Furthermore, she has known about Möbius for years and has been secretly copying his documents and using his scientific discoveries to construct an international empire.

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, Wolfgang Rindler, in his popular textbook on relativity, used the squeeze mapping form of Lorentz transformations in his demonstration of their characteristic property ( see equation 29. 5 on page 45 of the 1969 edition, or equation 2. 17 on page 37 of the 1977 edition, or equation 2. 16 on page 52 of the 2001 edition ).

Furthermore, a map f: A → B is a homomorphism of Boolean algebras if and only if it is a homomorphism of Boolean rings.

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, 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, 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, in Arabic the term can be generalized to mean any province of a country that is administered by a member of the ruling class, especially of a member ( usually styled emir ) of the royal family, as in Saudi Arabian governorates.

Furthermore, this can be generalized so that the entries in A can be real numbers representing connection strengths, as in a stochastic matrix.

Furthermore, if, then q is said to be a cyclic coordinate and the generalized momentum p defined by

Furthermore because of the Feuerbach conic theorem mentioned above, there exists a unique rectangular circumconic, centered at the common intersection point of the four nine-point circles, that passes through the four original arbitrary points as well as the orthocenters of the four triangles.

Furthermore there has been a fear in some circles that Chinese society has become too materialistic placing material wealth above all other social needs.

Furthermore, Carr notes that " tripped of its Islamic content, the broad contours of Ye ’ or ’ s preposterous thesis Eurabia: The Euro-Arab Axis recall the anti-Semitic conspiracy theories of the first half of the twentieth century and contemporary notions of the ‘ Zionist Occupation Government ’ prevalent in far-right circles in the US ".

Furthermore, it led to the recognition of his contributions to the evaluations of mineral deposits through the coining of the term ‘ kriging ’ that is used to describe a spatial mineral evaluation process known and practised in international mining circles.

Furthermore, in Germany proper, voices rose from various circles to speak for the sentenced men.

Furthermore, the exchange would not be expected to be sensitive to trace amounts of impurities because it would not be apt to be a chain reaction since the activation energy for abstraction of chlorine by a chlorine atom would be expected to be too high ; ;

Furthermore, one can find a neighborhood of Q in which the difference function is monotone, for since it is analytic it can have only a finite number of extrema in any interval.

Furthermore, since the wind varies in direction and the axis has to follow its changes, a wind vane or some other contrivance to fulfill the same purpose must be employed.

Furthermore, since 2002 more than 4 million refugees returned to Afghanistan.

Furthermore, transcripts made from the same gene may not have the same exon structure, since parts of the mRNA could be removed by the process of alternative splicing.

Furthermore, since the inscriptions were erected only in 17 to 18 BCE, the word may be a later addition to the text.

Furthermore, since 2 February 2007 an Italian, Claudio Graziano is the commander of the UN force in the country.

Furthermore, since all functions expecting more than one input can be transformed into equivalent functions accepting a single input ( via Currying ), the lambda calculus has no means for creating a function that accepts more than one argument.

Furthermore, since the AES was identical to its arcade counterpart, the MVS, arcade titles released for the home market were perfect translations.

Furthermore, since internal class conflict had been overcome, workers could now be duly rewarded for their qualifications and technical skills without contravening Marxism-Leninism.

Furthermore, the act provided that any bill rejected by the Lords would nevertheless become law if passed by the Commons in three successive sessions provided that two years had elapsed since its original passage.

) Furthermore, a ring of formal power series in one variable over a field is a PID since every ideal is of the form.

Furthermore, assassination attempts by radical Palestinian factions within the PLO since the early years of the peace process kept Arafat from expressing full, public support of the peace process or condemnation of terrorism without risking further danger to his own life.

Furthermore, although the transmission systems are still functional, receiving aerials in many places have long since been dismantled or are unmaintained.

Furthermore, compared to the United States, since 1971 Canadian core cities have not experienced as much population decline, have been allowed to annex more outlying areas, and have enacted zoning policies that are more tolerant of density.

Furthermore, since burglars often know likely hiding places, the house owner will experience greater risk of a burglary by hiding the key in this way, since the effort of finding the key is likely to be less effort to the burglar than breaking in by another means, such as through a glass window.

Furthermore, since Tantra dissolved the dichotomy of spiritual versus mundane, practitioners could entail every aspect of their daily lives into their spiritual growth process, seeking to realize the transcendent in the immanent.

Furthermore, since the brook-crossings do not always correspond to the beginning and ends of chapters, most editions of the book visually represent the crossings by breaking the text with several lines of asterisks ( * * * ).

Furthermore, both Anne and Maria Theresa had renounced their rights to the Spanish succession upon their marriages, although in the latter case the renunciation was widely seen as invalid, since it had been predicated upon Spain's payment of the Infanta's dowry, which was never paid.

* Furthermore, in practice, a signal can never be perfectly bandlimited, since ideal " brick-wall " filters cannot be realized.

Furthermore, since the Treaty of Lisbon took effect on 1 December 2009, the EU is expected to sign the Convention.

Furthermore, RS codes are suitable as multiple-burst bit-error correcting codes, since a sequence of b + 1 consecutive bit errors can affect at most two symbols of size b.

Furthermore, Catiline had little motive to participate in this conspiracy, especially since he had been denied very little.

Furthermore, it was impossible for the Umayyads to judge the size of Martel's army, since Charles had used the trees and forest to help conceal his true numbers.