Ernst denklemi, matematik'te doğrusal-olmayan bir kısmi diferansiyel denklem'dir.
Adı
Ünlü fizikçi Frederick J. Ernst tarafından bulunmuş olduğundan, "Ernst denklemi" olarak adlandırılmıştır.
Ernst denklemi
Sağ tarafında Birinci dereceden kısmî türevler içeren ve doğrusal olmayan terimleri olan bir denklemdir. Çözümü aranan u karmaşık fonksiyonunun gerçel kısmı R(u), denklemin sol tarafındaki İkinci dereceden kısmî türevlerin çarpımı halinde belirdiğinden, denklemin her iki tarafı da doğrusal-olmayan (non-linear) terimler ihtivâ etmektedir. Denklem aşağıdaki şekilde verilmektedir:
Kullanım amacı
Einstein alan denklemlerinin noksansız çözümlerini elde etmek için kullanılan doğrusal olmayan bir kısmi türevsel denklemdir.
Bibliyografya
- Zwillinger, Daniel (1989), Handbook of differential equations, Boston, MA: Academic Press, ISBN
İlgili yayınlar
Journal of Mathematical Physics mecmuasında
- 1971: Frederick J. Ernst, Exterior-Algebraic Derivation of Einstein Field Equations Employing a Generalized Basis
- 1974: Frederick J. Ernst, Complex potential formulation of the axially symmetric gravitational field problem
- 1974: Frederick J. Ernst, Weyl conform tensor for stationary gravitational fields
- 1975: Frederick J. Ernst, Black holes in a magnetic universe
- 1975: Frederick J. Ernst, Erratum: Complex potential formulation of the axially symmetric gravitational field problem
- 1975: John E. Economou & Frederick J. Ernst, Weyl conform tensor of =2 Tomimatsu–Sato spinning mass gravitational field
- 1976: Frederick J. Ernst & Walter J. Wild, Kerr black holes in a magnetic universe
- 1976: Frederick J. Ernst, New representation of the Tomimatsu–Sato solution
- 1976: Frederick J. Ernst, Removal of the nodal singularity of the C-metric
- 1977: Frederick J. Ernst, A new family of solutions of the Einstein field equations
- 1978: Frederick J. Ernst, Coping with different languages in the null tetrad formulation of general relativity
- 1978: Frederick J. Ernst & I. Hauser, Field equations and integrability conditions for special type N twisting gravitational fields
- 1978: Frederick J. Ernst, Generalized C-metric
- 1978: Isidore Hauser & Frederick J. Ernst, On the generation of new solutions of the Einstein–Maxwell field equations
- 1979: I. Hauser & Frederick J. Ernst, SU(2,1) generation of electrovacs from Minkowski space
- 1979: (Erratum) Coping with different languages in the null tetrad formulation of general relativity
- 1979: (Erratum) Generalized C metric
- 1980: Isidore Hauser & Frederick J. Ernst, A homogeneous Hilbert problem for the Kinnersley–Chitre transformations of electrovac space-times
- 1980: Isidore Hauser & Frederick J. Ernst, A homogeneous Hilbert problem for the Kinnersley–Chitre transformations
- 1981: Isidore Hauser & Frederick J. Ernst, Proof of a Geroch conjecture
- 1982: Dong-sheng Guo & Frederick J. Ernst, Electrovac generalization of Neugebauer's N = 2 solution of the Einstein vacuum field equations
- 1983: Y. Chen, Dong-sheng Guo & Frederick J. Ernst, Charged spinning mass field involving rational functions
- 1983: Cornelius Hoenselares & Frederick J. Ernst, Remarks on the Tomimatsu–Sato metrics
- 1987: Frederick J. Ernst, Alberto Garcia D & Isidore Hauser, Colliding gravitational plane waves with noncollinear polarization. I
- 1987: Frederick J. Ernst, Alberto Garcia D & Isidore Hauser, Colliding gravitational plane waves with noncollinear polarization. II
- 1988: Frederick J. Ernst, Alberto Garcia D & Isidore Hauser, Colliding gravitational plane waves with noncollinear polarization. III
- 1989: Wei Li & Frederick J. Ernst, A family of electrovac colliding wave solutions of Einstein's equations
- 1989: Isidore Hauser & Frederick J. Ernst, Initial value problem for colliding gravitational plane waves. I
- 1989: Isidore Hauser & Frederick J. Ernst, Initial value problem for colliding gravitational plane waves. II
- 1990: Isidore Hauser & Frederick J. Ernst, Initial value problem for colliding gravitational plane waves. III
- 1990: Cornelius Hoenselares & Frederick J. Ernst, Matching pp waves to the Kerr metric
- 1991: Wei Li, Isidore Hauser & Frederick J. Ernst, Colliding gravitational plane waves with noncollinear polarizations
- 1991: Wei Li, Isidore Hauser & Frederick J. Ernst, Colliding gravitational waves with Killing–Cauchy horizons
- 1991: Wei Li, Isidore Hauser & Frederick J. Ernst, Colliding wave solutions of the Einstein–Maxwell field equations
- 1991: Isidore Hauser & Frederick J. Ernst, Initial value problem for colliding gravitational plane waves. IV
- 1991: Wei Li, Isidore Hauser & Frederick J. Ernst, Nonimpulsive colliding gravitational waves with noncollinear polarizations
- 1993: Frederick J. Ernst & Isidore Hauser, On Gürses's symmetries of the Einstein equations
Kaynakça
- ^ Lisans-Fizik, Princeton Üniversitesi ve Doktora-Fizik, University of Wisconsin–Madison (Doktora Tezi: The Wave Functional Description of Elementary Particles with Application to Nucleon Structure); 1964 - 1969: Yardımcı Doçent, 1969 - 1980: Doçent, 1980 - 1987: Professör, Hepsi Fizik-Illinois Institute of Technology; 1987'den sonra Matematik-Kısmî Türevsel Denklemler ve Fizik-Genel Görelilik Kuramı Profesörü, Clarkson University Potsdam, New York.
- ^ "Weisstein, Eric W, Ernst denklemi, MathWorld--A Wolfram Web". 16 Ağustos 2017 tarihinde kaynağından . Erişim tarihi: 4 Mayıs 2015.
wikipedia, wiki, viki, vikipedia, oku, kitap, kütüphane, kütübhane, ara, ara bul, bul, herşey, ne arasanız burada,hikayeler, makale, kitaplar, öğren, wiki, bilgi, tarih, yukle, izle, telefon için, turk, türk, türkçe, turkce, nasıl yapılır, ne demek, nasıl, yapmak, yapılır, indir, ücretsiz, ücretsiz indir, bedava, bedava indir, mp3, video, mp4, 3gp, jpg, jpeg, gif, png, resim, müzik, şarkı, film, film, oyun, oyunlar, mobil, cep telefonu, telefon, android, ios, apple, samsung, iphone, xiomi, xiaomi, redmi, honor, oppo, nokia, sonya, mi, pc, web, computer, bilgisayar
Ernst denklemi matematik te dogrusal olmayan bir kismi diferansiyel denklem dir AdiUnlu fizikci Frederick J Ernst tarafindan bulunmus oldugundan Ernst denklemi olarak adlandirilmistir Ernst denklemiSag tarafinda Birinci dereceden kismi turevler iceren ve dogrusal olmayan terimleri olan bir denklemdir Cozumu aranan u karmasik fonksiyonunun gercel kismi R u denklemin sol tarafindaki Ikinci dereceden kismi turevlerin carpimi halinde belirdiginden denklemin her iki tarafi da dogrusal olmayan non linear terimler ihtiva etmektedir Denklem asagidaki sekilde verilmektedir ℜ u urr ur r uzz ur 2 uz 2 displaystyle displaystyle Re u u rr u r r u zz u r 2 u z 2 Kullanim amaci Einstein alan denklemlerinin noksansiz cozumlerini elde etmek icin kullanilan dogrusal olmayan bir kismi turevsel denklemdir BibliyografyaZwillinger Daniel 1989 Handbook of differential equations Boston MA Academic Press ISBN 978 0 12 784390 2 Ilgili yayinlar Journal of Mathematical Physics mecmuasinda 1971 Frederick J Ernst Exterior Algebraic Derivation of Einstein Field Equations Employing a Generalized Basis 1974 Frederick J Ernst Complex potential formulation of the axially symmetric gravitational field problem 1974 Frederick J Ernst Weyl conform tensor for stationary gravitational fields 1975 Frederick J Ernst Black holes in a magnetic universe 1975 Frederick J Ernst Erratum Complex potential formulation of the axially symmetric gravitational field problem 1975 John E Economou amp Frederick J Ernst Weyl conform tensor of 2 Tomimatsu