Abstract Recently, B. A. Kupershmidt have constructed a reflection symmetries of q-Bernoulli polynomials (see [9]). In this paper we give another construction of a q-Bernoulli polynomials, which form Barnes’ multiple Bernoulli polynomials at q = 1, cf. [1, 13, 14]. By using q-Volkenborn integration, we can also investigate the properties of the reflection symmetries of these’ q-Bernoulli polyno...

The open loop system of an Euler–Bernoulli plate with variable coefficients and partial boundary Neumann control and collocated observation is considered. Using the geometric multiplier method on Riemannian manifolds, we show that the system is well-posed in the sense of D. Salamon and regular in the sense of G. Weiss. Moreover, we determine that the feedthrough operator of this system is zero....

Two types of open-loop systems of an Euler–Bernoulli equation with variable coefficient and Dirichlet boundary control and collocated observation are considered. The uncontrolled boundary is either hinged or clamped. It is shown, with the help of multiplier method on Riemannian manifold, that in both cases, systems are well-posed in the sense of D. Salamon and regular in the sense of G. Weiss. ...

In this paper, an Euler-Bernoulli beam system under the local internal distributed control and a boundary point observation is studied. We design an infinite-dimensional observer for the open-loop system. The closed loop-system that is non-dissipative is obtained by estimated state feedback. By a detailed spectral analysis, it is shown that there is a set of generalized eigenfunctions, which fo...

The main goal of the present paper is to construct some families of the Carlitz's $q$-Bernoulli polynomials and numbers. We firstly introduce the modified Carlitz's $q$-Bernoulli polynomials and numbers with weight ($_{p}$. We then define the modified degenerate Carlitz's $q$-Bernoulli polynomials and numbers with weight ($alpha ,beta $) and obtain some recurrence relations and other identities...

Analytical approximations are developed to determine staffing levels that stabilize performance at designated targets in a many-server queueing model with time-varying arrival rates, customer feedback and abandonment. To provide a flexible model that can be readily fit to system data, Markovian routing is not assumed. Instead, the model has Bernoulli routing, with at most finitely many feedback...

Ahsrruct-It is shown that, for a ternary feedback random access channel with a Poisson arrival process, 0.5 is an upper bound to the throughput for all “degenerate intersection” algorithms (DIA’s) and firstcome first-served algorithms (FCFSA’S). As a by-product, the nested FCFSA with the largest throughput is found for the random access channel with a Bernoulli arrival process &ith parameter p....

We consider the stabilization problem for large-scale linear descriptor systems in continuousand discrete-time. We suggest a partial stabilization algorithm which preserves stable poles of the system while the unstable ones are moved to the left half plane using state feedback. Our algorithm involves the matrix pencil disk function method to separate the finite from the infinite generalized eig...

The present investigation deals with performance analysis of single server preemptive priority retrial queue with immediate Bernoulli feedback. There are two types of customers are considered, which are priority customers and ordinary customers. The priority customers do not form any queue and have an exclusive preemptive priority to receive their services over ordinary customers. After complet...

We consider customer joining behaviour for a system that consists of a FCFS queue with Bernoulli feedback. A consequence of the feedback characteristic is that the sojourn time of a customer already in the system depends on the joining decisions taken by future arrivals to the system. By establishing stochastic order results for coupled versions of the system, we prove the existence, and unique...