A simple illustration of such cause and effect is the case of experiencing the effects of what I cause: if I cause suffering, then as a natural consequence I will experience suffering ; if I cause happiness, then as a natural consequence I will experience happiness.

A consequence of the Jacobson density theorem is Wedderburn's theorem ; namely that any right artinian simple ring is isomorphic to a full matrix ring of n by n matrices over a division ring for some n. This can also be established as a corollary of the Artin – Wedderburn theorem.

A simple consequence of this formula is that if u is a harmonic function, then the value of u at the center of the sphere is the mean value of its values on the sphere.

The consequence of its application is that even a simple LAN connector jack can be considered to be a telecommunications facility in Canada, for tax purposes.

He demonstrated the resolution of forces before Pierre Varignon, which had not been remarked previously, even though it is a simple consequence of the law of their composition.

This is a simple consequence of the laws of modular arithmetic ; we are simply saying that we may first reduce a modulo p.

For example, Green parties often advocate simple living as a consequence of their " four pillars " or the " Ten Key Values " of the Green Party of the United States.

A direct consequence of this difference is that polygons are able to efficiently represent simple 3D structures with lots of empty or homogeneously filled space, while voxels are good at representing regularly sampled spaces that are non-homogeneously filled.

Note that because of the elliptical orbit, and as a simple consequence of Kepler's second law, θ does not progress exactly uniformly with time.

A similar case report in The Lancet, accompanied by a simple chemical experiment, concludes that the observed stones from a typical gallbladder flush actually are a consequence of the flush: they form in the stomach under the action of digestive enzymes on the mix of olive oil and lemon.

The great power in viewing a mind as a society of agents, as opposed to the consequence of some basic principle or some simple formal system, is that different agents can be based on different types of processes with different purposes, ways of representing knowledge, and methods for producing results.

Another remarkably simple and elegant consequence of the FT is the so-called " nonequilibrium partition identity " ( NPI ):

The first Fundamental theorem is a simple consequence

Would is the most common modal verb used in this sense, as it expresses simple consequence ( as opposed to the uncertainty involved with might or could ).

As a consequence of its definition, the Sobel operator can be implemented by simple means in both hardware and software: only eight image points around a point are needed to compute the corresponding result and only integer arithmetic is needed to compute the gradient vector approximation.

Informally, the case of a point charge in an arbitrary static electric field is a simple consequence of Gauss's law.

As a consequence, there are many finite-dimensional representations which are all built out of simple representations of dimension p.

A simple consequence of the first two axioms, positive homogeneity and the triangle inequality, is p ( 0 ) = 0 and thus

One consequence of this is a simple logical characterization of L: it contains precisely those languages expressible in first-order logic with an added commutative transitive closure operator ( in graph theoretical terms, this turns every connected component into a clique ).

Another consequence of this relation to triangular numbers is the simple recurrence relation for centered decagonal numbers

He took his degree in law at Pavia in 1810, and proceeded thence to Milan to exercise his profession ; but the Austrian government, suspecting his loyalty, interfered with his prospects, and in consequence Grossi was a simple notary all his life.

The weak maximum principle for harmonic functions is a simple consequence of facts from calculus.

simple: Quantum fluctuation

According to some simple New Keynesian macroeconomic models, insofar as the central bank keeps inflation stable, the degree of fluctuation in output will be optimized ( Blanchard and Gali call this property the ' divine coincidence ').

In mathematics, the classification of the finite simple groups is a theorem stating that every finite simple group belongs to one of four categories described below.

The classification theorem has applications in many branches of mathematics, as questions about the structure of finite groups ( and their action on other mathematical objects ) can sometimes be reduced to questions about finite simple groups.

Thanks to the classification theorem, such questions can sometimes be answered by checking each family of simple groups and each sporadic group.

The Sylow 2-subgroups are either cyclic, which is easy to handle using the transfer map, or generalized quaternion, which are handled with the Brauer – Suzuki theorem: in particular there are no simple groups of 2-rank 1.

The first case was done by the Gorenstein – Walter theorem which showed that the only simple groups are isomorphic to L < sub > 2 </ sub >( q ) for q odd or A < sub > 7 </ sub >, the second and third cases were done by the Alperin – Brauer – Gorenstein theorem which implies that the only simple groups are isomorphic to L < sub > 3 </ sub >( q ) or U < sub > 3 </ sub >( q ) for q odd or M < sub > 11 </ sub >, and the last case was done by Lyons who showed that U < sub > 3 </ sub >( 4 ) is the only simple possibility.

This is because if a group has sectional 2-rank at least 5 then MacWilliams showed that its Sylow 2-subgroups are connected, and the balance theorem implies that any simple group with connected Sylow 2-subgroups is either of component type or characteristic 2 type.

