These proofs were modeled upon Ken Ribet's proof of the converse to Herbrand's theorem ( so-called Herbrand-Ribet theorem ).

In mathematics, Ribet's theorem ( earlier called the epsilon conjecture or ε-conjecture ) is a statement in number theory concerning properties of Galois representations associated with modular forms.

A more elementary proof of Ribet's converse to Herbrand's theorem, a consequence of the theory of Euler systems, can be found in Washington's book.

His casual, dreamlike working methods, often as not in absentia, were an abrupt change from Harburg's, so that Arlen had to adjust again to another approach to collaboration.

But one cannot escape the suspicion that all this non-stop harping on the misdeeds of the long liquidated `` anti-party '' group would be totally unnecessary if there were not, inside the party, some secret but genuine opposition to Khrushchev on vital doctrinal grounds, on the actual methods to be employed in the `` transition to communism '' and, last but not least, on foreign policy.

Anti-A and anti-B activities were determined in fractions from the sera of group A, group B or group O donors by the following tube agglutination methods.

All samples were tested by both the saline and albumin methods.

In attempting to improve specificity of staining, the fluorescein-labeled antisera used in both direct and indirect methods were treated in one of several ways: ( 1 ) They were passed through Dowex-2-chloride twice and treated with acetone insoluble powders ( Coons, 1958 ) prepared from mouse liver or from healthy sweet clover stems or crown gall tissue produced by Agrobacterium tumefaciens ( E. F. Smith & Townsend ) on sweet clover stems.

Results of specific staining by the direct and the indirect methods were similar and showed the localization of WTV antigen in certain tissues of tumors.

There were two methods that could have been used for conducting the study within the resources available: ( 1 ) interviews in depth with a few selected companies, and ( 2 ) the more limited interrogation of a large number of companies by means of a mail questionnaire.

-- Electron-microscopical and physical-chemical methods were used to demonstrate the renaturation of heat-denatured collagen and ribonucleic acid.

Satisfactory methods for polyester foams and even prepolymer polyether foams were never fully achieved.

There were two possible methods of breaching the conservative barriers around the Rules Committee: 1 ) to pack it with additional liberals and break the conservative-liberal deadlock, or 2 ) to remove one of the conservatives -- namely Mississippi's 14-term William Meyers Colmer ( pronounced Calmer ).

Academic historical research supports that the alchemists were searching for a material substance using physical methods.

experimental methods used in the study of the personal equation were

AT promotes greater independence by enabling people to perform tasks that they were formerly unable to accomplish, or had great difficulty accomplishing, by providing enhancements to, or changing methods of interacting with, the technology needed to accomplish such tasks.

The intellectual society of this era was characterized by itinerant scholars, who were often employed by various state rulers as advisers on the methods of government, war, and diplomacy.

Some of the earliest attempts to apply scientific methods to the study of phenomena relating to an afterlife were conducted by this organization.

His innovative methods, however, were controversial, and he rarely stayed in one place very long.

She called him, " an intelligent, philosophic, modest man " and found his views on education " very attractive ". Locals in Cheshire were less supportive and became suspicious of his methods.

As usual, Alcott's methods were controversial ; a former student later referred to him as " the most eccentric man who ever took on himself to train and form the youthful mind.

Alcott's methods were not well received ; many found his conversations on the Gospels close to blasphemous.

The two men were leaders of Alcott House, an experimental school based on Alcott's methods from the Temple School located about ten miles outside of London.

Tacitus claims that Nero considered poisoning or stabbing her, but felt these methods were too difficult and suspicious, so he settled on building a self-sinking boat.

The 1910 Catholic Encyclopedia remarks that " Undeniably secular and ambitious, his moral life was not above reproach, and his unscrupulous methods in no wise accorded with the requirements of his high office ... the heinous crimes of which his opponents in the council accused him were certainly gravely exaggerated.

After World War II predicted methods were invariably applied but the fall of shot usually needed adjustment because of inaccuracy in locating the target, the proximity of friendly troops or the need to engage a moving target.

When debates polarise between techniques, the methods are often referred to by a colour code, based on the colours of the bindings of the two volumes from the first Oxford Conference, where the approaches were first distinguished.

As these methods are pushed to the limit, they approach the exact solution of the non-relativistic Schrödinger equation.

Depending on Cheka committees in various cities, the methods included: being skinned alive, scalped, " crowned " with barbed wire, impaled, crucified, hanged, stoned to death, tied to planks and pushed slowly into furnaces or tanks of boiling water, or rolled around naked in internally nail-studded barrels.

These methods might work for short-notice, or even long-notice threats, from solid objects that can be directly pushed, but probably not effective against loosely aggregated rubble piles.

