Bibliography for Rouche's Theorem

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  1. On the modification of Rouche's theorem for the queueing theory problems.  
    Klimenok, V.
    Queueing Syst. Theory Appl.  38  (2001),  no. 4, 431--434, MathSciNet.  
  2. Finding a cluster of zeros of univariate polynomials
    Yakoubsohn JC
    J Complexity 16 (3): 603-638 SEP 2000,Web of Science.    
  3. A generalization of the argument principle.
    Cristea, Mihai
    Complex Variables Theory Appl. 42 (2000), no. 4, 333--345, MathSciNet.  
  4. Winding numbers, complex currents, and non-Hermitian localization
    Shnerb, Nadav M.;   Nelson, David R.  
    Physical Review Letters, v 80, n 23, Jun 8, 1998, p 5172, Engineering Village.  
  5. On the integral giving the degree of a map and a Rouché type theorem.
    Hatziafratis, T.; Tsarpalias, A.
    Z. Anal. Anwendungen 16 (1997), no. 2, 239--247, MathSciNet.  
  6. The Argument Principle for Harmonic Functions (in Notes)  
    Peter Duren; Walter Hengartner; Richard S. Laugesen  
    American Mathematical Monthly, Vol. 103, No. 5. (May, 1996), pp. 411-415, Jstor.  
  7. Extensions of Rouche's theorem
    Lin, K.-J.; Juang, Y.-T.  
    Source: Journal of Control Systems and Technology, v 4, n 2, Jun, 1996, p 127-131, Engineering Village.  
  8. Homotopy methods and a generalization of Rouché theorem.
    Gao, Tang An; Wang, Ze Ke
    Complex analysis and its applications (Hong Kong, 1993), 174--177, Pitman Res. Notes Math. Ser., 305, Longman Sci. Tech., Harlow, 1994, MathSciNet.  
  9. Winding Number and the Number of Real Zeros of a Function  
    Lieven Smits; Willem Kuyk  
    Proceedings of the American Mathematical Society, Vol. 114, No. 4. (Apr., 1992), pp. 981-987, Jstor.  
  10. The Rouché theorem for holomorphic maps in complex Banach spaces.
    Wodarczyk, Kazimierz
    Complex Variables Theory Appl. 20 (1992), no. 1-4, 71--73, MathSciNet.  
  11. Plane Curves, Polar Coordinates and Winding Numbers  
    John A. Baker  
    Mathematics Magazine, Vol. 64, No. 2. (Apr., 1991), pp. 75-91, Jstor.  
  12. Rouche's Theorem for Polynomials (in Notes)  
    Michael Filaseta  
    American Mathematical Monthly, Vol. 97, No. 9. (Nov., 1990), pp. 834-835, Jstor.  
  13. Rotation and Winding Numbers for Planar Polygons and Curves  
    Branko Grunbaum; G. C. Shephard  
    Transactions of the American Mathematical Society, Vol. 322, No. 1. (Nov., 1990), pp. 169-187, Jstor.  
  14. A Version of Rouche's Theorem for Continuous Functions (in Notes)  
    A. Tsarpalias  
    American Mathematical Monthly, Vol. 96, No. 10. (Dec., 1989), pp. 911-913, Jstor.  
  15. Stability of perturbed polynomials based on the argument principle and Nyquist criterion.
    Lin, S. H.; Fong, I. K.; Juang, Y. T.; Kuo, T. S.; Hsu, C. F.
    Internat. J. Control 50 (1989), no. 1, 55--63, MathSciNet.  
  16. A reliable argument principle algorithm to find the number of zeros of an analytic function in a bounded domain.
    Ying, Xingren; Katz, I. Norman
    Numer. Math. 53 (1988), no. 1-2, 143--163, MathSciNet.  
  17. A generalization of Rouché's theorem with application to resonances.
    Siedentop, Heinz
    Resonances (Lertorpet, 1987), 77--85, Lecture Notes in Phys., 325, Springer, Berlin, 1989, MathSciNet.  
  18. A generalization of Rouché's theorem.
    Cristea, Mihai
    An. Univ. Bucuresti Mat. 36 (1987), 13--15, MathSciNet.  
