The rationalist philosophers, however, with a new emphasis on Reason as a tool of the intellect, brought the classical and medieval traditions under new scrutiny, exercising a new concept of doubt, with varying outcomes.

For a twentieth century thinker committed to the same ideal, government was an essential tool to the same end ... odern liberalism is instead the logical and sociological outcome of classical liberalism.

As central governments grew in power, a return to the citizen and mercenary armies of the classical period also began, as central levies of the peasantry began to be the central recruiting tool.

The transfer function was the primary tool used in classical control engineering.

This tool of war was unknown among the classical oriental civilizations.

* A free online tool to solve some classical queueing systems

* 1960 – 1965 – Dmitry Zubarev develops the method of non-equilibrium statistical operator, which becomes a classical tool in the statistical theory of non-equilibrium processes.

Besides military history, the Anabasis has found use as a tool for the teaching of classical philosophy ; the principles of leadership and government exhibited by the army can be seen as exemplifying Socratic philosophy.

The first sequent calculi, systems LK and LJ, were introduced by Gerhard Gentzen in 1934 as a tool for studying natural deduction in first-order logic ( in classical and intuitionistic versions, respectively ).

are a very useful tool in classical mechanics.

It is obvious that no one can collect any money off classical standards of beauty and form most of the time, so they are discouraged in a consumer society ; but an eye for beauty, for balance, is an essential Satanic tool and must be applied for greatest magical effectiveness.

Iranian classical music continues to function as a spiritual tool as it has throughout its history, and much less of a recreational activity.

Originally started to reconcile the philosophy of the ancient classical philosophers with medieval Christian theology, scholasticism is not a philosophy or theology in itself but a tool and method for learning which places emphasis on dialectical reasoning.

The main tool was Bohr – Sommerfeld quantization, a procedure for selecting out certain discrete set of states of a classical integrable motion as allowed states.

The Adams – Novikov spectral sequence is an analogue of the Adams spectral sequence using an extraordinary cohomology theory in place of classical cohomology: it is a computational tool of great potential scope.

Using this powerful tool one may then prove Cauchy's integral formula, and, just like in the classical case, that any vector-valued holomorphic function is analytic.

Rajaram questions how it was possible for 19th century European evangelical " Indologists / missionaries " to study and develop hypotheses on Indian history, claiming many of them were " functionally illiterate " in Indian languages, including even the fundamental classical language, Sanskrit, suggesting that " every available modern tool from archaeology to computer science " be used to " clearing away the cobwebs cast by questionable linguistic theories " as he chooses to refer to mainstream historical linguistics and philology.

Case control studies are a classical epidemiological tool.

Let R be a ( Noetherian, commutative ) regular local ring and P and Q be prime ideals of R. In 1958, Serre realized that classical algebraic-geometric ideas of multiplicity could be generalized using the concepts of homological algebra.

In classical mathematics, analytic geometry, also known as coordinate geometry, or Cartesian geometry, is the study of geometry using a coordinate system and the principles of algebra and analysis.

In Boolean-valued semantics ( for classical propositional logic ), the truth values are the elements of an arbitrary Boolean algebra, " true " corresponds to the maximal element of the algebra, and " false " corresponds to the minimal element.

Assign Boolean semantics to classical predicate calculus requires that the model be a complete Boolean algebra because the universal quantifier maps to the infimum operation, and the existential quantifier maps to the supremum ; this is called a Boolean-valued model.

It starts with the classical algebra of all ( smooth ) functionals over the configuration space.

The word problem was one of the first examples of an unsolvable problem to be found not in mathematical logic or the theory of algorithms, but in one of the central branches of classical mathematics, algebra.

In Boolean-valued semantics ( for classical propositional logic ), the truth values are the elements of an arbitrary Boolean algebra ; " true " corresponds to the maximal element of the algebra, and " false " corresponds to the minimal element.

In concise terms, loop quantization is the result of applying C *- algebraic quantization to a non-canonical algebra of gauge-invariant classical observables.

He worked mainly in the mathematical fields of calculus of variations, integration of algebraic functions, number theory, algebra, geometry, probability theory and in the fields of mathematical physics and classical mechanics.

However, the equations can be further generalized to then be extended to apply to quantum mechanics as well as to classical mechanics, through the deformation of the Poisson algebra over p and q to the algebra of Moyal brackets.

In linear algebra, the adjugate or classical adjoint ( occasionally referred to as adjunct ) of a square matrix is a matrix that plays a role similar to the inverse of a matrix ; it can, however, be defined for any square matrix without the need to perform any divisions.

However, Weyl's perception that the central place of classical analysis had been challenged by abstract algebra has subsequently been justified, as has his assessment of Serre's place in this change.

