" If the remainder of the Conservative Party could muster the electoral support necessary to form a government, then Disraeli was now guaranteed high office.

More than half of these can be found in the HSBC Money Gallery ( Gallery 68 ), while the remainder form part of the permanent displays throughout the Museum.

Now the remainder of dividing either a or b by d is also of the form ax + by since it is obtained by subtracting a multiple of from a or b, and on the other hand it has to be strictly smaller in absolute value than d. This leaves 0 as only possibility for such a remainder, so d divides a and b exactly.

* Every pair of congruence relations for an unknown integer x, of the form x ≡ k ( mod a ) and x ≡ l ( mod b ), has a solution, as stated by the Chinese remainder theorem ; in fact the solutions are described by a single congruence relation modulo ab.

In its basic form, the Chinese remainder theorem will determine a number n that when divided by some given divisors leaves given remainders.

Thus the division form of Euclid's algorithm starts with a pair of positive integers and forms a new pair that consists of the smaller number and the remainder obtained by dividing the larger number by the smaller number.

In a typical cluster perhaps only 5 % of the total mass is in the form of galaxies, maybe 10 % in the form of hot X-ray emitting gas and the remainder is dark matter.

: Comment: Take a formula φ of degree k + 1 of the form, where is the remainder of ( it is thus of degree k-1 ).

Even when a cluster such as the Pleiades does form, it may only hold on to a third of the original stars, with the remainder becoming unbound once the gas is expelled.

This follows from the Chinese remainder theorem and the fact that a ring of the form Z / kZ is a field if and only if k is a prime.

In that case the remainder of the Laplacian can be evaluated to its characteristic equation by considering solutions of the form

* Qin Jiushao publishes the original form of the Chinese remainder theorem.

* The remainder of the county was combined with the county of Kinross and the Angus parish of Kettins to form Perth and Kinross District in Tayside.

Then in 1817, in turn, a portion of Seneca County was combined with a piece of the remainder of Cayuga County to form Tompkins County.

In 1817, Seneca County was reduced in size by combining portions of Seneca and the remainder of Cayuga County to form Tompkins County.

Then in 1817, in turn, a portion of Seneca County was combined with a piece of the remainder of Cayuga County to form Tompkins County.

In 1804, after numerous acts of subdividing, Seneca County was formed by the splitting of Cayuga County, which, in turn, was reduced in size by combining portions of Seneca and the remainder of Cayuga County to form Tompkins County in 1817.

By July 2013, the business and housing components of BTH will be consolidated with the consumer components of SCSA to form the new Business, Consumer Services and Housing Agency ; the remainder of SCSA and the Technology Agency will merge into the new Government Operations Agency ; and the transportation components of BTH along with the formerly separate California Transportation Commission will become part of the new Transportation Agency.

As his poor form continued, the rotund striker was eventually released by Accrington Stanley, leaving the club to join a Finnish amateur side where he would see out the remainder of his playing days.

People of South Indian and Gujarati origin make up the majority of the Réunionnais of Indian origin ; Bihari and other origins form the remainder of the population.

The head coach for the remainder of the season became Ulseth's former assistant Steinar Nilsen, who managed to turn Tromsø IL's poor form around.

The remainder of the last column ( and last row ) must be zeros, and the product of any two such matrices has the same form.

A large prospective study followed a group of 715 homosexual men in the Vancouver, Canada area ; approximately half were HIV-seropositive or became so during the follow-up period, and the remainder were HIV-seronegative.

One study on genetic variations between different species of Drosophila suggests that if a mutation changes a protein produced by a gene, the result is likely to be harmful, with an estimated 70 percent of amino acid polymorphisms having damaging effects, and the remainder being either neutral or weakly beneficial.

Gerald spent the remainder of his life in academic study, most likely in Lincoln, producing works of devotional instruction and politics, and revising the works on Ireland and Wales he had written earlier in his life.

Researchers at the University of Strathclyde in August 2010 made a study ( old citation link broken ) of seventy women between the ages of 60 and 85 years ; half were Scottish country dancers and the remainder participated in other physical activities such as swimming, walking, golf and keep fit classes.

Beyond this, their study split the remainder of species into two broad groups, one including the Bryodesma species, the Articulatae, section Ericetorum and others, and the other centered around the broad Stachygynandrum group.

In his book 200 Years Together, Aleksandr Solzhenitsyn provides these numbers from Nahum Gergel's 1951 study of the pogroms in Ukraine: out of an estimated 1, 236 incidents of anti-Jewish violence, 887 mass pogroms occurred, the remainder being classified as " excesses " not assuming mass proportions.

The remainder of his life was spent in incessant, unremitting labour ; so keen was his devotion to study that he allowed himself only five hours a day for rest.

Operations in Burma over the remainder of 1942 and in 1943 were a study of military frustration.

A one-year study of scats in India's Keoladeo National Park found that fish comprised approximately three-quarters of the diet, with the remainder consisting of birds, insects, and small rodents.

The study also contains a complete collection of Governor General's Literary Award winning works ; prior to 2005, the library was lacking more than 25 % of the winning pieces, but, at the instigation of Governor General Adrienne Clarkson, the remainder were sought out.

This study contradicts the fossil evidence, which suggests that the Monoplacophora are the sister group to the remainder of the conchiferans, and that the cephalopods ( squid and octopus ) arose from within the monoplacophoran lineage.

Then, in August 2002, another NASA team led by Thomas-Keptra published a study indicating that 25 % of the magnetite in ALH 84001 occurs as small, uniform-sized crystals that, on Earth, is associated only with biologic activity, and that the remainder of the material appears to be normal inorganic magnetite.

On Hénault ' srecovery in his eightieth year from a dangerous malady ( 1765 ) he professed to have undergone religious conversion and retired into private life, devoting the remainder of his days to study and devotion.

Approximately one twentieth of the collection is on exhibition and the remainder in storage but available for study by interested persons.

For example, in a Munich study, part of a fleet of taxicabs were equipped with anti-lock brakes ( ABS ), while the remainder had conventional brake systems.

In the past the museum simply consisted of the entire collections being open to the public, but Karl Möbius instigated a clear split between a public exhibition space with a few choice specimens, together with explanations of their relevance, and the remainder of the collection held in archives for scientific study.

The remainder of his life he devoted to study, travel and literature.

He studied pharmaceutical chemistry from the age of 15 through the remainder of his teenage years, and aspired to study chemistry at university.

The College has nearly 200 residents, of whom about 150 are undergraduates ; the remainder are graduates undertaking further study or holding university positions.

For much of the remainder of the war, he travelled in the United States with another Bristol employee, Ian Duncan, to study their production line techniques in order to improve their own.

He retired from active service in 1932 and devoted the remainder of his life to the study of Dutch maritime history.

The remainder of his life was spent in the study of military sciences in which he became a pedant of the most pronounced type.

The study concluded that about fifty percent of the individual differences in IQ and personality were due to heredity and the remainder to environmental influences.

The remainder of the time in Hesder is designated for full time Torah study.