Abstract: The paper deals with the classical fiber bundle model
of equal load sharing, sometimes referred to as the Daniels’ bundle
or the democratic bundle. Daniels formulated a multidimensional
integral and also a recursive formula for evaluation of the
strength cumulative distribution function. This paper describes
three algorithms for evaluation of the recursive formula and also
their implementations with source codes in the Python high-level
programming language. A comparison of the algorithms are provided
with respect to execution time. Analysis of orders of magnitudes of
addends in the recursion is also provided.
Abstract: In this study integral form and new recursive formulas
for Favard constants and some connected with them numeric and
Fourier series are obtained. The method is based on preliminary
integration of Fourier series which allows for establishing finite
recursive representations for the summation. It is shown that the
derived recursive representations are numerically more effective than
known representations of the considered objects.
Abstract: Three novel and significant contributions are made in
this paper Firstly, non-recursive formulation of Haar connection
coefficients, pioneered by the present authors is presented, which
can be computed very efficiently and avoid stack and memory
overflows. Secondly, the generalized approach for state analysis of
singular bilinear time-invariant (TI) and time-varying (TV) systems
is presented; vis-˜a-vis diversified and complex works reported by
different authors. Thirdly, a generalized approach for parameter
estimation of bilinear TI and TV systems is also proposed. The unified
framework of the proposed method is very significant in that the
digital hardware once-designed can be used to perform the complex
tasks of state analysis and parameter estimation of different types
of bilinear systems single-handedly. The simplicity, effectiveness and
generalized nature of the proposed method is established by applying
it to different types of bilinear systems for the two tasks.
Abstract: In this paper, we extend the compound binomial model to the case where the premium income process, based on a binomial process, is no longer a linear function. First, a mathematically recursive formula is derived for non ruin probability, and then, we examine the expected discounted penalty function, satisfy a defect renewal equation. Third, the asymptotic estimate for the expected discounted penalty function is then given. Finally, we give two examples of ruin quantities to illustrate applications of the recursive formula and the asymptotic estimate for penalty function.
Abstract: An iterative definition of any n variable mean function is given in this article, which iteratively uses the two-variable form of the corresponding two-variable mean function. This extension method omits recursivity which is an important improvement compared with certain recursive formulas given before by Ando-Li-Mathias, Petz- Temesi. Furthermore it is conjectured here that this iterative algorithm coincides with the solution of the Riemann centroid minimization problem. Certain simulations are given here to compare the convergence rate of the different algorithms given in the literature. These algorithms will be the gradient and the Newton mehod for the Riemann centroid computation.