In this paper, the boundary-based estimation of pressure distribution in the cardiovascular system is investigated using two dimensional flow images. The conventional methods of non-invasive estimation of pressure distribution in the cardiovascular flow domain use the differential form of governing equations. This study evaluates the advantages of using the integral form of the equations in these calculations. The concepts provided with the Boundary Element Method (BEM) together with the boundary-based image segmentation tools are used to develop a fast calculation method. Boundary-based segmentation provides BEM with domain pixel extraction, boundary meshing, wall normal vector calculation, and accurate calculation of boundary element length. The integral form of the governing equations are reviewed in detail and the analytic value of integral constants at singular points are provided. The pressure data on boundary nodes are calculated to obtain the pressure data at every point in the domain. Therefore, the calculation of domain pressure could be considered as a post-processing procedure, which is an advantage of this approach. Both the differential and integral-based formulations are evaluated using mathematical Couette test flow image whose pressure domain is available. The resulting pressure distributions from both methods will be compared. According to the results obtained from this study, the use of BEM for estimating pressure values from a non-invasive flow image has the following advantages: reduced computational domain from two to one dimension, flexible calculation of pressure data at arbitrary points or at finer spatial resolutions, robustness against noise, less concern for its stability and compatibility, accuracy, and lower meshing attempts.

In this research paper, we introduce a new transform belonging to the class of Laplace transforms, called the Yasser-Jassim Transform (YJ Transform). We explore its properties and compare it to the classical Laplace transform. Furthermore, we provide proofs for the key properties associated with this transform and demonstrate its application in solving differential and integral equations. By employing this new transform, we can reduce the original problem to an algebraic equation that can be solved directly, followed by applying the inverse transform to obtain the solution to the original problem.

Today snow and avalanche studies have progressed dramatically throughout the world, and countries are experiencing avalanche phenomena have established advanced research and development centers in this regard. For many years, they have used their research and results. In Iran, despite the presence of snow in some parts of the country, no official observing centers have made in the country. One of the important issues in the avalanche studies are: the avalanche risk map that identifies avalanches in snowy and mountainous regions, but this map is very different from the avalanche risk map. Many domestic researchers find the two maps mistakenly the same. In this research, we have tried to determine the difference between avalanche hazard map and avalanche risk map.

This article investigates the problem of simultaneous attitude and vibration control of a flexible spacecraft to perform high precision attitude maneuvers and reduce vibrations caused by the flexible panel excitations in the presence of external disturbances, system uncertainties, and actuator faults. Adaptive integral sliding mode control is used in conjunction with an attitude actuator fault iterative learning observer (based on sliding mode) to develop an active fault tolerant algorithm considering rigid-flexible body dynamic interactions. The discontinuous structure of fault-tolerant control led to discontinuous commands in the control signal, resulting in chattering. This issue was resolved by introducing an adaptive rule for the sliding surface. Furthermore, the utilization of the sign function in the iterative learning observer for estimating actuator faults has not only enhanced its robustness to external disturbances through a straightforward design, but has also led to a decrease in computing workload. The strain rate feedback control algorithm has been employed with the use of piezoelectric sensor/actuator patches to minimize residual vibrations caused by rigid-flexible body dynamic interactions and the effect of attitude actuator faults. Lyapunov's law ensures finite-time overall system stability even with fully coupled rigid-flexible nonlinear dynamics. Numerical simulations demonstrate the performance and advantages of the proposed system compared to other conventional approaches.

These days, integral equations govern a wide range of physical processes, including those related to electricity, mechanics, fluid dynamics, ecology, soil moisture dynamics, shallow water wave propagation, and chemical science. As a result, creating new techniques and putting them into practice for solving integral equations becomes more crucial. In this paper, the Upadhyaya integral transform is employed for determining the analytical solutions of the non-linear Volterra integral equations (NVIEs) of the first kind. Four examples suggest the effectiveness of the Upadhyaya integral transform, particularly for NVIEs of the first kind. The calculation results suggest that the proposed method provides accurate solutions to the original problem and this method is a valuable tool for researchers and scientists working on the broader range of problems involving NVIEs of the first kind.