Feminist economists pushed for and produced gender aware theory and analysis, broadened the focus on economics and sought pluralism of methodology and research methods.

Despite his opposition to the treaty and his mistrust of the governments intentions and methods, the dwindling of the buffalo herds ultimately prevented his people from continuing to rely on this traditional food source and pushed the Cree to the point of starvation in less than a decade.

There are a variety of methods to secure medications, including caps that must be pinched or pushed down while turning.

" French Polishing " was the industry standard in Europe during the 18th and 19th centuries, pushed aside by the efficient advantage of modern methods in the Industrial Revolution.

The ESAS includes a number of recommendations for accelerating the development of the CEV and implementing Project Constellation, including strategies for flying manned CEV flights as early as 2012 ( now pushed back to at least 2015 ) and methods for servicing the International Space Station ( ISS ) without the use of the Space Shuttle, using cargo versions of the CEV.

Brown ( 1959 ) has reviewed generally the various methods of assaying TSH, and the reader is referred to her paper for further information on the subject.

In the 17th and 18th centuries, chemists provided a physical basis for this idea by showing that certain substances could not be further broken down by chemical methods.

In 1789, French nobleman and scientific researcher Antoine Lavoisier discovered the law of conservation of mass and defined an element as a basic substance that could not be further broken down by the methods of chemistry.

This section includes some minimal descriptions of methods, to give some feel for such a building's practicality, provide indexes to further information, and give a sense of modern trends.

Campbell-Bannerman tried to keep these forces together at the head of a moderate Liberal rump, but in 1901 he delivered a speech on the government's " methods of barbarism " in South Africa that pulled him further to the left and nearly tore the party in two.

The kinetic process of destabilisation can be rather long ( up to several months or even years for some products ) and it is often required for the formulator to use further accelerating methods in order to reach reasonable development time for new product design.

Almost all other elements found in nature, including some further hydrogen and helium created since then, were made by various natural or ( at times ) artificial methods of nucleosynthesis.

Their specifications, which go further than the West Country farmhouse Cheddar Protected Designation of Origin ( PDO ), require that Cheddar cheese be made in Somerset and with traditional methods, such as using raw milk, traditional animal rennet, and a cloth wrapping.

Elsewhere the reader may find further discussion of design methods for practical FIR filter design.

It is often required that the formulator use methods that further accelerate this process in order to reach a reasonable development time for new product designs.

This was further underpinned by the work of Justus von Liebig, which led to the development of modern food storage and food preservation methods.

DNA Gel electrophoresis is usually performed for analytical purposes, often after amplification of DNA via PCR, but may be used as a preparative technique prior to use of other methods such as mass spectrometry, RFLP, PCR, cloning, DNA sequencing, or Southern blotting for further characterization.

Public authorities should oppose laws which undermine natural law ; scientists should further study effective methods of natural birth control ; doctors should further familiarize themselves with this teaching, in order to be able to give advice to their patients, priests must spell out clearly and completely the Church's teaching on marriage.

By the mid 1960s, Viola Spolin's classes were handed over to her protégé, Jo Forsberg, who further developed Spolin's methods into a one-year course, which eventually became The Players Workshop, the first official school of improvisation in the USA.

But this information was used as a starting point by Muslim jurists who expounded the laws of inheritance even further using Hadith, as well as methods of juristic reasoning like Qiyas.

( The basicity methods were only suitable for lanthanum purification ; didymium could not be efficiently further separated in this manner.

Moving a step further, augmented systems for password-authenticated key agreement ( e. g., AMP, B-SPEKE, PAK-Z, SRP-6 ) avoid both the conflict and limitation of hash-based methods.

This approach is the conceptional basis of the Hartree – Fock method and further post Hartree – Fock methods.

< http :// www. scu. edu / ethics / publications / ethicalperspectives / profiling. html >.</ ref > It is argued that the passage of these laws and provisions by the national government leads to justification of preventative methods, such as racial profiling, that has been controversial for racial profiling and leads to further minority distrust in the national government.

Later transmission methods such as SONET and fiber optic transmission further advanced digital transmission.

Heaviside immediately ( 1887 ) proposed several methods of increasing the inductance, including spacing the conductors further apart and loading the insulator with iron dust.

The Morrill Act of 1862 propelled domestic science further ahead as land grant colleges sought to educate farm wives in running their households as their husbands were being educated in agricultural methods and processes.

The excavation methods he used, for example the grid system ( later developed further by Kathleen Kenyon and known as the Wheeler-Kenyon method ), were significant advances in archaeological method, although later superseded.

With both the ΔT and the ΔV charging methods, both manufacturers recommend a further period of trickle charging to follow the initial rapid charge.