modularadj.n.

Brit.

/ˈmɒdjᵿlə/,

/ˈmɒdʒᵿlə/, U.S.

/ˈmɑdʒələr/

Origin: Probably of multiple origins. Partly a borrowing from Latin Probably partly formed within English, by derivation. Etymons: Latin modularis ; module n., -ar suffix¹.

Etymology: In sense A. 1 < post-classical Latin modularis (in phrase modularis ratio (R. Cotes 1714, in Philos. Trans. Royal Soc. 29 6: see quot. 1815 at sense A. 1) < classical Latin modulus (see module n.) + -āris -ar suffix¹. In other senses probably directly < module n. + -ar suffix¹. Compare French modulaire (1845–6 in sense A. 2a; 1867 in Littré in sense A. 1).

A. adj.

1. Mathematics. Of or relating to a modulus or module. See modulus n. 2, module n. 5.The sense in quot. 1831 appears to be ‘of or belonging to a model’.

ΘΚΠ

the world > relative properties > number > mathematical number or quantity > [adjective] > prime > modular

modular1815

modulo1966

1815 C. Hutton Math. & Philos. Dict. (new ed.) II. 60 Modular Ratio, a term invented by Mr. Cotes, to denote the ratio or number whose logarithm is what he calls the modulus.

1831 C. Hutton & O. Gregory Course Math. (ed. 10) II. 385 [‘On Models’] If W were the greatest load which a modular wall, or column, could carry [etc.].

a1832 Encycl. Metrop. (1845) II. 385/1 Taking, therefore, ϕ a solution of the modular equation, which makes the above-mentioned equations consistent.

1844 Proc. Royal Irish Acad. 1840–4 2 453 It may happen that only one of them [sc. the curves] can be used in the generation of the surface by the modular method... A focal curve which can be so used shall be distinguished as a modular focal.

1860 J. F. W. Herschel Let. 23 Apr. in Athenæum 28 Apr. 581/3 A simple numerical relation between our actual parliamentary standard of length and the dimensions of the earth..puts us in easy possession of a ‘modular’ system, which might be decimalized.

a1883 H. J. S. Smith Coll. Math. Papers (1894) II. 560 The Modular Curves of an Uneven Order.

1894 A. R. Forsyth Theory Functions Complex Variable 633 The general definition of a modular function is that it is a uniform function such that an algebraical equation subsists between ψ^{αω + β}/ _{γω + δ} and ψ(ω), where α, β, γ, δ, are integers subject to the relation αδ − βγ = 1.

1943 J. M. Wolfe First Course Cryptanal. (rev. ed.) II. 19 The Vigenere operates on a modular addition while the Nihilist substitution does not.

1972 M. Kline Math. Thought xxix. 727 The earliest automorphic functions to be studied were the elliptic modular functions.

1990 Proc. London Math. Soc. 60 225 The modular representation theory of the finite general linear group GL_n(q) has been developed in a recent series of papers.

†a. Architecture. In the classical Greek and Roman orders: of, relating to, or measured in terms of a modulus or module. See module n. 3b. Obsolete. rare.

ΘΚΠ

society > leisure > the arts > visual arts > architecture > column > [adjective] > unit of proportion based on column diameter

modular1842

1842 J. Gwilt Encycl. Archit. Gloss. 1005 Modular Proportion, that which is regulated by a module.

b. Originally: designating or conforming to a system of building design or construction based on a standard module (see module n. 8). Hence more generally: involving or consisting of modules or discrete units as the basis of design, construction, or operation; (also) intended to form part of such a system. Also in extended use.

ΘΚΠ

the world > relative properties > wholeness > mutual relation of parts to whole > [adjective] > composed of or consisting in > modules

modular1936

modularized1936

modulized1981

the world > relative properties > wholeness > mutual relation of parts to whole > separation > action of dividing or divided condition > [adjective] > divided > divided into stages

modular1936

society > computing and information technology > programming language > program or code > [adjective] > sets of instructions

modular1973

1936 A. F. Bemis & J. Burchard Evolving House III. iv. 64 Cubical modular design..simply requires that all parts of the house..be proportioned to the same module in all three dimensions.

