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 norm of a Gaussian integer is the natural number defined as

The integer 2 factors as as a Gaussian integer, the second factorisation ( in which i is a unit ) showing that 2 is divisible by the square of a Gaussian prime ; it is the unique prime number with this property.

The necessary conditions can be stated as following: if a Gaussian integer is a Gaussian prime, then either its norm is a prime number, or its norm is a square of a prime number.

However, not every prime number is a Gaussian prime.

If is a Gaussian integer whose norm is a prime number, then is a Gaussian prime, because the norm is multiplicative.

It is easy to see graphically that every complex number is within units of a Gaussian integer.

Put another way, every complex number ( and hence every Gaussian integer ) has a maximal distance of

This paper not only introduced the Gaussian integers and proved they are a unique factorization domain, it also introduced the terms norm, unit, primary, and associate, which are now standard in algebraic number theory.

Gauss's circle problem does not deal with the Gaussian integers per se, but instead asks for the number of lattice points inside a circle of a given radius centered at the origin.

This is equivalent to determining the number of Gaussian integers with norm less than a given value.

Hartley did not work out exactly how the number M should depend on the noise statistics of the channel, or how the communication could be made reliable even when individual symbol pulses could not be reliably distinguished to M levels ; with Gaussian noise statistics, system designers had to choose a very conservative value of M to achieve a low error rate.

As described above, a Rayleigh fading channel itself can be modelled by generating the real and imaginary parts of a complex number according to independent normal Gaussian variables.

An integer is a prime for the Gaussian integers if it is a prime number ( in the normal sense ) that is congruent to 3 modulo 4.

A Gaussian quadrature rule is typically more accurate than a Newton – Cotes rule which requires the same number of function evaluations, if the integrand is smooth ( i. e., if it is sufficiently differentiable ).

It is known that the Gaussian source is the most " difficult " source to encode: for a given mean square error, it requires the greatest number of bits.

The condition number of the Vandermonde matrix may be large, causing large errors when computing the coefficients if the system of equations is solved using Gaussian elimination.

So as consistent with the meaning of the chi-squared distribution, we are measuring how probable the observed number of standard deviations away from the mean is under the Gaussian approximation ( which is a good approximation for large n ).

However a number of other beam types have been used to trap particles, including high order laser beams i. e. Hermite Gaussian beam ( TEM < sub > xy </ sub >), Laguerre-Gaussian ( LG ) beams ( TEM < sub > pl </ sub >) and Bessel beams.

In litters of eight mice from similar parents, the number of mice with straight instead of wavy hair is an integer from 0 to 8.

Time codes are usually published in the form of UTC, which differs from TAI by a well-known integer number of seconds.

He defines " A number be a multitude composed of units ": a counting number, a positive integer not including 0.

The atomic mass of these isotopes varied by integer amounts, called the whole number rule.

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 ).

All numbers which can be obtained from the integers using a finite number of integer additions, subtractions, multiplications, divisions, and taking nth roots ( where n is a positive integer ) are algebraic.

An algebraic integer is an algebraic number which is a root of a polynomial with integer coefficients with leading coefficient 1 ( a monic polynomial ).

The name algebraic integer comes from the fact that the only rational numbers which are algebraic integers are the integers, and because the algebraic integers in any number field are in many ways analogous to the integers.

# There is always an integer number of electrons orbiting the nucleus.

The principal quantum number, n, describes the energy of the electron and is always a positive integer.

The azimuthal quantum number,, describes the orbital angular momentum of each electron and is a non-negative integer.

The magnetic quantum number,, describes the magnetic moment of an electron in an arbitrary direction, and is also always an integer.

Therefore, given any positive integer n, it produces a string with Kolmogorov complexity at least as great as n. The program itself has a fixed length U. The input to the program GenerateComplexString is an integer n. Here, the size of n is measured by the number of bits required to represent n, which is log < sub > 2 </ sub >( n ).

( i may be an integer for a discrete-time process or a real number for a continuous-time process.

The data format of a DXF is called a " tagged data " format which " means that each data element in the file is preceded by an integer number that is called a group code.

( A proper divisor of a number is a positive integer divisor other than the number itself.

For example, the division example above is surjective ( or onto ) because every rational number may be expressed as a quotient of an integer and a natural number.

This shows in particular that is a natural number for any natural numbers n and k. There are many other combinatorial interpretations of binomial coefficients ( counting problems for which the answer is given by a binomial coefficient expression ), for instance the number of words formed of n bits ( digits 0 or 1 ) whose sum is k is given by, while the number of ways to write where every a < sub > i </ sub > is a nonnegative integer is given by.