Similarly, in Thermal quantum field theory a compactification of the euclidean time dimension leads to the Matsubara frequencies and thus to a discretized thermal energy spectrum.

Similarly, an arbitrary quantum operation can be implemented via introducing an ancilla and performing a suitable unitary evolution.

Similarly to a classical bit where the state of a transistor in a processor, the magnetization of a surface in a hard disk and the presence of current in a cable can all be used to represent bits in the same computer, an eventual quantum computer is likely to use various combinations of qubits in its design.

Similarly, Paul Dirac, one of the founders of quantum mechanics, began his academic career as an electrical engineer before proceeding to mathematics and later theoretical physics.

Similarly, in the de Broglie – Bohm theory, there are anomalous initial conditions which would produce measurement statistics in violation of the Born rule ( i. e., in conflict with the predictions of standard quantum theory ).

Similarly, a quantum particle moving in a potential can be described by a superposition of paths, each with a phase: the thermal variations in the shape across the collection have turned into quantum uncertainty in the path of the quantum particle.

Similarly, quantum fluctuations of the order parameter prevent most types of continuous symmetry breaking in one-dimensional systems even at zero-temperature ( an important exception is ferromagnets, whose order parameter, magnetization, is an exactly conserved quantitity and does not have any quantum fluctuations ).

A highest weight module is a module generated by a weight vector v, subject to for all weights μ, and for all i. Similarly, a quantum group can have a lowest weight representation and lowest weight module, i. e. a module generated by a weight vector v, subject to for all weights λ, and for all i.

Similarly, a quantum algorithm is a step-by-step procedure, where each of the steps can be performed on a quantum computer.

Similarly, let A be an observable of a quantum mechanical system.

Similarly, a periodic structure of alternating thin films of different materials may collectively form a so-called superlattice which exploits the phenomenon of quantum confinement by restricting electronic phenomena to two-dimensions.

Similarly, the argument for BPP almost goes through for BQP, but we have to additionally show that quantum queries can be performed in coherent superposition.

Similarly, quantum measurement tomography works to find out what measurement is being performed.

Similarly, in radio CDMA, each group of users is given a shared code.

Similarly, the multiplicative group of the field is a cyclic group.

Similarly, he accompanied Cardinal Ottobuono Fieschi, the future Pope Adrian V, to England in 1265 – 1268 to suppress a rebellion by a group of barons against King Henry III of England.

Similarly, in British law the phrase racial group means " any group of people who are defined by reference to their race, colour, nationality ( including citizenship ) or ethnic or national origin ".

Similarly, a meta-analysis of five studies of group psychotherapy for adult sexual abuse survivors showed moderate to strong effect sizes, and there is also good evidence for effectiveness with chronic traumatic stress in war veterans.

Similarly, the additive group Z of integers is not simple ; the set of even integers is a non-trivial proper normal subgroup.

Similarly, they were, at one time or another, at war with virtually every other Native American group living in the Great Plains, leaving opportunities for political maneuvering by European colonial powers and the United States.

Similarly, in British law the phrase racial group means " any group of people who are defined by reference to their race, colour, nationality ( including citizenship ) or ethnic or national origin ".

Similarly, in hexadecimal ( base 16 ), full spaces are usually used to group digits into twos.

Similarly, in a group of women who initially did not have difficulties achieving orgasm, 41 % acquired this problem during treatment with sertraline.

Similarly, if deaf parents were to raise a group of hearing children who have no contact with others until adulthood, they might develop an oral language among themselves and keep using it later, teaching it to their children, and so on.

Similarly, any set with 4 elements can be given two non-isomorphic group structures: one isomorphic to ; the other isomorphic to.

Similarly, if g and h are elements of a finite cyclic group G then a solution x of the equation g < sup > x </ sup > = h is called a discrete logarithm to the base g of h in the group G.

Similarly, in complex territorial and cooperative breeding bird communities ( such as the Australian magpie ) that have a high degree of etiquettes, rules, hierarchies, play, songs and negotiations, rule-breaking seems tolerated on occasions not obviously related to survival of the individual or group ; behaviour often appearing to exhibit a touching gentleness and tenderness.

