It may establish the relation of the figure of the dancer to light and color, in which case changes in the light or color will set off a kaleidescope of visual designs.

This is the principle which we will invoke in every case to set up a functional equation.

But in either event he was the wrong man for the kind of case outlined by Ben Gurion and set forth in the indictment.

We may now take up for consideration a hard case which seems to require either no action employing economic pressure or else action that would seem to violate the principles set forth above.

When they were forced to, Central Worlds shrugged its shoulders, arranged a tour of the Laboratory Schools and set the tour off to a big start by showing the members case histories, complete with photographs.

The committee decided it was important to support upper case 64-character alphabets, and chose to pattern ASCII so it could be reduced easily to a usable 64-character set of graphic codes.

But humans can do something equally useful, in the case of certain enumerably infinite sets: They can give explicit instructions for determining the nth member of the set, for arbitrary finite n. Such instructions are to be given quite explicitly, in a form in which they could be followed by a computing machine, or by a human who is capable of carrying out only very elementary operations on symbols.

However, that particular case is a theorem of Zermelo – Fraenkel set theory without the axiom of choice ( ZF ); it is easily proved by mathematical induction.

In the even simpler case of a collection of one set, a choice function just corresponds to an element, so this instance of the axiom of choice says that every nonempty set has an element ; this holds trivially.

** If S is a set of sentences of first-order logic and B is a consistent subset of S, then B is included in a set that is maximal among consistent subsets of S. The special case where S is the set of all first-order sentences in a given signature is weaker, equivalent to the Boolean prime ideal theorem ; see the section " Weaker forms " below.

It was intended to be a flexible set of laws that could only be strengthened, not weakened, by future case law.

If a is algebraic over K, then K, the set of all polynomials in a with coefficients in K, is not only a ring but a field: an algebraic extension of K which has finite degree over K. In the special case where K = Q is the field of rational numbers, Q is an example of an algebraic number field.

All units ran much faster than the original TRS-80, at 4 MHz, ( with a software selectable throttle to the original speed for compatibility purposes ) and the display supported upper and lower case, hardware snow suppression ( video ram bus arbitration logic ), and an improved character font set.

This is often the case for many precedents that have been set in the common law.

ASCII included the distinction of upper and lower case alphabets and a set of control characters to facilitate the transmission of written language as well as printing device functions, such as page advance and line feed, and the physical or logical control of data flow over the transmission media.

A binary relation is the special case of an n-ary relation R ⊆ A < sub > 1 </ sub > × … × A < sub > n </ sub >, that is, a set of n-tuples where the jth component of each n-tuple is taken from the jth domain A < sub > j </ sub > of the relation.

Bulgarian, along with the closely related Macedonian language ( collectively forming the East South Slavic languages ), has several characteristics that set it apart from all other Slavic languages: changes include the elimination of case declension, the development of a suffixed definite article ( see Balkan language area ) and the lack of a verb infinitive ; but it retains and has further developed the Proto-Slavic verb system.

Swiftsure, Alexander and Franklin were all set alight by falling wreckage although in each case teams of sailors with water buckets succeeded in extinguishing the flames, despite a secondary explosion on Franklin.

It can be done by systematically making explicit all the axioms, as in the case of the well-known book Naive Set Theory by Paul Halmos, which is actually a somewhat ( not all that ) informal presentation of the usual axiomatic Zermelo – Fraenkel set theory.

For example, civil law can be clearer than case law when the legislature has had the foresight and diligence to address the precise set of facts applicable to a particular situation.

Such a skill set would involve years of training, an extraordinary memory and numeracy, and / or acute visual or even aural observation, as in the case of wheel clocking in Roulette.

In 1960, Nicholas Poppe presented what was in effect a heavily revised version of Ramstedt ’ s volume on phonology that has since set the standard in Altaic studies.

* Meta-analysis – combines the results of several studies that address a set of related research hypotheses

In 1904, he travelled to Berlin to study philosophy, but set aside his studies soon and began a career as a professional chess player that same year.

