Page 372 - Determinants and Their Applications in Mathematical Physics

Bibliography 357

K. Kajiwara, Y. Ohta, Determinant structure of the rational solutions for the
e
Painlev´ IV equation. J. Phys. A: Math. Gen. 31 (1998), 2431–2446.
S. Kakei, Toda lattice hierarchy and Zamolodchikov’s conjecture. J. Phys. Soc.
Japan 65 (1996), 337–339.
S. Kakei, J. Satsuma, Multi-soliton solutions of a coupled system of the nonlinear
Schr¨odinger equation and the Maxwell–Bloch equations. J. Phys. Soc. Japan
63 (1994), 885–894.
S.A. Kamal, Determinant of a general tensor. Matrix Tensor Quart. 31 (1980/81),
64–66. [MR 82j: 15025; Zbl 524 (1984), 15005.]
F. Kaminski, On a method of order reduction for a tridiagonal determinant. Bull.
Acad. Pol. Sci. Ser. Sci. Technol. 29 (1981), 75–81, 419–425. [Zbl 487 (1983),
15005.]
T. Kanzaki, Y Watanabe, Determinants of r-fold symmetric multilinear forms.
J. Alg. 124 (1989), 219–229. [MR 90g: 11052.]
W. Kaplan, On Circulants. Complex Analysis, Birkh¨auser, Boston, 1988, pp.
121–130. [MR 90i: 15008.]
S. Karlin, Determinants and eigenfunctions of Sturm–Liouville equations. J.
Anal. Math. 9 (1961/62), 365–397. [MR 24A (1962), 3321.]
S. Karlin, J. McGregor, Determinants of orthogonal polynomials. Bull. Am. Math.
Soc. 68 (1962), 204–209. [MR 25 (1963), 2250.]
S. Karlin, J. McGregor, Some properties of determinants of orthogonal poly-
nomials. Theory and Applications of Special Functions (editor: R.A. Askey),
Academic Press, New York, 1975, pp. 521–550.
S. Karlin, G. Szeg¨o, On certain determinants whose elements are orthogonal
polynomials. J. Anal. Math. 8 (1960/1961), 1–157. [MR 26 (1963), 539.]
I. Katai, E. Rahmy, Computation of the determinant of five-diagonal symmetric
Toeplitz matrices. Ann. Univ. Sci. Budapest Sect. Comput. 1979, no. 2, (1981),
13–31. [MR 83e: 65081.]
Y. Kato, Fredholm determinants and the solution of the Korteweg–de Vries
equation. Prog. Theoret. Phys. 76 (1986), 768–783. [MR 88c: 35143.]
Y. Kato, Fredholm determinants and the Cauchy problem of a class of nonlin-
ear evolution equations. Prog. Theoret. Phys. 78 (1987), 198–213. [MR 89b:
35145.]
H. Kaufman, A bibliographical note on higher order sine functions. Scripta Math.
28 (1967), 29–36. [MR 35 (1968), 6871.]
1 {(n−1)! (n−2)!···1!}
T. Kawashima, On det i+j−1 = (2n−1)! (2n−2)!···n! . Res. Ref. Ashikaga Inst.
Technol. 9 (1983), 149–154 (Japanese, English summary). [Zbl 529 (1984),
15003.]
I. Kay, H.E. Moses, Reflectionless transmission through dielectrics and scattering
potentials. J. Appl. Phys. 27 (1956), 1503–1508. [PA 60 (1957), 4570.]
D. Kershaw, A note on orthogonal polynomials. Proc. Edin. Math. Soc. 17 (1970–
71), 83–93. [MR 42 (1971), 3326.]
J.B. Kim, J.E. Dowdy, Determinants of n-dimensional matrices. J. Korean Math.
Soc. 17 (1980/81), 141–146. [MR 81k: 15006.]