Araştırma Makalesi
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Eigenvalues of diffusion operators and Prime numbers

Yıl 2017, , 488 - 491, 30.09.2017
https://doi.org/10.17776/csj.340494

Öz

In this paper, the relationship between the positive eigenvalues of
diffusion operators and prime numbers is investigated. We also propose a Sturm-Liouville
problem with Coulomb singularity that shows eigenvalues the distribution of
prime numbers.

Kaynakça

  • [1]. M. Abramowitz, I. A. Stegun; Handbook of Mathematical Functions, Dover Publications, New York, 1972.
  • [2]. M. G. Gasymov and G. Sh. Guseinov, Determination of diffusion operator on spectral data, Dokl. Akad. Nauk Azerb. SSR, 37(2) (1981), 19-23.
  • [3]. B. Mingarelli; A note on Sturm-Liouville problems whose spectrum is the set of prime numbers, Electronic Journal of Differential Equations, Vol. 2011 (2011), No. 123, 1-4.
  • [4]. Amirov Rauf; Adalar Ibrahim, Eigenvalues of Sturm-Liouville operators and prime numbers. Electronic Journal of Differential Equations, Vol. 2017 (2017), No. 50, 1-3.
  • [5]. E. Ingham; The distribution of prime numbers, Cambridge Mathematical Librairy, Cambridge University Press, Cambridge, 1990. Reprint of the 1932 original, With a foreword by R. C. Vaughan.
  • [6]. P. T. Bateman and H. G. Diamond, Analytic Number Theory, World Scientific, Hackensack, NJ, 2004.
  • [7]. S. A. Buterin and V. A. Yurko, Inverse problems for second-order differential pencils with Dirichlet boundary conditions, Journal of Inverse and III-Posed Problems 20 (2012), 855–881.
  • [8]. Guo, Yongxia, and Guangsheng Wei. "Determination of differential pencils from dense nodal subset in an interior subinterval." Israel Journal of Mathematics 206.1 (2015), 213-231.
  • [9]. P. Dusart; Autour de la fonction qui compte le nombre de nombres premiers, Ph.D. thesis. Universite de Limoges, (1998).
  • [10]. J. E. Littlewood; Sur la distribution des nombres premiers, Comptes Rendus 158 (1914),1869-1872.
  • [11]. Amirov RK, Çakmak Y, Gulyaz S: Boundary value problem for second order differential equations with Coulomb singularity on a finite interval. Indian J. Pure Appl. Math. (2006), 37: 125-140.
  • [12]. Panaitopol, L. "A formula for pi(x) applied to a result of Koninck-Ivic." Nieuw Archief voor Wiskunde 1 (2000), 55-56.

Difüzyon Operatörlerinin Özdeğerleri ve Asal Sayılar

Yıl 2017, , 488 - 491, 30.09.2017
https://doi.org/10.17776/csj.340494

Öz

Bu makalede,
difüzyon operatörlerinin pozitif özdeğerleri ile asal sayılar arasındaki
ilişki incelenmiştir. Ayrıca, özdeğerleri, asal sayıların dağılımını gösteren
Coulomb singularitesine sahip bir Sturm-Liouville problemi önerilmiştir.

Kaynakça

  • [1]. M. Abramowitz, I. A. Stegun; Handbook of Mathematical Functions, Dover Publications, New York, 1972.
  • [2]. M. G. Gasymov and G. Sh. Guseinov, Determination of diffusion operator on spectral data, Dokl. Akad. Nauk Azerb. SSR, 37(2) (1981), 19-23.
  • [3]. B. Mingarelli; A note on Sturm-Liouville problems whose spectrum is the set of prime numbers, Electronic Journal of Differential Equations, Vol. 2011 (2011), No. 123, 1-4.
  • [4]. Amirov Rauf; Adalar Ibrahim, Eigenvalues of Sturm-Liouville operators and prime numbers. Electronic Journal of Differential Equations, Vol. 2017 (2017), No. 50, 1-3.
  • [5]. E. Ingham; The distribution of prime numbers, Cambridge Mathematical Librairy, Cambridge University Press, Cambridge, 1990. Reprint of the 1932 original, With a foreword by R. C. Vaughan.
  • [6]. P. T. Bateman and H. G. Diamond, Analytic Number Theory, World Scientific, Hackensack, NJ, 2004.
  • [7]. S. A. Buterin and V. A. Yurko, Inverse problems for second-order differential pencils with Dirichlet boundary conditions, Journal of Inverse and III-Posed Problems 20 (2012), 855–881.
  • [8]. Guo, Yongxia, and Guangsheng Wei. "Determination of differential pencils from dense nodal subset in an interior subinterval." Israel Journal of Mathematics 206.1 (2015), 213-231.
  • [9]. P. Dusart; Autour de la fonction qui compte le nombre de nombres premiers, Ph.D. thesis. Universite de Limoges, (1998).
  • [10]. J. E. Littlewood; Sur la distribution des nombres premiers, Comptes Rendus 158 (1914),1869-1872.
  • [11]. Amirov RK, Çakmak Y, Gulyaz S: Boundary value problem for second order differential equations with Coulomb singularity on a finite interval. Indian J. Pure Appl. Math. (2006), 37: 125-140.
  • [12]. Panaitopol, L. "A formula for pi(x) applied to a result of Koninck-Ivic." Nieuw Archief voor Wiskunde 1 (2000), 55-56.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Bölüm Makaleler
Yazarlar

Rauf Amirov

İbrahim Adalar

Yayımlanma Tarihi 30 Eylül 2017
Gönderilme Tarihi 29 Mayıs 2017
Kabul Tarihi 7 Ağustos 2017
Yayımlandığı Sayı Yıl 2017

Kaynak Göster

APA Amirov, R., & Adalar, İ. (2017). Eigenvalues of diffusion operators and Prime numbers. Cumhuriyet Science Journal, 38(3), 488-491. https://doi.org/10.17776/csj.340494