A Reply to S. K. Goyal

Journal of the Operational Research Society -     

Equations of Pseudo-Spherical Type (After S.S. Chern and K. Tenenblat)

This paper surveys some recent developments around the notion of a scalar partial differential equation describing pseudo-spherical surfaces due to Chern and Tenenblat. It is shown how conservation laws, pseudo-potentials, and linear problems arise naturally from geometric considerations, and it is also explained how Darboux and B?cklund transformations can be constructed starting from geometric data. Classification results for equations in this class are stated, and hierarchies of equations of pseudo-spherical type are introduced, providing a connection between differential geometry and the study of hierarchies of equations which are the integrability condition of sl(2, R)-valued linear problems. Furthermore, the existence of correspondences between any two solutions to equations of pseudo-spherical type is reviewed, and a correspondence theorem for hierarchies is also mentioned. As applications, an elementary immersion result for pseudo-spherical metrics arising from the Chern?CTenenblat construction is proven, and non-local symmetries of the Kaup?CKupershmidt, Sawada?CKotera, fifth order Korteweg?Cde Vries and Camassa?CHolm (CH) equation with non-zero critical wave speed are considered. It is shown that the existence of a non-local symmetry of a particular type is enough to single the first three equations out from a whole family of equations describing pseudo-spherical surfaces while, in the CH case, it is shown that it admits an infinite-dimensional Lie algebra of non-local symmetries which includes the Virasoro algebra.     

Dedicated to S.K. Godunov on the Occasion of His 90th Birthday

Computational Mathematics and Mathematical Physics -     

Proper S(t,K,v)'s for t ≥ 3,v ≤ 16, |K| > 1 and Their Extensions

We characterize the proper t-wise balanced designs t-(v,K,1) for t ≥ 3, λ = 1 and v ≤ 16 with at least two block sizes. While we do not examine extensions of S(3,4,16)'s, we do determine all other possible extensions of S(3,K,v)'s for v ≤ 16. One very interesting extension is an S(4, {5,6}, 17) design.©1995 John Wiley & Sons, Inc.     

Konvergenzbetrachtungen bei quasikonformen Abbildungen im ℝ3 mittels Sätzen von K. Strebel

Ohne Zusammenfassung     

A note on “Some inequalities in inner product spaces related to the generalized triangle inequality” by S.S. Dragomir et al.

In this note, we present an affirmative answer to a question presented in the paper “Some inequalities in inner product spaces related to the generalized triangle inequality” by S.S. Dragomir et al. [Appl. Math. Comput. 217 (18) (2011) 7462-7468].     

Accelerated dynamical approaches for finding the unique positive solution of K S $\mathcal {K}\mathcal {S}$ -tensor equations

Numerical Algorithms - A new class of tensors called $\mathcal {K}\mathcal {S}$ -tensors, which is a subset of non-singular $\mathcal {P}$ -tensors and generalization of ${\mathscr{H}}^{+}$...     

S.K. Godunov and Kinetic Theory at the Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences

Computational Mathematics and Mathematical Physics - The history of the cooperation between the staff of the Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences and S.K....