1945 Archit. Rec. Jan. 102/2 The modular system does not necessarily involve making every product come out to even multiples of 4 inches... The system does suggest, however, that the 4-in. unit be considered as an increment wherever possible.

1956 W. H. Whyte Organization Man (1957) 398 Modular construction is a condition of moderate-cost housing.

1960 Missiles & Rockets 8 Aug. 20/1 Apollo will be a three-man modular spacecraft that can perform as an earth-orbiting space station or circle man around the moon and bring him back.

1960 House & Garden Dec. 31/1 As the houses are based on modular units, it is relatively simple to add a wing.

1973 Computers & Humanities 7 144 This program is modular in design, that is, it consists of several steps each doing a simple task.

1984 Times 24 May 3/1 British Rail's hot meals go ‘modular’ over the next five years. Food for lunch and dinner will be prepared ‘ashore’..then heated in microwave ovens in the restaurant car.

1999 Materials World July 404/3 By adopting a modular approach it has been possible to make steering wheels of different sizes from just a few key components.

c. Education. Designating or relating to an educational course composed of a number of independent units of study, which can be combined in a variety of ways.

ΘΚΠ

society > education > teaching > means of teaching > [adjective] > type of course

1011929

modular1968

1968 Economist 25 May 18/2 The board has developed proposals both for the retraining of adults for skilled jobs, and for a so-called ‘modular’ scheme of training for young entrants to industry.

1972 Accountant 19 Oct. 483/1 Public sector institutions..have succeeded wherever possible in providing oral tuition on a modular basis, so that students of different bodies are able to share studies.

1990 Times Educ. Suppl. 8 June a22/1 There is considerable support for the modular approach as it appears to impart flexibility to a system having two interrelated examinations.

B. n.

1. Mathematics. A non-negative functional acting on a linear space and representing a generalization of the concept of magnitude in that space (see quot. 1950 and cf. modulus n. 2e).

ΚΠ

1950 H. Nakano Modulared Semi-ordered Linear Spaces 4 A functional m(a)(a ∈ R) is called a modular on R if it satisfies modular conditions: (1 0 ≦ m(a) ≦ +∞; 2) if m(ξa) = 0 for every ξ ≧ 0, then a = 0; 3) to any a ∈ R there exists an α > 0 such that m(αa) < +∞; 4) m(ξa) is a convex function of ξ ≧ 0; 5) |a| ≦ |b| implies m(a) ≦ m(b); 6) a ∩ b = 0 implies m(a+b) = m(a) + m(b); and 7) 0 ≦ a_λ ↑_{λ ∈ Λ}a implies m(a) = sup_{λ ∈ Λ}m(a_λ).

1959 Trans. Amer. Math. Soc. 90 291 The relations between the modular and its norms are the most important problem in the theory of Nakano spaces.

1975 Proc. Amer. Math. Soc. 50 202 Let m be the conjugate modular of an L_p,q modular m.

1994 Ann. Probability 22 1762 We immediately obtain the comparison of generalized Orlicz modulars, that is, functionals of the form Φ(·) = Eϕ(‖·‖), where ϕ is a nondecreasing function on the positive half-line, ϕ(0) = 0.

2. Chiefly U.S. Something composed of modules; esp. a building constructed from standardized prefabricated components; (occasionally) any of these components.

ΘΚΠ

the world > relative properties > wholeness > mutual relation of parts to whole > [noun] > a structure > modular

modular1969

1969 Automation in Housing Aug. 61/2 A two-section modular, the home includes kitchen, bathroom, toilet facility, laundry room and five rooms for sleeping, eating and living in its well-organized plan.