He was a champion of the classical approach to geometry, in a period when the tendency was to approach geometry more and more via algebra.

In 1957, Artin wrote a book on geometric algebra an insightful development of the classical groups in a Kleinian context.

In commutative algebra and algebraic geometry, elimination theory is the classical name for algorithmic approaches to eliminating between polynomials of several variables.

To get a more classical set theory one can look at toposes in which it is moreover a Boolean algebra, or specialising even further, at those with just two truth-values.

In classical logic, and in particular in Boolean algebra, the operations OR and AND, which are also denoted by and, also satisfy the lattice axioms, including the absorption law.

Analytic vectors are dense by a classical argument of Edward Nelson, amplified by Roe Goodman, since vectors in the image of a heat operator e < sup >– tD </ sup >, corresponding to an elliptic differential operator D in the universal enveloping algebra of G, are analytic.

The notion of " algebras for a monad " generalizes classical notions from universal algebra, and in this sense, monads can be thought of as " theories ".

It provides, in the classical setting of field theory, an alternative perspective to that of Emil Artin based on linear algebra, which became standard from about the 1930s.

Chern – Simons theory is a gauge theory, which means that a classical configuration in the Chern – Simons theory on M with gauge group G is described by a principal G-bundle on M. The connection of this bundle is characterized by a connection one-form A which is valued in the Lie algebra g of the Lie group G. In general the connection A is only defined on individual coordinate patches, and the values of A on different patches are related by maps known as gauge transformations.

108: 171 .</ ref > Moreover, Jaynes elaborated an interpretation of probability theory as generalized Aristotelian logic, a view very convenient for linking fundamental physics with digital computers, because these are designed to implement the operations of classical logic and, equivalently, of Boolean algebra.

With classical art, all is settled.

Experience is not seen, as it is in classical rationalism, as presenting us initially with clear and distinct objects simply located in space and registering their character, movements, and changes on the tabula rasa of an uninvolved intellect.

The recent history of the Dominican Republic is an almost classical study of the way in which even a professedly benevolent dictatorship tends to become oppressive.

One had to manage the given subjects, three diverse recent events, so as to make them part of a classical frieze, -- that is, a pattern of large figures filling the space, with not much else, against a blank background.

-- On the basis of a differentiability assumption in function space, it is possible to prove that, for materials having the property that the stress is given by a functional of the history of the deformation gradients, the classical theory of infinitesimal viscoelasticity is valid when the deformation has been infinitesimal for all times in the past.

And then, some churchmen remarked, there is a more classical church-state problem:

The Leningrad Kirov Ballet, which opened a series of performances Friday night at the Opera House, is, I think, the finest `` classical '' ballet company I have ever seen, and the production of the Petipa-Tschaikowsky `` Sleeping Beauty '' with which it began the series is incomparably the finest I have ever had the pleasure of witnessing.

The mushrooming of FM outlets, offering concerts ( both jazz and classical ), lectures, and other special events, is a phenomenon which has had a fair amount of publicity.

Andalusian so-called Algerian classical music is a musical style that was reported in Algeria by Andalusian refugees who fled the inquisition of the Christian Kings from the 11th century, it will develop considerably in the cities of the North of the Algeria.

In classical Greece the emphasis is not given to the illusive imaginative reality represented by the ideal forms, but to the analogies and the interaction of the members in the whole, a method created by Polykleitos.

Since the widespread adoption of digital setting circles, any classical engraved setting circle is now specifically identified as an " analog setting circle " ( ASC ).

Wormwood, a genus that includes the sagebrush, is used as a source of flavoring for absinthe, a bitter classical liquor of European origin.

ZFC, however, is still formalized in classical logic.

Alex is then subjected to a relentless barrage of classical music, prompting him to attempt suicide by leaping from a high window.

Due to the near-identity of the Aramaic and the classical Hebrew alphabets, Aramaic text is mostly typeset in standard Hebrew script in scholarly literature.

Poirot, as mentioned in Curtain and The Clocks, is extremely fond of classical music, particularly Mozart and Bach.

and Nagaoka himself recognized a fundamental defect in the theory even at its conception, namely that a classical charged object cannot sustain orbital motion because it is accelerating and therefore loses energy due to electromagnetic radiation.

The majority Arminian view accepts classical theism – the belief that God's power, knowledge, and presence have no external limitations, that is, outside of His divine nature.

André-Marie Ampère ( 20 January 1775 – 10 June 1836 ) was a French physicist and mathematician who is generally regarded as one of the main founders of the science of classical electromagnetism, which he referred to as " electrodynamics ".

However, in the classical interpretation, it is zero and the thermal energy of matter vanishes.

Note that the above formula is only applicable to classical ideal gases and not Bose – Einstein or Fermi gases.