Since an abbreviation is also employed for the word ‘ equals ’, Diophantus took a fundamental step from verbal algebra towards symbolic algebra .”

Since this also results in a prediction for the relative strengths of the fundamental interactions which we observe, in particular the weak mixing angle, Grand Unification ideally reduces the number of independent input parameters, but is also constrained by observations.

Since knowledge is used to achieve intelligent behavior, the fundamental goal of knowledge representation is to facilitate reasoning, inferencing, or drawing conclusions.

Since independence, with Jaja Wachuku as the first Minister of Foreign Affairs and Commonwealth Relations, later called External Affairs, Nigerian foreign policy has been characterized by a focus on Africa as a Regional power and by attachment to several fundamental principles: African unity and independence ; Capability to exercise hegemonic influence in the region: peaceful settlement of disputes ; nonalignment and nonintentional interference in the internal affairs of other nations ; and regional economic cooperation and development.

Since reason is the means of human knowledge, it is therefore each person's most fundamental means of survival and is necessary to the achievement of values.

Since the 1960s, the term has also been used in numerous non-scientific contexts to describe a profound change in a fundamental model or perception of events, even though Kuhn himself restricted the use of the term to the hard sciences.

Since all realistic systems with more than a handful of degrees of freedom are expected to be chaotic, this puts the fundamental postulate on firm footing.

Since many materials can form crystals — such as salts, metals, minerals, semiconductors, as well as various inorganic, organic and biological molecules — X-ray crystallography has been fundamental in the development of many scientific fields.

Since it is absurd to have no logical method by which to settle on one hypothesis amongst an infinite number of equally data-compliant hypotheses, we should choose the simplest theory: " either science is irrational the way it judges theories and predictions probable or the principle of simplicity is a fundamental synthetic a priori truth " ( Swinburne 1997 ).

Since ( 9 / 8 ) / ( 10 / 9 ) = ( 81 / 80 )— the syntonic comma — the fundamental characteristics of meantone systems are that all intervals are generated from fifths, and the syntonic comma is tempered to a unison.

Since the fundamental theorem of arithmetic applied to a non-zero integer n that is neither 1 nor − 1 also asserts uniqueness of the representation for p < sub > i </ sub > prime and e < sub > i </ sub > positive, a primary decomposition of ( n ) is essentially unique.

Since the local tradition to erect wooden churches depended on those who built and used them, it is fundamental to identify the local builders and founders.

Since modchips oftentimes hook into fundamental functions of the host system that cannot be removed or adjusted, these measures may not completely prevent a modchip from functioning but only prompt an adjustment of its installation process or programming, e. g. to include measures to make it undetectable (" stealth ") to its host system.

Since the Canadian Bill of Rights was an ordinary statute, it was not until 1982 when the term fundamental justice was first constitutionalized.

Since provincial prohibitions touching on the fundamental freedoms of speech, religion, assembly and association were declared unconstitutional by the courts, and in light of the expansive obiters in the leading cases, the writers were able to claim that there was a bill of rights implicit in the Constitution.

Since X is a compact oriented manifold, X has a fundamental class.

Since the late 1970s, despite periodic reversals, media in mainland China have frequently criticized party cadres and have published debates on such fundamental issues as the rule of law, freedom of the press, and universal human rights.

Since the 1970s fundamental rights, recognised as general principles of European Union law, have become part of primary legislation in European Union law.

Since the university and its graduates were fundamental to the building of the United States pharmaceutical industry, the university archives are of interest to anyone researching the origins of the pharmaceutical industry.

Since Canada's federal government and any of its provincial governments can suspend for five years at a time the Charter rights to fundamental freedoms in section 2, to legal rights in sections 7 through 14, and to equality rights in section 15 by a simple majority vote of the legislature which invokes the Charter of Rights and Freedoms ' override clause, section 33, emergency powers can always be very easily created even without using the Emergency Act.

Since this time the X window system has gone through many fundamental changes and no longer bears any significant resemblance to W.

Since Isenkrahe's proposal on the connection between density, temperature and weight was based purely on the anticipated effects of changes in material density, and since temperature at a given density can be increased or decreased, Isenkrahe's comments do not imply any fundamental relation between temperature and gravitation.

Since under contemporary inheritance law George would have been able to lay claim to Sir John's property on his death, Sir John engaged in a lengthy parliamentary campaign to disinherit his son via a private Act, setting out to " reverse the fundamental laws of hereditary succession ".