Similarly, his 78 knockout wins make him a member of an exclusive group of boxers to have won 50 or more fights by knockout.

* Similarly, the free group F < sub > n </ sub > has p < sup > n </ sup > − 1 subgroups of index p.

Similarly, the title for Harry Potter and the Order of the Phoenix did not make it obvious whether the word " Order " referred to a group of people or to a directive.

Similarly, the multiplicative group of adeles, called the group of ideles, is a locally compact group with respect to its topology defined below.

Similarly, the group of ideles has a nontrivial translation invariant measure using which one defines a zeta integral.

Similarly, section 7482 of the Internal Revenue Code provides that the U. S. Supreme Court and the federal courts of appeals may impose penalties where the taxpayer's appeal of a U. S. Tax Court decision was " maintained primarily for delay " or where " the taxpayer's position in the appeal is frivolous or groundless.

Similarly, most patented medications cost more in the U. S. than in other countries with a ( presumed ) poorer customer base.

Similarly, at a cost of $ 36 per pint, " Opium Concentrated, for U. S. P.

" Similarly, among U. S. authorities, such a sense of collective guilt was " considered a prerequisite to any long-term education of the German people.

Similarly, at a cost of $ 36 per pint, " Opium Concentrated, for U. S. P.

Similarly, in an article by CNN Money, Yorba Linda was one of the richest U. S. cities and the richest in Orange County as reported by the Census data, showing a median household income of more than $ 120K: " Among towns of between 65, 000 and 250, 000 in population, Yorba Linda, California, where six-figure incomes are the rule, had the highest median income at $ 121, 075 "

Similarly, low interest rate policies by the U. S. Federal Reserve in the 2001-2004 are believed to have exacerbated housing and commodities bubbles.

Similarly, M was a one-hit wonder in the U. S. with the 1979 # 1 pop hit " Pop Muzik ," but in the UK, where the original " Pop Muzik " hit # 2, the improbably titled " Moonlight & Muzak " made it to # 33, a re-mix of " Pop Muzik " hit # 15 in 1989 and two other singles (" That's the Way the Money Goes " and " Official Secrets ") charted, albeit missing the UK top 40.

Similarly, in Minnesota v. Clover Leaf Creamery Co., 449 U. S. 456 ( 1981 ) the Court upheld a state law that banned nonreturnable milk containers made of plastic, but permitted other nonreturnable milk containers.

Similarly, if U > U *, inflation tends to slow.

Similarly, at high unemployment rates ( greater than U *) lead to low inflation

Similarly, for i < j, the joint probability density function of the two order statistics U < sub > i </ sub > < U < sub > j </ sub > can be shown to be

Similarly, if T is a subtype of U, then there is an inclusion predicate of domain type T and codomain type U that satisfies the same equation ; there are additional function symbols associated with other ways of constructing new types out of old ones.

Similarly brokers attending the U. S., Mexico, Colombia, Brazil, Tanzania, Costa Rica, Kenya, Belgium, Venezuela, Canada and others.

Similarly, the term " Strategic Corporal " refers to the special responsibilities conferred upon a Marine corporal over the other branches of the U. S. armed forces.

Similarly, Georg Rickhey, who came to the United States under Operation Paperclip in 1946, was returned to Germany to stand trial at the Mittelbau-Dora war crimes trial in 1947, was acquitted, and returned to the United States in 1948, eventually becoming a U. S. citizen.

Similarly, all lunar meteorites collected by the U. S. and Japanese Antarctic programs are, by treaty, held by those governments for research and education purposes only.

Similarly, if a player is short on Energy, some land plots won't produce any output, while a shortage of Smithore will raise the price of M. U. L. E. s in the store and prevent the store from manufacturing new M. U. L. E. s to make use of one's land.

Similarly, in 1991, when Shi ' a across Iraq revolted against Hussein's regime ( partially in response to the televised rallying call to do so by U. S. President George H. W. Bush ), the U. S. justification for ultimately staying out of the revolt and allowing Hussein's security forces to suppress the rebels was that the U. S. had strategically decided Hussein's rule was better than the risk of a mujahideen-or Iranian Revolution-style takeover.