On a linear homogeneous congruence

On Local Congruence of Immersions in Homogeneous or Nonhomogeneous Spaces

We show how to find a complete set of necessary and sufficient conditions that solve the fixed-parameter local congruence problem of immersions in G-spaces, whether homogeneous or not, provided that a certain k order jet bundle over the G-space admits a G-invariant local coframe field of constant structure. As a corollary, we note that the differential order of a minimal complete set of congrue...

on the effect of linear & non-linear texts on students comprehension and recalling

چکیده ندارد.

Quadratic and Linear Congruence*

The number of simultaneous solutions of a quadratic and a linear congruence does not seem to be discussed in the literature, yet a knowledge of the invariants necessary to specify this number should lead to an arithmetical classification of the form-pairs involved. This preliminary investigation is confined to congruences with modulus odd and prime to the g.c.d.'s of the two sets of coefficient...

Enumeration Problems for a Linear Congruence Equation

Let m ≥ 2 and r ≥ 1 be integers and let c ∈ Zm = {0, 1, . . . , m− 1}. In this paper, we give an upper bound and a lower bound for the number of unordered solutions x1, . . . , xn ∈ Zm of the congruence x1 + x2 + · · · + xr ≡ c mod m. Exact formulae are also given when m or r is prime. This solution number involves the Catalan number or generalized Catalan number in some special cases. Moreover...

On Mapping Homogeneous Graphs on a Linear Array-Processor Model