( All the meanings and derivations cited above are based upon Sanskrit English Dictionary of Monier-Williams ).

However, the above derivations suggest an error proportional to.

* the above component vali ahad meaning ' successor by virtue of a covenant ' ( or various forms and etymological derivations ) was adopted by many oriental monarchies, even some non-Muslim, e. g. Walet as alternative title for the Nepali ( Hindu ) royal heir apparent ; first used Crown Prince Trailokya in the middle of the nineteenth century, taken from the Mughal title ' Vali Ahad '

It should be noted that the above derivations make the following assumptions:

Early derivations of Kin selection theory and the related field of Sociobiology, encouraged some biologists such as Darwinian anthropologists and evolutionary psychologists to approach human kinship with the assumption that kin selection theory predicts that kinship relations in humans are indeed expected to depend on genetic relatedness, which they readily connected with the genealogy approach of early anthropologists such as Morgan ( see above sections ).

Using the above derivations we can substitute the universal constants h, G, and c, and determine physical values for the particle's mass and radius.

ﯨطر could represent the root ' see ' as above, but also ' protect ', ' pride ', ' clitoris ' or ' with flint ', as well as several inflections and derivations of each of these root words.

In differential equations, the function e < sup > ix </ sup > is often used to simplify derivations, even if the final answer is a real function involving sine and cosine.

He read an unabridged dictionary ( the 13th edition of Webster ’ s ) through, word for word, studying not only the definitions of the words but also their derivations from ancient languages.

That expansion, in turn, serves as the starting point for one of the derivations of precise error estimates for Stirling's approximation of the factorial function.

Such derivations are today proposed only by a minority since being refuted by Grimm, who was skeptical of theories proposing non-Germanic origins for German folklore traditions.

* Pictographic ideograms or pictograms ( 象形字 ) -- characters that adhere most to the pictorial origins of the word-form surviving from Bronze-age China, e. g. the characters for " human ", " big ", " mountain ", " mouth " and " sun ", which are easily recognisable as straightforward pictorial derivations from their Bronze-age counterparts ;

These derivations form a real vector space if we define addition and scalar multiplication for derivations by

" The hat-passing game in Waiting For Godot and Lucky's inability to think without his hat on are two obvious Beckett derivations from Laurel and Hardy – a substitution of form for essence, covering for reality ," wrote Gerald Mast in The Comic Mind: Comedy and the Movies ( Univ.

In addition, local dialects employ derivations of the Malay word then in use for ' silver ', in contrast to the term used in wider Melanesian society, which has etymological roots in Chinese, a consequence of the regional trade with China that was developed in the 6th and 7th centuries.

In the New Hacker's Dictionary, two derivations for chad are offered, a back-formation from a personal name Chadless and an acronym for Card Hole Aggregate Debris.

Cognac-producing regions should not be confused with the northeastern region of Champagne, a wine region that produces sparkling wine by that name, although they do share a common etymology – both being derivations of a French term for chalky soil.

The original river Uck name was most likely related to the ancient Celtic word for ' water ' or ' stream ' - Uisge, derivations uske, usci, that give river names still existing such as the Usk.

It would appear from both these later derivations that the only assumptions really needed for the inequality itself ( as opposed to the method of estimation of the test statistic ) are that the distribution of the possible states of the source remains constant and the detectors on the two sides act independently.

Various derivations for the meaning of the town ’ s name have been put forward.

The exact meaning of the name Ojibwe is not known ; the most common explanations for the name derivations are:

Instead of viewing the rules as descriptions for legal derivations in predicate logic, one may also consider them as instructions for the construction of a proof for a given statement.

The rule of cut is different: It states that, when a formula A can be concluded and this formula may also serve as a premise for concluding other statements, then the formula A can be " cut out " and the respective derivations are joined.

Aubrey compiled a list of some 5, 000 place-names, but managed to provide derivations for only a relatively small proportion of them: many are correct, but some are wildly wrong.

* Top-down parsing-Top-down parsing can be viewed as an attempt to find left-most derivations of an input-stream by searching for parse trees using a top-down expansion of the given formal grammar rules.

In a similar way, compression waves in solids depend both on compressibility and density — just as in liquids — but in gases the density contributes to the compressibility in such a way that some part of each attribute factors out, leaving only a dependence on temperature, molecular weight, and heat capacity ( see derivations below ).

For example, when the film is only four minutes old, Neitzbohr refers to a small, Victorian piano stool as `` Wilhelmina '', and we are thereupon subjected to a flashback that informs us that this very piano stool was once used by an epileptic governess whose name, of course, was Doris ( the English equivalent, when passed through middle-Gaelic derivations, of Wilhelmina ).

( Some of the terms used below are defined in Uniform polychoron # Geometric derivations.

There are two major derivations of this segment, both presupposing that it belongs to the family of Indo-European languages: from ' cow ' and from ' warrior.

The versions sampled in the following sections are representative of the most common derivations of the argument.

Below are three examples of increasing complexity, with derivations of the formulas governing velocity and acceleration.

* Axiomatic proof: Proofs are deductive derivations of propositions from primitive premises that are ‘ true ’ in some sense.

* Analytic proof: Proofs are non-deductive derivations of hypotheses from problems.

The derivations of all of the inhabited islands of the Hebrides and some of the larger uninhabited ones are listed below.

In several axiomatic derivations of logic, this is effectively resolved by showing that ( P ∨ ¬ P ) and its negation are constants, and simply defining TRUE as ( P ∨ ¬ P ) and FALSE as ¬( P ∨ ¬ P ), without taking a position as to the principle of bivalence or the law of excluded middle.

Influential to thinkers associated with Postmodernism are Heidegger's critique of the subject-object or sense-knowledge division implicit in Rationalism, Empiricism and Methodological Naturalism, his repudiation of the idea that facts exist outside or separately from the process of thinking and speaking them ( however, Heidegger is not specifically a Nominalist ), his related admission that the possibilities of philosophical and scientific discourse are wrapped up in the practices and expectations of a society and that concepts and fundamental constructs are the expression of a lived, historical exercise rather than simple derivations of external, apriori conditions independent from historical mind and changing experience ( see Johann Gottlieb Fichte, Heinrich von Kleist, Weltanschauung and Social Constructionism ), and his Instrumentalist and Negativist notion that Being ( and, by extension, reality ) is an action, method, tendency, possibility and question rather than a discreet, positive, identifiable state, answer or entity ( see also Process Philosophy, Dynamism, Instrumentalism, Pragmatism and Vitalism ).

Both the noun (* rīkijan ) and the adjective (* rīkijaz ) are derivations based on a Common Germanic * rīks " ruler, king ", reflected in Gothic as reiks, glossing " leader, ruler, chieftain ".

Most of the individual islands have Norse names, although the derivations of some are obscure and may represent pre-Norse, possibly Pictish or even pre-Celtic names or elements.

To illustrate how derivations are done, we will work in a very simplified formal system.

These derivations are quite productive but there are a few adjectives from which adverbs may not be derived.

This is a focus on the highly-specialized and highly-accurate algorithmic derivations and statistical calculations that are less often observed in the typical general business environment.

Below are six derivations all of which are very different and lead to different ways of understanding and extending this theory.