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 equation was eventually solved by Euler in the early 18th century, who also solved a number of other Diophantine equations.

The Euler – Maclaurin formula provides expressions for the difference between the sum and the integral in terms of the higher derivatives ƒ < sup >( k )</ sup > at the end points of the interval m and n. Explicitly, for any natural number p, we have

For closed ( orientable or non-orientable ) surfaces with positive genus, the maximum number p of colors needed depends on the surface's Euler characteristic χ according to the formula

Euler worked in almost all areas of mathematics: geometry, infinitesimal calculus, trigonometry, algebra, and number theory, as well as continuum physics, lunar theory and other areas of physics.

The Swiss mathematician Leonhard Euler pioneered the modern approach to congruence in about 1750, when he explicitly introduced the idea of congruence modulo a number N.

The Euler number E < sub > 2n </ sub > can be expressed as a sum over the even partitions of 2n,

Alternatively, it is possible to show that any bridgeless bipartite planar graph with n vertices and m edges has by combining the Euler formula ( where f is the number of faces of a planar embedding ) with the observation that the number of faces is at most half the number of edges ( because each face has at least four edges and each edge belongs to exactly two faces ).

This means that as the number of contours increases, Euler diagrams are typically less visually complex than the equivalent Venn diagram, particularly if the number of non-empty intersections is small.

The non-orientable genus, demigenus, or Euler genus of a connected, non-orientable closed surface is a positive integer representing the number of cross-caps attached to a sphere.

In number theory, Euler's theorem ( also known as the Fermat – Euler theorem or Euler's totient theorem ) states that if n and a are coprime positive integers, then

If the Euler criterion formula is used modulo a composite number, the result may or may not be the value of the Jacobi symbol.

Orientation-free metrics of a group of connected or surrounded pixels include the Euler number, the perimeter, the area, the compactness, the area of holes, the minimum radius, the maximum radius.

In number theory, an odd composite integer n is called an Euler – Jacobi pseudoprime to base a, if a and n are coprime, and

Note that for orientable compact surfaces without boundary, the Euler characteristic equals, where is the genus of the surface: Any orientable compact surface without boundary is topologically equivalent to a sphere with some handles attached, and counts the number of handles.

More generally, if the polyhedron has Euler characteristic ( where g is the genus, meaning " number of holes "), then the sum of the defect is

The difference between the nth harmonic number and the natural logarithm of n converges to the Euler – Mascheroni constant.

In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic ( or Euler – Poincaré characteristic ) is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent.

where B < sub > k </ sub > is a Bernoulli number and R < sub > m, n </ sub > is the remainder term in the Euler – Maclaurin formula.

Bridge 8: Euler walks are possible if exactly zero or two nodes have an odd number of edges.

Amongst the fruits of his industry may be mentioned a laborious investigation of the disturbances of Jupiter by Saturn, the results of which were employed and confirmed by Euler in his prize essay of 1748 ; a series of lunar observations extending over fifty years ; some interesting researches in terrestrial magnetism and atmospheric electricity, in the latter of which he detected a regular diurnal period ; and the determination of the places of a great number of stars, including at least twelve separate observations of Uranus, between 1750 and its discovery as a planet.

The numbers indicate the number of nearest neighbors.

A constant is a number that remains the same regardless of the other numbers used in the formula and the resultant equation.

I used the alias of Robert C. Richards, gave the first three letters and the first and last figure of the license number on the agency heap, but a couple of phony numbers in between.

The importance of this 5 can largely be explained by the natural mathematical properties of the middle number and its special relationship to all the rest of the numbers -- quite apart from any numerological considerations, which is to say, any symbolic meaning arbitrarily assigned to it.

Furthermore, the middle number of the Lo Shu is not only the physical mean between every opposing pair of the other numbers, by reason of its central position ; ;

Although the primary mathematical properties of the middle number at the center of the Lo Shu, and the interrelation of all the other numbers to it, might seem enough to account for the deep fascination which the Lo Shu held for the Old Chinese philosophers, this was actually only a beginning of wonders.

Since is the distance from a given number to the mean, one way to interpret this property is as saying that the numbers to the left of the mean are balanced by the numbers to the right of the mean.

* If it is required to use a single number X as an estimate for the value of numbers, then the arithmetic mean does this best, in the sense of minimizing the sum of squares ( x < sub > i </ sub > − X )< sup > 2 </ sup > of the residuals.

The numbers of species cited above follow Frost and the total number of known amphibian species is approximately 7, 000, of which nearly 90 % are frogs.

Synthesis of new elements is accomplished by bombarding target atoms of heavy elements with ions, such that the sum of the atomic numbers of the target and ion elements equals the atomic number of the element being created.

In general, the half-life becomes shorter as atomic number increases, though an " island of stability " may exist for undiscovered isotopes with certain numbers of protons and neutrons.

In particular, this applies where large numbers of amateur astronomers with small telescopes are more effective than the relatively small number of large telescopes that are available to professional astronomers.

One of the simplest algorithms is to find the largest number in an ( unsorted ) list of numbers.

While Nicomachus ' algorithm is the same as Euclid's, when the numbers are prime to one another it yields the number " 1 " for their common measure.

Albanians, Arabs, Armenians, Assyrians, Bosnians, Arameans, Circassians, Georgians, Greeks, Jews, Hemshin, Laz, Gagauz, Yezidi, Abkhazians and a number of other ethnic groups also live in Anatolia in smaller numbers.

Six astatine isotopes, with mass numbers of 214 to 219, are present in nature as the products of various decay routes of heavier elements, but neither the most stable isotope of astatine ( with mass number 210 ) nor astatine-211 ( which is used in medicine ) is produced naturally.

Isotopes were then explained as elements with the same number of protons, but different numbers of neutrons within the nucleus.

The standard structure is where is the set of natural numbers, is the successor function and is naturally interpreted as the number 0.

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.

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.

Each orbital is defined by a different set of quantum numbers ( n, l, and m ), and contains a maximum of two electrons each with their own spin quantum number.

For example, the prime number theorem states that the number of prime numbers less than or equal to N is asymptotically equal to N / ln N. Therefore the proportion of prime integers is roughly 1 / ln N, which tends to 0.

After describing the manifestation of the Gospel in the Ogdoad and Hebdomad, he adds that the Basilidians have a long account of the innumerable creations and powers in the several ' stages ' of the upper world ( diastemata ), in which they speak of 365 heavens and say that " their great archon " is Abrasax, because his name contains the number 365, the number of the days in the year ; i. e. the sum of the numbers denoted by the Greek letters in ΑΒΡΑΣΑΞ according to the rules of isopsephy is 365: