interval analysis

interval analysis

1) <engin.> expose

पदम् [पद्-अच्]

1 A foot (said to be m. also in this sense); पदेन on foot; शिखरिषु पदं न्यस्य Me.13; अपथे पदमर्पयन्ति हि R.9.74 'set foot on (follow) a wrong road'; 3.5;12.52; पदं हि सर्वत्र गुणैर्निधीयते 3.62 'good qualities set foot everywhere' i. e. command notice or make themselves felt; जनपदे न गदः पदमादधौ 9.4. 'no disease stepped into the country'; यदवधि न पदं दधाति चित्ते Bv.2.14; पदं कृ (a) to set foot in, on or over (lit.); शान्ते करिष्यसि पदं पुनराश्रमे$स्मिन् Ś.4.2. (b) to enter upon or into, take possession of, occupy (fig.); कृतं वपुषि नवयौवनेन पदम् K.137; कृतं हि मे कुतूहलेन प्रश्नाशया हृदि पदम् 133; so Ku.5.21; Pt.1.24; कृत्वा पदं नो गले Mu.3.26 'in defiance of us'; (lit. planting his foot on our neck); मूर्ध्नि पदं कृ 'to mount on the head of', 'to humble'; पदं मूर्ध्नि समाधत्ते केसरी मत्तदन्तिनः Pt.1.327; आकृतिविशेषेष्वादरः पदं करोति M.1 'good forms attract attention (command respect); जने सखी पदं कारिता Ś.4; 'made to have dealings with (to confide in)'; धर्मेण शर्वे पार्वतीं प्रति पदं कारिते Ku.6.14.

-2 A step, pace, stride; तन्वी स्थिता कतिचिदेव पदानि गत्वा Ś.2.13; पदे पदे 'at every step'; अक्षमालामदत्त्वा पदात् पदमपि न गन्तव्यम् or चलितव्यम् 'do not move even a step' &c.; पितुः पदं मध्यममुत्पतन्ती V.1.19 'the middle pace or stride of Viṣṇu.'; i. e. the sky (for mythologically speaking, the earth, sky, and lower world are considered as the three paces of Viṣṇu in his fifth or dwarf incarnation वामनावतार); so अथात्मनः शब्दगुणं गुणज्ञः पदं विमानेन विगाहमानः R.13.1.

-3 A foot-step, foot- print, foot-mark; पदपङ्क्तिः Ś.3.7; or पदावली foot-prints; पदमनुविधेयं च महताम् Bh.2.28 'the foot-steps of the great must be followed'; पदैगृर्ह्यते चौरः Y.2.286.

-4 A trace, mark, impression, vestige; रतिवलयपदाङ्के चापमासज्य कण्ठे Ku.2.64; Me.37,98; M.3.

-5 A place, position, station; अधो$धः पदम् Bh.2.1; आत्मा परिश्रमस्य पदमुपनीतः Ś.1, 'brought to the point of or exposed to trouble'; तदलब्धपदं हृदि शोकघने R.8.91, 'found no place in (left no impression on) the heart'; अपदे शङ्कितो$स्मि M.1, 'my doubts were out of place', i. e. groundless; कृशकुटुम्बेषु लोभः पदमधत्त Dk.162; Ku.6.72;3.4; R.2.5;9.82; कृतपदं स्तनयुगलम् U.6.35, 'brought into relief or bursting forth'.

-6 Dignity, rank, office, station or position; भगवत्या प्रश्निकपदमध्यासितव्यम् M.1; यान्त्येवं गृहिणीपदं युवतयः Ś.4.18, 'attain to the rank or position, &c.; स्थिता गृहिणीपदे 4.19; so सचिव˚, राज˚ &c.

-7 Cause, subject, occasion, thing, matter, business, affair; व्यवहारपदं हि तत् Y.2.5; 'occasion or matter of dispute, title of law, judicial proceeding'; Ms.8.7; सतां हि सन्देहपदेषु वस्तुषु Ś.1.22; वाञ्छितफलप्राप्तेः पदम् Ratn.1.6.

