A mathematical model for the first-pass dynamics of antibiotics acting on the cardiovascular system

We present a preliminary first-pass dynamic model for delivery of drug compounds to the lungs and heart. We use a compartmental mass-balance approach to develop a system of nonlinear differential equations for mass accumulated in the heart as a result of intravenous injection. We discuss sensitivity analysis as well as methodology for minimizing mass in the heart while maximizing mass delivered to the lungs on a first circulatory pass.     

A mathematical model for the 3d location estimation of 2D echocardiography data

The recovery of 3D left ventricle(LV) shape using 2D echocardiography is very attractable topic in the field of ultrasound imaging. In this paper, we propose a mathematical model to determine the 3D position of LV contours extracted from multiple 2D echocardiography images. We formulate the proposed model as a non-convex constrained minimization problem. To solve it, we propose a proximal alternating minimization algorithm with a solver OPTI for quadratically constrained quadratic program. For validating the proposed model, numerical experiments are performed with real ultrasound data. The experimental results show that the proposed model is promising and available for real echocardiography data.     

A computational model of a bonus-malus system with a variable trend

The paper considers a model of a bonus-malus system with a variable trend in the case of a three-parameter gamma distribution. The parameters of the distribution and the value of the trend are selected based on statistical data. The indexes of the bonus-malus system are obtained.     

A new way of investigating the asymptotic behaviour of a stochastic SIS system with multiplicative noise

In this paper, we investigate a nonlinear stochastic SIS epidemic system with multiplicative noise. First, we transform the Itô’s integral into an equivalent Stratonovich integral. Then, by using the solution of Langevin equation and Ornstein–Uhlenbeck process, we prove that the system generates a random dynamical system which has a tempered compact random absorbing set, implying the condition for the extinction of the disease. Finally, the discussion and numerical simulation are given to demonstrate the obtained result.     

A simple mathematical model for free vibration analysis of combined system consisting of framed tube,shear core,belt truss and outrigger system with geometrical discontinuities

Dynamic analysis of beam-like structure is significantly important in modeling real cases such as tall buildings, aircraft wings, spacecraft antennas and many other applications. This paper tries to determine the first natural frequency of tall buildings including framed tube, shear core, belt truss and outrigger system with multiple jumped discontinuities in the cross section of framed tube and shear core. In this regard, the entire length of the tall building is partitioned into uniform segments between each two successive discontinuity points. The effect of belt truss and outrigger system is modeled as a concentrated rotational spring applied at the belt truss and outrigger system location. Many cantilevered tall structures can be treated as cantilever bars with multiple jumped discontinuities in the cross section for the analysis of their free vibration. In this paper, the continuous approach was accepted and by using the Hamilton’s variational principle, the general form of governing equation for free vibration of tall building can be obtained. By applying the separation of variable method on time and space, the governing Partial Differential Equation (PDE) of motion is reduced to an Ordinary Differential Equation (ODE) with one variable coefficient while the other coefficients are constant based on the assumption that the transverse displacement is a harmonic vibration. To find exact solution of ODE, we must have exact distribution of EI(x), AG(x), N(x) and m(x) in the height of the structure. Some of these parameters such as EI(x), AG(x) and m(x), are constant throughout the height of each segment. These parameters can be expressed exactly by using of multi criteria function, while N(x) is variable in the height of each segment. Therefore, the ODE by using the method of variable separation and partitioned method can be expressed for each segment. We must apply the continuity conditions in conjunction with different segments for obtaining unique mode shape for mentioned system. Tall building characteristics matrix can be derived based on the boundary conditions and the continuity conditions applied at the partitioned points. This matrix is particularly used to find combined system first natural frequency and mode shape. Three numerical examples with different stepped discontinuities in their cross sections are studied to demonstrate the reliability of this method. The results of the proposed mathematical model give a good understanding of the structure’s dynamic characteristics; it is easy to use, yet reasonably accurate and suitable for quick evaluations during the preliminary design stages which require less time.     

A new mathematical model towards the integration of cell formation with operator assignment and inter-cell layout problems in a dynamic environment

This paper proposes a new mathematical model to solve the cell formation, operator assignment and inter-cell layout problems, simultaneously. The objectives of proposed model are minimization of inter–intra cell part trips, machine relocation cost and operator related issues. Since the objective function of the proposed model consists of none commensurable statements, the preferred solution is obtained by the LP-metric approach. In order to validate the proposed model, some numerical examples are generated randomly and solved by branch and bound technique. Moreover; a real case study is illustrated in order to verify its applicability in an automobile producer company. Moreover the sensitivity analysis of proposed model shows that considering the operator assignment problem has significant impact on the overall system efficiency.     

Some modified mathematical analytic derivations of the annual total relevant cost of the inventory model with two levels of trade credit in the supply chain system

Several recent studies in supply chain system and related areas explored various economic order quantity (EOQ) models for noninstantaneous deteriorating items with imperfect quality and trade credit financing. In particular, in the year 2007, Teng et al investigated an EOQ model in which the supplier offers the retailer the permissible delay period M and the retailer, in turn, provides the trade credit period N (with ) to his/her customers. The main purpose of this article is twofold: (a) It modifies the annual total relevant cost TVC(T) in the study of Teng et al and presents the correct derivations of TVC(T) by applying mathematical analytic tools and techniques. (b) It exposes some logical and mathematical problems in the proof of Theorem 1 in Teng et al. It also corrects and overcomes all of the errors and shortcomings by systematically presenting the complete and mathematical solution procedures in order to locate all optimal solutions for the model in Teng et al.     

A proposed model for measuring the aggregative risk degree of implementing an RFID digital campus system with the consistent fuzzy preference relations

An RFID digital campus system implementation can enhance convenience in teaching environment, teaching quality and administrative efficiency. When administrators decide to implement an RFID digital campus system, they often encounter unexpected internal and external risk factors and difficulties. Therefore, this study proposes a novel analytic hierarchy model for helping administrators to identify the critical risk factors affecting the RFID digital campus system initiation, and measuring the aggregative risk of implementing an RFID digital campus system. The importance weights of risk factors and possible occurrence ratings of four risk grades (high, medium, low and none) are determined by using consistent fuzzy preference relations. The relative priority weights of evaluators are considered simultaneously by using simple additive weighting method. Multiplying the importance weights of risk factors, the possible occurrence ratings of risk grades and the relative priority weights of evaluators, the aggregative risk degree of implementing an RFID digital campus system is derived. University A in Taiwan is used to demonstrate the computation procedures of this proposed methodology.