Mathematics |
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2004, No. 4
G.P. Yarovoy, Y.N. Radayev
ON A NEW TRANSLATION OF WHITEHEAD AND RUSSELL'S "PRINCIPIA MATHEMATICA"
O.F. Menshikh
Point transformation groups technique is applied to the second-order quasilinear partial differential equations with their all functionally invariant smooth solutions. Infinitesimal operators of these equations are always depend on arbitrary functions. A criterion for separating the equations with the above characteristics are found. The two classes of such equations with two and three independent variables are obtained. Transformation groups are calculated for a number of particular equations, two of them being of special intrest: the equation obtained by G.Monge describing a class of ruled surfaces, and the implicit form of the Born-Infeld equation wich is well-known in physics.
G.V. Voskresenskaya
MODULAR FORMS AND GROUPS OF ORDER 2n
In the paper groups of order 16 and 32 are studied. It is shown that their cusp forms associated with all elements of these groups by a faithful representation are modular forms from the special class with multiplicative Fourier coefficients.