A final class of exceptional lines is identifiable from the following considerations: Since no two generators of Af can intersect, it follows that their image curves can have no free intersections.

Since I have already discussed his moral position, that discussion is incorporated by reference into the following pages, which will focus on the empirical and analytic side of Fromm's treatment.

Since the change to better nutrition, he feels he can report on improvements in health, though he considers the following statements observations and not scientific proof.

Since the Catholic Church expresses such desire that the Sacred Scriptures be read, the following taken from the Holy Bible ( New Catholic Edition ) will prove a means of grace and a source of great spiritual blessing.

Since the administrative reforms in Bavaria in the 1970s, the town also encompasses the following Ortsteile:

Since we require the process to be adiabatic, the following equation needs to be true

Since its video release it has acquired a cult following, along with the other two films in the trilogy.

Since the area has been referred to as the Balkans, notable conflicts have included the following

Since 1964, following clashes between the two communities, the Turkish Cypriot seats in the House remained vacant, while the Greek Cypriot Communal Chamber was abolished.

Since the 1980s, following the popularization of computer technology, it has become fashionable in marketing for names of products and companies, and for 1990s online video games where players use pseudonyms ( when spaces were not allowed ).

Since the corona has been photographated at high resolution in the X-rays by the satellite Skylab in 1973, and then later by Yohkoh and the other following space instruments, it has been seen that the structure of the corona is very various and complex: different zones have been immediately classified on the coronal disc

Since the Iraq War, evangelicalism has begun to make inroads in Iraq, capitalizing on a new openness to Western missionaries following the US-led invasion of the country, although the vast majority of converts are from other sects of Christianity present in Iraq .< ref >

Since Arafat's death, he is formally head of Fatah's political bureau and chairman, but his actual political following within Fatah appears limited.

Since July 2007, following the 2006 Palestinian legislative election and the following Battle of Gaza, Hamas has functioned as the de-facto ruler in the Gaza Strip, forming an alternative Hamas Government in Gaza.

Since then, and even in recent years, public spokesmen in Haiti as well as international academics and statesmen have denounced this event as the payment of an illegitimate debt, in several cases calling on the French government to repay it ( the French government has never been willing to repay it, though there was a hoax following the 2010 Haiti Earthquake involving a fake website purporting to offer reparation payment on behalf of the French Government ).

Since homomorphisms are morphisms, the following specific kinds of morphisms defined in any category are defined for homomorphisms as well.

Since 1990, Hezbollah has been accused of the following attacks and attempted attacks.

Since cast iron was becoming cheaper and more plentiful, it also became a major structural material following the building of the innovative Iron Bridge in 1778 by Abraham Darby III.

Since the 1950s, following the lead of D. W. Jefferson, there are those who argue that, whatever its legacy of influence may be, Tristram Shandy in its original context actually represents a resurgence of a much older, Renaissance tradition of " Learned Wit " – owing a debt to such influences as the Scriblerian approach.

Since 1980, linguists studying children, such as Melissa Bowerman, and psychologists following Jean Piaget, like Elizabeth Bates and Jean Mandler, came to suspect that there may indeed be many learning processes involved in the acquisition process, and that ignoring the role of learning may have been a mistake.

Since July 2012, Odyssey has been back in full, nominal operation mode following three weeks of ' safe ' mode on remote maintenance.

Since 2003, following the death in custody of a prisoner, Naseem, the Maldives experienced several anti-government demonstrations calling for political reforms, more freedoms and, and end to torture and oppression.

Since its economy was highly dependent on the rest of the former Soviet Union for energy and raw materials, the breakdown in trade following the breakup of the Soviet Union had a serious effect, exacerbated at times by drought and civil conflict.

Since two of these could be trustees of the college, actually it would be necessary to have the consent of only one elected official to impose a levy of millions of dollars of tax revenue.

Since accurate base maps are necessary for any planning program, the first step taken by the planning division to implement the long-range state plan has been to prepare two series of base maps -- one at a scale of 1 inch to a mile, and the second a series of 26 sheets at a scale of 1 inch to 2000 feet, covering the entire state.