In 2003, Mitchell set up a web site on which he posted most all of the publications of Victor T. Houteff, Ben and Lois Roden, and his own new studies, including a detailed presentation of what he calls The Warfare of Vernon Howell ( a. k. a. David Koresh ) and others against the Branch Davidian Seventh Day Adventists, in which he gives a detailed and documented overview of the controversy regarding the church and its adversaries.

Recent studies, based on a larger data set, indicate the cut-off inclination of 12 ° ( instead of 5 °) between the cold and hot populations while confirming the distinction between the homogenous red cold population and the bluish hot population.

Alain Silver, the most widely published American critic specializing in film noir studies, refers to film noir as a " cycle " and a " phenomenon ", even as he argues that it has — like certain genres — a consistent set of visual and thematic codes.

Because abstract algebra studies sets endowed with operations that generate interesting structure or properties on the set, functions which preserve the operations are especially important.

Several studies have suggested that hedge funds are sufficiently diversifying to merit inclusion in investor portfolios, but this is disputed for example by Mark Kritzman who performed a mean-variance optimization calculation on an opportunity set that consisted of a stock index fund, a bond index fund, and ten hypothetical hedge funds.

" But Maloy adds that " The totalitarian thesis in Rousseau studies has, by now, been discredited as an attribution of real historical influence .” Arthur Melzer, however, while conceding that Rousseau would not have approved of modern nationalism, observes that his theories do contain the " seeds of nationalism ", insofar as they set forth the " politics of identification ", which are rooted in sympathetic emotion.

Recent studies in neuroscience have indicated that as people fall in love, the brain consistently releases a certain set of chemicals, including pheromones, dopamine, norepinephrine, and serotonin, which act in a manner similar to amphetamines, stimulating the brain's pleasure center and leading to side effects such as increased heart rate, loss of appetite and sleep, and an intense feeling of excitement.

Experimental studies dating from the 1990s have shown that circadian rhythms are generated by a " genetic clock " consisting of a special set of genes whose expression level rises and falls over the course of the day.

Critics say that analogous problems with meta-analysis have been documented in medicine, where it has been shown different investigators performing meta-analyses of the same set of studies have reached contradictory conclusions.

He was set to work on astronomical and calendar studies, a project which was intended to bring the year back into synchronization with the seasons.

Clement X confirmed the exemptions granted by Pope Gregory XIII ( 1572 – 85 ) to the German College at Rome in 1671 ; and then, on 16 October 1672, he ordered the pupils to swear that at the close of their studies they would set out for Germany without a day's delay.

Pointless topology then studies lattices like these abstractly, without reference to any underlying set of points.

In most statistical studies, the goal is to generalize from the observed units to a larger set consisting of all comparable units that exist but are not directly observed.

After meeting Samuel Beckett while delivering a series of lectures in Paris the same year, Adorno set to work on " Trying to Understand Endgame ," which, along with studies of Proust, Valéry and Balzac, formed the central texts of the 1961 publication of the second volume of his Notes to Literature.

Usability testing measures the usability, or ease of use, of a specific object or set of objects, whereas general human-computer interaction studies attempt to formulate universal principles.

Otto Kitzler, Bruckner's last composition teacher, set him three final tasks as the climax of his studies: a choral work ( Psalm 112 ), an overture ( the Overture in G minor ), and a symphony.

Goodall also set herself apart from the traditional conventions of the time by naming the animals in her studies of primates, instead of assigning each a number.

He cited studies that showed that people were more likely to engage in dangerous deviant behavior, such as drug taking, if someone else had set the example first.

In 1826 Clementi completed his very large collection of keyboard studies, Gradus ad Parnassum, and set off for Paris with the intention of publishing the third volume of the work simultaneously in Paris, London and Leipzig.

From these studies, we will begin to set our course toward the Great Society.

These studies further suggest that pollinators may maintain a fidelity to either male or hermaphroditic flowers ( trees ), thus limiting pollination and fruit set under natural conditions where crossing between male and female flowers is required.