  19. A Rouché's type theorem in several complex variables.
    Lupacciolu, Guido
    Rend. Accad. Naz. Sci. XL Mem. Mat. (5) 9 (1985), no. 1, 33--41, MathSciNet.  
  20. Counting Zeros of Real Polynomials within the Unit Disk  
    Charles W. Schelin  
    SIAM Journal on Numerical Analysis, Vol. 20, No. 5. (Oct., 1983), pp. 1023-1031, Jstor.  
  21. A Converse to Rouche's Theorem (in Notes)
    David Challener; Lee Rubel
    American Mathematical Monthly, Vol. 89, No. 5. (May, 1982), pp. 302-305, Jstor.  
  22. Generalized Rouché's theorem and its application to multivariate autoregressions.
    Monden, Yoshimi; Arimoto, Suguru
    IEEE Trans. Acoust. Speech Signal Process. 28 (1980), no. 6, 733--738, MathSciNet.  
  23. Rouché's and related theorems for analytic functions of several complex variables.
    Shih, Mau Hsiang
    Bull. Inst. Math. Acad. Sinica 8 (1980), no. 4, 527--533, MathSciNet.  
  24. A note on Rouché's theorem. (Spanish)
    Ruiz, Francisco; Uriz, Zenaida
    Proceedings of the sixth conference of Portuguese and Spanish mathematicians, Part I (Santander, 1979). Rev. Univ. Santander No. 2, part 1 (1979), 233--235, MathSciNet.  
  25. Remarks on generalising Rouché's theorem.  
    Lloyd, N. G.
    J. London Math. Soc. (2)  20  (1979), no. 2, 259--272, MathSciNet.  
  26. Generalized argument principle for commutative Banach algebras.
    Naghshineh-Ardjmand, Mohsen
    J. London Math. Soc. (2) 18 (1978), no. 1, 140--146, MathSciNet.  
  27. Hurwitz' theorem implies Rouché's theorem.
    Abian, Alexander
    J. Math. Anal. Appl. 61 (1977), no. 1, 113--115, MathSciNet.  
  28. A Remark on Rouche's Theorem (in Mathematical Notes)  
    I. Glicksberg  
    American Mathematical Monthly, Vol. 83, No. 3. (Mar., 1976), pp. 186-187, Jstor.  
  29. An Algorithm for Winding Numbers for Closed Polygonal Paths  
    Kenneth O. Leland  
    Mathematics of Computation, Vol. 29, No. 130. (Apr., 1975), pp. 554-558, Jstor.  
  30. A Winding Number Algorithm for Closed Polygonal Paths  
    J. V. Petty  
    Mathematics of Computation, Vol. 27, No. 122. (Apr., 1973), pp. 333-337, Jstor.  
  31. A note on Rouché's theorem.
    Chatterjea, S. K.
    Mat. Vesnik 10(25) (1973), 297--298, MathSciNet.  
  32. A Functional Analytic Proof of Rouche's Theorem (in Mathematical Notes)  
    D. van Dulst  
    American Mathematical Monthly, Vol. 78, No. 7. (Aug. - Sep., 1971), pp. 770-771, Jstor.  
  33. On a theorem of N. Rouche.
    Gambardella, Lucia; Tenneriello, Catello
    Rend. Accad. Sci. Fis. Mat. Napoli (4) 38 (1971), 145--150, MathSciNet.  
  34. A note on an extension of Rouche's theorem.
    Ghosh, A.
    Bull. Calcutta Math. Soc. 61 1969 115--117, MathSciNet.  
  35. A lesson on Rouché's theorem. (Spanish)
    Cuesta, N.
    Gac. Mat. (Madrid) (1) 18 1969 28--43, MathSciNet.  
  36. A note on Rouché's theorem.
    Bank, S. B.; Orland, G. H.
    Fund. Math. 63 1968 137--141, MathSciNet.  
  37. On Rouche's Theorem and the Integral-Square Measure of Approximation  
    J. L. Walsh  
    Proceedings of the American Mathematical Society, Vol. 2, No. 5. (Oct., 1951), pp. 671-681, Jstor.  
  38. Errata: On Rouche's Theorem and the Integral-Square Measure of Approximation  
    J. L. Walsh  
    Proceedings of the American Mathematical Society, Vol. 2, No. 6. (Dec., 1951), p. 993, Jstor.  

 

 

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