-8 Abode, object, receptacle; पदं दृशः स्याः कथमीश मादृशाम् Śi.1.37; 15.22; अगरीयान्न पदं नृपश्रियः Ki.2.14; अविवेकः परमापदां पदम् 2.3; के वा न स्युः परिभवपदं निष्फलारम्भयत्नाः Me.56; संपदः पदमापदाम् H.4.65.

-9 A quarter or line of a stanza, verse; विरचितपदम् (गेयम्) Me.88,15; M.5.2; Ś.3.14.

-1 A complete or inflected word; सुप्तिडन्तं पदम् P.I. 4.14. वर्णाः पदं प्रयोगार्हानन्वितैकार्थबोधकाः S. D.9; R.8.77; Ku.4.9.

-11 A name for the base of nouns before all consonantal case-terminations except nom. singular.

-12 Detachment of the Vedic words from one another, separation of a Vedic text into its several constituent words; वेदैः साङ्गपदक्रमोपनिषदैर्गायन्ति यं सामगाः Bhāg.12.13.1.

-13 A pretext; अनिभृतपदपातमापपात प्रियमिति कोपपदेन कापि सख्या Śi.7.14.

-14 A sqare root.

-15 A part, por- tion or division (as of a sentence); as त्रिपदा गायत्री.

-16 A measure of length.

-17 Protection, preservation; ते विंशतिपदे यत्ताः संप्रहारं प्रचक्रिरे Mb.7.36.13.

-18 A square or house on a chessboard; अष्टापदपदालेख्यैः Rām.

-19 A quadrant.

-2 The last of a series.

-21 A plot of ground.

-22 (In Arith.) Any one in a set of numbers the sum of which is required.

-23 A coin; माता पुत्रः पिता भ्राता भार्या मित्रजनस्तथा । अष्टापदपदस्थाने दक्षमुद्रेव लक्ष्यते ॥ Mb.12.298.4. (com. अष्टापदपदं सुवर्णकार्षापणः).

-24 A way, road; षट्पदं नवसंख्यानं निवेशं चक्रिरे द्विजाः Mb.14.64.1.

-25 Retribution (फल); ईहोपरमयोर्नॄणां पदान्यध्यात्मचक्षुषा Bhāg.7.13.2.

-दः A ray of light.

-Comp. -अङ्कः, चिह्नम् a foot-print.

-अङ्गुष्ठः the great toe, thumb (of the foot).

-अध्ययनम् study of the Vedas according to the पदपाठ q. v.

-अनुग a.

1 following closely, being at the heels of (gen.).

-2 suitable, agreeable to. (

-गः) a follower, companion; एतान्निहत्य समरे ये चृ तस्य पदानुगाः । तांश्च सर्वान् विनिर्जित्य सहितान् सनराधिपान् ॥ Mb.3.12.6.

-अनुरागः 1 a servant.

-2 an army.

-अनुशासनम् the science of words, grammar.

-अनुषङ्गः anything added to a pada.

-अन्तः 1 the end of a line of a stanza.

-2 the end of a word.

-अन्तरम् another step, the interval of one step; पदान्तरे स्थित्वा Ś.1; अ˚ closely, without a pause.

-अन्त्य a. final.

-अब्जम्, -अम्भोजम्, -अरविन्दम्, -कमलम्, -पङ्कजम्, -पद्मम् a lotus-like foot.

-अभिलाषिन् a. wishing for an office.

-अर्थः 1 the meaning of a word.

-2 a thing or object.

-3 a head or topic (of which the Naiyāyikas enumerate 16 subheads).

-4 anything which can be named (अभिधेय), a category or predicament; the number of such categories, according to the Vaiśeṣikas, is seven; according to the Sāṅkhyas, twentyfive (or twenty-seven according to the followers of Patañjali), and two according to the Vedāntins.

