Further, suppose that no one can look inside another's box, and each claims to know what a " beetle " is only by examining their own box.

Further, suppose there exists u in L such that f ( u ) ≤ u and that any chain in the subset

Further suppose that the discount factor from now ( time zero ) until time is.

Further, suppose that G is irreducible: there is no subspace V other than 0 and the whole space which is invariant under the action of G. In other words,

Further suppose that the host also allows the contestant to take $ 500 instead of choosing a door.

Further suppose that

Further suppose that the fair market value of a ticket to the dance is 75 USD, and that the donor pays 375 USD to purchase a ticket.

Further, suppose that you are asked to perform the computation ' 68 + 57 '.

Further suppose that V is acted on by the Virasoro algebra in such a way that the adjoint of the operator L < sub > i </ sub > is L < sub >- i </ sub >, that the central element of the Virasoro algebra acts as multiplication by 24, that any vector of V is the sum of eigenvectors of L < sub > 0 </ sub > with non-negative integral eigenvalues, and that all eigenspaces of L < sub > 0 </ sub > are finite-dimensional.

Further suppose g is a function for which the two expectations E ( g ( X ) ( X − μ ) ) and E ( g ′( X ) ) both exist ( the existence of the expectation of any random variable is equivalent to the finiteness of the expectation of its absolute value ).

Further suppose, that the market has a 50 % chance of increasing, a 30 % chance of staying even, and a 20 % chance of decreasing.

Further, in 1945, about 100 filtration camps were set for repatriated Ostarbeiter, PoWs, and other displaced persons, which processed more than 4, 000, 000 people.

Further, landowners with 50 % or more of their income from agriculture were able to deduct the donation at a rate of 100 % of their AGI.

Further on, he departed from the date of the foundation of the Realms in Exile, calculated at 3320 of the Second Age on the basis of average reigns of the Kings in Númenor ; from the duration of the time of peace before the war of the Last Alliance, approximated at 100 years ; and from the date of the failing of the Kings in Gondor, proposed as T. A.

Further, the intense heat usually causes the halogen lamp to fail quickly, often lasting less than 100 hours before failing and requiring replacement.

Further major repairs were carried out in 1968 ( at a cost of £ 650 ) and 1976 (£ 2, 100 ).

Further, chainsaws, rock concerts, rocket engines, pneumatic drills, small firecrackers, and ambulance sirens are rated at 100 to 140 dB.

Further use for his discoveries was realised by researchers at IBM who, by 1980, had assembled an experimental computer switch structure, which would permit switching speeds from 10 to 100 times faster than those possible with conventional silicon-based chips, vastly increasing data processing capabilities.

Further 1 100 men were under command of Colonel Gustaf Mauritz Armfelt.

Further Confusion donated over $ 100, 000 to various charitable beneficiaries ( including animal shelters, rescue groups, and the Comic Book Legal Defense Fund ) in the period 1999-2008.

Further downstream, where it is bridged by the Kasama-Mpika road and the Tazara Railway, the permanent main channel is about 100 m wide, and up to 400 m wide in flood.

Further confirmation of this sighting was provided by a 1986 conversation American Everest historian Tom Holzel had with Wang's tent-mate from the 1975 expedition, Zhang Junyanon, who admitted that Wang had come back from a short excursion lasting about 20 minutes and described finding " a foreign mountaineer " at " 8, 100 m ."

Further upgrading of the trackwork at this station is ongoing as of July 2011 to facilitate higher speed running up to 100 MPH.

Further building work was planned with planning permission being sought to build a visitor's centre incorporating a 100 seater auditorium and cafe.

Further expansion plans in the late 1990s resulted in the demolition of more than 100 houses along the eastern part of the road.

Further superzoom was a 100 – 500 mm / 1: 8 Rokkor from Minolta and a 360-1200 / 1: 11 Nikkor from 1976.

Further, the 100 paintings ' sold ' after Rothko's death by the estate executors through Marlborough were not sold to bona fide purchasers, but were instead retained by the gallery which shuffled the sale monies through its accounts in Europe, and which then quickly're-sold ' the works to actual purchasers for 5 to 6 times the value declared by the estate.

Further singles from the album included " Heart Turns to Stone ", which had peaked at # 7 on the Hot Mainstream Rock Tracks chart in an earlier non-commercial release only to rock radio but only managed # 56 on the Hot 100 several months later, and the harder " Can't Wait ", which matched the # 18 Mainstream Rock Tracks charting of " I Don't Want To Live Without You " but failed to crack the Hot 100.

