The arbelos is the shape bounded by three mutually tangent semicircles with collinear diameters. Recently, Sondow introduced the parabolic analog, the parbelos and proved several properties of the parbelos similar to properties of the arbelos. In this paper we give one step further and generalize the situation considering the figure bounded by (quite) arbitrary similar curves, the f -belos. We ...

In many industrial applications one wants to determine the temperature on the surface of a body, where the surface itself is inaccessible to measurement [2, 4]. In this case it is necessary to determine surface temperature from a measured temperature history at a fixed location inside the body. This problem is called an inverse heat conduction problem (IHCP). In a one-dimensional setting, assum...

We introduce a generalized version of a q-Schur algebra (of parabolic type) for arbitrary Hecke algebras over extended Weyl groups. We describe how the decomposition matrix of a finite group with split BN -pair, with respect to a non-describing prime, can be partially described by the decomposition matrices of suitably chosen q-Schur algebras. We show that the investigated structures occur natu...

In this paper we study the equation ut = ∆[φ(u(x, [t/τ ]τ))u(x, t)] , x ∈ Ω , t > 0, with homogeneous Neumann boundary conditions in a bounded domain in R. We show existence and uniqueness for the initial value problem, and prove some results that show the aggregating behaviour exhibited by the solutions.

Complete complex parabolic geometries (including projective connections and conformal connections) are flat and homogeneous.

We use the general theory developed in our article [1] in the setting of parabolic geometries to reprove known results on special infinitesimal automorphisms of projective and conformal geometries.

0.1. Let G be a connected reductive algebraic group over an algebraically closed field k. Let Z be the variety (of the same dimension as G) consisting of all pairs (P, gUP ) where P runs through a fixed conjugacy class P of parabolics of G and gUP ∈ G/UP (UP is the unipotent radical of P ). Now G acts on Z by h : (P, gUP ) 7→ (hPh , hghUhPh−1). In this paper we study a class of simple G-equivar...

In non-relativistic Brueckner calculations of nuclear matter, the self-consistent single particle potential is strongly momentum dependent. To simplify the calculations, a parabolic approximation is often used in the literature. The variation in the binding energy value introduced by the parabolic approximation is quantitatively analyzed in detail. It is found that the approximation can introdu...

Hecke algebras are beautiful q-extensions of Coxeter groups. In this paper, we prove several results on their characters, with an emphasis on characters induced from trivial and sign representations of parabolic subalgebras. While most of the results in type A are known, our proofs are of a combinatorial nature, and generalize to (partial) results in types B and C. We also present complete desc...