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1 bounded frontier
Большой англо-русский и русско-английский словарь > bounded frontier
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2 bounded frontier
Математика: ограниченная область -
3 bounded frontier
мат. -
4 bounded
1) граничить
2) ограниченный
3) ограниченно
4) разграниченный
5) связанный ∙ absolutely bounded form ≈ абсолютно ограниченная форма absolutely bounded function ≈ ограниченная по абсолютной величине функция absolutely bounded matrix ≈ абсолютно ограниченная матрица algebra of bounded representation type ≈ алгебра с ограниченными степенями представлений algebra of linearly bounded degree ≈ алгебра линейно ограниченной степени almost bounded function ≈ функция, ограниченная почти всюду bounded above function ≈ ограниченная сверху функция bounded above operator ≈ ограниченый сверху оператор bounded above subset ≈ ограниченное сверху подмножество bounded below function ≈ ограниченная снизу функция bounded below operator ≈ ограниченный снизу оператор bounded below subset ≈ ограниченное снизу подмножество bounded closed interval ≈ ограниченный замкнутый интервал bounded distance decoding ≈ декодирование с ограниченным расстоянием bounded from one side ≈ полуограниченный bounded open interval ≈ ограниченный открытый интервал bounded partial quotient ≈ ограниченное неполное частное bounded pure subgroup ≈ ограниченная сервантная подгруппа bounded random variable ≈ ограниченная случайная величина bounded universal hypothesis ≈ ограниченная универсальная гипотеза bounded variable technique ≈ метод ограниченной переменной collectively bounded set ≈ ограниченное в совокупности множество completely bounded set ≈ вполне ограниченное множество completely bounded space ≈ вполне органическое пространство completely bounded statistic ≈ вполне ограниченная статистика derivative of bounded variation ≈ производная с ограниченной вариацией doubly bounded quantifier ≈ ограниченный с двух сторон квантор essentially bounded function ≈ существенно ограниченная функция essentially bounded random variable ≈ существенно ограниченная случайная величина essentially bounded sequence ≈ существенно ограниченная последовательность explicitly bounded function ≈ явно ограниченная функция finitely bounded germ ≈ конечно ограниченный росток function of bounded characteristic ≈ функция с ограниченной характеристикой function of bounded type ≈ функция ограниченного вида function of bounded variation ≈ функция с ограниченным изменением linearly bounded automaton ≈ линейно ориентированный автомат linearly bounded set ≈ линейно ограниченное множество locally bounded curvature ≈ локально ограниченная кривизна locally bounded density ≈ локально ограниченная плотность locally bounded function ≈ локально ограниченная функция locally bounded game ≈ локально ограниченная игра locally bounded space ≈ локально ограниченное пространство metrically bounded functional ≈ метрически ограниченный функционал metrically bounded set ≈ метрически ограниченное множество nontangentially bounded function ≈ нетангенциально ограниченная функция nontangentially bounded integral ≈ некасательно ограниченный интеграл order bounded functional ≈ ограниченный по упорядоченности функционал pointwise bounded function ≈ точечно ограниченная функция polynomially bounded function ≈ полиномиально ограниченная функция process with bounded aftereffect ≈ процесс с ограниченным последействием progressively bounded graph ≈ прогрессивно ограниченный граф recursively bounded quantifier ≈ рекурсивно ограниченный квантор regressively bounded graph ≈ регрессивно ограниченный граф relatively bounded form ≈ относительно ограниченная форма sequentially bounded net ≈ последовательно ограниченная сеть simply bounded subset ≈ поточечно ограниченное подмножество smoothly bounded region ≈ гладко ограниченная область stochastically bounded sequence ≈ стохастически ограниченная последовательность strictly