1. CMB 2007 (vol 50 pp. 547)
 Iakovlev, Serguei

Inverse Laplace Transforms Encountered in Hyperbolic Problems of NonStationary FluidStructure Interaction
The paper offers a study of the inverse Laplace
transforms of the functions $I_n(rs)\{sI_n^{'}(s)\}^{1}$ where
$I_n$ is the modified Bessel function of the first kind and $r$ is
a parameter. The present study is a continuation of the author's
previous work %[\textit{Canadian Mathematical Bulletin} 45]
on the
singular behavior of the special case of the functions in
question, $r$=1. The general case of $r \in [0,1]$ is addressed,
and it is shown that the inverse Laplace transforms for such $r$
exhibit significantly more complex behavior than their
predecessors, even though they still only have two different types
of points of discontinuity: singularities and finite
discontinuities. The functions studied originate from
nonstationary fluidstructure interaction, and as such are of
interest to researchers working in the area.
Categories:44A10, 44A20, 33C10, 40A30, 74F10, 76Q05 

2. CMB 2002 (vol 45 pp. 399)
 Iakovlev, Serguei

On the Singular Behavior of the Inverse Laplace Transforms of the Functions $\frac{I_n(s)}{s I_n^\prime(s)}$
Exact analytical expressions for the inverse Laplace transforms of
the functions $\frac{I_n(s)}{s I_n^\prime(s)}$ are obtained in the
form of trigonometric series. The convergence of the series is
analyzed theoretically, and it is proven that those diverge on an
infinite denumerable set of points. Therefore it is shown that the
inverse transforms have an infinite number of singular points. This
result, to the best of the author's knowledge, is new, as the
inverse transforms of $\frac{I_n(s)}{s I_n^\prime(s)}$ have
previously been considered to be piecewise smooth and continuous.
It is also found that the inverse transforms have an infinite
number of points of finite discontinuity with different left and
rightside limits. The points of singularity and points of finite
discontinuity alternate, and the sign of the infinity at the
singular points also alternates depending on the order $n$. The
behavior of the inverse transforms in the proximity of the singular
points and the points of finite discontinuity is addressed as well.
Categories:65R32, 44A10, 44A20, 74F10 
