This conjecture was proven for all θ < 1 / 2 by Enrico Bombieri and A. I. Vinogradov ( the Bombieri – Vinogradov theorem, sometimes known simply as " Bombieri's theorem "); this result is already quite useful, being an averaged form of the generalized Riemann hypothesis.

To provide the continuous flow of information basic to administrative decisions, a number of institutions have established offices of institutional research.

A number of strong independent agencies, established in some cases with governmental or royal support, have conducted large medical, social, educational and research operations in particular parts of the Congo and Ruanda-Urundi.

In the last decade the number of Negro-appeal radio program hours has risen at least 15 per cent, and the number of Negro-appeal stations has increased 30 per cent, according to a research man quoted by Sponsor.

The school is involved in a study of the prehistoric and historic landscape at Slievemore, incorporating a research excavation at a number of sites within the deserted village of Slievemore.

Today, it is estimated that fewer than 100 speakers of the language remain, while other research places the number at fewer than 15 speakers – the language has been regarded as “ endangered ”.

The growth in the number of published literature makes it virtually impossible to read every paper, resulting in disjointed subfields of research.

Kusche's research revealed a number of inaccuracies and inconsistencies between Berlitz's accounts and statements from eyewitnesses, participants, and others involved in the initial incidents.

This practice can lead to the controversial question of which research group actually discovered an element, a question that has delayed naming of elements with atomic number of 104 and higher for a considerable time.

There are a number of institutions and organizations which provide community college research to inform practice and policy.

There are a number of research organizations and publications who focus upon the activities of community college, junior college, and technical college institutions.

* ACT-R, a cognitive architecture used in a large number of research projects.

It was announced in February 2011 that the company name would revert to Meritor, Inc. Cummins, Inc. is by far the region's largest employer, and the Infotech Park accounts for a sizable number of research jobs in Columbus proper.

As an example, the subject " research in the cure of tuberculosis of lungs by x-ray conducted in India in 1950 " results in a call number

Throughout the world there are many organizations and institutions dedicated to the area of computer and electronic music study and research, including the ICMA ( International Computer Music Association ), IRCAM, GRAME, SEAMUS ( Society for Electro Acoustic Music in the United States ), CEC ( Canadian Electroacoustic Community ), and a great number of institutions of higher learning around the world.

Dalhousie also houses a number of marine research pools, a wet laboratory and a benthic flume, which are collectively known as the Aquatron laboratory.

The institute, which is a partnership between a number of private industries, government and post-secondary institutions, was designed to help increase the scale, quality, internationalization and impact of marine research in the region.

Students are required to complete coursework in a number of core areas of law, as well as to submit a thesis which is to be " an original work on the approved subject or other contribution to the knowledge showing that he / she has carried out sufficient research therein ".

When that research was repeated in 2007, the number of senior management posts held by women had fallen to 22 %.

This led to tremendous advances in number theory, and the study of Diophantine equations (" Diophantine geometry ") and of Diophantine approximations remain important areas of mathematical research.

An increasing number of economists have called for increased emphasis on environmental sustainability ; this area of research is known as Ecological economics.

The TU / e participates in a large number of research institutes which balance in different ways between pure science and applied science research.

To be assigned an Erdős number, an author must co-write a research paper with an author with a finite Erdős number.

The dissection of scientific theory, the examination of a theory from the vantage-points of language, epistemology, and ethics, is itself a distinct contribution to knowledge, no less so because of its removal from empirical research.

Two related strands of research on altruism have emerged from traditional evolutionary analyses and from game theory.

His research program vastly extended the scope of the field, incorporating major elements of commutative algebra, homological algebra, sheaf theory, and category theory into its foundations.

The proposed mechanism of chronic nicotine causing desensitisation of nicotinic receptors, thereby leading to an antidepressant effect, is consistent with the theory first proposed over 30 years ago and subsequent research that confirmed excessive acetylcholine activity in the brain leads to depressive symptoms.

On the other hand, the theory of infinite abelian groups is an area of current research.

Pascal was an important mathematician, helping create two major new areas of research: he wrote a significant treatise on the subject of projective geometry at the age of sixteen, and later corresponded with Pierre de Fermat on probability theory, strongly influencing the development of modern economics and social science.

Over the last half of the 20th century, historical and archaeological research has increasingly supported the theory that the remnants of the Celtic Boii were absorbed into the Roman Empire and later intermingled with other Germanic peoples who chose to stay ( or were stationed by the Romans ) in the area.

Recent empirical research has lent support to the theory that psychological projection plays a role in conspiracy belief.

As the field is highly interdisciplinary, research often cuts across multiple areas of study, drawing on research methods from psychology, neuroscience, computer science and systems theory.

Philipp Lenard also contributed a great deal to cathode ray theory, winning the Nobel prize for physics in 1905 for his research on cathode rays and their properties.

Holzkamp, who had written two books on theory of science and one on sensory perception before publishing the Grundlegung der Psychologie in 1983, thought this major work provided a solid paradigm for psychological research, as he viewed psychology as a pre-paradigmatic scientific discipline ( T. S.

Holzkamp mostly based his sophisticated attempt to provide a comprehensive and integrated set of categories defining the field of psychological research on Aleksey Leontyev's approach to cultural – historical psychology and activity theory.

Much research in graph theory was motivated by attempts to prove that all maps, like this one, could be graph coloring | colored with four color theorem | only four colors.

In graph theory, much research was motivated by attempts to prove the four color theorem, first stated in 1852, but not proved until 1976 ( by Kenneth Appel and Wolfgang Haken, using substantial computer assistance ).

The early debates were made before the much greater calculating powers of modern computers became available but also before research on chaos theory.

Expander constructions have spawned research in pure and applied mathematics, with several applications to complexity theory, design of robust computer networks, and the theory of error-correcting codes.

In practice, the accumulation of evidence for or against any particular theory involves planned research designs for the collection of empirical data, and academic rigor plays a large part of judging the merits of research design.

Although Abel had already proved the impossibility of a " quintic formula " by radicals in 1824 and Ruffini had published a solution in 1799 that turned out to be flawed, Galois ' methods led to deeper research in what is now called Galois theory.

For example, educational psychologists have conducted research on the instructional applicability of Jean Piaget's theory of development, according to which children mature through four stages of cognitive capability.