on both the Billboard R & B and the Billboard Hot 100 chart.

Furthermore, Type B personalities may have a poor sense of time schedule and can be predominately right brained thinkers.

Hay found that form F was significantly easier than Form D. Furthermore, Kazmier found Form B to be the most difficult of the five forms and, thus, recommended that it " not be regarded as directly equivalent to any of the forms.

Furthermore, another newly constructed highway, the B. P.

Furthermore, with the hit singles, " La Schmoove " ( featuring Phife Dawg of A Tribe Called Quest ) and " True Fu-Schnick ", the album reached the Top 20 in the Top R & B / Hip-Hop Albums chart and was certified gold by the RIAA.

Furthermore, the above can be expressed in a more strict logical form ( where K ( x ) means " x is the king of France ", B ( x ) means " x is bald ", the bullet means " and ", and the arrow means " if-then "):

Furthermore, if B is deceived by A as to the ownership or boundaries of C's land, A may be jointly liable with B for B's trespass.

Furthermore, if a new use of nearby land interferes with a land owner's quiet enjoyment of his rights, there may be an action for nuisance, as where a disagreeable aroma or noise from A drifts across the land of B.