bounded set ≈ строго ограниченное множество strongly bounded set ≈ сильно ограниченное множество strongly bounded space ≈ сильно ограниченное пространство theor of semigroups of linear bounded operators ≈ теория полугрупп линейных ограниченных операторов topology of bounded convergence ≈ топология ограниченной сходимости totally bounded measure ≈ вполне ограниченная мера totally bounded set ≈ вполне ограниченное множество totally bounded space ≈ вполне ограниченное пространство totally bounded subset ≈ вполне ограниченное подмножество totally bounded uniformity ≈ вполне ограниченная равномерность uniformly bounded convergence ≈ равномерно ограниченная сходимость uniformly bounded curvature ≈ равномерно ограниченная кривизна uniformly bounded error ≈ равномерно ограниченная ошибка uniformly bounded family ≈ равномерно ограниченное семейство uniformly bounded function ≈ равномерно ограниченная функция uniformly bounded kernel ≈ равномерно ограниченное ядро uniformly bounded sequence ≈ равномерно ограниченная последовательность uniformly bounded series ≈ равномерно ограниченный ряд uniformly bounded set ≈ равномерно ограниченное множество uniformly bounded variation ≈ равномерно ограниченная вариация weakly bounded set ≈ слабо ограниченное множество weakly bounded subset ≈ слабо ограниченное подмножество - almost bounded - bounded above - bounded acceptor - bounded accuracy - bounded adele - bounded aggregate - bounded approximation - bounded automaton - bounded axonometry - bounded below - bounded characteristic - bounded collection - bounded compactness - bounded completeness - bounded continuum - bounded convergence - bounded curvature - bounded decomposition - bounded deficiency - bounded degree - bounded derivation - bounded derivative - bounded deviation - bounded difference - bounded distribution - bounded domain - bounded duality - bounded extension - bounded field - bounded flow - bounded form - bounded frontier - bounded function - bounded functional - bounded group - bounded homomorphism - bounded index - bounded integral - bounded integrand - bounded intersection - bounded invertibility - bounded kernel - bounded language - bounded lattice - bounded mapping - bounded martingale - bounded matrix - bounded measure - bounded metric - bounded module - bounded monotonicity - bounded morphism - bounded motion - bounded network - bounded norm - bounded operator - bounded order - bounded path - bounded polyhedron - bounded potential - bounded predicate - bounded problem - bounded product - bounded projection - bounded quality - bounded quantification - bounded quantifier - bounded quantity - bounded quotient - bounded region - bounded representation - bounded retract - bounded semigroup - bounded sequence - bounded series - bounded set - bounded solution - bounded space - bounded spectrum - bounded spline - bounded string - bounded subset - bounded subtraction - bounded sum - bounded summand - bounded support - bounded term - bounded topology - bounded transformation - bounded utility - bounded variance - bounded variation - bounded varying - bounded vector - essentially bounded - explicitly bounded - exponentially bounded - power bounded - uniformly bounded - weakly bounded (математика) ограниченный -
5 frontier
граница || краевой; пограничный -
6 ограниченная область
Большой англо-русский и русско-английский словарь > ограниченная область
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7 ограниченная область
bounded domain, bounded frontier, bounded region, restricted domainРусско-английский научно-технический словарь Масловского > ограниченная область
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8 ограниченная область
1) Mathematics: bounded domain, bounded frontier, bounded region, restricted domain2) Metrology: localized region3) Makarov: bounded area, enclosed areaУниверсальный русско-английский словарь > ограниченная область
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9 set
