While the U. S. Department of Labor has a program of projecting industry and occupational employment trends and publishing current outlook statements, there is little tangible evidence that these projections have been used extensively in local curriculum planning.

While there, he initiated an important series of historical monographs on the history of Malaya, publishing the very first of the series in 1960.

" While his intentions for publishing a fresh Latin translation are clear, it is less clear why he included the Greek text.

While competing printers and their associated control languages offered some of the capabilities of PostScript, they were limited in their ability to reproduce free-form layouts ( as a desktop publishing application might produce ), use outline fonts, or offer the level of detail and control over the page layout.

While desktop publishing software still provides extensive features necessary for print publishing, modern word processors now have publishing capabilities beyond those of many older DTP applications, blurring the line between word processing and desktop publishing.

While a Privatdozent, Zschokke created a sensation by publishing the extravagant novel, Abällino, der grosse Bandit ( 1793 ; subsequently also dramatized ), modelled on Schiller's Die Räuber, and the melodramatic tragedy Julius von Sassen ( 1796 ).

While Annenberg ran his publishing empire as a business, he was not afraid to use it for his own ends.

While the fourth volume is generally regarded as Rodríguez de Montalvo's own work, he claimed to be publishing earlier sources and it is generally accepted that the first three volumes derive from a previous manuscript or oral tradition.

While Knight had sought an outright release from Ruthless Records for Dr. Dre, the JDL and Ruthless Records management negotiated a release in which the record label would continue to receive money and publishing rights from future Dr. Dre projects with Death Row Records, founded by Dr. Dre with Suge Knight.

While Rand was working as a script reader for Paramount Pictures, her boss there, Richard Mealand, offered to introduce her to his publishing contacts.

While the term " electronic publishing " is primarily used today to refer to the current offerings of online and web-based publishers, the term has a history of being used to describe the development of new forms of production, distribution, and user interaction in regard to computer-based production of text and other interactive media.

While in the hospital, Jackson signed a publishing deal with Columbia Records.

While his intentions for publishing a fresh Latin translation are clear, it is less clear why he included the Greek text.

While in Breslau, Dirichlet continued his number theoretic research, publishing important contributions to the biquadratic reciprocity law which at the time was a focal point of Gauss ' research.

While out of office in the mid-1960s he served as editor of The Spectator, where he caused further controversy by publishing in early 1964 a candid account of the 1963 party leadership contest.

While this was a little outside the main centres of British mathematical research, Burnside remained a very active researcher, publishing more than 150 papers in his career.

While plasma cosmology has never had the support of most astronomers or physicists, a few researchers have continued to promote and develop the approach, publishing mostly in the IEEE journal Transactions on Plasma Science.

While the publishing history of the work is not absolutely clear, there is reason to believe that Histriomastix was published late in 1632 by the bookseller Michael Sparke, although it had been in preparation by its author for almost ten years prior to its final printing.

While at Columbia University, Charles wrote the original version of the desktop publishing application FrameMaker, which was the main product of the company he soon co-founded.

While working for a brief time with Maxim Gorky at the World Literature publishing company, he criticized the Soviet regime.

While living on the road, Oppen began writing poems and publishing in local magazines.

While in normal typography these are just alternate font variants, they may have different meanings as mathematical symbols.

While some of Euler's proofs are not acceptable by modern standards of mathematical rigour ( in particular his reliance on the principle of the generality of algebra ), his ideas led to many great advances.

While the patent was initially rejected by the patent office as being a purely mathematical invention, following 12 years of appeals, Pardo and Landau won a landmark court case at the CCPA ( Predecessor Court of the Federal Circuit ) overturning the Patent Office in 1983 — establishing that " something does not cease to become patentable merely because the point of novelty is in an algorithm.

While areas of many simple surfaces have been known since antiquity, a rigorous mathematical definition of the area requires a lot of care.

While other such approaches have been developed, those based on moments are advantageous in terms of mathematical and computational simplicity.

While these result in some contradictions and lack completeness in a mathematical sense ( being based on axioms that are " merely " self-evident, but not robust under the stresses of radical scepticism ), the paradoxes can nonetheless be analysed rationally using the subatomic applications of quantum cosmology-particularly through the employment of the Schrödinger wave equations.

While Lobachevsky created a non-Euclidean geometry by negating the parallel postulate, Bolyai worked out a geometry where both the Euclidean and the hyperbolic geometry are possible depending on a parameter k. Bolyai ends his work by mentioning that it is not possible to decide through mathematical reasoning alone if the geometry of the physical universe is Euclidean or non-Euclidean ; this is a task for the physical sciences.

While it is often assumed that those with this intelligence naturally excel in mathematics, chess, computer programming and other logical or numerical activities, a more accurate definition places less emphasis on traditional mathematical ability and more on reasoning capabilities, recognizing abstract patterns, scientific thinking and investigation and the ability to perform complex calculations.

While Bolzano had developed a reasonably rigorous definition of a limit as early as 1817 ( and possibly even earlier ) his work remained unknown to most of the mathematical community until years later,

While Hilbert's tenth problem is not a formal mathematical statement as such the nearly universal acceptance of the ( philosophical ) identification of a decision algorithm with a total computable predicate allows us to use the MRDP theorem to conclude the tenth problem is unsolvable.

While the advanced mathematical nature of such adaptive systems has kept neural networks for financial analysis mostly within academic research circles, in recent years more user friendly neural network software has made the technology more accessible to traders.

While the complexity of real food webs connections are difficult to decipher, ecologists have found mathematical models on networks an invaluable tool for gaining insight into the structure, stability, and laws of food web behaviours relative to observable outcomes.

While the theorems of Gödel and Gentzen are now well understood by the mathematical logic community, no consensus has formed on whether ( or in what way ) these theorems answer Hilbert's second problem.

While infinitesimals eventually disappeared from the calculus, their mathematical study continued through the work of Levi-Civita and others, throughout the late nineteenth and the twentieth centuries, as documented by Philip Ehrlich ( 2006 ).

While the mathematical probability of an event has a value in the range from zero to one, " the odds " in favor of that same event lie between zero and infinity.

While they have useful mathematical properties, they can produce counter-intuitive results: an event with an 80 % probability of occurring is four times more likely to happen than an event with a 20 % probability, but the odds are 16 times higher on the less likely event ( 4 – 1 against, or 4 ) than on the more likely one ( 1 – 4, or 4 – 1 on, or 0. 25 ).

While some coders specialize in developing system-level functionality ( such as providing wrappers and APIs for other coders to base their code on ), others code effects which are usually visual representations of mathematical formulas, such as fractals or metaballs.

" While Javits said any government official who sought to use the bill for busing purposes " would be making a fool of himself ," two years later the Department of Health, Education and Welfare said that Southern school districts would be required to meet mathematical ratios of students by busing.

While admitting that it made him " a little sore ", Patrick has said that the research he and his students conducted was seminal in developing mathematical models against which further research could be compared.

While complex problems can be broken down into simpler multiplications, the answers to these basic operations themselves are essential for more complex mathematical operations.

While content validity depends on a theoretical basis for assuming if a test is assessing all domains of a certain criterion ( e. g. does assessing addition skills yield in a good measure for mathematical skills?

While possibly following Pythagorean modes of thinking, Vincenzo is known to have discovered a new mathematical relationship between string tension and pitch, thus suggesting a generalization of the idea that music and musical instruments can be mathematically quantified and described.