Mean square stability with general decay rate of nonlinear neutral stochastic function differential equations in the $ G $-framework

<abstract><p>Few results seem to be known about the stability with general decay rate of nonlinear neutral stochastic function differential equations driven by $ G $-Brownain motion ($ G $-NSFDEs in short). This paper focuses on the $ G $-NSFDEs, and the coefficients of these considered $ G $-NSFDEs can be allowed to be nonlinear. It is first proved the existence and uniqueness of the global solution of a $ G $-NSFDE. It is then obtained the trivial solution of the $ G $-NSFDE is mean square stable with general decay rate (including the trivial solution of the $ G $-NSFDE is mean square exponentially stable and the trivial solution of the $ G $-NSFDE is mean square polynomially stable) by $ G $-Lyapunov functions technique. In this paper, auxiliary functions are used to dominate the Lyapunov function and the diffusion operator. Finally, an example is presented to illustrate the obtained theory.</p></abstract>

APLIKASI INTEGRAL DALAM BIDANG EKONOMI DAN FINANSIAL

The characteristics of a function are usually investigated by looking at the continuity of the function. But what happens if a function does not have continuous properties? To what extent can the characteristics of continuous function be maintained for discontinuous cases? The stochastic function that is widely involved in solving problems in the field of average financial mathematics is a discontinuous function. This is reflected by the acquisition of a smooth curve from the modeling drawing obtained. Today, the nature of continuous functions in [a, b] has been widely studied and developed. Some properties of the continuous function can be extended to the appropriate discontinuous function. In this paper, there will be some integral reviews for discontinuous functions which are closely related to stochastic functions.

Stochastic Analysis of Multi-Reaction Model for Non-Linear Thermal History

This paper investigates the effect of non-linear thermal profile on the numerical solution of the multi-reaction model. According to the practical perspective, the temperature distribution at a different section of pyrolysis reactor is not necessarily following the ideal thermal history; therefore, it is necessary to predict the behaviour of the system for the higher degree of freedom. TG thermogram is obtained by the thermal degradation of pine needles sample in the thermogravimetric analyser (TGA). The activation energy, frequency factor, reaction order and the scale, shape and location parameters of a stochastic function are estimated for the non-linear parabolic thermal profile. The conventional Laplace integral is used to approximate the multi-reaction model. Activation energy obtained for the non-thermal profile lies in the range of 57.5–60 kJ·mol−1, whereas the frequency factor varies from 103–105 min-1. The obtained value of reaction order (n) lies in the domain of (0.9, 1.6).

Review of Roundabout Capacity Based on Gap Acceptance

Circulating vehicles have priority at modern roundabouts. Entrance vehicles can enter the roundabout when there is a time gap larger than the critical gap; otherwise, the vehicles need to wait until there is a large enough gap. The gap acceptance theory was used to analyze the entrance capacity of roundabouts, which can be derived by queuing theory involving two vehicle streams. The paper introduces the main styles of headway distribution, which are named as bunched exponential distribution or M3 distribution. The calculation model of free stream ratio is also introduced. The entrance capacity models can be classified by different entrance vehicle types, which are piecewise function or linear function, or by different critical gap types, which are constant or stochastic function. For each form, the typical capacity expressions are given. The calculation values show a very small difference between these kinds of models. The capacity value based on the critical gap of stochastic function is more realistic and more complex in function style. Some conclusions were derived that drivers’ nonhomogeneous and inconsistent character is more realistic than the fixed critical gap and following gap. The calculation results of capacity are similar to the field capacity under the assumption of homogeneity and continuance, with only a minor percent deviation. Finally, the paper points out additional problems and the suggested research in capacity of roundabouts.