1) набор; комплект- semiconductor assembly set - set of Belleville springs - set of conventional set - set of drawing instruments - set of gate patterns - set of gauge blocks - set of logical elements - set of statistical data - set of technical aids- snap set2) партия3) совокупность; множество4) установка; агрегат- desk telephone set - dial telephone set- gear set- local-battery telephone set - man-pack radio set - multi-operator welding set - sound-powered telephone set - wall telephone set5) регулировка; настройка || регулировать; настраивать6) группа; ансамбль7) класс; семейство9) схватывание || схватываться10) затвердевание || затвердевать11) крепление || закреплять12) геол. свита пород13) осадка (грунта) || оседать ( о грунте)14) радиоточка15) спорт сет16) включать, приводить в действие17) мат. множествоset closed under operation — множество, замкнутое относительно операции
- absolutely compact set - absolutely continuous set - absolutely convex set - absolutely irreducible set - absolutely measurable set - affinely independent set - affinely invariant set - algebraically independent set - almost finite set - almost full set - angular cluster set - asymptotically indecomposable set - at most denumerable set - centro-symmetric set - completely bounded set - completely continuous set - completely generating set - completely improper set - completely irreducible set - completely nonatomic set - completely normal set - completely ordered set - completely productive set - completely reducible set - completely separable set - constructively nonrecursive set - convexly independent set - countably infinite setto set aside — не учитывать, не принимать во внимание; откладывать
- cut set- cyclically ordered set - deductively inconsistent set - derived set - doubly well-ordered set - dual set of equations - dynamically disconnected set - effectively enumerable set - effectively generating set - effectively nonrecursive set - effectively simple set - enumeration reducible set - finely perfect set - finitely definite set - finitely measurable set- flat set- full set- fully reducible set - functionally closed set - functionally complete set - functionally open set - fundamental probability set - generalized almost periodic set- goal set- internally stable set- knot set- left directed set - left normal set - left-hand cluster set - linearly ordered set - local peak set - locally arcwise set - locally closed set - locally compact set - locally connected set - locally contractible set - locally convex set - locally finite set - locally invariant set - locally negligible set - locally null set - locally polar set - locally polyhedral set - metrically bounded set - metrically dense set - multiply ordered set - nearly analytic set - nearly closed set - nonvoid set - normally ordered set- null set- open in rays set - partitioned data set- peak set- pole set- positively homothetic set- pure set- radially open set - rationally independent set - recursively creative set - recursively indecomposable set - recursively isomorphic set - recursively productive set - regularly convex set - regularly situated sets - relatively closed set - relatively compact set - relatively dense set - relatively interpretable set - relatively open set - right normal set - right-hand cluster set- scar set- sequentially complete set - serially ordered set - set of elementary events - set of first category - set of first kind - set of first species - set of possible outcomes - set of probability null - set of second category - set of second species - shift invariant set - simply connected set - simply ordered set - simply transitive set- skew set- star set- strongly bounded set - strongly closed set - strongly compact set - strongly connected set - strongly convex set - strongly dependent set - strongly disjoint sets - strongly enumerable set - strongly independent set - strongly minimal set - strongly polar set - strongly reducible set - strongly separated set - strongly simple set - strongly stratified set- tame set- tautologically complete set - tautologically consistent set - tautologically inconsistent set- test set- thin set- tie set- time set- totally disconnected set - totally imperfect set - totally ordered set - totally primitive set - totally unimodular set - totally unordered set - truth-table reducible set - uniformly bounded set - uniformly continuous set - uniformly convergent set - uniformly integrable set - uniformly universal set - unilaterally connected set- unit set- vacuous set- void set- weakly compact set - weakly convex set - weakly n-dimensional set - weakly stratified set - weakly wandering set - well chained set - well founded set - well measurable set - well ordering set - well quasiordered set -
10 अन्त _anta
अन्त a. [अम्-तन् Uṇ.3.86]1 Near.-2 Last.-3 Handsome, lovely; Me.23; दन्तोज्ज्वलासु विमलोपलमे- खलान्ताः Śi.4.4, (where, however, the ordinary sense of 'border' or 'skirt' may do as well, though Malli. renders अन्त by रम्य, quoting the authority of शब्दार्णव - 'मृताववसिते रम्ये समाप्तावन्त इष्यते').-4 Lowest, worst.-5 Youngest.-तः (n. in some senses)1 (a) End, limit, boundary (in time or space); final limit, last or extreme point; स सागरान्तां पृथिवीं प्रशास्ति H.4.5 bounded by the ocean, as far as the sea; अपाङ्गौ नेत्रयो- रन्तौ Ak.; उद्युक्तो विद्यान्तमधिगच्छति H.3.114 goes to the end of, masters completely; श्रुतस्य यायादयमन्तमर्भकस्तथा परेषां युधि चेति पार्थिवः (where अन्त also means end or destruction); जीवलोकसुखानामन्तं ययौ K.59 enjoyed all worldly pleasures; आलोकितः खलु रमणीयानामन्तः K.124 end, furthest extremity; दिगन्ते श्रूयन्ते Bv.1.2.-2 Skirt, border, edge, precinct; a place or ground in general; यत्र रम्यो वनान्तः U.2.25 forest ground, skirts of the forest; ओदकान्तात् स्निग्धो जनो$नुगन्तव्यः Ś.4; उपवनान्तलताः R.9.35 as far as the borders or skirts; वृत्तः स नौ संगतयोर्वनान्ते R.2.58,2.19; Me.23. Upper part (शिरोभाग); महा- र्हमुक्तामणिभूषितान्तम् Rām.5.4.3.-3 End of a texture, edge, skirt, fringe or hem of a garment; वस्त्र˚; पवनप्रनर्तितान्तदेशे दुकूले K.9 (by itself in Veda).-4 Vicinity, proximity, neighbourhood, presence; नाधीयीत श्मशानान्ते ग्रामान्ते Ms. 4.116; Y.2.162; जलान्ते छन्दसां कुर्यादुत्सर्गं विधिवद् बहिः 1.143; गङ्गाप्रपातान्तविरूढशष्पम् (गह्वरम्) R.2.26; पुंसो यमान्तं व्रजतः P.2.115 going into the vicinity or presence of Yama; अन्योन्यामन्त्रणं यत्स्याज्जनान्ते तज्जनान्तिकम् S. D.; यां तु कुमारस्यान्ते वाचमभाषथास्तां मे ब्रूहि Śat. Br. (These four senses are allied).-5 End, conclusion, termination (opp. आरम्भ or आदि); सेकान्ते R.1.51; दिनान्ते निहितम् R.4.1; मासान्ते, पक्षान्ते, दशाहान्ते &c.; एकस्य दुःखस्य न यावदन्तं गच्छाम्यहं पारमिवार्णवस्य Pt.2.175; व्यसनानि दुरन्तानि Ms.7.45; दशान्तमुपेयिवान् R.12.1 going to the end of the period of life (end of the wick); व्यसनं वर्धयत्येव तस्यान्तं नाधिगच्छति Pt.2.18; oft. in comp. in this sense, and meaning 'ending in or with', 'ceasing to exist with', 'reaching to the end'; तदन्तं तस्य जीवितम् H.1.91 ends in it; कलहान्तानि हर्म्याणि कुवाक्यान्तं च सौहृदम् । कुराजान्तानि राष्ट्राणि कुकर्मान्तं यशो नृणाम् ॥ Pt.5.76; विशाखान्ता गता मेघा प्रसूत्यन्तं च यौवनम् । प्रणामान्तः सतां कोपो याचनान्तंहि गौरवम् ॥ Subhā. फलोदयान्ताय तपःसमाधये Ku.5.6 ending with (lasting till) the attainment of fruit; यौवनान्तं वयो यस्मिन् Ku.6.44; R.11.62,14.41; विपदन्ता ह्यविनीतसंपदः Ki.2.52; युगसहस्रान्तं ब्राह्मं पुण्यमहर्विदुः Ms.1.73 at the end of 1 Yugas; प्राणान्तं दण़्डम् Ms.8.359 capital punishment (such as would put an end to life).-6 Death, destruc- tion; end or close of life; धरा गच्छत्यन्तं Bh.3.71 goes down to destruction; योगेनान्ते तनुत्यजाम् R.1.8; एका भवेत्स्वस्तिमती त्वदन्ते 2.48;12.75; ममाप्यन्ते Ś.6; अद्य कान्तः कृतान्तो वा दुःखस्यान्तं करिष्यति Udb.; औषध्यः फलपाकान्ताः Ms.1.46; अन्तं या To be destroyed, perish, be ruined.-7 (In gram.) A final syllable or letter of a word; अजन्त ending in a vowel; so हलन्त, सुबन्त, तिडन्त &c.-8 The last word in a compound.-9 Ascertainment, or settlement (of a question); definite or final settle- ment; pause, final determination, as in सिद्धान्त; न चैव रावणस्यान्तो दृश्यते जीवितक्षये Rām.6.17.58 उभयोरपि दृष्टोन्तस्त्वनयोस्तत्त्वदर्शिभिः Bg.2.16 (सदसतोः इत्यर्थः).-1 The last portion or the remainder (n. also); निशान्तः; वेदान्तः &c. वेदांश्चैव तु वेदाङ्गान् वेदान्तानि तथा स्मृतीः । अधीत्य ब्राह्मणः पूर्वं शक्तितो$न्यांश्च संपठेत् ॥ Bṛihadyogi- yājñavalkya Smṛiti 12.34.-11 Underneath, inside, inner part; युष्मदीयं च जलान्ते गृहम् Pt.4 in water, underneath water; सुप्रयुक्तस्य दम्भस्य ब्रह्माप्यन्तं न गच्छति Pt.1.22 does not penetrate or dive into, sound, fathom; आशङ्कितस्यान्तं गच्छामि M.3 shall dive deep into, fully satisfy, my doubts.-12 Total amount, whole number or quantity.-13 A large number.-14 Nature, condition; sort, species; मम मोक्षस्य को$न्तो वै ब्रह्मन्ध्यायस्व वै प्रभो Mb.12.282.32. एतदन्तास्तु गतयो ब्रह्माद्याः समुदाहृताः Ms.1.5.-15 Disposition; essence; शुद्धान्तः-16 Division (विभाग); ते$नया कात्यायन्या$न्तं करवाणीति Bri. Up.2.4.1. [cf. Goth. andeis, and; Germ. ende and ent; also Gr. anti; L. ante]. cf. अन्तस्तु भागे$- वसिते रचनायां च तत्परे । मृतौ निषेवणे रम्ये समाप्तावग्रमध्ययोः ॥ स्वरूपे च समीपे च पुंलिङ्गे$पि प्रकीर्तितः । Nm.-Comp. -अवशा- यिन् m. [अन्ते पर्यन्तदेशे अवशेते] a chāṇḍāla.-अवसायिन् [नखकेशानामन्तं अवसातुं छेत्तुं शीलमस्य, सो-णिनि]1 a barber.-2 a chāṇḍāla, low caste.-3 N. of a sage, see अन्त्याव- सायिन् (अन्ते पश्चिमे वयसि अवस्यति तत्त्वं निश्चिनोति).-उदात्त a. having the acute accent on the last syllable. (-त्तः) the acute accent on the last syllable; P.VI,1.199.-ओष्ठः The lower lip (अधरोष्ठ); रुधिरं न व्यतिक्रामदन्तोष्ठादम्ब मा शुचः Mb.11.15.16.-कर, -करण,-कारिन् a. causing death or destruction, fatal, mortal, destructive; क्षत्रिया- न्तकरणो$पि विक्रमः R.11.75 causing the destruction of; राज्यान्तकरणावेतौ द्वौ दोषौ पृथिवीक्षिताम् Ms.9.221; अहमन्तकरो नूनं ध्वान्तस्येव दिवाकरः Bk.-कर्मन् n. death, destruction; षो अन्तकर्मणि Dhātupāṭha.-कालः, -वेला time or hour of death; स्थित्वा स्यामन्तकाले$पि ब्रह्मनिर्वाणमृच्छति Bg.2.72.-कृत् m. death; वर्जयेदन्तकृन्मर्त्यं वर्जयेदनिलो$नलम् Rām.-कृद्दशाः N. of the eighth of the twelve sacred Aṅga texts of the Jainas (containing ten chapters).-ग a. having gone to the end of, thoroughly conversant or familiar with, (in comp.); शाखान्तगमथाध्वर्युम् Ms.3.145.-गति, -गामिन् a. perishing. प्राप्तो$न्तगामी विपरीतबुद्धिः Rām.6.59.94.-गमनम् 1 going to the end, finishing, completing; प्रारब्धस्य ˚नं द्वितीयं बुद्धिलक्षणम्-2 death, perishing, dying.-चक्रम् Reading of omens and augury; Kau. A.-चर a.1 walking about, going to the borders or frontiers.-2 completing or finishing (as a business &c.).-ज a. last born.-दीपकम् a figure of speech (in Rhetoric).-परिच्छदः a. cover, covering utensil. राजतान्तपरिच्छदां दिव्यपायससंपूर्णां पात्रीम् Rām.1.16.14.-पालः 1 a frontier-guard, guarding the frontiers; विनीतैरन्तपालैश्च रक्षोभिश्च सुरक्षितम् Rām.5.6.9. ˚दुर्गे M.1; त्वदीयेनान्तपाले- नावस्कन्द्य गृहीतः ibid.-2 a door-keeper (rare). सुद्युम्न- स्त्वन्तपालेभ्यः श्रुत्वा लिखितमागतम् Mb.12.23.29.-भव, -भाज् a. being at the end, last.-लीन a. hidden, con- cealed.-लोपः dropping of the final of a word. (न्ते˚)-वासिन् a. dwelling near the frontiers, dwelling close by. -m. [अन्ते गुरुसमीपे वस्तुं शीलं यस्य]1 a pupil (who always dwells near his master to receive instruction); P.IV.3.14;VI.2.36.; Ms.4.33.-2 a chāṇḍāla (who dwells at the extremity of a village).-वेला = ˚कालः q. v.-व्यापत्तिः f. change of the final syllable, as in मेघ from मिह् Nir.-शय्या 1 a bed on the ground.-2 the last bed, death-bed; hence death itself.-3 a place for burial or burning.-4 a bier or funeral pile.-संश्लेषः union (सन्धि), joint; सुखदुःखान्तसंश्लेषम् (काल- चक्रम्) Mb.14.45.3.-सत्क्रिया last rites, funeral ceremonies, obsequies.-सढ् m. pupil; तमुपासते गुरुमिवा- न्तसदः Ki.6.34.-स्वरितः the svarita accent on the last syllable of a word. -
