1. This, the Riemann curvature tensor, quantifies space-time curvature.

2. The Riemann sphere still describes the array of physically distinct possibilities, but now only abstractly.

3. Riemann, who was a student of Gauss, initiated the analysis of curved spaces with more than two dimensions in 1846.

4. Can mathematicians prove the Riemann hypothesis?

5. Bernhard Riemann pioneered elliptic geometry.

6. These two airfoils lie on different Riemann sheets in the hodograph plane.

7. A geometer like Riemann might almost have foreseen the more important features of the actual world.

8. It was this concept that Riemann generalized, thereby opening up new vistas in non - Euclidean geometry.

9. Furthermore, we compute the Riemann solution by using a bisection method combined with the phase-plane analysis.

10. We solve the Riemann problem for C - J model and Z - N - D model under the entropy conditions.

11. The classical elementary waves in Riemann solutions include rarefaction wave, shock wave and contact discontinuity.

12. H. C. Whitehead theorem in Riemann manifolds is extended into Finsler manifolds.

13. In his lecture Riemann covered an enormous variety of topics.

14. Riemann doesn't analyze the absolute music and title music from the viewpoint of music form and content, and finds a way to reconcile between title music and absolute music.

15. To see how the array of possibilities is again the Riemann sphere, imagine the photon to be travelling vertically upwards.

16. We shall now briefly bring out the relationship between the Gaussian curvature and the Riemann curvature tensor.

17. Appendix B contains more details on the mathematical properties of the Riemann tensor.

18. A more complete and compact description of curvature in n dimensions is embodied in the Riemann tensor.

19. Christoffel's major concern was to reconsider and amplify the theme already treated somewhat sketchily by Riemann.

20. This article discusses the analyzing nature of Dirichlet function and Riemann function .

21. Einstein did not, but his brilliant intuition led him to study and adopt the obscure non-Euclidean geometry of Riemann and Gauss for his geometric theory of gravity.

22. In this paper, we use the method of the estimated characteristic function to estimate a lower bound of the first eigenvalue on compact Riemann manifold.

23. To our surprise, the Godunov scheme can not be performed well for this system when the Riemann solution contains a weak backward rarefaction wave and a strong forward shock.

24. The major contents include tensor analysis, principle of equivalence, Riemann geometry ...

25. Based on Darboux theory, this paper discussed the integrability of the Riemann Integral and provides a necessary and sufficient condition for integrability.

26. Analytic theory is fortunate to have one of the most famous unsolved problems, the Riemann hypothesis.