Operator (computer programming)

About: Operator (computer programming) is a research topic. Over the lifetime, 40896 publications have been published within this topic receiving 671452 citations. The topic is also known as: operator symbol & operator name.

Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties

Abstract: We presented an analysis of evolutions equations generated by three fractional derivatives namely the Riemann–Liouville, Caputo–Fabrizio and the Atangana–Baleanu fractional derivatives. For each evolution equation, we presented the exact solution for time variable and studied the semigroup principle. The Riemann–Liouville fractional operator verifies the semigroup principle but the associate evolution equation does not. The Caputo–Fabrizio fractional derivative does not satisfy the semigroup principle but surprisingly, the exact solution satisfies very well all the principle of semigroup. However, the Atangana–Baleanu for small time is the stretched exponential derivative, which does not satisfy the semigroup as operators. For a large time the Atangana–Baleanu derivative is the same with Riemann–Liouville fractional derivative, thus satisfies semigroup principle as an operator. The solution of the associated evolution equation does not satisfy the semigroup principle as Riemann–Liouville. With the connection between semigroup theory and the Markovian processes, we found out that the Atangana–Baleanu fractional derivative has at the same time Markovian and non-Markovian processes. We concluded that, the fractional differential operator does not need to satisfy the semigroup properties as they portray the memory effects, which are not always Markovian. We presented the exact solutions of some evolutions equation using the Laplace transform. In addition to this, we presented the numerical solution of a nonlinear equation and show that, the model with the Atangana–Baleanu fractional derivative has random walk for small time. We also observed that, the Mittag-Leffler function is a good filter than the exponential and power law functions, which makes the Atangana–Baleanu fractional derivatives powerful mathematical tools to model complex real world problems.

Regular linear systems with feedback

Abstract: We consider a rather general class of infinite-dimensional linear systems, called regular linear systems, for which convenient representations are known to exist both in time and in the frequency domain. We introduce and study the concept of admissible feedback operator for such a system and of well-posedness radius. We show that the closed-loop system obtained from a regular linear system with an admissible feedback operator is again regular and we describe the relationship between the generating operators of the open-loop and closed-loop systems.

Intuitionistic fuzzy geometric aggregation operators based on einstein operations

Abstract: Intuitionistic fuzzy information aggregation plays an important part in Atanassov's intuitionistic fuzzy set theory, which has emerged to be a new research direction receiving more and more attention in recent years In this paper, we first introduce some operations on intuitionistic fuzzy sets, such as Einstein sum, Einstein product, Einstein exponentiation, etc, and further develop some new geometric aggregation operators, such as the intuitionistic fuzzy Einstein weighted geometric operator and the intuitionistic fuzzy Einstein ordered weighted geometric operator, which extend the weighted geometric (WG) operator and the ordered weighted geometric (OWG) operator to accommodate the environment in which the given arguments are intuitionistic fuzzy values We also establish some desirable properties of these operators, such as commutativity, idempotency and monotonicity, and give some numerical examples to illustrate the developed aggregation operators In addition, we compare the proposed operators with the existing intuitionistic fuzzy geometric operators and get the corresponding relations Finally, we apply the intuitionistic fuzzy Einstein weighted geometric operator to deal with multiple attribute decision making under intuitionistic fuzzy environments © 2011 Wiley Periodicals, Inc © 2011 Wiley Periodicals, Inc

The Algebra of Timed Processes, ATP

Abstract: The algebra of timed processes, ATP, uses a notion of discrete global time and suggests a conceptual framework for introducing time by extending untimed languages. The action vocabularly of ATP contains a special element representing the progress of time. The algebra has, apart from standard operators of process algebras such as prefixing by an action, alternative choice, and parallel composition, a primitive unit-delay operator. For two arguments, processes P and Q, this operator gives a process which behaves as P before the execution of a time event and behaves as Q afterwards. It is shown that several d-unit delay constructs such as timeouts and watchdogs can be expressed in terms of the unit-delay operator and standard process algebra operators. A sound and complete axiomatization for bisimulation semantics is studied and two examples illustrating the adequacy of the language for the description of timed systems are given. Finally we provide a comparison with existing timed process algebras.