11 bound
граница имя прилагательное:непременный (bound, irremissible)имя существительное: глагол:быстро бежать (bound, spank)служить границей (bound, limit) -
12 limitary
пограничный имя прилагательное: -
13 Introduction
Portugal is a small Western European nation with a large, distinctive past replete with both triumph and tragedy. One of the continent's oldest nation-states, Portugal has frontiers that are essentially unchanged since the late 14th century. The country's unique character and 850-year history as an independent state present several curious paradoxes. As of 1974, when much of the remainder of the Portuguese overseas empire was decolonized, Portuguese society appeared to be the most ethnically homogeneous of the two Iberian states and of much of Europe. Yet, Portuguese society had received, over the course of 2,000 years, infusions of other ethnic groups in invasions and immigration: Phoenicians, Greeks, Celts, Romans, Suevi, Visigoths, Muslims (Arab and Berber), Jews, Italians, Flemings, Burgundian French, black Africans, and Asians. Indeed, Portugal has been a crossroads, despite its relative isolation in the western corner of the Iberian Peninsula, between the West and North Africa, Tropical Africa, and Asia and America. Since 1974, Portugal's society has become less homogeneous, as there has been significant immigration of former subjects from its erstwhile overseas empire.Other paradoxes should be noted as well. Although Portugal is sometimes confused with Spain or things Spanish, its very national independence and national culture depend on being different from Spain and Spaniards. Today, Portugal's independence may be taken for granted. Since 1140, except for 1580-1640 when it was ruled by Philippine Spain, Portugal has been a sovereign state. Nevertheless, a recurring theme of the nation's history is cycles of anxiety and despair that its freedom as a nation is at risk. There is a paradox, too, about Portugal's overseas empire(s), which lasted half a millennium (1415-1975): after 1822, when Brazil achieved independence from Portugal, most of the Portuguese who emigrated overseas never set foot in their overseas empire, but preferred to immigrate to Brazil or to other countries in North or South America or Europe, where established Portuguese overseas communities existed.Portugal was a world power during the period 1415-1550, the era of the Discoveries, expansion, and early empire, and since then the Portuguese have experienced periods of decline, decadence, and rejuvenation. Despite the fact that Portugal slipped to the rank of a third- or fourth-rate power after 1580, it and its people can claim rightfully an unusual number of "firsts" or distinctions that assure their place both in world and Western history. These distinctions should be kept in mind while acknowledging that, for more than 400 years, Portugal has generally lagged behind the rest of Western Europe, although not Southern Europe, in social and economic developments and has remained behind even its only neighbor and sometime nemesis, Spain.Portugal's pioneering role in the Discoveries and exploration era of the 15th and 16th centuries is well known. Often noted, too, is the Portuguese role in the art and science of maritime navigation through the efforts of early navigators, mapmakers, seamen, and fishermen. What are often forgotten are the country's slender base of resources, its small population largely of rural peasants, and, until recently, its occupation of only 16 percent of the Iberian Peninsula. As of 1139—10, when Portugal emerged first as an independent monarchy, and eventually a sovereign nation-state, England and France had not achieved this status. The Portuguese were the first in the Iberian Peninsula to expel the Muslim invaders from their portion of the peninsula, achieving this by 1250, more than 200 years before Castile managed to do the same (1492).Other distinctions may be