Furthermore, all solutions x of this system are congruent modulo the product, N = n < sub > 1 </ sub > n < sub > 2 </ sub >… n < sub > k </ sub >.

Furthermore, this fixed point can be found as follows: start with an arbitrary element x < sub > 0 </ sub > in X and define an iterative sequence by x < sub > n </ sub >

Furthermore, the inclusion is proper if and only if m is a proper divisor of n ( i. e., with k not equal to either 1 or − 1 ).

Furthermore, one can use a generalization of this formula to find explicit expressions for the nth roots of unity, that is, complex numbers z such that z < sup > n </ sup >

Furthermore, the theorem says that if two subsets U and V of R < sup > n </ sup > are homeomorphic, and U is open, then V must be open as well.

Furthermore, he proved that as n tends to infinity, the number of primes between 3n and 4n also goes to infinity, thereby generalizing Erdős ' and Ramanujan's results ( see the section on Erdős ' theorems above ).

Furthermore, P < sub > 0 </ sub >( T ) = 1 − T, P < sub > 2n </ sub >( T ) = 1 − q < sup > n </ sup > T, and for, P < sub > i </ sub >( T ) factors over C as for some numbers α < sub > ij </ sub >.

Furthermore, the theta function of an even unimodular lattice of rank n is actually a modular form of weight n / 2.

Furthermore, if the highest excitation level in the operator is n,

Furthermore, the trial factors need go no further than because, if n is divisible by some number p, then n

Furthermore, they performed the songs " Desayuno Continental " and " No Puedo Soportar Perderte ", in addition to " Separados ", to a small audience at their own Pop ' n ' Roll bar in Madrid.

) Furthermore, a similar factorization holds for any n × n rotation matrix.

* 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, it is a nontrivial ideal: let n be the finite dimension of the algebra of matrices, then

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 when n is odd, the number of ordinary lines is at least 3n / 4 − C, for some constant C. Thus, the constructions of Böröczky for even and odd ( discussed above ) are best possible.

Furthermore, the theta function of an even unimodular lattice of rank n is actually a modular form of weight n / 2.

Furthermore, in the wake of the Shuttle's retirement, further redesign of the Propulsion Module would have been necessary.

Furthermore, despite the many challenges faced with the control policy affecting student-intake for the alleged qualitative improvement of universities, which was introduced in the wake of the 5. 16 Military Coup in 1961, CAU was able to appoint Dr. Sung-Hee Yim as its second chancellor on 2 October 1961.

Furthermore, if the Lieutenant Governor becomes incapacitated while serving in the office of Governor, the next most senior judge of the Supreme Court is sworn in as the Administrator.

Furthermore, it has been argued that the Supreme Court should have been able to issue the writ on original jurisdiction based on the fact that Article III of the Constitution granted it the right to review on original jurisdiction " all cases affecting … public ministers and consuls ," and that James Madison, Secretary of State at the time and defendant of the suit, should have fallen into that category of a " public minister consul.

Furthermore, while the courts in the United Kingdom are undoubtedly amongst the most independent in the world, the Law Lords, who were the final arbiters of judicial disputes in the UK sat simultaneously in the House of Lords, the upper house of the legislature, although this arrangement ceased in 2009 when the Supreme Court of the United Kingdom came into existence.

Furthermore, the Supreme Commander of the Unified Armed Forces of the Warsaw Treaty Organization was also a First Deputy Minister of Defense of the USSR, and the head of the Warsaw Treaty Combined Staff also was a First Deputy Chief of the General Staff of the Armed Forces of the USSR.

Furthermore, constitutional issues, such as the establishment of the Supreme Court of New Zealand, may be done without a referendum.

Furthermore, self discovered in the Supreme experience is not a single universal Ātman.

Furthermore, the Nevada Supreme Court ruled that absent a statutory revision by the legislature, elected constables ( but not their deputies ) were exempt from the provisions of NRS 289. 550, the primary statute establishing peace officer standards.

Furthermore, a confidential letter sent on October 29, 2005 by the Chairman of the Command Headquarters of the Armed Forced in Iran states that the Supreme Leader of Iran, Ayatollah Khamenei has instructed the Command Headquarters to identify people who adhere to the Bahá ' í Faith and to monitor their activities and gather any and all information about the members of the Bahá ' í Faith.

