Such a position entails the negation of philosophy in its Platonic form as something soaring above and embracing the empirical and mathematical sciences.

Such concerns include mathematical well-posedness: the existence, uniqueness, and stability of any solutions to econometric equations.

Such a limit is possible only in mathematical settings, where accurate repetitions unto infinity may be made ( e. g. such as counting the relative fraction of even numbers less than n < sub > t </ sub >: one may easily compute the limit.

Such techniques can help evolve mathematical solutions to certain types of otherwise difficult problems.

Such are distinguished from mathematical formalisms for theories developed prior to the early 1900s by the use of abstract mathematical structures, such as infinite-dimensional Hilbert spaces and operators on these spaces.

Such relationships are then amenable to mathematical treatment by the established methods of continuum mechanics.

Such mathematical identities will hold for referentially transparent functions such as.

Such languages are a form of mathematical recreation, in which programmers work out how to achieve basic programming constructs in an extremely difficult but mathematically Turing-equivalent language.

Such axiomatizations were most famously used by Russell and Whitehead in their mathematical treatise Principia Mathematica.

Such a formulation is called an optimization problem or a mathematical programming problem ( a term not directly related to computer programming, but still in use for example in linear programming-see History below ).

Such a fundamental understanding can result in what looks like slowness and can hide a mathematical intelligence potentially higher than that of a child who quickly memorizes the multiplication table despite possessing a less detailed understanding of the process of multiplication.

Such questions are usually more difficult to solve than regular mathematical exercises like " 5 − 3 ", even if one knows the mathematics required to solve the problem.

Such a model would formalize a link between the lambda calculus as a purely syntactic system and the lambda calculus as a notational system for manipulating concrete mathematical functions.

Such phrases are known as mathematical jargon.

Such mathematical formulas can be a part of speech in a natural-language phrase, or even assume the role of a full-fledged sentence.

Such denotations are often mathematical objects inhabiting a mathematical space, but it is not a requirement that they should be so.

Such a proof generally shows that a system or a protocol is secure by showing that an attacker must require impossible behavior from the oracle, or solve some mathematical problem believed hard, in order to break the protocol.

( Such asymmetrical normalizations are sometimes found in both purely mathematical and engineering contexts.

Such mathematical areas as calculus, probability theory, statistics, linear algebra, abstract algebra, graph theory, combinatorics, algebraic geometry, topology, dynamical systems, differential equations and coding theory are now being applied in biology.

( Such attempts are not pseudomathematical unless accepted mathematical methods are disregarded ; perhaps there really is an uncorrectable error in the published proof, and it has not been conclusively demonstrated that Fermat was mistaken in his supposed " proof " or that some other " simpler " proof cannot be found.

Such applications include numerical analysis, mathematics of engineering, linear programming, optimization and operations research, continuous modelling, mathematical biology and bioinformatics, information theory, game theory, probability and statistics, financial mathematics, actuarial science, cryptography and hence combinatorics and even finite geometry to some extent, graph theory as applied to network analysis, and a great deal of what is called computer science.

Such time to MRCA ( TMRCA ) estimates can be given based on DNA test results and established mutation rates as practiced in genetic genealogy, or by reference to a non-genetic, mathematical model or computer simulation.

Such decreases in heat capacity were among the first signs to physicists of the 19th century that classical physics was incorrect and that a new, more subtle, scientific model was required.

Such mental models are akin to architects ' models or to physicists ' diagrams in that their structure is analogous to the structure of the situation that they represent, unlike, say, the structure of logical forms used in formal rule theories of reasoning.

Such research is the common interdisciplinary domain of interest of the philosophy of mind, artificial intelligence and different systemic and meta-systemic approaches with a strong contribution from physicists and mathematicians.

Such " spooky communication " experiments have never been successfully conducted, and only attempted a limited number of times, since most physicists believe that they would violate the no-communication theorem.

Such terms are primarily understood as negative attitudes towards certain categories of people or other things, used in an analogy with the medical usage of the term.