Sato spinning mass gravitational field 1976 Frederick J Ernst amp Walter J Wild Kerr black holes in a magnetic universe 1976 Frederick J Ernst New representation of the Tomimatsu Sato solution 1976 Frederick J Ernst Removal of the nodal singularity of the C metric 1977 Frederick J Ernst A new family of solutions of the Einstein field equations 1978 Frederick J Ernst Coping with different languages in the null tetrad formulation of general relativity 1978 Frederick J Ernst amp I Hauser Field equations and integrability conditions for special type N twisting gravitational fields 1978 Frederick J Ernst Generalized C metric 1978 Isidore Hauser amp Frederick J Ernst On the generation of new solutions of the Einstein Maxwell field equations 1979 I Hauser amp Frederick J Ernst SU 2 1 generation of electrovacs from Minkowski space 1979 Erratum Coping with different languages in the null tetrad formulation of general relativity 1979 Erratum Generalized C metric 1980 Isidore Hauser amp Frederick J Ernst A homogeneous Hilbert problem for the Kinnersley Chitre transformations of electrovac space times 1980 Isidore Hauser amp Frederick J Ernst A homogeneous Hilbert problem for the Kinnersley Chitre transformations 1981 Isidore Hauser amp Frederick J Ernst Proof of a Geroch conjecture 1982 Dong sheng Guo amp Frederick J Ernst Electrovac generalization of Neugebauer s N 2 solution of the Einstein vacuum field equations 1983 Y Chen Dong sheng Guo amp Frederick J Ernst Charged spinning mass field involving rational functions 1983 Cornelius Hoenselares amp Frederick J Ernst Remarks on the Tomimatsu Sato metrics 1987 Frederick J Ernst Alberto Garcia D amp Isidore Hauser Colliding gravitational plane waves with noncollinear polarization I 1987 Frederick J Ernst Alberto Garcia D amp Isidore Hauser Colliding gravitational plane waves with noncollinear polarization II 1988 Frederick J Ernst Alberto Garcia D amp Isidore Hauser Colliding gravitational plane waves with noncollinear polarization III 1989 Wei Li amp Frederick J Ernst A family of electrovac colliding wave solutions of Einstein s equations 1989 Isidore Hauser amp Frederick J Ernst Initial value problem for colliding gravitational plane waves I 1989 Isidore Hauser amp Frederick J Ernst Initial value problem for colliding gravitational plane waves II 1990 Isidore Hauser amp Frederick J Ernst Initial value problem for colliding gravitational plane waves III 1990 Cornelius Hoenselares amp Frederick J Ernst Matching pp waves to the Kerr metric 1991 Wei Li Isidore Hauser amp Frederick J Ernst Colliding gravitational plane waves with noncollinear polarizations 1991 Wei Li Isidore Hauser amp Frederick J Ernst Colliding gravitational waves with Killing Cauchy horizons 1991 Wei Li Isidore Hauser amp Frederick J Ernst Colliding wave solutions of the Einstein Maxwell field equations 1991 Isidore Hauser amp Frederick J Ernst Initial value problem for colliding gravitational plane waves IV 1991 Wei Li Isidore Hauser amp Frederick J Ernst Nonimpulsive colliding gravitational waves with noncollinear polarizations 1993 Frederick J Ernst amp Isidore Hauser On Gurses s symmetries of the Einstein equationsKaynakca Lisans Fizik Princeton Universitesi ve Doktora Fizik University of Wisconsin Madison Doktora Tezi The Wave Functional Description of Elementary Particles with Application to Nucleon Structure 1964 1969 Yardimci Docent 1969 1980 Docent 1980 1987 Professor Hepsi Fizik Illinois Institute of Technology 1987 den sonra Matematik Kismi Turevsel Denklemler ve Fizik Genel Gorelilik Kurami Profesoru Clarkson University Potsdam New York Weisstein Eric W Ernst denklemi MathWorld A Wolfram Web 16 Agustos 2017 tarihinde kaynagindan Erisim tarihi 4 Mayis 2015