One purpose of this paper is to define the twisted q-Bernoulli numbers by using p-adic invariant integrals on Zp. Finally, we construct the twisted q-zeta function and q-L-series which interpolate the twisted q-Bernoulli numbers.

In this paper, we considered a batch arrival feedback retrial queue with two phase of service under Bernoulli vacation schedule and orbit search. At the arrival epoch of a batch, if the server is busy, under repair or on vacation then the whole batch joins the orbit. Where as if the server is free, then one of the arriving customers starts his service immediately and the rest join the orbit. At...

pollution has become a very serious threat to our environment. monitoring pollution is the rst step toward planning to save the environment. the use of dierential equations, monitoring pollution has become possible. in this paper, a ritz-collocation method is introduced to solve non-linear oscillatory systems such as modelling the pollution of a system of lakes. the method is based upon bernoul...

The principal aim of this paper is to serve the numerical solution of an integral-algebraic equation (IAE) by using the Bernoulli polynomials and the residual correction method. After implementation of our scheme, the main problem would be transformed into a system of algebraic equations such that its solutions are the unknown Bernoulli coefficients. This method gives an analytic solution when ...

In this paper, we study the Fourier series related to higher-order Bernoulli functions and give new identities for higher-order Bernoulli functions which are derived from the Fourier series of them.

We show that Bernoulli Conjecture holds for sets with small one-dimensional projections, i.e. any bounded Bernoulli process indexed by such set may be represented as a sum of uniformy bounded process and a process dominated by bounded Gaussian process.

This paper presents two new fault models for networked systems. These are more realistic and generalized systems in the sense that they can represent effects of at node network levels. At layer, uncertain lines modeled using a Markov chain with complex transition probabilities simultaneously stochastic behavior Bernoulli process. A output feedback-based controller, which is two-mode dependent c...