| 释义 |
▪ I. † adjoint, pa. pple. and n.1 Obs.
Also 4 anioynt.
[a. OFr. ajoint:—L. adjunct-um adjunct.]
A. pple. Adjoined, united.
c1325E.E. Allit. P. A. 894 And to the gentyl lombe hit arn anioynt [ed. amoynt].
B. n. [The pple. used subst.] A helper, aider; an adjunct, addition.
1597Daniel Civ. Wares iv. lxix, Here with these grave Adjoynts (Then learned Maisters) they were taught to see Themselves. 1639H. Ainsworth On Pentat., Lev. xiii. 1, 66 Sapachath is an adjoynt to the swelling, and an adjoynt to the Bright-spot. c1700Gentlem. Instr. (1732) 108 You are, Madam, I perceive, said he, a publick Minister, and this Lady is your Adjoint.
▪ II. adjoint, n.2 and a.|ˈædʒɔɪnt|
[mod.Fr. adjoint, pa. pple. of adjoindre to adjoin, used as an appellative. Mod.Fr. form of prec.]
‖A. n.2 (with pronunc. adʒwɛ̃). Official title of a French civil officer who assists the maire; also, an assistant professor in a French college.
1835Blackw. Mag. XXXVIII. 19 The lower professors or adjoints cannot, in one instance out of twenty, rise above their actual position. 1864Sala in Daily Tel. 16 Aug., Halting to exchange official commonplaces with..the adjoint of the mayor. 1865Pall Mall G. 6 Nov. 10, Arab adjoints are to be associated with European mayors in towns and villages.
2. Math. An adjoint matrix, equation, etc.
1889T. Craig Treat. Linear Differential Equations I. xiii. 471 When Chapter I was written..I had not seen Forsyth's memoir, and had not been able to find an adopted English term for Lagrange's ‘équation adjointe’, so I used the word adjunct, suggested by the German ‘adjungirte’, and not unlike the French ‘adjointe’. It seems better now, however, to employ the word associate, or, when speaking simply of Lagrange's ‘équation adjointe’, the word adjoint. Ibid. 483 The adjoint of the quantic S. 1902A. R. Forsyth Theory Differential Equations IV. vi. 253 It is clear that wp(v) is a perfect differential if P(w) = 0, shewing that the original equation is the adjoint of the Lagrangian derived equation. 1907M. Bôcher Introd. Higher Algebra vi. 77 By the adjoint A of a matrix a is understood another matrix of the same order in which the element in the ith row and jth column is the cofactor of the element in the jth row and ith column of a. 1942R. P. Agnew Differential Equations xii. 254 If L denotes the operator L = a0D2 + a1D + a2, then the adjoint (or adjoint operator) is L* = a0D2 + (2a0′ - a1′)D + (a0{pp} - a1′ + a2) . 1972M. Kline Math. Thought xxxix. 936 The integrals are of the form ∫ ϕ(x, y) / ∂f/∂y dx where ϕ is a polynomial (an adjoint) of..the degree n - 3. 1976M. A. Morrison et al. Quantum States vi. 153 These matrix elements are defined by simple matrix multiplication—for example, 〈χ1S21χ′〉 ≡ χ† S2χ′, where the row vector χ′ is the adjoint of χ, the complex conjugate of the transpose of χ. 1980A. J. Jones Game Theory iii. 145 If we define the adjoint of M by adjM = (Aij)T if r >1, adjM = 1 if r = 1, then for all square matrices M we have MadjM = (detM)I, where I is the identity matrix.
B. adj. Math. Of a matrix: equal to the transpose of the cofactors (or in quantum mechanics, of the complex conjugate) of a given square matrix. Of a differential equation: related to a given differential equation in such a way that its solutions are integrating factors and its integrating factors solutions of the given equation. Of a transformation or operator: (see quot. 1959). Generally, pertaining to adjoint quantities or their relationships.
1889T. Craig Treat. Linear Differential Equations I. xiii. 478 The typical variable of the set is the variable of the Lagrangian adjoint equation. Ibid. 482 Suppose the quantics..to be adjoint. 1902A. R. Forsyth Theory Differential Equations IV. vi. 253 The two equations are reciprocally adjoint to one another. 1923J. Hadamard Lect. Cauchy's Probl. ii. 59 The relation between two adjoint polynomials is a reciprocal one. 1937E. C. Kemble Fund. Princ. Quantum Mech. x. 350 We define the adjoint matrix to A as a matrix obtained..by replacing each element by its conjugate complex quantity and then interchanging rows and columns. We denote the adjoint of A by A† . Ibid. 353 The matrix of the operator adjoint to α is readily seen to be the adjoint α† of the matrix α. 1942R. P. Agnew Differential Equations xii. 254 Prove that the adjoint of the adjoint of the operator L..is L itself. 1959G. & R. C. James Math. Dict. 6/1 Two linear transformations T1 and T2 are said to be adjoint if (T1x, y) = (x, T2y) for any x in the domain of T1 and y in the domain of T2. 1978Nature 19 Oct. 643/1 According to Pontryagin's maximum principle, (1) can be minimised by maximising the hamiltonian H(c, t) = -[αs2(t)+βδc3(t)+γc(t)p(t)] with unknown adjoint variable p(t). 1984S. L. Ross Differential Equations xi. 574 The special situation in which the adjoint equation..of Equation (11.110) is also Equation (11.110) itself. |