Determinants and Their Applications in Mathematical Physics

Bibliography 359

J. de Leeuw, A note on partitioned determinants.Psychometrika 47 (1982), 531–

534. [MR 84h: 15009.]

A. Lenard, Some remarks on large Toeplitz determinants.Pacific J. Math. 42

(1972), 137–145. [MR 48 (1974), 9440.]

F.A. Lewis, On a determinant of Sylvester.Am. Math. Monthly 57 (1950), 324–

326. [MR 11 (1950), 710.]

D.C. Lewis, The multiplication of determinants.Am. Math. Monthly 83 (1976),

268–270. [MR 53 (1977), 472.]

C. Li, The maximum determinant of ann×nlower Hessenberg matrix.Linear

Alg. Applic. 183 (1993), 147–153. [Zbl 769 (1993/19), 15008.]

Q.-M. Liu, Casorati determinant form of the superposition formula of the two-

dimensional Toda lattice.Phys. Lett. A 135 (1989), 443–446. [PA 92 (1989),

68413.]

Q.-M. Liu, Transformation formulae of the solutions of the two-dimensional Toda

lattices.J. Phys. A: Math. Gen. 22 (1989), 4737–4742. [PA 93 (1990), 11916.]

Q.-M. Liu, Double Wronskian solutions of the AKNS and the classical Boussinesq

hierarchies.J. Phys. Soc. Japan 59 (1990), 3520–3527. [PA 94 (1991), 6983.]

R. Loewy, Determinants of nonprincipal submatrices of positive semidefinite

matrices.Linear Alg. Applic. 56 (1984), 1–16. [Zbl 523 (1984), 15009.]

J.S. Lomont, M.S. Cheema, Properties of Pfaffians.Rocky Mountain J. Math. 15

(1985), 493–512. [MR 87c: 15016.]

L. Lorch, Turanians and Wronskians for the zeros of Bessel functions.SIAM J.

Math. Anal. 11 (1980), 223–227. [Zbl 446 (1981), 33011.]

I. Loris, R. Willox, Soliton solutions of Wronskian form to the nonlocal Boussinesq

equation.J. Phys. Soc. Japan 65 (1996), 383–388.

I. Loris, R. Willox, On the solution of the constrained KP equation.J. Math.

Phys. 38 (1997), 283–291.

O.P. Lossers, Solution of Problem 74-14 (1974) proposed by S. Venit [A

generalization of the Vandermonde determinant]. SIAM Rev. 17 (1975),

694–695.

P.J. McCarthy, A generalization of Smith’s determinant.Can. Math. Bull. 29

(1986), 109–113. [Zbl 588 (1986), 10005.]

B.M. McCoy, Physical applications and extensions of Szeg ̈o’s theorem on Toeplitz

determinants.Abstr. AMS 3 (1982), 344.

B.R. McDonald, A characterization of the determinant.Linear Multilinear Alg.

12 (1982), 31–36. [MR 83j: 15009.]

P.A. Macmahon, On anx-determinant which includes as particular cases both

determinants and permanents.Proc. Roy. Soc. Edin. 44 (1923/1924), 21–22.

P.A. Macmahon, Researches in the theory of determinants.Trans. Camb. Phil.

Soc. 23 (1924), 89–135.

P.A. Macmahon, The symmetric functions of which the general determinant is a

particular case.Proc. Camb. Phil. Soc. 22 (1925), 633–654.

P.A. Macmahon, The structure of a determinant.J. Lond. Math. Soc. 2 (1927),

273–286.