-5 the sense of another word which is not expressed but has to be supplied. ˚अनुसमयः preforming one detail with reference to all things or persons concerned; then doing the second, then the third and so on (see अनुसमय). Hence पदार्थानुसमयन्याय means: A rule of interpretation according to which, when several details are to be performed with reference to several things or persons, they should be done each to each at a time.

-आघातः 'a stroke with the foot', a kick.

-आजिः a foot-soldier.

-आदिः 1 the beginning of the line of a stanza.

-2 the beginning or first letter of a word. ˚विद् m. a bad student (knowing only the beginnings of stanzas).

-आयता a shoe.

-आवली a series of words, a continued arrangement of words or lines; (काव्यस्य) शरीरं तावदिष्टार्थव्यवच्छिन्नापदावली Kāv. 1.1; मधुरकोमलकान्तपदावलीं शृणु तदा जयदेवसरस्वतीम् Gīt.1.

-आसनम् a foot-stool.

- आहत a. kicked.

-कमलम् lotus-like foot.

-कारः, -कृत् m. the author of the Padapāṭha.

-क्रमः 1 walking, a pace; न चित्रमुच्चैः श्रवसः पदक्रमम् (प्रशशंस) Śi.1.52.

-2 a particular method of reciting the Veda; cf. क्रम.

-गः a foot-soldier.

-गतिः f. gait, manner of going.

-गोत्रम् a family supposed to preside over a particular class of words.

-छेदः, -विच्छेदः, -विग्रहः separation of words, resolu- tion of a sentence into its constituent parts.

-च्युत a. dismissed from office, deposed.

-जातम् class or group of words.

-दार्ढ्यम् fixedness or security of text.

-न्यासः 1 stepping, tread, step.

-2 a foot-mark.

-3 position of the feet in a particular attitude.

-4 the plant गोक्षुर.

-5 writing down verses or quarters of verses; अप्रगल्भाः पदन्यासे जननीरागहेतवः । सन्त्येके बहुलालापाः कवयो बालका इव ॥ Trivikramabhaṭṭa.

-पङ्क्तिः f.

1 a line of foot-steps; द्वारे$स्य पाण्डुसिकते पदपङ्क्तिर्दृश्यते$भिनवा Ś.3.7; V.4.6.

-2 a line or arrangement of words, a series of words; कृतपदपङ्क्तिरथर्वणेव वेदः Ki.1.1.

-3 an iṣtakā or sacred brick.

-4 a kind of metre.

-पाठः an arrangement of the Vedic text in which each word is written and pronounced in its original form and independently of phonetic changes (opp. संहितापाठ).

-पातः, विक्षेपः a step, pace (of a horse also).

-बन्धः a foot-step, step.

-भञ्जनम् analysis of words, etymology.

-भञ्जिका 1 a commentary which separates the words and analyses the compounds of a passage.

-2 a register, journal.

-3 a calendar.

-भ्रंशः dismissal from office.

-माला a magical formula.

-योपनम् a fetter for the feet (Ved.).

-रचना 1 arrangement of words.

-2 literary composition.

-वायः Ved. a leader.

-विष्टम्भः a step, footstep.

-वृत्तिः f. the hiatus between two words.

-वेदिन् a linguist, philologist.

-व्याख्यानम् interpreta- tion of words.

-शास्त्रम् the science of separately written words.

-संघातः (टः) 1 connecting the words which are separated in the संहिता.

-2 a writer, an annotator.

-संधिः m. the euphonic combination of words.

-स्थ a.

1 going on foot.

-2 being in a position of authority or high rank.

-स्थानम् a foot-print.

