A finite group G is said to be simply reducible (SR-group) if it has the following two properties: 1) each element of G is conjugate to its inverse; 2) the tensor product of every two irreducible representations is decomposed as a sum of irreducible representations of G with multiplicities not exceeding 1. It is proved that a finite SR-group is solvable if it has no composition factors isomorph...

We prove that if a mapping F : X → → Y , where X and Y are Banach spaces, is metrically regular at x̄ for ȳ and its inverse F−1 is convex and closed valued locally around (x̄, ȳ), then for any function G : X → Y with lipG(x̄) · regF (x̄ | ȳ)) < 1, the mapping (F + G)−1 has a continuous local selection x(·) around (x̄, ȳ + G(x̄)) which is also calm.

Let G be a simple complex algebraic group. Lusztig and Vogan have conjectured the existence of a natural bijection between the set of dominant integral weights of G, and the set of pairs consisting of a nilpotent orbit and a finite-dimensional irreducible representation of the isotropy group of the orbit. This conjecture has been proved by Bezrukavnikov. In this paper, we develop combinatorial ...

of a known kernel k(ω, λ). The problem is difficult in part because the integral operator K : Γ 7→ G is smoothing, making the “inverse problem” K−1 : G 7→ Γ ill-posed in the sense that small changes in G may be associated with large changes in Γ. The most common approaches to solving Equation (1) for the unknown Γ begin by approximating this infinite-dimensional continuous problem with the fini...

We reduce the regular version of the Inverse Galois Problem for any finite group G to finding one rational point on an infinite sequence of algebraic varieties. As a consequence, any finite group G is the Galois group of an extension L/P (x) with L regular over any PAC field P of characteristic zero. A special case of this implies that G is a Galois group over Fp(x) for almost all primes p.

Throughout this paper, G will denote a nondegenerate continuous collection of atriodic continuous curves (i.e. arcs or simple closed curves) filling up a compact metric continuum M. As is well known, we may regard G itself as a compact metric continuum, with the elements of the collection G as the points of the space G and with G, as a space, the image of M under an open continuous mapping whos...

Given a group G and a subgroup H, under what circumstances can we find a homomorphism φ : G −→ G', such that H is the kernel of φ? Clearly a necessary condition is that H is normal in G. Somewhat surprisingly this trivially necessary condition is also in fact sufficient. The idea is as follows. Given G and H there is an obvious map of sets, where H is the inverse image of a point. We just put X...

It is well known that the degree-raised Bernstein-B ezier coeecients of degree n of a polynomial g converge to g at the rate 1=n. In this paper we consider the polynomial An(g) of degree n interpolating the coeecients. We show how An can be viewed as an inverse to the Bernstein polynomial operator and that the derivatives An(g) (r) converge uniformly to g (r) at the rate 1=n for all r. We also ...

the major lipoprotein classes are heterogenous. human serum high-density-lipoproteins (hdl) are separated into two major subfractions (hdl2, d=1.063-1.125 g/ml, hdl3, d=1.125-1.210 g/ml) by a simple double precipitation method. there was a strong inverse relation between hdl-cholesterol (hdl-c) and subfractions hdl2-c and hdl3-c with atherosclerosis. this study demonstrated that hdl-c (p<0.001)...

It is well known that the degree-raised Bernstein-Bézier coefficients of degree n of a polynomial g converge to g at the rate 1/n. In this paper we consider the polynomial An(g) of degree ≤ n interpolating the coefficients. We show how An can be viewed as an inverse to the Bernstein operator and that the derivatives An(g) (r) converge uniformly to g at the rate 1/n for all r. We also give an as...