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.
Anahtar Kelimeler
Inverse problem spectrum prime numbers diffusion operator coulomb singularity
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.
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.
Anahtar Kelimeler
Ters problem spektrum asal sayılar difüzyon operator coulomb singularite
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.
Ayrıntılar
| Bölüm | Makaleler |
|---|---|
| Yazarlar | |
| Yayımlanma Tarihi | 30 Eylül 2017 |
| Gönderilme Tarihi | 29 Mayıs 2017 |
| Kabul Tarihi | 7 Ağustos 2017 |
| Yayımlandığı Sayı | Yıl 2017 |