On One Number-theoretic Conception: towards a New Theory Rom Varshamov and Armen Bagdasaryan
نویسنده
چکیده
In this paper we present a new mathematical conception based on a new method for ordering the integers. The method relies on the assumption that negative numbers are beyond infinity, which goes back to Wallis and Euler. We also present a new axiom system, the model of which is arithmetics. We define regular method for summation of infinite series which allows us to discover general and unified approach to summation of divergent series, and determine the limits of unbounded and oscillating functions. Several properties for divergent series and explicit formulas for sums of some infinite series are established. A number of finite and new recurrence formulas for Bernoulli numbers are obtained. We rederive some known results, but in a simpler and elementary way, and establish new results by means of techniques of the theoretical background developed. Date: September 9, 2009. 2000 Mathematics Subject Classification. Primary 26A03, 40C15; Secondary 26A09, 11B68, 03H05, 00A05.
منابع مشابه
A New Lower Bound for Mathieu’s Series
In this paper, we establish a new lower bound for Mathieu’s series and present a simple and short proof of the Mathieu’s inequality. We also give a simple derivation of the integral form of the series.
متن کاملSystem Theoretic Viewpoint on Modeling of Complex Systems: Design, Synthesis, Simulation, and Control
We consider the basic features of complex dynamic and control systems, including systems having hierarchical structure. Special attention is paid to the problems of design and synthesis of complex systems and control models, and to the development of simulation techniques and systems. A model of complex system is proposed and briefly analyzed. Key–Words: Systems, Complexity, Control, Modeling, ...
متن کاملGraph Theoretic Methods in Coding Theory
This paper is a tutorial on the application of graph theoretic techniques in classical coding theory. A fundamental problem in coding theory is to determine the maximum size of a code satisfying a given minimum Hamming distance. This problem is thought to be extremely hard and still not completely solved. In addition to a number of closed form expressions for special cases and some numerical re...
متن کاملMathematical Tool of Discrete Dynamic Modeling of Complex Systems in Control Loop
In this paper we present a method of discrete modeling and analysis of multi-level dynamics of complex largescale hierarchical dynamic systems subject to external dynamic control mechanism. In a model each state describes parallel dynamics and simultaneous trends of changes in system parameters. The essence of the approach is in analysis of system state dynamics while it is in the control loop.
متن کامل