The earliest known formulation is Aristotle's principle of non-contradiction, first proposed in On Interpretation, where he says that of two contradictory propositions ( i. e. where one proposition is the negation of the other ) one must be true, and the other false.

Examples of A and B are propositions using a wave description of S and a corpuscular description of S. The latter statement is one part of Niels Bohr's original formulation, which is often equated to the principle of complementarity itself.

In mathematics, axiomatization is the formulation of a system of statements ( i. e. axioms ) that relate a number of primitive terms in order that a consistent body of propositions may be derived deductively from these statements.

The logical formulation of pure mathematics suggested by Bertrand Russell in terms of a quantifier structure of propositions seemed more and more plausible, as large parts of mathematics became axiomatised and thus subject to the simple criteria of rigorous proof.

A systematic understanding of its consequences has led to the phase space formulation of quantum mechanics, which works in full phase space instead of Hilbert space, so then with a more intuitive link to the classical limit thereof.

Peano's original formulation of the axioms used 1 instead of 0 as the " first " natural number.

In the Bazaar, written towards the end of his life, Nestorius denies the heresy for which he was condemned and instead affirms of Christ " the same one is twofold " – an expression that some consider similar to the formulation of the Council of Chalcedon.

This is another formulation of a composite Simpson's rule: instead of applying Simpson's rule to disjoint segments of the integral to be approximated, Simpson's rule is applied to overlapping segments, yielding:

An alternative problem formulation uses rice and chopsticks instead of spaghetti and forks.

In the above formulation, if the bit rate constraint is neglected by setting equal to 0, or equivalently if it is assumed that a fixed-length code ( FLC ) will be used to represent the quantized data instead of a variable-length code ( or some other entropy coding technology such as arithmetic coding that is better than an FLC in the rate – distortion sense ), the optimization problem reduces to minimization of distortion alone.

In the 15 April 2009 episode of Mythbusters, Jamie Hyneman and Adam Savage built a small boat out of a modified formulation of Pykrete ( using newspaper instead of wood pulp ).

After the formulation of the Nicene Creed, its initial liturgical use was in baptism, which explains why the text uses the singular " I ... instead of " we ...." The text was gradually incorporated into the liturgies, first in the east and in Spain, and gradually into the north, from the sixth to the ninth century.

The Italian adopted it as filite, in cord instead of flake form, but realising its drawbacks changed to a formulation with nitroglycerine they called solenite.

The manifolds that are used in this formulation are 4 dimensional Riemannian manifolds instead of pseudo Riemannian manifolds.

Specifically, the scaled inverse chi-squared distribution can be used as a conjugate prior for the variance parameter of a normal distribution ; however, it is more common to use the inverse gamma distribution formulation instead.

A permanent, unified and politically neutral civil service, in which appointments were made on merit, was introduced on the recommendations of the Northcote-Trevelyan Report of 1854, which also recommended a clear division between staff responsible for routine (" mechanical ") work, and those engaged in policy formulation and implementation in an " administrative " class.

During their wanderings abroad the chancellor wrote for the instruction of the young Prince Edward his celebrated work De laudibus legum Angliae (" concerning the praises of the laws of England "), in which he made the first expression of what would later become known as Blackstone's formulation, stating that " one would much rather that twenty guilty persons should escape the punishment of death, than that one innocent person should be condemned, and suffer capitally ".

In the United Kingdom, the permanent and politically neutral Her Majesty's Civil Service, in which appointments were made on merit, was introduced on the recommendations of the 1854 Northcote-Trevelyan Report, which also recommended a clear division between staff responsible for routine (" mechanical ") work, and those engaged in policy formulation and implementation in an " administrative " class.

Its formulation is often attributed to the legendary sage Laozi (" Old Master "), who is said to predate Confucius, and Zhuangzi ( 369 – 286 BC ).

Its main foreign policy decision was to contribute to Operation Iraqi Freedom, although its formulation (" political " but not " military " support ) gave it an ambivalent character.

Through the state of exception, Schmitt included all types of violence under right, in the case of the authority of Hitler leading to the formulation " The leader defends the law " (" Der Führer schützt das Recht ").

The national coffee fund (" Fondo Nacional del Café ") ( FNC ) has served for several decades as the primary instrument of Colombian coffee policy formulation and implementation.

The Society's most authoritative formulation of Mother mythology was not produced by the sect itself, but is a spirit-written work that dates back to the year 1880 (" The Golden Basin of Jade Dew ").

He regarded heat as a form of motion, suggested the wave theory of light, contributed to the formulation of the kinetic theory of gases, and stated the idea of conservation of matter in the following words: " All changes in nature are such that inasmuch is taken from one object insomuch is added to another.