* * *

фу́нкция A перехо́дит в фу́нкцию B — (the) function A goes into (the) function B

воспроизводи́ть фу́нкцию — approximate [implement, mechanize, realize] a function

задава́ть фу́нкцию нея́вно или я́вно — define a function implicitly or explicitly

иссле́довать фу́нкцию на ма́ксимумы и ми́нимумы [на экстре́мумы] — examine [test] a function for maxima and minima

фу́нкция обраща́ется в нуль — a function vanishes

фу́нкция определя́ется в о́бласти … — a function is defined on an interval

фу́нкция периоди́чна по, напр. t — a function is periodic in, e. g., t

фу́нкция периоди́чна с пери́одом T — a function is periodic with period T

преобразо́вывать фу́нкцию по Лапла́су — apply the Laplace transformation to a function, take the Laplace transform of a function

прибли́зить сло́жную фу́нкцию бо́лее просто́й — approximate a complex function by a simpler one

прибо́р мо́жет выполня́ть сле́дующие фу́нкции — the instrument offers the following services

а́белева фу́нкция — Abelian function

автокорреляцио́нная фу́нкция — autocorrelation function

аддити́вная фу́нкция — additive function

амплиту́дная фу́нкция тлв. — amplitude function

аналити́ческая фу́нкция — analytical function

ана́логовая фу́нкция — analog function

аннули́рующая фу́нкция — nullifier

аркгиперболи́ческая фу́нкция — arc-hyperbolic [antihyperbolic, inverse hyperbolic] function

фу́нкция без ограниче́ний — unconstrained function

фу́нкция Бе́сселя — Bessel's function

фу́нкция большинства́ — majority function

бу́лева фу́нкция — Boolean function

ве́кторная фу́нкция — vector function

вероя́тностная фу́нкция — distribution [probability] function

весова́я фу́нкция — weighting function

весова́я фу́нкция поме́хи тлв. — noise weighting function

фу́нкция взаи́мной когере́нтности — mutual coherence function

фу́нкция влия́ния — influence [Green's] function

фу́нкция возбужде́ния — excitation [drive] function

возраста́ющая фу́нкция — increasing function

волнова́я фу́нкция — wave function

фу́нкция вы́годы киб. — objective [return] function

вы́рожденная фу́нкция — confluent function

вычисли́мая фу́нкция — computable function

фу́нкция Га́мильтона — Hamiltonian function

гармони́ческая фу́нкция — harmonic (function)

