On Contact-Transformations

On Certain Groups of Birational Contact Transformations*

Complex Contact and Lift Transformations

We study mappings from sets of real variables into complex variables, which extend features of lift and contact transformations between real variables that we explored in a previous paper. In particular the relationship between lifts in R and the CauchyRiemann equations for functions of n complex variables is discussed. Explicit examples are given to illustrate the anatomy of such transformatio...

On p-semilinear transformations

In this paper, we introduce $p$-semilinear transformations for linear algebras over a field ${bf F}$ of positive characteristic $p$, discuss initially the elementary properties of $p$-semilinear transformations, make use of it to give some characterizations of linear algebras over a field ${bf F}$ of positive characteristic $p$. Moreover, we find a one-to-one correspondence between $p$-semiline...

Comparison of Union-Preserving and Contact Transformations.

a given group then it is not possible for one of them to be contained in the other. If the operators which are commutative with one of the non-invariant operators of one of the groups under consideration do not always constitute an Abelian group then the prime number of the conjugates for each of its sets of conjugate operators of its non-invariant operators must be the same and hence these gro...

On descent for coalgebras and type transformations

We find a criterion for a morphism of coalgebras over a Barr-exact category to be effective descent and determine (effective) descent morphisms for coalgebras over toposes in some cases. Also, we study some exactness properties of endofunctors of arbitrary categories in connection with natural transformations between them as well as those of functors that these transformations induce between co...