Nevertheless, the theory that the determining influence of the hypothalamic balance has a profound influence on the clinical behavior of neuropsychiatric patients has not yet been tested on an adequate number of patients.

Connes has applied his work in areas of mathematics and theoretical physics, including number theory, differential geometry and particle physics.

The exact number and placement of Endosymbiotic theory | endosymbiotic events is currently unknown, so this diagram can be taken only as a general guide It represents the most parsimonious way of explaining the three types of endosymbiotic origins of plastids.

They are a set of axioms strong enough to prove many important facts about number theory and they allowed Gödel to establish his famous second incompleteness theorem.

In number theory, if P ( n ) is a property of positive integers, and if p ( N ) denotes the number of positive integers n less than N for which P ( n ) holds, and if

This is an example of renormalization in quantum field theory — the field theory being necessary because the number of particles changes from one to two and back again.

Wallace was one of the leading evolutionary thinkers of the 19th century and made a number of other contributions to the development of evolutionary theory besides being co-discoverer of natural selection.

Supporting literature includes: the work of social impact theory, which discusses persuasion in part through the number of persons engaging in influence ; as well as studies made on the relative influence of communicator credibility in different kinds of persuasion ; and examinations of the trustworthiness of the speaker.

It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex analysis, topology and number theory.

He is especially known for his foundational work in number theory and algebraic geometry.

He made substantial contributions in many areas, the most important being his discovery of profound connections between algebraic geometry and number theory.

Atle Selberg ( 14 June 1917 – 6 August 2007 ) was a Norwegian mathematician known for his work in analytic number theory, and in the theory of automorphic forms, in particular bringing them into relation with spectral theory.

Sir Andrew John Wiles, KBE, FRS ( born 11 April 1953 ) is a British mathematician and a Royal Society Research Professor at Oxford University, specializing in number theory.

His construction of new cohomology theories has left deep consequences for algebraic number theory, algebraic topology, and representation theory.

Alexander Grothendieck's work during the ` Golden Age ' period at IHÉS established several unifying themes in algebraic geometry, number theory, topology, category theory and complex analysis.

In that setting one can use birational geometry, techniques from number theory, Galois theory and commutative algebra, and close analogues of the methods of algebraic topology, all in an integrated way.

* abc conjecture, a concept in number theory

On a more abstract level, model theoretic arguments hold that a given set of symbols in a theory can be mapped onto any number of sets of real-world objects — each set being a " model " of the theory — providing the interrelationships between the objects are the same.

The axons of some neurons branch to form axon collaterals, that can be divided into a number of smaller branches called telodendria.

Arithmetic or arithmetics ( from the Greek word ἀριθμός, arithmos " number ") is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations.

Many branch lines ( and a number of main lines ) were closed because they were deemed uneconomic (" the Beeching Axe " of 1963 ), removing much feeder traffic from main line passenger services.

By attempting to predict which branch ( or path ) a conditional instruction will take, the CPU can minimize the number of times that the entire pipeline must wait until a conditional instruction is completed.

Cranial nerve number 5 ( CN V ), and its ophthalmic branch ( V < sub > 1 </ sub >) are responsible for the afferent arm of the reflex, and the cranial nerve number 7 ( CN VII ) also known a facial nerve, is responsible for the efferent arm, causing contraction of the muscle orbicularis oculi resulting in closing of the eyes.

The scheme functions slightly differently in each area, and is managed by each branch, but the overall rule is that each participating pub is allowed to purchase beer from whatever brewery they wish, but if it the beer is to be promoted as a ' LocAle ' it must come from a brewery within a predetermined number of miles ( which is set by each CAMRA branch, but generally is around 20 or 25 miles, although, the North London branch has set it at 30 miles ) from brewery to pub door, even if it comes from a distribution centre further away ; in addition, each participating pub must keep at least one LocAle for sale at all times.

Though the Church is prohibited by the Manual from publishing membership figures, the number of branch churches in the United States has fallen steadily since World War II.

In addition, each chakra has a number of ' spokes ' or ' petals ', which branch off into thousands of subtle channels running to every part of the body, and each contains a Sanskrit syllable.

** Social Security number, followed by " AF " indicating branch of service

** Social Security number, followed by " AF " indicating branch of service

** Social Security number, no dashes or spaces, followed immediately by branch ( i. e., 123456789USCG )

" On the basis of the existing name records, a number of scholars suggest that the Huns spoke a Turkic language of the Oghur branch, which also includes Bulgar, Avar, Khazar and Chuvash languages.

