Word Finder - analysis

definition

Decomposition into components in order to study (a complex thing, concept, theory etc.).

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The result of such a process.

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The mathematical study of functions, sequences, series, limits, derivatives and integrals.

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Proof by deduction from known truths.

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The process of breaking down a substance into its constituent parts, or the result of this process.

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The analytical study of melodies, harmonies, sequences, repetitions, variations, quotations, juxtapositions, and surprises.

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Psychoanalysis.

After careful analysis, he decided not to go.

The atomic weight of the element has been determined by analysis.

The analysis must be deeper, if we are to gain any further conclusions.

He needed to brush up on his analysis techniques.

But analysis has failed to find such differences.

These last articles show a keen analysis and interpretation of facts.

Regression analysis was used to predict the outcome.

This prediction is verified by the result of analysis.

He compiled the history and did an analysis of the writings of all the ecclesiastical writers of the first thirteen centuries.

The analysis of the consolidated data was set for a later date.

An analysis of the case has been made elsewhere, and Miss Keller has written her account of it.

Mathematics has influenced the form and the terminology of the science, and has sometimes been useful in analysis; but mathematical methods of reasoning, in their application to economics, while possessing a certain fascination, are of very doubtful utility.

Between them the general theory of the complex variable, and of the various "infinite" processes of mathematical analysis, was established, while other mathematicians, such as Poncelet, Steiner, Lobatschewsky and von Staudt, were founding modern geometry, and Gauss inaugurated the differential geometry of surfaces.

The analysis of the Hong Kong flora indicates that about threefifths of the species are common to the Indian region, and nearly all the remainder are either Chinese or local forms. The number of species common to southern China, Japan and northern Asia is small.

For the subjects of this general heading see the articles ALGEBRA, UNIVERSAL; GROUPS, THEORY OF; INFINITESIMAL CALCULUS; NUMBER; QUATERNIONS; VECTOR ANALYSIS.

Notable service was also rendered by Augustus de Morgan, who applied logical analysis to the laws of mathematics.

In the following year he published a paper on the analysis of one of the London pump-waters (from Rathbone Place, Oxford Street), which is closely connected with the memoirs just mentioned, since it shows that the calcareous matter in that water is held in solution by the "fixed air" present and can be precipitated by lime.

A second great service was the publication in the British Association Reports for 1833 of his "Report on the Recent Progress and Present State of certain branches of Analysis."

It all seems a very hurried and imperfectly studied philosophical analysis.

This section treats of the qualitative detection and separation of the metals, and the commoner methods employed in quantitative analysis.

Martin Heinrich Klaproth showed the necessity for igniting precipitates before weighing them, if they were not decomposed by this process; and he worked largely with Louis Nicolas Vauquelin in perfecting the analysis of minerals.

The evolution of mathematical thought in the invention of the data of analysis has thus been completely traced in outline.

Thus the current applications of mathematics to the analysis of phenomena can be justified by no a priori necessity.

For the subjects of this general heading see the articles Mechanics; Dynamics, Analytical; Gyroscope; Harmonic Analysis; Wave; HYDROMechanics; Elasticity; Motion, Laws Of; Energy; Energetics; Astronomy (Celestial Mechanics); Tide.

The 18th century witnessed a rapid development of analysis, and the period culminated with the genius of Lagrange and Laplace.

All these views have, however, been cast in the shade by more recent investigations based on minute literary analysis of the Pentateuch, begun by Graf, continued by Kuenen, and culminating in the work of Wellhausen and Robertson Smith.

The argument is supported by an analysis of the phenomena of dreams, which are ascribed to direct spiritual influences.

So also any exhaustive survey of the temperature and salinity of the sea at a great number of points on and below the surface reveals a complexity of conditions that may defy mathematical analysis and could not easily be predicted.

At present, however, the methods of analysis usually employed are not sufficiently delicate to afford all the necessary information as to the intrinsic value of the higher grades of rubber, and do not go much beyond the exclusion of inferior rubber.

It was also a distributory tax (impot de repartition); every year the king in his council fixed the total sum which the taille was to produce in the following year; he drew up and signed the brevet de la taille (warrant), and the contribution of the individual taxpayer was arrived at in the last analysis by a series of subdivisions.

Arithmetical groups, connected with the theory of quadratic forms and other branches of the theory of numbers, which are termed "discontinuous," and infinite groups connected with differential forms and equations, came into existence, and also particular linear and higher transformations connected with analysis and geometry.

Under Abel's guidance, the prevailing obscurities of analysis began to be cleared, new fields were entered upon and the study of functions so advanced as to provide mathematicians with numerous ramifications along which progress could be made.

Dr. Stone returned to the UK in January 2001 to begin data analysis.

It should know what the food on my fork weighs, run a chemical analysis of every bite I take, and log it in my Digital Echo file for my future reference.

The importance of ascertaining the proximate composition of bodies was clearly realized by Otto Tachenius; but the first systematic investigator was Robert Boyle, to whom we owe the introduction of the term analysis.

Having completed the dry analysis we may now pass on to the wet and more accurate investigation.

In the above account we have indicated the procedure adopted in the analysis of a complex mixture of salts.

We see however the similarity of the metal-working of both countries at approximately the same time; both are in the same style of artistic development, the Egyptian perhaps the more advanced of the two, and (if the published analysis by Mosso is to be relied upon) with the additional technique of the alloy with tin, making the metal bronze, and so easier for the heads to be cast.

But his great strength lay in metaphysical analysis, as was shown in his answer to the objections raised against the appointment of Sir John Leslie to the mathematical professorship (1805).

Often this felsitic devitrified glass is so fine-grained that its constituents cannot be directly determined even with the aid of the microscope, but chemical analysis leaves little doubt as to the real nature cf the minerals which have been formed.

In addition to many other researches besides those here mentioned, he wrote or edited various books on chemistry and chemical technology, including Select Methods of Chemical Analysis, which went through a number of editions; and he also gave a certain amount of time to the investigation of psychic phenomena, endeavouring to effect some measure of correlation between them and ordinary physical laws.

There is much keen analysis and original investigation in his two essays Der jiidische Stamm (1869) and Der jiidische Stamm in nicht jiidischen Spriich-wortern (1881-1882).

It is shown in the article on Combinatorial Analysis that (w; 0,n) is the coefficient of a e z w in the ascending expansion of the fraction 1-a.

These are effects of pedantry, and seem rather to be founded on a cold-blooded analysis of celebrated sermons than on any instinctive sense of the duty of the preacher.

The results, together with the chemical analysis of each sample, are given in a table contained in this paper, some of them being also represented graphically.

The second and third implements of analysis above cited are of the nature of cautions or checks.

Laplace was, moreover, the first to offer a complete analysis of capillary action based upon a definite hypothesis - that of forces "sensible only at insensible distances"; and he made strenuous but unsuccessful efforts to explain the phenomena of light on an identical principle.

In this neighbourhood fragments and lumps of glass are still constantly being dug up, and analysis proves that the glass contains a considerable proportion of magnesia.

An analysis of the glass of a Cairene mosque lamp shows that it is a soda-lime glass and contains as much as 4% of magnesia.

In regard to methods and apparatus, mention should be made of his improvements in the technique of organic analysis, his plan for determining the natural alkaloids and for ascertaining the molecular weights of organic bases b y means of their chloroplatinates, his process for determining the quantity of urea in a solution - the first step towards the introduction of precise chemical methods into practical medicine - and his invention of the simple form of condenser known in every laboratory.