Since two curves of symbol Af on Q intersect in Af points, it follows that there are Af lines of Af which are tangent to Aj.

Since Parts 1, and 2, were prepared independently, the abbreviation schemes and the chemical symbols used differ in the two parts.

Since the days when their two thousand pairs of skis outnumbered those assembled anywhere else in the United States, the students have stopped regarding the Olympic Ski Team as another name for their own.

( page 33 ) On the other hand, a little later on he says: `` Since 1692 a great but superficial change has wiped out God's beard and the Devil's horns, but the world is still gripped between two diametrically opposed absolutes.

Since the hero, a sterling and upright fellow, is a rich Brown senior, while two Yalies are cast as virtual rapists, I suppose I should disqualify myself from sitting in judgment on `` Where The Boys Are '', but I shall do nothing of the sort.

Since the 1950s, this type of fiction has to a large extent merged with science fictional tropes involving cross-time travel between alternate histories or psychic awareness of the existence of " our " universe by the people in another ; or ordinary voyaging uptime ( into the past ) or downtime ( into the future ) that results in history splitting into two or more time-lines.

Since complex scalar fields admit two different kinds of annihilation operators, which are related by conjugation, such fields describe charged bosons.

Since the 1960s, composite airframes and quieter, more efficient engines have become available, and Concorde provided supersonic passenger service for more than two decades, but the most important lasting innovations have taken place in instrumentation and control.

Since the English Reformation, the Church of England has been more explicitly a state church and the choice is legally that of the British crown ; today it is made in the name of the Sovereign by the Prime Minister, from a shortlist of two selected by an ad hoc committee called the Crown Nominations Commission.

Since 1990, Bulgaria has an unstable party system, in the past two decades differently dominated by the post-communist Bulgarian Socialist Party or by the right Union of Democratic Forces and recently by the new right-oriented party-Citizens for European Development of Bulgaria.

Since 1961, only two new parties ( Bündnis 90 / Die Grünen and PDS / Die Linke ) have entered the Bundestag.

Since these two constructions are inverses of each other, we can say that every Boolean ring arises from a Boolean algebra, and vice versa.

* Since Big Brother 2, the UK series always opens with a twist which have included the public being able to choose the final housemate out of three possibilities ( Big Brother 2 ), the public voting for a housemate to leave during the first week and then the housemates choosing between the two housemates with the least number of votes ( Big Brother 3 ), First Night Nominations ( Big Brother 4 ), Suitcase Nominations ( Big Brother 5 ), Unlucky Housemate 13 ( Big Brother 6 ), Big Brother Hood ( Big Brother 7 ), an all-female House and the first inclusion of twins as contestants ( Big Brother 8 ), the first couple to enter as housemates and set a secret task to hide their real relationship ( Big Brother 9 ), all " housemates " really being " non-housemates " who had to earn their housemate status ( Big Brother 10 ), a mole entering the House with an " Impossible Task " ( Big Brother 11 ), Jackie Stallone entering a house containing her son's ex-wife ( Celebrity Big Brother 3 ), the entrance of a non-celebrity in a celebrity edition ( Celebrity Big Brother 4 ) and Jade Goody's family announced to be visiting.

Since these are a basis, any quantum state of the particle can be expressed as a linear combination ( i. e., quantum superposition ) of these two states:

Since then, with several relaunches, an increase in funding and resources from the BBC and improvements in digital television technology, the channel has been able to diversify content, with two minute looped bulletins available to view via BBC Red Button, BBC News Online and the BBC's mobile website, alongside individual weather and sport bulletins.

Since this is a second-order differential equation, there must be two linearly independent solutions.

Since the late nineteenth century, only two brief periods of violence have marred its democratic development.

Since 1974, the internationally recognised Republic of Cyprus has controlled the south two thirds, and the Turkish Republic of Northern Cyprus the northern one-third.

Since these are two very different referents, the validity of the term has been called into question.