Stochastic (Markovian) process algebra extend classical process algebra with probabilistic exponentially distributed time durations denoted by rates (the parameter of the exponential distribution). Defining a semantics for such an algebra, so to derive Continuous Time Markov Chains from system specifications, requires dealing with transitions labeled by rates. With respect to standard process a...

In the analysis of queueing network models, the response time plays an important role in studying the various characteristics. In this paper data based recurrence relation is used to compute a sequence of response time. The sample means from those response times, denoted by r̂1 and r̂2 are used to estimate true mean response time r1 and r2. Further we construct some confidence intervals for mean ...

In this paper, we are primarily concerned with the oscillation of solutions to higher-order dynamic equations. We first extend some recent results which have been obtained for second-order dynamic equations to even-order neutral delay dynamic equations. Our technique depends on making use of the Riccati substitution and the use of properties of the generalized Taylor monomials on time scales. W...

On the occasion of Laurens de Haan’s 70th birthday, we discuss two aspects of the statistical inference on the extreme value behavior of time series with a particular emphasis on his important contributions. First, the performance of a direct marginal tail analysis is compared with that of a model-based approach using an analysis of residuals. Second, the importance of the extremal index as a m...

Let Hn be the number of claw-free cubic graphs on 2n labeled nodes. Combinatorial reductions are used to derive a second order, linear homogeneous differential equation with polynomial coefficients whose power series solution is the exponential generating function for {Hn}. This leads to a recurrence relation for Hn which shows {Hn} to be P -recursive and which enables the sequence to be comput...

The paper proposes a new stability test for two-dimensional (2D) discrete systems. It is a tabular test; that is, it builds for the tested bivariate polynomial of degree (n1, n2) a sequence of n2 (or n1) bivariate polynomials or matrices (the “2D table”) of increasing row and decreasing column sizes. It is an immittance-type test, which means that it uses a three-term recurrence relation to obt...

Products of the Laplace transforms of exponential distributions with different parameters are inverted to give a mixture of Erlang densities, i.e. an expression for the convolution of exponentials. The formula for these inversions is expressed both as an explicit sum and in terms of a recurrence relation which is better suited to numerical computation. The recurrence for the inversion of certai...

In this paper, we arithmetically describe the convex hull of a digital straight segment by three recurrence relations. This characterization gives new insights into the combinatorial structure of digital straight segments of arbitrary length and intercept. It also leads to two on-line algorithms that computes a part of the convex hull of a given digital straight segment. They both run in consta...

with A. being a given m × m-matrix function, has been an intensively discussed field in both theory and practice. This problem can be seen in many real problems, such as in electric circuits, chemical reactions, and vehicle systems. März in 1 has dealt with the question whether the zero-solution of 1.1 is asymptotically stable in the Lyapunov sense with f t, x′ t , x t Bx t g t, x′ t , x t , wi...

insufficient sleep may lead to adverse cardio-metabolic effects by influencing body weight, blood pressure, and glucose tolerance. we aimed to assess the relation between sleep duration and indices of obesity including body mass index (bmi) and waist circumference in a sample population in central iran. we selected a sub-sample of 1770 individuals from isfahan healthy heart program. the data re...