The three classes are groups of GF ( 2 ) type ( classified mainly by Timmesfeld ), groups of " standard type " for some odd prime ( classified by the Gilman – Griess theorem and work by several others ), and groups of uniqueness type, where a result of Aschbacher implies that there are no simple groups.

simple: Four color theorem

simple: Fundamental theorem of arithmetic

* By the convolution theorem, Fourier transforms turn the complicated convolution operation into simple multiplication, which means that they provide an efficient way to compute convolution-based operations such as polynomial multiplication and multiplying large numbers.

Baudhayana ( c. 8th century BCE ) composed the Baudhayana Sulba Sutra, the best-known Sulba Sutra, which contains examples of simple Pythagorean triples, such as:,,,, and as well as a statement of the Pythagorean theorem for the sides of a square: " The rope which is stretched across the diagonal of a square produces an area double the size of the original square.

However, even though it cannot be determined whether a particular file is incompressible, a simple theorem about incompressible strings shows that over 99 % of files of any given length cannot be compressed by more than one byte ( including the size of the decompressor ).

In the simple case of periodic functions, this result is based on the theorem that any continuous periodic function can be represented as the sum of a series of sine waves and cosine waves:

If the polygon can be drawn on an equally spaced grid such that all its vertices are grid points, Pick's theorem gives a simple formula for the polygon's area based on the numbers of interior and boundary grid points.

An important advance in the theory of simple modules was the Jacobson density theorem.

A theorem might be simple to state and yet be deep.

Consider a simple, closed, plane curve C which is a real-analytic image of the unit circle, and which is given by Af.

It was a simple ivory crucifix which my mother had given me.

When the Athenian line was ready, according to one source, the simple signal to advance was given by Miltiades: " At them ".

A simple one is given in pseudocode below.

A circle is a simple shape of Euclidean geometry that is the set of points in the plane that are equidistant from a given point, the

Context-free grammars are simple enough to allow the construction of efficient parsing algorithms which, for a given string, determine whether and how it can be generated from the grammar.

A more accurate value of the limit than that given by this simple model requires adjusting for various factors, including electrostatic interactions between the electrons and nuclei and effects caused by nonzero temperature.

For the simple electric dipole given above, the electric dipole moment points from the negative charge towards the positive charge, and has a magnitude equal to the strength of each charge times the separation between the charges.

A simple example would consist of looking up a given word in a dictionary, then proceeding to look up the words found in that word's definition, etc., also comparing with older dictionaries from different periods in time, and such a process would never end.

For a simple metal where there is only one type of charge carrier ( electrons ) the Hall voltage V < sub > H </ sub > is given by

The simple formula for the Hall coefficient given above becomes more complex in semiconductors where the carriers are generally both electrons and holes which may be present in different concentrations and have different mobilities.

Bradley explained this effect in the context of Newton's corpuscular theory of light, by showing that the aberration angle was given by simple vector addition of the Earth's orbital velocity and the velocity of the corpuscles of light, just as vertically falling raindrops strike a moving object at an angle.

When PNG development started in early 1995, developers decided not to incorporate support for animation, because the majority of the PNG developers felt that overloading a single file type with both still and animation features is a bad design, both for users ( who have no simple way of determining to which class a given image file belongs ) and for web servers ( which should use the image / foo MIME type for stills and video / foo for animations -- GIF notwithstanding ).

However, the ancient Romans recognized the health benefits of a simple or " frugal " diet ( from the Latin fruges, the common name given to cereals, vegetables and legumes ) and thick vegetable soups and vegetables remained a staple.

These discourses, transcribed or worked up by close disciples from points given by Baba, address many aspects of the spiritual life and provide practical and simple direction for the spiritual aspirant.

Because of their low-rise construction ( most were simple one-story buildings, anything more than two floors with outside corridors being rare ) with large car parks, the number of rooms which would fit on any given amount of land was low compared to the high-rise urban hotels which had grown around railway stations.

The meaning of terms that stand for complex properties can be given by using terms for their constituent properties in a definition ; simple properties cannot be defined, because they are made up only of themselves and there are no simpler constituents to refer to.

Similarly to curved mirrors, thin lenses follow a simple equation that determines the location of the images given a particular focal length () and object distance ():

For a non-self-intersecting ( simple ) polygon with n vertices, the area and centroid are given by:

If any two simple polygons of equal area are given, then the first can be cut into polygonal pieces which can be reassembled to form the second polygon.

A simple but slow method of verifying the primality of a given number n is known as trial division.

In countries with a simple plurality voting system, parties elected tend to be few ( often only two in any given jurisdiction ).

He found an essential clue in a 1924 paper by Edmund C. Stoner which pointed out that for a given value of the principal quantum number ( n ), the number of energy levels of a single electron in the alkali metal spectra in an external magnetic field, where all degenerate energy levels are separated, is equal to the number of electrons in the closed shell of the noble gases for the same value of n. This led Pauli to realize that the complicated numbers of electrons in closed shells can be reduced to the simple rule of one per state, if the electron states are defined using four quantum numbers.

If W isn't irreducible, then the dominant species ( or quasispecies ) that develops can depend on the initial population, as is the case in the simple example given below.