1983 Motor Trend Jan. 76/1 At the opposite end of the scale are the high-zoot modulars—racing wheels, really.

1994 Hartford (Connecticut) Courant (ed. 3) b2/5 The connector was intended to provide students with some protection from the weather as they moved between the new modulars and the main school building.

Compounds

modular arithmetic n. Mathematics any system of arithmetic having an arbitrary but fixed modulus, in which all integers that have the same remainder when divided by the modulus are equivalent and are represented by that remainder (see modulus n. 2b, congruent adj. 5).

ΚΠ

1941 D. Harkin Fund. Math. v. 53 (heading) Finite modular arithmetic.

1962 W. J. LeVeque Elem. Theory Numbers iii. 56 The strong distinction between real and complex numbers sometimes disappears in this ‘modular’ arithmetic.

1988 T. Peterson Math. Tourist ii. 17 As in many modern cryptographic systems for sending secret messages, modular arithmetic plays an important role in the oblivious transfer.

modular form n. Mathematics a holomorphic function that is invariant under transformation by elements of the modular group (see modular group n.).

ΚΠ

1918 Ann. Math. 19 201 (title) Covariant expansion of a modular form.

1997 S. Singh Fermat's Last Theorem v. 195 The key feature of modular forms is their inordinate level of symmetry.

modular group n. Mathematics the group of linear transformations z → ^{az + b}/ _{cz + d}, where ad − bc = 1 (cf. modulus n. 2d(c), Möbius transformation n. at Möbius n. 2).

ΚΠ

1898 Science 16 Sept. 362/2 The subgroups of the generalized modular group.

1990 Glasgow Math. Jrnl. 32 317 Let Γ denote the modular group, consisting of the Möbius transformations z → ^{az + b}/ _{cz + d}..ad − bc = 1.

This entry has been updated (OED Third Edition, September 2002; most recently modified version published online March 2022).

