Armen Bagdasaryan

New Symmetric Identities Involving q-Zeta Type Functions

The main object of this paper is to obtain several symmetric properties of the q-zeta type functions. As applications of these properties, we give some new interesting identities for the modified q-Genocchi polynomials. Finally, our applications are shown to lead to a number of interesting results which we state in the present paper.

Discrete dynamic simulation models and technique for complex control systems

Abstract The method for dynamic model synthesis and discrete simulation of complex hierarchical control systems is presented. The method provides integration of large data sets, monitoring data and expert knowledge with the process of simulation and analysis of system state dynamics, thus providing an extensible and evolvable environment and reuse of knowledge and simulation models. The method is based on the hierarchical state diagrams technique and control scenarios methodology. The general structure of corresponding computer simulation system is also proposed. We also outline general principles of computer realization of our simulation approach, and schemes of model-based knowledge representation. The proposed method is based on the object-oriented paradigm and is especially powerful in information-intensive environments.

The Legendre Polynomials Associated with Bernoulli, Euler, Hermite and Bernstein Polynomials

In the present paper, we deal mainly with arithmetic properties of Legendre polynomials by using their orthogonality property. We show that Legendre polynomials are proportional with Bernoulli, Euler, Hermite and Bernstein polynomials.

Elementary Evaluation of the Zeta and Related Functions: An Approach From a New Perspective

The zeta and related functions are explicitly known at either even values as for the ζ(s), λ(s) and η(s) functions or at odd function values as for the Dirichlet β(s) function. In this paper, the values at integers are obtained for the zeta and related functions by applying new analytical tool that naturally arises within a new theoretical setting. This allows a simple and elementary derivation of the function values at integer points from quite a different point of view. It is based on the hypothesis that negative numbers might be beyond infinity, advanced by Wallis and Euler. I will first define the basic concepts of our theory: (1) a new ordering relation on the set of integer numbers; (2) a new class of real functions, called regular, and the definition of sum that extends the classical definition to the case when the upper limit of summation is less than the lower; (3) a set of conditions imposed on regular functions that defines a new regular method for summation of infinite series.

Computing the maximum violation of a Bell inequality is an NP-problem

The number of steps required in order to maximize a Bell inequality for arbitrary number of qubits is shown to grow exponentially with the number of parties involved. The proof that the optimization of such correlation measure is an NP-problem based on an operational perspective involving a Turing machine, which follows a general algorithm. The implications for the computability of the so-called nonlocality for any number of qubits is similar to recent results involving entanglement or similar quantum correlation-based measures.

Dynamic Simulation and Synthesis Technique for Complex Control Systems

A method for dynamic model synthesis and simulation of complex hierarchical control systems is developed. The method provides integration of large data sets, monitoring data and expert knowledge with the process of simulation, analysis and prediction of system state dynamics, based on the control scenarios methodology. The proposed technique is based on object-oriented approach and is powerful for information rich environments.

Mathematical Model and Analysis of Reliability and Safety of Large Database Systems

In this paper we consider and analyze the problems of reliability and safety of database systems operation. One of the methods of improving the reliability and quality of functioning of database systems is the registration of information about events and processes occuring in the system. In this direction, we introduce some new concepts related to the problem, and then develop and analyze a corresponding graph-theoretical mathematical model. In conclusion, several future directions of research are also briefly outlined.

A Model of Hierarchically Consistent Control of Nonlinear Dynamical Systems

Most of the real modern systems are complex, nonlinear, and large-scale. A natural approach for reducing the complexity of large scale systems places a hierarchical structure on the system architecture. In hierarchical control models, the notion of consistency is much important, as it ensures the implementation of high-level objectives by the lower level systems. In this work, we present a model for synthesis of hierarchically consistent control systems for complex nonlinear multidimensional and multicoupled dynamical systems, using invariant manifold theory.