Determinants and Their Applications in Mathematical Physics

(Chris Devlin) #1

370 Bibliography


P.R. Vein, Determinantal solutions of two difference–differential equations. Tech.


Rep. TR 90005, Dept. Comp. Sci. & Appl. Maths., Aston University,

Birmingham, U.K., 1990.

P.R. Vein, P. Dale, Determinants, their derivatives and nonlinear differential


equations.J. Math. Anal. Applic. 74 (1980), 599–634. [MR 81f: 15013; Zbl

459 (1982), 15009.]

P.R. Vein, P. Dale, Two verifications of the determinantal solutions of the


Korteweg–de Vries and the Kadomtsev–Petviashvili equations.Applic. Anal.

25 (1987), 79–100. [Zbl 602 (1987), 35114; PA 90 (1987), 134523.]

R. Vermes, Hankel determinants formed from successive derivatives.Duke Math.


J. 37 (1970), 255–259. [MR 41 (1971), 3843.]

V. Vinnikov, Determinantal representations of real cubics and canonical forms


of corresponding triples of matrices. Math. theory of networks and systems.

Proc. Int. Symp. Beer Sheva, Israel, 1983.Lect. Notes Control Inf. Sci. 58

(1984), 882–898. [Zbl 577 (1986), 14040.]

V.S. Vladimirov, I.V. Volovich, Superanalysis II. Integral calculus.Theoret. Math.


Phys. 60 (1984), 743–765. [MR 86c: 58015b.]

H. Waadeland,
̈
Uber eine determinante.Norske Vid. Selsk. Forh. Trondheim 24


(1952), 108–109. [MR 14 (1953), 1054.]

M. Wadati, The modified KdV equation.J. Phys. Soc. Japan 34 (1973), 1289–



  1. [PA 76 (1973), 37905.]


M. Wadati, M. Toda, The exactn-soliton solution of the Korteweg–de Vries


equation.J. Phys. Soc. Japan 32 (1972), 1403–1411.] [PA 75 (1972), 69553.]

A.W. Walker, A proof of the product rule for determinants.Math. Gaz. 33 (1949),


213–214.

C.R. Wall, Analogs of Smith’s determinant.Fibonacci Quart. 25 (1987), 343–345.


[MR 88i: 15022.]

C.L. Wang, Gramian expansions and their applications.Util. Math. 15 (1979),


97–111. [MR 80e: 15013.]

G. Wang, A Cramer’s rule for minimum-norm (T) least-squares (S) solution of


the inconsistent linear equations.Linear Alg. Applic. 74 (1986), 213–218. [Zbl

588 (1986), 15005.]

K. Wang On the generalization of circulants.Linear Alg. Applic. 25 (1979), 197–



  1. [MR 81i: 15022.]


K. Wang, On the generalization of a retrocirculant.Linear Alg. Applic. 37 (1981),


35–43. [MR 83i: 15026.]

T. Watanabe, On a determinant sequence in the lattice path counting.J. Math.


Anal. Applic. 123 (1987), 401–414.

W.C. Waterhouse, Twisted forms of the determinant.J. Alg. 86 (1984), 60–75.


[MR 85c: 11040.]

W.C. Waterhouse, How often do determinants over finite fields vanish?Discrete


Math. 65 (1987), 103–104. [MR 88d: 11127.]

W.C. Waterhouse, Automorphisms of determinant (Xij): The group scheme


approach.Adv. Math. 65 (1987), 171–203. [Zbl 651 (1989), 4028.]
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