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Page "Algebraic number" ¶ 22
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Examples and algebraic
Examples are the product of sets ( see Cartesian product ), groups ( described below ), the product of rings and of other algebraic structures.
Examples include piecewise definitions, induction or recursion, algebraic or analytic closure, limits, analytic continuation, infinite series, and as solutions to integral and differential equations.
Examples are linear dependence of arbitrary subsets of infinite-dimensional vector spaces ( but not infinite dependencies as in Hilbert and Banach spaces ), and algebraic dependence in arbitrary subsets of field extensions of possibly infinite transcendence degree.
Examples of algebraic functions are rational functions and the square root function.
Examples come from fractional ideals in algebraic number theory, so that the definition captures that theory.
Examples of algebraic surfaces include ( κ is the Kodaira dimension ):
In mathematics, a Severi – Brauer variety over a field K is an algebraic variety V which becomes isomorphic to projective space over an algebraic closure of K. Examples are conic sections C: provided C is non-singular, it becomes isomorphic to the projective line over any extension field L over which C has a point defined.
Examples are homomorphisms, which preserve algebraic structures ; homeomorphisms, which preserve topological structures ; and diffeomorphisms, which preserve differential structures.

Examples and integers
Examples of Euclidean domains include fields, polynomial rings in one variable over a field, and the Gaussian integers.

Examples and are
Examples are in public utilities, making military aircraft and accessories, or where the investment and risk for a proprietorship would be too great for a much needed project impossible to achieve by any means other than the corporate form, e.g. constructing major airports or dams.
Examples of such situations are ( aerial ) night reconnaissance, the recording of radioactive tracers in live body tissues, special radiography in medical or industrial applications, track recording of high energy particles, etc..
Examples of applied anthropology are ubiquitous.
Examples include Web accessibility a set of guidelines and two accessible web portals designed for people developing reading skills are peepo. com — try typing a letter with your keyboard for more — and peepo. co. uk with enhanced graphics, unique style controls and improved interactivity ( requires an SVG supported browser ).
Examples of present-day abjads are the Arabic and Hebrew scripts ; true alphabets include Latin, Cyrillic, and Korean hangul ; and abugidas are used to write Tigrinya, Amharic, Hindi, and Thai.
Examples are parsley ( Petroselinum crispum ), coriander ( Coriandrum sativum ), and dill ( Anethum graveolens ).
Examples among the Egyptian monks of this submission to the commands of the superiors, exalted into a virtue by those who regarded the entire crushing of the individual will as a goal, are detailed by Cassian and others, e. g. a monk watering a dry stick, day after day, for months, or endeavoring to remove a huge rock immensely exceeding his powers.
Examples of substitutional alloys include bronze and brass, in which some of the copper atoms are substituted with either tin or zinc atoms.
Examples of applications often classified as applets are all of the accessories bundled in Microsoft Windows ( such as Windows Notepad or Microsoft Paint ).
Examples of non-benzene compounds with aromatic properties are furan, a heterocyclic compound with a five-membered ring that includes an oxygen atom, and pyridine, a heterocyclic compound with a six-membered ring containing one nitrogen atom.
Examples of benzene compounds with just one substituent are phenol, which carries a hydroxyl group, and toluene with a methyl group.
Examples from the nineteenth century are the transposition of " Horatio Nelson " into " Honor est a Nilo " ( Latin = Honor is from the Nile ); and of " Florence Nightingale " into " Flit on, cheering angel ".
Examples of prayer which are unique to Luke include Jesus's prayers at the time of his baptism (), his praying all night before choosing the twelve (), and praying for the transfiguration ().
Examples of pre-historic art are rare.
Examples are the local anesthetic and stimulant cocaine ; the psychedelic psilocin ; the stimulant caffeine ; nicotine ; the analgesic morphine ; the antibacterial berberine ; the anticancer compound vincristine ; the antihypertension agent reserpine ; the cholinomimeric galatamine ; the spasmolysis agent atropine ; the vasodilator vincamine ; the anti-arhythmia compound quinidine ; the anti-asthma therapeutic ephedrine ; and the antimalarial drug quinine.
Examples of thermosetting adhesives are: epoxy, polyurethane, cyanoacrylate and acrylic polymers.
Examples of hardware noise reduction are the use of shielded cable, analog filtering, and signal modulation.
Examples of software noise reduction are digital filtering, ensemble average, boxcar average, and correlation methods.
Examples of rapidly expanding fields in this area are:
Examples of such groups are Take 6, Glad and Acappella.
Examples of addition reactions are hydrohalogenation, halogenation, halohydrin formation, oxymercuration, hydroboration, dichlorocarbene addition, Simmons-Smith reaction, catalytic hydrogenation, epoxidation, radical polymerization and hydroxylation.
Examples are the Sushruta Samhita written in the 3rd or 4th century CE, which recommends beef for certain patients and for pregnant women, and the Charaka Samhita which describes meat as superior to all other kinds of food for convalescents.

Examples and Note
( Note that the Simple Examples below are not quotes from the Focal Points, but are based on the descriptions of activities found in the Focal Points.

Examples and therefore
Examples might include an organizational structure which is unclear and therefore makes it confusing to know who to communicate with.
Examples: The 427 Chevy bore is 4. 312 in, and the stroke is 3. 65 in, therefore the displacement for this eight-cylinder engine is:
Examples of good leaving groups are therefore the halides ( except fluoride ) and tosylate, whereas HO < sup >-</ sup > and H < sub > 2 </ sub > N < sup >-</ sup > are not.
Examples are FIFA in soccer and FIBA in basketball, which have regulated international gameplay rules that are even practiced within US sports leagues today, despite not practicing them historically ( which therefore meant that many US sports leagues weren't recognized by international governing bodies in the past, until they began to adopt international rules ).
Examples of arithmetic groups include therefore the groups GL < sub > n </ sub >( Z ).
) Examples of the negative aspect of fairness include consumers " boycotting " firms they disapprove of by not buying products they otherwise would ( and therefore settling for second-best ); and employees sabotaging firms they feel hard done by.
Examples include dense clays with a small pore size and therefore a low hydraulic conductivity and clean sands and gravels, which contain small amounts of fine particles and whose pore sizes are too open to promote capillary flow.
Examples include threats to self-esteem and to one's worldview ; the DTA paradigm can therefore assess the role of death-thoughts in self-esteem and worldview defenses.

Examples and constitute
Examples of loose interpretation exist not only in California, but also in other states such as Colorado where similar code ( Colorado Code § 18-1-901 ( 3 )( g )) applies in cases even when a shooting at an detached garage that does not traditionally constitute a dwelling or house.
Examples of the last case constitute the towns of Yutupiza on the Santiago River and Japaime on the Nieva.

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