Further, the settlement includes a supplemental environmental project ( SEP ) valued at $ 100, 000 to plant vegetation along the banks of Horse Creek to decrease erosion and sedimentation, thereby improving water quality in Horse Creek.

Further bequests included £ 1, 400 and two houses in Marylebone and Argyll Ground Westminster to John Sherwine of Soho plus £ 100 to be given to a charity of Sherwine's daughters choice, to Robert Pringle of Clifton a Cavendish Square house and £ 400 and to Cosmo Alexander ( 1724 – 1772 ) a Scottish painter " my house I live in withall its furniture as it stands with pictures bustoes etc ".

Further bequests of £ 100 each went to William Thomas, Dr William King, St. Bartholomew's Hospital and the Foundling Hospital.

Further, most arbitrage opportunities were found to have small magnitudes, with 94 % of JPY and CHF opportunities existing at a difference of 1 basis point, which translates into a potential arbitrage profit of $ 100 USD per $ 1 million USD transacted.

Further theories arose after a journalist had a heart attack whilst on board the 2012 commemorative cruise that followed the same journey 100 years later.

Further improvements came in 2004, when she improved to 8. 07 s and 13. 08 s in the 60 and 100 metre hurdles.

Further, Alexander observed that many individuals commonly tightened the musculature of the upper torso as he had done, in anticipation of many other activities besides speech.

" Further, when asked if he felt ideologically closer to his father's engagement with politics or to other evangelicals who have tried to avoid civic involvement, he answered, " The gospel is for individuals.

Further, charges can also be brought against individuals or corporations who have sued or filed criminal charges against a defendant.

Further, since the suit was settled, other individuals have come forth, in class action lawsuits, claiming individual damages.

Further, Gay. com states that closeted individuals are reported to be at increased risk for suicide.

Further critics, learning from the broadly-defined psychoanalytic tradition, criticize the Homo economicus model as ignoring the inner conflicts that real-world individuals suffer, as between short-term and long-term goals ( e. g., eating chocolate cake and losing weight ) or between individual goals and societal values.

Further, while engaged in projection, individuals can be unable to access truthful memories, intentions, and experiences, even about their own nature, as is common in deep trauma.

Further, the individuals that inhabit these social structures are capable of consciously reflecting upon, and changing, the actions that produce them — a practice that is in part facilitated by social scientific research.

Further, individuals will not be able to take a member state to court for failing to uphold the rights in the Charter unless the member state in question was implementing EU law.

Further studies during the 1950s on immunosuppressed individuals showed that the disease was not as benign as once thought, and the search for various therapeutic and preventive measures began.

Beginning in 1999 with attendance of 691 individuals, Further Confusion has grown rapidly.

Further, he argues that the Establishment Clause ought not be considered a right that attaches to individuals pursuant to the Incorporation Doctrine, because he believes the clause only prohibits interference by the federal government in the right of individual states to establish their own official religions-notwithstanding current majority opinion on the question is against states having such a right, as a result of the Incorporation Doctrine.

Further damage was the reduction of investment: both large companies and individuals were unwilling and unable to invest in new ventures.

The IMA provides Education Grants of up to £ 600 to allow individuals from the UK working in schools or Further / Higher Education to help with the attendance at or the organisation of a mathematics educational activity such as attendance at a conference, expenses to cover a speaker coming into a school, organising a session for a conference.

Further ahead, by 2025-26 the number of middle class households in India is likely to more than double from the 2015-16 levels to 113. 8 million households or 547 million individuals.

Further criticisms of the JTPA stem from the argument that individuals can take advantage of the system due to the way that it is set up.

" Further, Barclays will not acquire Lehman's Eagle Energy unit, but will have entities known as Lehman Brothers Canada Inc, Lehman Brothers Sudamerica, Lehman Brothers Uruguay and its Private Investment Management business for high net-worth individuals.

Further suggestions for individuals to be honored were solicited in 1808 from Swiss historian Johannes von Müller.

Further studies have suggested that people who already have Alzheimer's disease have more clusterin in their blood, and that clusterin levels in blood correlate with faster cognitive decline in individuals with Alzheimer's disease, but have not found that clusterin levels predicted the onset of Alzheimer's disease.

" Further, when asked if he felt ideologically closer to his father's engagement with politics or to other evangelicals who have tried to avoid civic involvement, he answered, " The gospel is for individuals.

Further research has shown that mortality salient individuals also prefer leaders who are members of the same group, as well as men rather than women ( Hoyt et al.