单词	modular
释义	modularadj.n. Brit. /ˈmɒdjᵿlə/, /ˈmɒdʒᵿlə/, U.S. /ˈmɑdʒələr/ Origin: Probably of multiple origins. Partly a borrowing from Latin Probably partly formed within English, by derivation. Etymons: Latin modularis ; module n., -ar suffix¹. Etymology: In sense A. 1 < post-classical Latin modularis (in phrase modularis ratio (R. Cotes 1714, in Philos. Trans. Royal Soc. 29 6: see quot. 1815 at sense A. 1) < classical Latin modulus (see module n.) + -āris -ar suffix¹. In other senses probably directly < module n. + -ar suffix¹. Compare French modulaire (1845–6 in sense A. 2a; 1867 in Littré in sense A. 1). A. adj. 1. Mathematics. Of or relating to a modulus or module. See modulus n. 2, module n. 5.The sense in quot. 1831 appears to be ‘of or belonging to a model’. ΘΚΠ the world > relative properties > number > mathematical number or quantity > [adjective] > prime > modular modular1815 modulo1966 1815 C. Hutton Math. & Philos. Dict. (new ed.) II. 60 Modular Ratio, a term invented by Mr. Cotes, to denote the ratio or number whose logarithm is what he calls the modulus. 1831 C. Hutton & O. Gregory Course Math. (ed. 10) II. 385 [‘On Models’] If W were the greatest load which a modular wall, or column, could carry [etc.]. a1832 Encycl. Metrop. (1845) II. 385/1 Taking, therefore, ϕ a solution of the modular equation, which makes the above-mentioned equations consistent. 1844 Proc. Royal Irish Acad. 1840–4 2 453 It may happen that only one of them [sc. the curves] can be used in the generation of the surface by the modular method... A focal curve which can be so used shall be distinguished as a modular focal. 1860 J. F. W. Herschel Let. 23 Apr. in Athenæum 28 Apr. 581/3 A simple numerical relation between our actual parliamentary standard of length and the dimensions of the earth..puts us in easy possession of a ‘modular’ system, which might be decimalized. a1883 H. J. S. Smith Coll. Math. Papers (1894) II. 560 The Modular Curves of an Uneven Order. 1894 A. R. Forsyth Theory Functions Complex Variable 633 The general definition of a modular function is that it is a uniform function such that an algebraical equation subsists between ψ^{αω + β}/ _{γω + δ} and ψ(ω), where α, β, γ, δ, are integers subject to the relation αδ − βγ = 1. 1943 J. M. Wolfe First Course Cryptanal. (rev. ed.) II. 19 The Vigenere operates on a modular addition while the Nihilist substitution does not. 1972 M. Kline Math. Thought xxix. 727 The earliest automorphic functions to be studied were the elliptic modular functions. 1990 Proc. London Math. Soc. 60 225 The modular representation theory of the finite general linear group GL_n(q) has been developed in a recent series of papers. 2. †a. Architecture. In the classical Greek and Roman orders: of, relating to, or measured in terms of a modulus or module. See module n. 3b. Obsolete. rare. ΘΚΠ society > leisure > the arts > visual arts > architecture > column > [adjective] > unit of proportion based on column diameter modular1842 1842 J. Gwilt Encycl. Archit. Gloss. 1005 Modular Proportion, that which is regulated by a module. b. Originally: designating or conforming to a system of building design or construction based on a standard module (see module n. 8). Hence more generally: involving or consisting of modules or discrete units as the basis of design, construction, or operation; (also) intended to form part of such a system. Also in extended use. ΘΚΠ the world > relative properties > wholeness > mutual relation of parts to whole > [adjective] > composed of or consisting in > modules modular1936 modularized1936 modulized1981 the world > relative properties > wholeness > mutual relation of parts to whole > separation > action of dividing or divided condition > [adjective] > divided > divided into stages modular1936 society > computing and information technology > programming language > program or code > [adjective] > sets of instructions modular1973 1936 A. F. Bemis & J. Burchard Evolving House III. iv. 64 Cubical modular design..simply requires that all parts of the house..be proportioned to the same module in all three dimensions. 1945 Archit. Rec. Jan. 102/2 The modular system does not necessarily involve making every product come out to even multiples of 4 inches... The system does suggest, however, that the 4-in. unit be considered as an increment wherever possible. 1956 W. H. Whyte Organization Man (1957) 398 Modular construction is a condition of moderate-cost housing. 