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* Duality principle ( optimization theory )
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Duality and principle
* Duality principle in functional analysis, used in the large sieve method of analytic number theory
Duality and optimization
Duality and theory
* Duality: Every statement, theorem, or definition in category theory has a dual which is essentially obtained by " reversing all the arrows ".
This formulation of Poincaré Duality has become quite popular as it provides a means to define Poincaré Duality for any generalized homology theories provided one has a Thom Isomorphism for that homology theory.
A treatment of this theory, Residues and Duality ( 1966 ) by Robin Hartshorne, became an accessible reference.
principle and optimization
The more broad concept of optimism is the understanding that all of nature, past, present and future, operates by laws of optimization along the lines of Hamilton's principle of optimization in the realm of physics.
* Progressive lenses can use the optimization principle, which is based on linearization and represents the lens surface using special spline functions.
According to the end-to-end principle, protocol features are only justified in the lower layers of a system if they are a performance optimization, hence, TCP retransmission for reliability is still justified, but efforts to improve TCP reliability should stop after peak performance has been reached.
In convex optimization, the maximum principle states that the maximum of a convex function on a compact convex set is attained on the boundary.
Thus the learning algorithm defined by ERM principle consists in solving the above optimization problem.
In applied mathematics, highly optimized tolerance ( HOT ) is a method of generating power law behavior in systems by including a global optimization principle.
principle and theory
Corpuscularianism is similar to the theory of atomism, except that where atoms were supposed to be indivisible, corpuscles could in principle be divided.
Also, as we now know, bosons also have antiparticles, but since bosons do not obey the Pauli exclusion principle ( only fermions do ), hole theory does not work for them.
In quantum field theory, this process is allowed only as an intermediate quantum state for times short enough that the violation of energy conservation can be accommodated by the uncertainty principle.
His emphasis on the role of universal properties brought category theory into the mainstream as an important organizing principle.
Grothendieck took them to a higher level of abstraction and turned them into a key organising principle of his theory.
The Big Bang theory depends on two major assumptions: the universality of physical laws and the cosmological principle.
** Microevolution: species — speciation — adaptation — selection — natural selection — directional selection — sexual selection — genetic drift — sexual reproduction — asexual reproduction — colony — allele frequency — neutral theory of molecular evolution — population genetics — Hardy-Weinberg principle
* the equivalence principle, whether or not Einstein's general theory of relativity is the correct theory of gravitation, and if the fundamental laws of physics are the same everywhere in the universe.
With an essential principle like " when the epoch changed, the ways changed ", it upholds the rule of law and is thus a theory of jurisprudence.
Dropping the principle that the wave function is a complete description results in a hidden variable theory.
Conjecture is contrasted by hypothesis ( hence theory, axiom, principle ), which is a testable statement based on accepted grounds.
The central principle to this theory was that “ all parts of a catapult, including the weight or length of the projectile, were proportional to the size of the torsion springs ”.
" Han independence " was therefore scrapped in favor of the Five Races Under One Union principle, which later developed into the theory of Zhonghua minzu.
In turn, imposing restrictions on the available resources is what distinguishes computational complexity from computability theory: the latter theory asks what kind of problems can, in principle, be solved algorithmically.
The theory of supply and demand is an organizing principle for explaining how prices coordinate the amounts produced and consumed.
Later empiricism referred to a theory of knowledge in philosophy which adheres to the principle that knowledge arises from experience and evidence gathered specifically using the senses.
Boas developed the principle of cultural relativism and Malinowski developed the theory of functionalism as guides for producing non-ethnocentric studies of different cultures.
The Hausdorff maximal principle is one of many statements equivalent to the axiom of choice over Zermelo – Fraenkel set theory.
The holographic principle resolves the black hole information paradox within the framework of string theory.
Using Huygens ' theory and the principle of superposition of waves, the complex amplitude at a further point P is found by summing the contributions from each point on the sphere of radius r < sub > 0 </ sub >.
The domino theory principle may indeed explain why a chain of dominoes collapses, but an independent argument is necessary to explain why a similar principle would hold in other circumstances.
Anarchist communism ( also known as anarcho-communism and occasionally as free communism or libertarian communism ) is a theory of anarchism which advocates the abolition of the state, capitalism and private property ( while retaining respect for personal property ), and in favor of common ownership of the means of production, direct democracy and a horizontal network of voluntary associations and workers ' councils with production and consumption based on the guiding principle: " from each according to his ability, to each according to his need ".
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