Furthermore, < u > The United States Supreme Court: A Political and Legal Analysis </ u > discussed the results of a 1991 survey, stating that: " The Court's school prayer decisions were, and still are, deeply unpopular with the public, many politicians and most religions organisations.

Furthermore, CHP officers act as bailiffs for the California Supreme Court and security at State of California buildings.

Furthermore, he defied the Supreme Court in enforcing the policy of ethnically cleansing Native American tribes (" Indian Removal "); he stated, " John Marshall has made his decision.

Furthermore, the California Supreme Court expanded this amendment to class actions in Arias v. Superior Court by holding that “ unaffected ” plaintiffs no longer may bring a class action lawsuit unless they satisfy the regular requirements laid out in Cal.

Furthermore, a referendum in California had overturned the California Supreme Court's earlier decision ( California v. Anderson ) holding that the death penalty violated the California constitution.

Furthermore, in 2009 the United States Supreme Court found in a unanimous opinion in Rivera v. Illinois that " there is no freestanding constitutional right to peremptory challenges ," even when a court was mistaken in applying Batson.

Furthermore, the Court was well aware that nearly a century before the Supreme Court decision in Chisholm v. Georgia,, holding that states could be sued in federal courts by citizens of other states, had sparked negative reaction and two years later Congress and the states expressed their will in the Eleventh Amendment.

Furthermore, in his capacity as secretary of the Supreme Council, he was also familiar with other aristocrats like Clanricarde and James Dillon, whose thoughts and actions during 1641-42 he recounts extensively in his history of the period.

Furthermore, when federal law limits the states ’ ability to change the definition of state-created legal interests, the Supreme Court has jurisdiction to review the state court ’ s characterization of the law both before and after the change.

Furthermore, the Court declared that the concept of terra nullius ( un-owned land ) did not apply to the territory.

Furthermore, the Court refused to apply the proportionality standards of the Fourteenth Amendment or the free-speech standards in the First Amendment to limit Congress's ability to confer copyrights for limited terms.

Furthermore, Samuel A ' Court Ashe was convinced that the colonists had relocated westward to the banks of the Chowan River in Bertie County, and Conway Whittle Sams claimed that after being attacked by Wanchese and Powhatan, the colonists scattered to multiple locations: the Chowan River, and south to the Pamlico and Neuse Rivers.

Furthermore, the Court ruled that slaves, as chattels or private property, could not be taken away from their owners without due process.

Furthermore, when the office of the Solicitor General endorses a petition for certiorari, review is frequently granted, which is remarkable given that only 75 – 125 of the over 7, 500 petitions submitted each term are granted review by the Court.

Furthermore, the Court held the exercise of editorial judgment is a protected First Amendment activity.

" Furthermore, the Court pointed out that in neither case was there an " ' express jurisdictional element which might limit its reach ( to those instances that ) have an explicit connection with or effect on interstate commerce.

Furthermore, he was an opponent of the 1972 Anti-Ballistic Missile Treaty, the International Criminal Court and the Chemical Weapons Convention which he criticized as ineffective and dangerous to U. S. interests.

Furthermore, the Danish Constitution provides for the Court of Impeachment of the Realm ( Rigsretten ) to hear cases brought against ministers concerning their administration.

Furthermore, he advocated Soviet entry into several important international organizations, such as the CSCE and International Court of Justice.

Furthermore, the parties to the proposed partnership must not be within the prohibited degrees of relationship specified in part 1 of schedule 1, paragraphs 1 and 2 of the Act ( paragraph 3 was not brought into force following a ruling from the European Court of Human Rights against similar provisions for marriage ).

Furthermore, the Court went on to state that blacks were not citizens of the United States and could not become citizens and therefore they could not sue in a court.

Furthermore, it did not believe that the Divisional Court had " acknowledged the constitutional enormity, as the law stands, of requiring a Secretary of State to act contrary to the clearly expressed will of Parliament when the unlawfulness of that expression has yet to be established.

Furthermore, the Court contended that the Amish community was a very successful social unit in American society, a self-sufficient, law-abiding member of society, which paid all of the required taxes and rejected any type of public welfare.