1960 Missiles & Rockets 8 Aug. 20/1 Apollo will be a three-man modular spacecraft that can perform as an earth-orbiting space station or circle man around the moon and bring him back. 1960 House & Garden Dec. 31/1 As the houses are based on modular units, it is relatively simple to add a wing. 1973 Computers & Humanities 7 144 This program is modular in design, that is, it consists of several steps each doing a simple task. 1984 Times 24 May 3/1 British Rail's hot meals go ‘modular’ over the next five years. Food for lunch and dinner will be prepared ‘ashore’..then heated in microwave ovens in the restaurant car. 1999 Materials World July 404/3 By adopting a modular approach it has been possible to make steering wheels of different sizes from just a few key components. c. Education. Designating or relating to an educational course composed of a number of independent units of study, which can be combined in a variety of ways. ΘΚΠ society > education > teaching > means of teaching > [adjective] > type of course 1011929 modular1968 1968 Economist 25 May 18/2 The board has developed proposals both for the retraining of adults for skilled jobs, and for a so-called ‘modular’ scheme of training for young entrants to industry. 1972 Accountant 19 Oct. 483/1 Public sector institutions..have succeeded wherever possible in providing oral tuition on a modular basis, so that students of different bodies are able to share studies. 1990 Times Educ. Suppl. 8 June a22/1 There is considerable support for the modular approach as it appears to impart flexibility to a system having two interrelated examinations. B. n. 1. Mathematics. A non-negative functional acting on a linear space and representing a generalization of the concept of magnitude in that space (see quot. 1950 and cf. modulus n. 2e). ΚΠ 1950 H. Nakano Modulared Semi-ordered Linear Spaces 4 A functional m(a)(a ∈ R) is called a modular on R if it satisfies modular conditions: (1 0 ≦ m(a) ≦ +∞; 2) if m(ξa) = 0 for every ξ ≧ 0, then a = 0; 3) to any a ∈ R there exists an α > 0 such that m(αa) < +∞; 4) m(ξa) is a convex function of ξ ≧ 0; 5) \|a\| ≦ \|b\| implies m(a) ≦ m(b); 6) a ∩ b = 0 implies m(a+b) = m(a) + m(b); and 7) 0 ≦ a_λ ↑_{λ ∈ Λ}a implies m(a) = sup_{λ ∈ Λ}m(a_λ). 1959 Trans. Amer. Math. Soc. 90 291 The relations between the modular and its norms are the most important problem in the theory of Nakano spaces. 1975 Proc. Amer. Math. Soc. 50 202 Let m be the conjugate modular of an L_p,q modular m. 1994 Ann. Probability 22 1762 We immediately obtain the comparison of generalized Orlicz modulars, that is, functionals of the form Φ(·) = Eϕ(‖·‖), where ϕ is a nondecreasing function on the positive half-line, ϕ(0) = 0. 2. Chiefly U.S. Something composed of modules; esp. a building constructed from standardized prefabricated components; (occasionally) any of these components. ΘΚΠ the world > relative properties > wholeness > mutual relation of parts to whole > [noun] > a structure > modular modular1969 1969 Automation in Housing Aug. 61/2 A two-section modular, the home includes kitchen, bathroom, toilet facility, laundry room and five rooms for sleeping, eating and living in its well-organized plan. 1983 Motor Trend Jan. 76/1 At the opposite end of the scale are the high-zoot modulars—racing wheels, really. 1994 Hartford (Connecticut) Courant (ed. 3) b2/5 The connector was intended to provide students with some protection from the weather as they moved between the new modulars and the main school building. Compounds modular arithmetic n. Mathematics any system of arithmetic having an arbitrary but fixed modulus, in which all integers that have the same remainder when divided by the modulus are equivalent and are represented by that remainder (see modulus n. 2b, congruent adj. 5). ΚΠ 1941 D. Harkin Fund. Math. v. 53 (heading) Finite modular arithmetic. 1962 W. J. LeVeque Elem. Theory Numbers iii. 56 The strong distinction between real and complex numbers sometimes disappears in this ‘modular’ arithmetic. 1988 T. Peterson Math. Tourist ii. 17 As in many modern cryptographic systems for sending secret messages, modular arithmetic plays an important role in the oblivious transfer. modular form n. Mathematics a holomorphic function that is invariant under transformation by elements of the modular group (see modular group n.). ΚΠ 1918 Ann. Math. 19 201 (title) Covariant expansion of a modular form. 1997 S. Singh Fermat's Last Theorem v. 195 The key feature of modular forms is their inordinate level of symmetry. modular group n. Mathematics the group of linear transformations z → ^{az + b}/ _{cz + d}, where ad − bc = 1 (cf. modulus n. 2d(c), Möbius transformation n. at Möbius n. 2). ΚΠ 1898 Science 16 Sept. 362/2 The subgroups of the generalized modular group. 1990 Glasgow Math. Jrnl. 32 317 Let Γ denote the modular group, consisting of the Möbius transformations z → ^{az + b}/ _{cz + d}..ad − bc = 1. This entry has been updated (OED Third Edition, September 2002; most recently modified version published online March 2022). < adj.n.1815
随便看	sit fast upon sit fast upon something sit flat down sit generals sit hard on sit heavily sit heavy sit in sit in a person's pocket sit in for sit in formerly at judgement sit in judgement sit in one's own light sit in wait sit in waits sit light sit light on sit light upon sit lightly sit like piffy sit like piffy on a rock bun sit loose sit mum sit mumchance sit near one's heart