гиперболи́ческая фу́нкция — hyperbolic function

действи́тельная фу́нкция — real-valued function

действи́тельно-зна́чная фу́нкция — real-valued function

фу́нкция де́йствия мех. — action function

де́льта-фу́нкция — delta function

диссипати́вная фу́нкция — dissipative function

доброка́чественная фу́нкция — well-behaved function

до́норная фу́нкция ( атома) — donor function

за́данная фу́нкция — prescribed function

задаю́щая фу́нкция — driving function

фу́нкция запомина́ния — storage function

фу́нкция запре́та — inhibit function

фу́нкция изоба́рного потенциа́ла — isobaric potential function

и́мпульсная фу́нкция — impulse function

интегри́рующая фу́нкция — integrator

фу́нкция и́стинности — truth function

квадрати́чная фу́нкция — quadratic function

фу́нкция кисло́тности — acidity junction

классифици́рующая фу́нкция — discriminant function, discriminator

ко́мплексная фу́нкция — complex(-valued) function

корреляцио́нная фу́нкция — correlation function

-кра́тно дифференци́руемая фу́нкция — n times differentiable function

фу́нкция крите́рия — test function

фу́нкция Лагра́нжа — Lagrangian function

фу́нкция Лежа́ндра — Legendre function

лине́йная фу́нкция — linear function

лине́йно-возраста́ющая фу́нкция — ramp function

логарифми́ческая фу́нкция — logarithmic function

логи́ческая фу́нкция — logical function

логи́ческая фу́нкция включа́ющее ИЛИ — inclusive OR function

логи́ческая фу́нкция И — AND function

логи́ческая фу́нкция И—ИЛИ — AND-to-OR function

логи́ческая фу́нкция ИЛИ — OR function

логи́ческая фу́нкция исключа́ющее ИЛИ — exclusive OR function

логи́ческая фу́нкция НЕ — NOT function

фу́нкция логи́ческого сложе́ния — logical addition function

фу́нкция логи́ческого умноже́ния — collate function

мажори́рующая фу́нкция — majorant

фу́нкция Матьё́ — Mathieu's function

многозна́чная фу́нкция — multiple valued function

моното́нная фу́нкция — monotonic function

невычисли́мая фу́нкция — noncomputable function

фу́нкция неопределё́нности — ambiguity [Woodward] function

непреры́вная фу́нкция — continuous function

нечё́тная фу́нкция — odd function

нея́вная фу́нкция — implicit function

обобщё́нная фу́нкция — generalized function

обра́тная фу́нкция — inverse function

обра́тная, гиперболи́ческая фу́нкция — inverse hyperbolic [arc-hyperbolic, antihyperbolic] function

обра́тная, тригонометри́ческая фу́нкция — inverse trigonometric [antitrigonometric] function

ограни́ченная фу́нкция — bounded function

однозна́чная фу́нкция — single-valued function

опо́рная фу́нкция — function of support, support [supporting] function

фу́нкция отсчё́тов ( в теории сообщений и теории информации) — sampling function

первоо́бразная фу́нкция — antiderivative, primitive

переда́точная фу́нкция — transfer function

реализова́ть переда́точную фу́нкцию на … — implement the transfer function with

переда́точная, дискре́тная фу́нкция — sampled-data transfer [pulse transfer] function

переда́точная фу́нкция нелине́йного элеме́нта — describing function

переда́точная, опти́ческая фу́нкция — optical transfer function

переда́точная фу́нкция по возде́йствию — actuating transfer function

переда́точная фу́нкция по возмуще́нию — the transfer function to [on] the extraneous signal

переда́точная фу́нкция по входно́му сигна́лу — the transfer function to [on] the input signal

переключа́тельная фу́нкция — switching function

фу́нкция перехо́да ( цифрового мата) — transition [next-state] function

перехо́дная фу́нкция — unit step function

периоди́ческая фу́нкция — periodic function

разлага́ть периоди́ческую фу́нкцию на слага́емые гармо́ники ме́тодом ана́лиза Фурье́ — resolve a periodic function into harmonic components by Fourier analysis

пилообра́зная фу́нкция — saw-tooth function

фу́нкция пло́тности — density function

фу́нкция пло́тности состоя́ний — density-of-states function

подынтегра́льная фу́нкция — integration function, integrand

показа́тельная фу́нкция — exponential function

поро́говая фу́нкция — threshold function

порожда́ющая фу́нкция — generator

потенциа́льная фу́нкция — potential function

потенциа́льная фу́нкция скоросте́й — velocity potential function

фу́нкция правдоподо́бия — likelihood function

фу́нкция преобразова́ния — transfer function

произво́дная фу́нкция — derived function

производя́щая фу́нкция — generating function

произво́льная фу́нкция — arbitrary function

проста́я фу́нкция — simple function

фу́нкция разбие́ния — partition function

фу́нкция распределе́ния — distribution function; стат. frequency function

фу́нкция распределе́ния вероя́тности — probability distribution function

фу́нкция распростране́ния — propagation function, propagator

фу́нкция рассе́яния — scattering function

рациона́льная фу́нкция — rational function

регуля́рная фу́нкция — well-behaved function

рекурси́вная фу́нкция — recursive function

реша́ющая фу́нкция — decision function

фу́нкция ри́ска — risk function

силова́я фу́нкция — force function

синусоида́льная фу́нкция — sine function

фу́нкция скачко́в — saltus [step, jump] function

сло́жная фу́нкция — composite function

случа́йная фу́нкция — random function

со́бственная фу́нкция — eigenfunction, characteristic [fundamental] function

фу́нкция с ограниче́нном — constrained function

фу́нкция с ограни́ченным измене́нием — function of bounded variation

фу́нкция состоя́ния — function of state, point function

спектра́льная фу́нкция — spectrum, spectral function, integrated spectrum

степенна́я фу́нкция — power function

ступе́нчатая фу́нкция — step [jump] function

сфери́ческая фу́нкция — spherical [surface] harmonic, spherical function

фу́нкция то́ка — stream [flow] function

трансценде́нтная фу́нкция — transcendental function

тригонометри́ческая фу́нкция — trigonometrical function

фу́нкция управле́ния — control function

фи-фу́нкция Э́йлера — phi function, Euler's function (of an integer)

