Abstract: The generalization of relativistic theory of gravity based essentially on the principle of equivalence stipulates that for all bodies, the grave mass is equal to the inert mass which leads us to believe that gravitation is not a property of the bodies themselves, but of space, and the conclusion that the gravitational field must curved space-time what allows the abandonment of Minkowski space (because Minkowski space-time being nonetheless null curvature) to adopt Riemannian geometry as a mathematical framework in order to determine the curvature. Therefore the work presented in this paper begins with the evolution of the concept of gravity then tensor field which manifests by Riemannian geometry to formulate the general equation of the gravitational field.
Abstract: Analytical techniques for measuring and planning
railway capacity expansion activities have been considered in this
article. A preliminary mathematical framework involving track
duplication and section sub divisions is proposed for this task. In
railways, these features have a great effect on network performance
and for this reason they have been considered. Additional motivations
have also arisen from the limitations of prior models that have not
included them.
Abstract: Super steel materials play a vital role in the
construction and fabrication of structural, piping and pipeline
components. In assuring the integrity of onshore and offshore
operating systems, they enable life cycle costs to be minimized. In
this context, Duplex stainless steel (DSS) material related welding on
constructions and fabrications plays a significant role in maintaining
and assuring integrity at an optimal expenditure over the life cycle of
production and process systems as well as associated structures. In
DSS welding, factors such as gap geometry, shielding gas supply
rate, welding current, and type of the welding process are vital to the
final joint performance. Hence, an experimental investigation has
been performed using an engineering robust design approach
(ERDA) to investigate the optimal settings that generate optimal
super DSS (i.e. UNS S32750) joint performance. This manuscript
illustrates the mathematical approach and experimental design,
optimal parameter settings and results of the verification experiment.
Abstract: In communication networks where communication nodes are connected with finite capacity transmission links, the packet inter-arrival times are strongly correlated with the packet length and the link capacity (or the packet service time). Such correlation affects the system performance significantly, but little attention has been paid to this issue. In this paper, we propose a mathematical framework to study the impact of the correlation between the packet service times and the packet inter-arrival times on system performance. With our mathematical model, we analyze the system performance, e.g., the unfinished work of the system, and show that the correlation affects the system performance significantly. Some numerical examples are also provided.
Abstract: The mathematical framework for studying of a fuzzy approximate reasoning is presented in this paper. Two important defuzzification methods (Area defuzzification and Height defuzzification) besides the center of gravity method which is the best well known defuzzification method are described. The continuity of the defuzzification methods and its application to a fuzzy feedback control are discussed.
Abstract: Cryptographic protocols are widely used in various
applications to provide secure communications. They are usually
represented as communicating agents that send and receive messages.
These agents use their knowledge to exchange information and
communicate with other agents involved in the protocol. An agent
knowledge can be partitioned into explicit knowledge and procedural
knowledge. The explicit knowledge refers to the set of information
which is either proper to the agent or directly obtained from other
agents through communication. The procedural knowledge relates to
the set of mechanisms used to get new information from what is
already available to the agent.
In this paper, we propose a mathematical framework which specifies
the explicit knowledge of an agent involved in a cryptographic
protocol. Modelling this knowledge is crucial for the specification,
analysis, and implementation of cryptographic protocols. We also,
report on a prototype tool that allows the representation and the
manipulation of the explicit knowledge.