A well-known and widely used approach in the study of algebraic objects is the investigation of their sub-objects and quotient objects. Consider the set of Boolean functions on F2 of degree less than or equal to r for 0 ≤ r ≤ n, which can also be seen as the Reed-Muller code RM(r, n) of order r. The automorphism group of RM(r, n) is equal to the general affine group AGL(n, 2) for all 1 ≤ r ≤ n ...

To understand the larger context, first note that Casselman’s subrepresentation theorem asserts that any irreducible representation [1] π of G is a subrepresentation of some one of the principal series representations Is defined below. [2] Further, the quotient Is/π (or a further quotient that is irreducible) again imbeds in some Is′ with another parameter value s′. Thus, any irreducible π appe...

Let R be a Krull ring with quotient field K and a1, . . . , an in R. If and only if the ai are pairwise incongruent mod every height 1 prime ideal of infinite index in R does there exist for all values b1, . . . , bn in R an interpolating integer-valued polynomial, i.e., an f ∈ K[x] with f(ai) = bi and f(R) ⊆ R. If S is an infinite subring of a discrete valuation ring Rv with quotient field K a...

Let R be an associative ring in which an identity element is not assumed. A right quotient ring of P is an overring 5 such that for each aQS there corresponds rQR such that arQR and ar 9*0. A theorem of R. E. Johnson [l ] states that R possesses a right quotient ring S which is a (von Neumann) regular ring if and only if P has vanishing right singular ideal. In this case P possesses a unique (u...

Let G be a co-compact Fuchsian group. As such, it acts discontinuously on the hyperbolic plane H and the quotient is a closed hyperbolic 2-orbifold. The structure theory for co-compact Fuchsian groups yields a canonical presentation for such groups. This information is described by the signature s s g ; m , . . . , m 1 Ž . Ž . 1 r where g is the genus of the base surface of the quotient 2-orbif...

Recent results in geometric invariant theory (GIT) for non-reductive linear algebraic group actions allow us to stratify quotient stacks of the form [X/H ], where X is a projective scheme and H is a linear algebraic group with internally graded unipotent radical acting linearly onX , in such a way that each stratum [S/H ] has a geometric quotient S/H . This leads to stratifications of moduli st...

in this paper, the rayleigh's quotient and the inverse vector iteration method are presented. the latter approach helps to obtain the natural frequencies and mode shapes of a structure. inverse vector iteration method with shifting enables to determine the higher modes. some basic theorems of linear algebra are presented and extended to study the free vibration of structures. the variation...

The space of inequivalent representations of a compact surface S with χ(S) < 0 as a quotient of a convex domain in RP by a properly discontinuous group of projective transformations is a cell of dimension