Riemann's theorem shows the reason why Seeliger's paradox occurs, and it also demonstrates that its origin is mathematical, not physical.

Buser, Geometry and spectra of compact

Riemann surfaces, Progress in Mathematics, 106, Birkhauser Boston, Inc., Boston, MA, 1992.

The scalar constructed out of this projected

Riemann tensor becomes

Shen [28] considered the

Riemann problem of pressureless Euler system (4).

It has been shown that delta-shocks and vacuum states do occur in the

Riemann solutions of (3).

Tenney withholds a filiation for the clang in

Riemann's Klang, which was translated into English as early as the 1890s (see Dictionary of Music, trans.

"The inspired idea of incorporating into the symphony a minuet in the form of a typical folksy medley of coarse revelry, the philistine affability and naive grace was also undoubtedly in compliance with the new spirit, which had been brought into orchestral music in the city on the Rhine and Neckar by the settled Bohemian [bohmisch], and Moravian, musicians Stamitz, Filtz and Richter." In a footnote, with reference to a work by Adolf Sandberg,

Riemann added yet another name--that of Jan Zach (whereas Filtz would be omitted from the group in the future).

Thus, the

Riemann tensors on the middle surface S are defined by (cf.

In 1859, on the occasion of being elected as a corresponding member of the Berlin Academy, Bernard

Riemann presented a lecture with the title On the Number of Primes Less Than a Given Magnitude, in which he presented a mathematics formula, derived from complex integration, which gave a precise count of the primes on the understanding that one of the terms in the formula, which depended on a knowledge of the non-trivial zeros of the zeta function, could be evaluated.

Among the topics are modular functions and Eisenstein series, the

Riemann zeta function, Euler's formulas and functional equations, functional equations, a linear space of solutions, and the multidimensional Poisson summation formula.

In 2013, Cheng [7] considered the

Riemann problem and two kinds of interactions of elementary waves for system (3) with the state equation for Chaplygin gas: