The main results are listed as following:If G is a (3,4)—regular maximal planar graph on n vertices, then n = 5.If G is a (3,5)-regular maximal planar graph on n vertices, then n = 8.If G is a (3,6)-regular maximal planar graph on n vertices, then n > 5, and also n ≡ 0(mod2).
If R is a zero commutative ring, the authors obtain that (1) R is strongly regular if and only if every essential left ideal of R which is an annihilator is left GP-injective or R contains a maximal left ideal K such that the annihilator of every element of K is left GP-injective;
Based on the investigation and study of the maximum assembly at regular railway stations, a new method, the probability method, is proposed to calculate the maximum assembling at passenger-railway-line station.
Finally we show for more than half of the infinite series that a presentation for the fundamental group of the space of regular orbits ofW can be derived from our presentations.
Let ζ-1/2 be the inverse on the set of regular elements ofu of a square root of the discriminant of.
We obtain a criterion for rational smoothness of an algebraic variety with a torus action, with applications to orbit closures in flag varieties, and to closures of double classes in regular group completions.
A theorem of Richardson states that the algebra of regular functions ofG is a free module over the subalgebra of regular class functions.
The F-valued points of the algebra ofstrongly regular functions of a Kac-Moody group