'Ht moi, ..., si j'avait su comment en revenir, One lemce mathematics has rendered the je n'y serai. point aile.' human race. It has put common sense back Jule. Verne ..... "'" it belong., on the topmost shelf next to the dusty caniller labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a...

1. Preliminaries, Notation, and Terminology n n 1.1. Sets and functions in lR. Throughout the book, lR. stands for the n-dimensional arithmetic space of points x = (X}, X2, '," xn)j Ixl is the length of n n a vector x E lR. and (x, y) is the scalar product of vectors x and y in lR., i.e., for x = (Xl, X2, ., xn) and y = (y}, Y2, ..., Yn), Ixl = Jx + x + ... + x, (x, y) = XIYl + X2Y2 + ... + XnYn. n Given arbitrary points a and b in lR., we denote by a, b] the segment that joins n them, i.e. the collection of points x E lR. of the form x = >.a + I'b, where>. + I' = 1 and >. 0, I' O. n We...

The book contains a survey of research on non-regular Riemannian geome try, carried out mainly by Soviet authors. The beginning of this direction oc curred in the works of A. D. Aleksandrov on the intrinsic geometry of convex surfaces. For an arbitrary surface F, as is known, all those concepts that can be defined and facts that can be established by measuring the lengths of curves on the surface relate to intrinsic geometry. In the case considered in differential is defined by specifying its first geometry the intrinsic geometry of a surface fundamental form. If the surface F is non-regular,...

1. Preliminaries, Notation, and Terminology n n 1.1. Sets and functions in lR. * Throughout the book, lR. stands for the n-dimensional arithmetic space of points x = (X},X2,'" ,xn)j Ixl is the length of n n a vector x E lR. and (x, y) is the scalar product of vectors x and y in lR. , i.e., for x = (Xl, X2, *.* , xn) and y = (y}, Y2,**., Yn), Ixl = Jx~ + x~ + ...+ x~, (x, y) = XIYl + X2Y2 + ...+ XnYn. n Given arbitrary points a and b in lR. , we denote by [a, b] the segment that joins n them, i.e. the collection of points x E lR. of the form x = >.a + I'b, where>. + I' = 1 and >. ~ 0, I' ~ O....

'Ht moi, ..., si j'avait su comment en revenir, One lemce mathematics has rendered the je n'y serai. point aile.' human race. It has put common sense back Jule. Verne ..."'" it belong., on the topmost shelf next to the dusty caniller labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a...

One service mathematics has rendered the "Et moi, ...si j'a'ait su comment en revenir, human race. It has put common sense back je n'y scrais point alit: Jules Verne where it belongs, on the topmost shelf next to the dusty canister labcled 'discarded non- The series is divergent; therefore we may be sense'. Eric T. 8cl able to do something with it. O. Hcaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a...