характеристи́ческая фу́нкция — characteristic [fundamental] function, eigenfunction

фу́нкция хране́ния — storage function

це́лая фу́нкция — entire [integral] function

целева́я фу́нкция ( в исследовании операций) — ( для каждого решения по каждой цели) efficiency function; ( для каждого решения по всем целям) effectiveness function

цилиндри́ческая фу́нкция — Bessel's function

чё́тная фу́нкция — even function

экспоненциа́льная фу́нкция — exponential function

фу́нкция эне́ргии Ги́ббса — Gibbous function

эргоди́ческая фу́нкция — ergodic function

- прогнозирование объёмов продаж

SUBJECT AREA: Medical technology, Photography, film and optics

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At the age of 19 Marey went to Paris to study medicine, becoming particularly interested in the problems of the circulation of the blood. In an early communication to the Académie des Sciences he described a much improved device for recording the pulse, the sphygmograph, in which the beats were recorded on a smoked plate. Most of his subsequent work was concerned with methods of recording movement: to study the movement of the horse, he used pneumatic sensors on each hoof to record traces on a smoked drum; this device became known as the Marey recording tambour. His attempts to study the wing movements of a bird in flight in the same way met with limited success since the recording system interfered with free movement. Reading in 1878 of Muybridge's work in America using sequence photography to study animal movement, Marey considered the use of photography himself. In 1882 he developed an idea first used by the astronomer Janssen: a camera in which a series of exposures could be made on a circular photographic plate. Marey's "photographic gun" was rifle shaped and could expose twelve pictures in approximately one second on a circular plate. With this device he was able to study wing movements of birds in free flight. The camera was limited in that it could record only a small number of images, and in the summer of 1882 he developed a new camera, when the French government gave him a grant to set up a physiological research station on land provided by the Parisian authorities near the Porte d'Auteuil. The new design used a fixed plate, on which a series of images were recorded through a rotating shutter. Looking rather like the results provided by a modern stroboscope flash device, the images were partially superimposed if the subject was slow moving, or separated if it was fast. His human subjects were dressed all in white and moved against a black background. An alternative was to dress the subject in black, with highly reflective strips and points along limbs and at joints, to produce a graphic record of the relationships of the parts of the body during action. A one-second-sweep timing clock was included in the scene to enable the precise interval between exposures to be assessed. The fixed-plate cameras were used with considerable success, but the number of individual records on each plate was still limited. With the appearance of Eastman's Kodak roll-film camera in France in September 1888, Marey designed a new camera to use the long rolls of paper film. He described the new apparatus to the Académie des Sciences on 8 October 1888, and three weeks later showed a band of images taken with it at the rate of 20 per second. This camera and its subsequent improvements were the first true cinematographic cameras. The arrival of Eastman's celluloid film late in 1889 made Marey's camera even more practical, and for over a decade the Physiological Research Station made hundreds of sequence studies of animals and humans in motion, at rates of up to 100 pictures per second. Marey pioneered the scientific study of movement using film cameras, introducing techniques of time-lapse, frame-by-frame and slow-motion analysis, macro-and micro-cinematography, superimposed timing clocks, studies of airflow using smoke streams, and other methods still in use in the 1990s. Appointed Professor of Natural History at the Collège de France in 1870, he headed the Institut Marey founded in 1898 to continue these studies. After Marey's death in 1904, the research continued under the direction of his associate Lucien Bull, who developed many new techniques, notably ultra-high-speed cinematography.

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See also: Demenÿ, Georges

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