Mathematical modeling of non-Newtonian fluid in arterial blood flow through various stenoses

Since the stenosis geometry of some cardiovascular patients cannot be described by a vertically symmetric function throughout the stenosis, so it motivates us to study the blood flow through a vertically asymmetric stenosis. In addition, we compare the flow quantities in bothvertically symmetric and asymmetric stenoses. The vertically symmetric stenosis is explained by a vertically symmetric function such as an exponential function in bell shape and a cosine function in cosine shape. The vertically asymmetric stenosis is interpreted by a vertically asymmetric function such as the combination of two different stenosis shapes. Blood is treated as a non-Newtonian fluid which is represented in the power-law model. The finite difference scheme is used to solve governing equations for obtaining the flow quantities such as axial velocity, radial velocity, flow rate, resistance to flow, and skin friction. We investigated the way that the stenosis height, stenosis length, and non-Newtonian behavior affect the flow quantities through three various stenoses. The flow quantities in the bell shape and cosine shape of stenosis show significantly different behavior. Moreover, we found that the flow quantities in the single shape (bell shape or cosine shape) have the same behavior as the flow quantities in the combined shape in the first half part, but have a slightly different behavior in the last half part.

Optimal control of production with improvement

This article considers a process that produces items and in which the process mean is observed periodically. We use a state-space model to describe the relationship between the process mean and the quality characteristic of the items. At each observation, one of the following actions can be taken: production, repair, replacement, or improvement. When production is chosen, some number of items are produced. The quality characteristic of the items has a target value, and the quality loss is expressed by an asymmetric function of the deviation of the quality characteristic from the target value. Replacement resets the process mean to an initial value. When improvement is selected, the process mean is returned to the same initial value as in replacement. When improvement is repeated, it becomes less likely that the process mean will increase. There are several kinds of repairs, and each repair returns the process mean to some value greater than the initial value. For this model, we obtain a total expected discount cost for an unbounded horizon, and we show that under several reasonable assumptions, a control-limit policy is optimal. Furthermore, we derive the sufficient conditions to ensure that the optimal control policy has monotonic structures.

Asymmetric Volatility and Risk-Return Relationship in International Stock Markets

This paper investigates daily stock market volatility of 9 developed and 11 emerging stock markets of the world using different symmetnc, as well as asymmetric GARCH models. The symmetric GARCH parameters suggest that though market behaves differently for different countries in terms of reaction and persistence in volatility, the return generating process in all markets is charactenzed by a high degree of persistence in conditional variance. The estimated parameters of TGARCH model reveal that in all markets, volatility is an asymmetric function of past innovation. Finally, the results of TGARCH-M model indicate insignificant risk-return relationship of most of the markets.