Among the new features are a number of management features for branch offices, file serving, printing and company-wide identity integration.

Hezbollah has a military branch known as Al-Muqawama al-Islamiyya (" The Islamic Resistance ") and is the possible sponsor of a number of lesser-known militant groups, some of which may be little more than fronts for Hezbollah itself, including the Organization of the Oppressed, the Revolutionary Justice Organization, the Organization of Right Against Wrong, and Followers of the Prophet Muhammad.

In 1692, as a result of the inheritance of the Palatinate by a Catholic branch of the Wittelsbach family, which threatened to upset the religious balance of the College of Electors, the number of electors was increased to nine, with a seat being granted to the Duke of Brunswick-Lüneburg, who became known as the Elector of Hanover ( the Reichstag officially confirmed the creation in 1708 ).

It includes the domestic bank account number, branch identifier, and potential routing information.

Before IBAN, differing national standards for bank account identification ( i. e., bank, branch, routing codes, and account number ) were confusing for some users.

The theory of automorphic forms, an important branch of modern number theory, deals extensively with analogues of Lie groups over adele rings ; p-adic Lie groups play an important role, via their connections with Galois representations in number theory.

In addition to establishing Mongolia as an independent, sovereign republic and guaranteeing a number of rights and freedoms, the new constitution restructured the legislative branch of government, creating a unicameral legislature, the State Great Khural ( SGKh ).

In the common elk ( A. a. alces ) this branch usually expands into a broad palmation, with one large tine at the base, and a number of smaller snags on the free border.

One of the most interesting aspects of the axiom of choice is the large number of places in mathematics that it shows up.

In mathematics, the absolute value ( or modulus ) of a real number is the numerical value of without regard to its sign.

In mathematics, an algebraic number is a number that is a root of a non-zero polynomial in one variable with rational coefficients ( or equivalently — by clearing denominators — with integer coefficients ).

In mathematics, the unit square is defined to have area one, and the area of any other shape or surface is a dimensionless real number.

In mathematics, the phrase " almost all " has a number of specialised uses.

In mathematics, an associative algebra A is an associative ring that has a compatible structure of a vector space over a certain field K or, more generally, of a module over a commutative ring R. Thus A is endowed with binary operations of addition and multiplication satisfying a number of axioms, including associativity of multiplication and distributivity, as well as compatible multiplication by the elements of the field K or the ring R.

Realism in the philosophy of mathematics is the claim that mathematical entities such as number have a mind-independent existence.

* Bell number, in mathematics

In mathematics, the Bernoulli numbers B < sub > n </ sub > are a sequence of rational numbers with deep connections to number theory.

With large sets, it becomes necessary to use more sophisticated mathematics to find the number of combinations.

* Catalan number, a concept in mathematics

In mathematics, a countable set is a set with the same cardinality ( number of elements ) as some subset of the set of natural numbers.

Although a " bijection " seems a more advanced concept than a number, the usual development of mathematics in terms of set theory defines functions before numbers, as they are based on much simpler sets.

In 1879, Peirce was appointed Lecturer in logic at the new Johns Hopkins University, which was strong in a number of areas that interested him, such as philosophy ( Royce and Dewey did their PhDs at Hopkins ), psychology ( taught by G. Stanley Hall and studied by Joseph Jastrow, who coauthored a landmark empirical study with Peirce ), and mathematics ( taught by J. J. Sylvester, who came to admire Peirce's work on mathematics and logic ).

The Langlands program is a far-reaching web of these ideas of ' unifying conjectures ' that link different subfields of mathematics, e. g. number theory and representation theory of Lie groups ; some of these conjectures have since been proved.

In mathematics, any number of cases supporting a conjecture, no matter how large, is insufficient for establishing the conjecture's veracity, since a single counterexample would immediately bring down the conjecture.

* Cardinal number, a concept in mathematics

In mathematics, the Cantor set is a set of points lying on a single line segment that has a number of remarkable and deep properties.

In mathematics, the cardinality of a set is a measure of the " number of elements of the set ".

In mathematics, a contraction mapping, or contraction, on a metric space ( M, d ) is a function f from M to itself, with the property that there is some nonnegative real number < math > k < 1 </ math > such that for all x and y in M,