3D vector tomography has been explored and results have been achieved in the last few decades. Among these was a reconstruction formula for the solenoidal part of a vector field from its Doppler transform with sources on a curve. The Doppler transform of a vector field is the line integral...
This paper is a classification of 181 problems, each of which involves the evaluation or application of determinants. The problems are those which have appeared in the "Problems and Solutions" sections of the American Mathematical Monthly, Deutsche Mathematiker-Vereinigung Jahresbricht, Mathematics Magazine, and School Science and Mathematics. The problems are classified,...
Let H be a cyclically-presented group on n generators with a single defining relator. Attempts have been made to classify such groups by their order, their status as a 3-manifold group, and the asphericity status of their presentations. For groups with a defining relator of length 3 these classifications are...
In this paper we investigate the Lyapunov mapping
P --> AP + PA *
where A is a positive stable matrix and P is a hermitian
matrix. In particular, for special positive stable A we
characterize the image of the cone of positive definite matrices
under this mapping. In Section...
It is well- known that a real number can be defined as an equivalence
class of fundamental rational sequences. In fact, it is also possible
to define a real number as an equivalence class of sequences of
nested closed rational intervals. This paper is devoted to the latter
case.
A set of axioms of incidence and order for geometry was formulated
by David Hilbert in 1898. In this paper these axioms are reformulated
and particular care is taken with the two relations of order
and incidence. Such phrases as " point P lies on line [cursive small letter L]"...
Given two rational maps φ and ψ on Ρ¹ of degree at least two, we study a symmetric, nonnegative real-valued pairing〈φ, ψ〉which is closely related to the canonical height functions hφ and hψ associated to these maps. Our main results show a strong connection between the value of〈φ, ψ〉and the...