Such methods are used primarily for the fabrication of materials ( typically a metal oxide ) starting from a chemical solution which acts as the precursor for an integrated network ( or gel ) of either discrete nanoparticles or network polymers.

Such a derivation would find support only in epigraphic documents, primarily from the Osco-Sabellic area.

Such clubs may also offer social activities and facilities, and some members may join primarily to take advantage of the social opportunities.

" By the eighteenth century, " man " had come to refer primarily to males ; some writers who wished to use the term in the older sense deemed it necessary to spell out their meaning: Anthony Trollope, for example, writes of " the infinite simplicity and silliness of mankind and womankind " and when " Edmund Burke, writing of the French Revolution, used men in the old, inclusive way, he took pains to spell out his meaning: ' Such a deplorable havoc is made in the minds of men ( both sexes ) in France ....'"

Such planets are often described with no pretense to scientific accuracy ; their strange characteristics are primarily intended to amuse.

Such definitions fail to distinguish between erotic and romantic slash, and between slash, het ( works focusing primarily on heterosexual relationships ) and gen ( works which do not include a romantic focus ).

Such debris disks are rare among M-type star systems older than about 10 million years, having been primarily cleared away by drag from the stellar wind.

Such books were written primarily for housewives and occasionally domestic servants as opposed to professional cooks, and at times books such as The Joy of Cooking ( USA ), La bonne cuisine de Madame E. Saint-Ange ( France ), The Art of Cookery ( UK, USA ), Il cucchiaio d ' argento ( Italy ), and A Gift to Young Housewives ( Russia ) have served as references of record for national cuisines.

Such independent secondary schools are often called public schools, though this term is primarily used of schools which are members of the Headmasters ' and Headmistresses ' Conference.

This movement was centered in Bakersfield, California with musicians like Buck Owens (" Act Naturally "), Merle Haggard (" Sing a Sad Song ") and Wynn Stewart (" It's Such a Pretty World Today ") helping to define the sound among the community, made up primarily of Oklahoman immigrants to California, who had fled unemployment and drought.

Such systems are primarily used for electric meter reading.

Such is the case in nations such as Argentina, Nicaragua, and Panama, or in the case of Brazil, persons of primarily African descent who also have Portuguese ancestors.

Such development was primarily geared toward agricultural needs and was concentrated near the cities of Landsberg and Küstrin, and the Neumark did not become nearly as industrialized or densely-populated as other German areas such as the Ruhr, Saxony, or Upper Silesia.

Such comments invigorated Kellogg chairman William E. LaMothe to improve, which primarily involved approaching the demographic of 80 million baby boomers rather than marketing children-oriented cereals.

Such people, however, obtain their food primarily from farm plots cleared from the forest and hunt and forage within the forest to supplement this. The issue arising is between the independent farmer providing for his family and the needs and wants of the globe as a whole.

Such units were primarily defensive and although there were examples of RF and PF units successfully defending themselves, they rarely conducted offensive operations ; even when they did these operations were usually limited and lacked initiative or aggression.

Such central reservations are also sometimes found on more minor or residential streets, where they serve primarily as a traffic-calming or landscaping element rather than a safety enhancement to restrict turns and separate opposite directions of high-volume traffic flow.

Such methods are used primarily for the fabrication of materials ( typically a metal oxide ) starting from a chemical solution ( sol, short for solution ) which acts as the precursor for an integrated network ( or gel ) of either discrete particles or network polymers.

Such issues were made salient primarily by W. V.

Such proposals often include excising Albany ( and presumably the Hudson River Valley ) along with New York City, due to a perception that Albany is primarily controlled by politicians from the New York City area.

Such action gives Springer the possibility to prove to the older generations that, while his TV show ( which appeals primarily to younger adults ) was empty-minded, he may nevertheless be well-suited to representing citizens.

Such methods are used primarily for the fabrication of materials ( typically metal oxides ) starting from a colloidal solution ( sol ) that acts as the precursor for an integrated network ( or gel ) of either discrete particles or network polymers.

Such conventions focused primarily on improving working conditions in relation to hours of work, women's and children's labor, and the use of hazardous materials.