Since it relied on fundamental bugs, software upgrades made systems immune to Staog.

Since then, and since the pure grain had gotten him divorced from every decent -- and even indecent -- group from Greenwich Village to the Embarcadero, he had become a sucker-rolling freight-jumper.

Since most European cars average more miles per gallon of gasoline than American cars, it naturally follows that the cost per kilometer for these models will be less, but the greater seating capacity of the large American cars will equalize this, provided your group is sufficiently large to fill a 7-passenger limousine.

Since the writer had not noticed this characteristic in married students scattered throughout the various sections previous to this experiment, nor, as a matter of fact, in those who were continuing in `` single sections '', he can only conclude that there must have been something `` contagious '' within the specific group which caused this to occur.

Since its inception in the early 1990s, the group has carried out bombings, kidnappings, assassinations and extortion in what they describe as their fight for an independent Islamic province in the Philippines.

Since over the course of any single dance, individuals interact with not just their partners but everyone else in the set, contra dancing might be considered a group activity.

Since the consolidation of newspaper comics by the first quarter of the 20th century, most cartoonists have used a group of assistants ( with usually one of them credited ).

Since the reunions in the UK and Australia in 1957, two generations of Christadelphians have grown up with little awareness of the existence of the minority " fellowships ", or awareness that the main group is called " Central " by the minority groups.

Since its origins, the viability of the carrier battle group has been dependent on its ability to remain at sea for extended periods.

Since Cauchy sequences can also be defined in general topological groups, an alternative to relying on a metric structure for defining completeness and constructing the completion of a space is to use a group structure.

Since the Somalis were one main ethnic group, they could only elect a single candidate and the two main fractions of that tribe in Djibouti, the Issa and the Gadabuursi each strove to win.

Since then, the tariff is calculated by a formula based on various factors such as the number of twist and somersaults, the height, the group etc., and divers are free to submit new combinations.

Since 1988, the group has also hosted Earth Celebration, which brings artists and enthusiasts from all over the world to Sado Island.

Since the American Civil War the term " discrimination " generally evolved in American English usage as an understanding of prejudicial treatment of an individual based solely on their race, later generalized as membership in a certain socially undesirable group or social category.

Since 1990 there has been an emergence of a German minority group, Elbinger Minderheit.

Since 20 July 2004, ELDR is politically represented in the European Parliament by the Alliance of Liberals and Democrats for Europe ( ALDE ) parliamentary group, formed in conjunction with the European Democratic Party.

Since the player names were being used as a group, the players had assigned their publicity rights to the players association who then signed licensing deals.

Since the stored energy in the barrier is less than the energy stored in a barrier-free region of the same length due to destructive interference, the group delay for the energy to escape the barrier region is shorter than it would be in free space, which according to Winful is the explanation for apparently superluminal tunneling.

Since the 1980s, various experiments have verified that it is possible for the group velocity of laser light pulses sent through specially prepared materials to significantly exceed the speed of light in vacuum.

Since each element of G is represented as a permutation, a group action is also known as a permutation representation.

Since then, Japanese noise rock group Boredoms have borrowed elements of grind, and toured with Brutal Truth in 1993.

Since then, pop singers in the latter group have included KK, Baba Sehgal, Alisha Chinai, Shantanu Mukherjee aka Shaan, Sagarika, Colonial Cousins ( Hariharan, Leslie Lewis ), Lucky Ali, and Sonu Nigam, and music composers like Jawahar Wattal, who made top selling albums with, Daler Mehndi, Shubha Mudgal, Baba Sehgal, Swetha Shetty and Hans Raj Hans.

Since the emergence of the post-1943 state and after the destruction of the Ottoman Caliphate, national policy has been determined largely by a relatively restricted group of traditional regional and sectarian leaders.

* The atomic mass unit ( u ) is defined so that a single carbon-12 atom has a mass of 12 u ; 1 u is approximately .< ref group =" note "> Since the Avogadro constant N < sub > A </ sub > is defined as the number of atoms in 12 g of carbon-12, it follows that 1 u is exactly 1 /( 10 < sup > 3 </ sup > N < sub > A </ sub >) kg .</ ref > The atomic mass unit is convenient for expressing the masses of atoms and molecules.

Since the mid-1980s, geometric group theory, which studies finitely generated groups as geometric objects, has become a particularly active area in group theory.