All the characteristic temperatures associated to phases transformation, glass transitions and melting points, occurring during a sinterisation cycle of a particular ceramics formulation ( i. e., tails and frits ) can be easily obtained by observing the expansion-temperature curves during optical dilatometer thermal analysis.

All point numbers refer to Barker's formulation.

All three differ slightly, however more information regarding the Surge formulation can be gleaned from both syrup variations, as they were to be mixed using a ratio of 4. 4 parts cold, carbonated water to 1 part syrup.

All these cases were solved within a year of the formulation of the Schrödinger equation.

All modern theories of syntax have some part of the theory which deals with the correct formulation of the rules for wh-movement.

USAID has programming in the following areas: economic policy reform and restructuring ; private sector development ( the Business Development Program ); infrastructure rebuilding ; democratic reforms in the media, political process and elections, and rule of law / legal code formulation ; and training programs for women and diplomats.

* Afri-Cola, a German brand, had a higher caffeine content ( about 250 mg / L ) until the product was relaunched with a new formulation in 1999.

For at least the IV formulation, a loading dose of 20 mg / kg is required.

Another way of stating the same is that for every prime factor p of n, the prime p does not divide n / p. Yet another formulation: n is square-free if and only if in every factorization n = ab, the factors a and b are coprime.

A similar criticism, responding to large software company complaints about the slow pace of W3C's formulation of XML / web services standards, appeared in Cnet's news. com in 2002:

The propellant grain is longer and of a different formulation than that of the MK40 / MK4, however, the stabilizing rod and igniter are essentially the same design.

According to Gerry / Gerald Butters, the former head of Lucent's Optical Networking Group at Bell Labs, there is another version, called Butter's Law of Photonics, a formulation which deliberately parallels Moore's law.

The phenomenological tie-in with the sociology of knowledge stems from two key historical sources for Mannheim's analysis: Mannheim was dependent on insights derived from Husserl's phenomenological investigations, especially the theory of meaning as found in Husserl's Logical Investigations of 1900 / 1901 ( Husserl: 2000 ), in the formulation of his central methodological work: " On The Interpretation of Weltanschauung " ( Mannheim: 1993: see fn41 & fn43 )-this essay forms the centerpiece for Mannheim's method of historical understanding and is central to his conception of the sociology of knowledge as a research program ; and The concept of " Weltanschauung " employed by Mannheim has its origins in the hermeneutic philosophy of Wilhelm Dilthey, who relied on Husserl's theory of meaning ( above ) for his methodological specification of the interpretive act ( Mannheim: 1993: see fn38 ).

There are some temperature / humidity ranges that prohibit or restrict the formulation of a snowball.

The calibration of the recording and playback circuitry is therefore critical for faithful reproduction of the original program content, and this is easily offset by poor quality tape, dirty recording / playback heads, or using inappropriate bias levels / frequency for the tape formulation, as well as tape speed, when recording or duplicating.

Joining the Advanced Program Laboratory in 1978, he began working on the concept formulation and subsequent proposal for the SYNCON IV / LEASAT Program.

This is in analogy to the 4 / 3 problem of the electromagnetic mass of electrons, where similar methods were employed by Enrico Fermi ( 1921 ) and Fritz Rohrlich ( 1960 ): In the standard formulation of relativistic dynamics the hyperplanes of simultaneity of any observer can be used, while in the Fermi / Rohrlich definition the hyperplane of simultaneity of the object's rest frame should be used.

Individual manufacturers can use their own " formulation standards " in which the ethanol content usually ranges from 70-99 % v / v.

During the 1970s and early 1980s, Merrell Dow Pharmaceuticals sold similar cough syrups ( differing slightly in flavor, but pharmacologically identical ) under the names " 2 / G " ( a reference to " glyceryl guaiacolate ," an older name for guaifenesin ) for the base expectorant formulation, and " 2G / DM " for the guaifenesin / dextromethorphan formulation.

Bale walls can be tied together with pins of bamboo, rebar, or wood ( internal to the bales or on their faces ), or with surface wire meshes, and then stuccoed or plastered, either with a cement-based mix, lime-based formulation, or earth / clay render.

This includes training in the role of economic and political factors in public decision-making and policy formulation ; microeconomic analysis of policy options and issues ; resource allocation and decision modeling ; cost / benefit analysis ; statistical methods ; and various applications to specific public policy topics.

Surfboard wax ( also known as surfwax ) is a formulation of natural and / or synthetic wax for application to the deck of a surfboard, bodyboard, or skimboard, to keep the surfer from slipping off the board when paddling out or riding a wave.

This section presents a simple formulation of plural logic / quantification approximately the same as given by Boolos in Nominalist Platonism ( Boolos 1985 ).