noted. Portugal conquered the first overseas empire beyond the Mediterranean in the early modern era and established the first plantation system based on slave labor. Portugal's empire was the first to be colonized and the last to be decolonized in the 20th century. With so much of its scattered, seaborne empire dependent upon the safety and seaworthiness of shipping, Portugal was a pioneer in initiating marine insurance, a practice that is taken for granted today. During the time of Pombaline Portugal (1750-77), Portugal was the first state to organize and hold an industrial trade fair. In distinctive political and governmental developments, Portugal's record is more mixed, and this fact suggests that maintaining a government with a functioning rule of law and a pluralist, representative democracy has not been an easy matter in a country that for so long has been one of the poorest and least educated in the West. Portugal's First Republic (1910-26), only the third republic in a largely monarchist Europe (after France and Switzerland), was Western Europe's most unstable parliamentary system in the 20th century. Finally, the authoritarian Estado Novo or "New State" (1926-74) was the longest surviving authoritarian system in modern Western Europe. When Portugal departed from its overseas empire in 1974-75, the descendants, in effect, of Prince Henry the Navigator were leaving the West's oldest empire.Portugal's individuality is based mainly on its long history of distinc-tiveness, its intense determination to use any means — alliance, diplomacy, defense, trade, or empire—to be a sovereign state, independent of Spain, and on its national pride in the Portuguese language. Another master factor in Portuguese affairs deserves mention. The country's politics and government have been influenced not only by intellectual currents from the Atlantic but also through Spain from Europe, which brought new political ideas and institutions and novel technologies. Given the weight of empire in Portugal's past, it is not surprising that public affairs have been hostage to a degree to what happened in her overseas empire. Most important have been domestic responses to imperial affairs during both imperial and internal crises since 1415, which have continued to the mid-1970s and beyond. One of the most important themes of Portuguese history, and one oddly neglected by not a few histories, is that every major political crisis and fundamental change in the system—in other words, revolution—since 1415 has been intimately connected with a related imperial crisis. The respective dates of these historical crises are: 1437, 1495, 1578-80, 1640, 1820-22, 1890, 1910, 1926-30, 1961, and 1974. The reader will find greater detail on each crisis in historical context in the history section of this introduction and in relevant entries.LAND AND PEOPLEThe Republic of Portugal is located on the western edge of the Iberian Peninsula. A major geographical dividing line is the Tagus River: Portugal north of it has an Atlantic orientation; the country to the south of it has a Mediterranean orientation. There is little physical evidence that Portugal is clearly geographically distinct from Spain, and there is no major natural barrier between the two countries along more than 1,214 kilometers (755 miles) of the Luso-Spanish frontier. In climate, Portugal has a number of microclimates similar to the microclimates of Galicia, Estremadura, and Andalusia in neighboring Spain. North of the Tagus, in general, there is an Atlantic-type climate with higher rainfall, cold winters, and some snow in the mountainous areas. South of the Tagus is a more Mediterranean climate, with hot, dry, often rainless summers and cool, wet winters. Lisbon, the capital, which has a fifth of the country's population living in its region, has an average annual mean temperature about 16° C (60° F).For a small country with an area of 92,345 square kilometers (35,580 square miles, including the Atlantic archipelagos of the Azores and the Madeiras), which is about the size of the state of Indiana in the United States, Portugal has a remarkable diversity of regional topography and scenery. In some respects, Portugal resembles an island within the peninsula, embodying a unique fusion of European and non-European cultures, akin to Spain yet apart. Its geography is a study in contrasts, from the flat, sandy coastal plain, in some places unusually wide for Europe, to the mountainous Beira districts or provinces north of the Tagus, to the snow-capped mountain range of the Estrela, with its unique ski area, to the rocky, barren, remote Trás-os-Montes district bordering Spain. There are extensive forests in central and northern Portugal that contrast with the flat, almost Kansas-like plains of the wheat belt in the Alentejo district. There is also the unique Algarve district, isolated somewhat from the Alentejo district by a mountain range, with a microclimate, topography, and vegetation that resemble closely those of North Africa.Although Portugal is small, just 563 kilometers (337 miles) long and from 129 to 209 kilometers (80 to 125 miles) wide, it is strategically located on transportation and communication routes between Europe and North Africa, and the Americas and Europe. Geographical location is one key to the long history of Portugal's three overseas empires, which stretched once from Morocco to the Moluccas and from lonely Sagres at Cape St. Vincent to Rio de Janeiro, Brazil. It is essential to emphasize the identity of its neighbors: on the north and east Portugal is bounded by Spain, its only neighbor, and by the Atlantic Ocean on the south and west. Portugal is the westernmost country of Western Europe, and its shape resembles a face, with Lisbon below the nose, staring into theAtlantic. No part of Portugal touches the Mediterranean, and its Atlantic orientation has been a response in part to turning its back on Castile and Léon (later Spain) and exploring, traveling, and trading or working in lands beyond the peninsula. Portugal was the pioneering nation in the Atlantic-born European discoveries during the Renaissance, and its diplomatic and trade relations have been dominated by countries that have been Atlantic powers as well: Spain; England (Britain since 1707); France; Brazil, once its greatest colony; and the United States.Today Portugal and its Atlantic islands have a population of roughly 10 million people. While ethnic homogeneity has been characteristic of it in recent history, Portugal's population over the centuries has seen an infusion of non-Portuguese ethnic groups from various parts of Europe, the Middle East, and Africa. Between 1500 and 1800, a significant population of black Africans, brought in as slaves, was absorbed in the population. And since 1950, a population of Cape Verdeans, who worked in menial labor, has resided in Portugal. With the influx of African, Goan, and Timorese refugees and exiles from the empire—as many as three quarters of a million retornados ("returned ones" or immigrants from the former empire) entered Portugal in 1974 and 1975—there has been greater ethnic diversity in the Portuguese population. In 2002, there were 239,113 immigrants legally residing in Portugal: 108,132 from Africa; 24,806 from Brazil; 15,906 from Britain; 14,617 from Spain; and 11,877 from Germany. In addition, about 200,000 immigrants are living in Portugal from eastern Europe, mainly from Ukraine. The growth of Portugal's population is reflected in the following statistics:1527 1,200,000 (estimate only)1768 2,400,000 (estimate only)1864 4,287,000 first census1890 5,049,7001900 5,423,0001911 5,960,0001930 6,826,0001940 7,185,1431950 8,510,0001960 8,889,0001970 8,668,000* note decrease1980 9,833,0001991 9,862,5401996 9,934,1002006 10,642,8362010 10,710,000 (estimated)
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