On Fuzzy Contractive Mappings in Fuzzy Metric Spaces

In this paper we introduce a new fuzzy contraction mapping and prove that such mappings have fixed point in $\tau$-complete fuzzy metric spaces. As an application, we shall utilize the results obtained to show the existence and uniqueness of random solution for the following random linear random operator equation. Moreover, we shall show that the existence and uniqueness of the solutions for nonlinear Volterra integral equations on a kind of particular fuzzy metric space.

Successive approximations for random coupled Hilfer fractional differential systems

In this paper, we study the global convergence of successive approximations as well as the uniqueness of the random solution of a coupled random Hilfer fractional differential system. We prove a theorem on the global convergence of successive approximations to the unique solution of our problem. In the last section, we present an illustrative example.

AN APPLICATION OF LINEAR DIOPHANTINE EQUATIONS TO CRYPTOGRAPHY

In this chapter we propose a Key exchange protocol based on a random solution of linear Diophantine equation in n variables, where the considered linear Diophantine equation satisfies the condition for existence of infinitely many solutions. Also the crypt analysis of the protocol is analysed.

Stochastic Model of the Absorption of Drugs Problem in the Cells and Organs

In this paper we create the stochastic differential equation for the problem of the Absorption of Drugs Problem in the Cells and Organs with fixed volume and then solve this equation and study the stability of the random solution.

The Riccati-Bernoulli Sub-ODE Technique for Solving the Deterministic (Stochastic) Generalized-Zakharov System

This article concerns with the construction of the analytical traveling wave so- lutions for the Generalized-Zakharov System by the Riccati-Bernoulli Sub- ODE technique. Also, we will discuss this technique in random case by using random traveling wave trans- formation in order to find what is the effect of the randomness input for this technique. We presented the Generalized-Zakharov System as an example to show the difference effect between the deterministic and stochastic Riccati-Bernoulli Sub-ODE technique. The first moment of random solution is computed for different statistical probability distributions.

Fluctuations in 1D stochastic homogenization of pseudo-elliptic equations with long-range dependent potentials

This paper deals with the homogenization problem of one-dimensional pseudo-elliptic equations with a rapidly varying random potential. The main purpose is to characterize the homogenization error (random fluctuations), i.e., the difference between the random solution and the homogenized solution, which strongly depends on the autocovariance property of the underlying random potential. It is well known that when the random potential has short-range dependence, the rescaled homogenization error converges in distribution to a stochastic integral with respect to standard Brownian motion. Here, we are interested in potentials with long-range dependence and we prove convergence to stochastic integrals with respect to the Hermite process.

How to Avoid Random Market Segmentation Solutions

Tourism researchers and the tourism industry rely heavily on data-driven market segmentation analysis for both knowledge development and market insight. Most algorithms used in data-driven market segmentation are exploratory; they do not generate one single stable result. Only when data are well-structured (when very clear, distinct market segments exist in the data) are repeated calculations likely to generate the same segmentation solution. When data lack structure, which is frequently the case in empirical consumer data sets, repeated calculations lead to different solutions. Running a market segmentation analysis once only can therefore lead to an entirely random solution that does not represent a strong foundation for developing a long-term market segmentation strategy. The present study (1) explains the problem, (2) assesses how high the risk is of random solutions occurring in tourism market segmentation studies, and (3) recommends an approach that can be used to avoid random solutions.

A Random Solution to Ice-Induced Vibrations of Conical Structures

Offshore installations designed to withstand extreme ice actions, such as the multi-leg structures in Cook Inlet, the gravity based Molikpaq during its mobilization in the Beaufort Sea, lighthouses and channel markers in the Baltic Sea, jackets and mooring poles in Bohai Bay and multi-leg structures offshore Sakhalin, have experienced ice-induced vibrations (IIVs). Full-scale data from Bohai Bay also demonstrate that a conical waterline geometry of the structure does reduce the magnitude of the ice forces, but it still experiences IIVs that can be treated as a stochastic process. ISO 19906 recommends that the dynamic ice actions and the corresponding IIVs shall be considered in the design as the fatigue limit state (FLS). ISO 19906 provides the guidance for the time-domain random dynamic ice action on conical structures. The dynamic structural response to such ice action can take the form of a random vibration. As an alternative to the time-domain approach, random vibration analysis can also be done in the frequency domain by the spectral approach. In addition to the time-domain random dynamic ice action on conical structures provided in ISO 19906, a type of ice-force spectrum on conical structures has been developed. In this paper, a simplified single-degree-of-freedom system (SDOF system) and the ice-force spectrum are used to derive an analytical random solution to assess the IIVs of conical structures. As ISO 19906 points out that particular attention shall be given to dynamic actions on narrow structures and flexible structures, the developed random solution can be useful for designers to make a fast estimate of IIVs (i.e., displacement, velocity and acceleration) and to efficiently screen out the key design parameters of a conical ice-resistant structure.

Input Control in Production System by Simulation Optimization

The paper deals with the problem of simulation optimization and presents its usage for input control in a production system. The paper gives an overview of typical concepts of input control. Authors propose different approaches. The basic principles of simulation optimization are explained. A general procedure with each step is defined and this procedure is explained by an example. The solution is focused on the minimization of the production costs, which is included in the objective function. Realization of the simulation optimization is based on the combination of three different algorithms: Adaptive Thermostatistical Simulated Annealing, Random Solution and All Combination algorithm. The proposed procedure definitely leads to exact determination of input interval for given production system and short time period.