Pfaffiann.adj.

Brit.

/ˈ(p)fɑːfɪən/,

/ˈ(p)fafɪən/, U.S.

/ˈ(p)fɑfiən/

Origin: From a proper name, combined with an English element. Etymons: proper name Pfaff , -ian suffix.

Etymology: < the name of Johann Friedrich Pfaff (1765–1825), German mathematician + -ian suffix.

Mathematics.

A. n.

Any of various mathematical objects occurring in or derived from the work of Pfaff on differential equations. Originally: spec. (A. Cayley's term for) a function involving permutations arising from this work.

ΚΠ

1852 A. Cayley Coll. Math. Papers II. 19 The permutants of this class (from their connexion with the researches of Pfaff on differential equations) I shall term ‘Pfaffians’.

1860 A. Cayley Coll. Math. Papers IV. 600 A skew symmetrical determinant of any even order is the square of a Pfaffian.

1922 Amer. Math. Monthly 29 13 The determinant of the sum of an axisymmetric matrix and a zero-axial skew matrix is expressible as a Pfaffian.

1989 Encycl. Brit. XIX. 972/2 An important combination of the curvature forms is given by the Pfaffian.

1997 Trans. Amer. Math. Soc. 349 3804 They were able to show that the homogeneous ideal of every such scheme arises as the Pfaffian of a skew symmetric matrix.

B. adj.

Of or relating to (mathematical objects occurring in) the work of Pfaff; spec. designating a differential equation of the form f₁dx₁ +…+ f_ndx_n = 0, where each f_i is a function of the variables x_i.

ΚΠ

1860 A. Cayley Coll. Math. Papers (1891) IV. 515 Pfaffian equations.

1904 Amer. Jrnl. Math. 26 106 In this case the determinant of the above system..is equal to the square of a certain integral function of the elements (the so-called Pfaffian function).

1910 Encycl. Brit. VIII. 231/2 This method for a single Pfaffian equation can..be generalized to a simultaneous system of (n-r) Pfaffian equations dx_j=c_1jdx₁+..+c_rjdx_r.

1995 Daily Tel. 31 Jan. 19/5 Is the Carathéodry theorem always needed to show that the Pfaffian form for the heat increment has an integrating factor?

This entry has been updated (OED Third Edition, December 2005; most recently modified version published online March 2022).

单词	pfaffian
释义	Pfaffiann.adj. Brit. /ˈ(p)fɑːfɪən/, /ˈ(p)fafɪən/, U.S. /ˈ(p)fɑfiən/ Origin: From a proper name, combined with an English element. Etymons: proper name Pfaff , -ian suffix. Etymology: < the name of Johann Friedrich Pfaff (1765–1825), German mathematician + -ian suffix. Mathematics. A. n. Any of various mathematical objects occurring in or derived from the work of Pfaff on differential equations. Originally: spec. (A. Cayley's term for) a function involving permutations arising from this work. ΚΠ 1852 A. Cayley Coll. Math. Papers II. 19 The permutants of this class (from their connexion with the researches of Pfaff on differential equations) I shall term ‘Pfaffians’. 1860 A. Cayley Coll. Math. Papers IV. 600 A skew symmetrical determinant of any even order is the square of a Pfaffian. 1922 Amer. Math. Monthly 29 13 The determinant of the sum of an axisymmetric matrix and a zero-axial skew matrix is expressible as a Pfaffian. 1989 Encycl. Brit. XIX. 972/2 An important combination of the curvature forms is given by the Pfaffian. 1997 Trans. Amer. Math. Soc. 349 3804 They were able to show that the homogeneous ideal of every such scheme arises as the Pfaffian of a skew symmetric matrix. B. adj. Of or relating to (mathematical objects occurring in) the work of Pfaff; spec. designating a differential equation of the form f₁dx₁ +…+ f_ndx_n = 0, where each f_i is a function of the variables x_i. ΚΠ 1860 A. Cayley Coll. Math. Papers (1891) IV. 515 Pfaffian equations. 1904 Amer. Jrnl. Math. 26 106 In this case the determinant of the above system..is equal to the square of a certain integral function of the elements (the so-called Pfaffian function). 1910 Encycl. Brit. VIII. 231/2 This method for a single Pfaffian equation can..be generalized to a simultaneous system of (n-r) Pfaffian equations dx_j=c_1jdx₁+..+c_rjdx_r. 1995 Daily Tel. 31 Jan. 19/5 Is the Carathéodry theorem always needed to show that the Pfaffian form for the heat increment has an integrating factor? This entry has been updated (OED Third Edition, December 2005; most recently modified version published online March 2022). < n.adj.1852
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