In many industrial and non-industrial applications, it is necessary to identify the largest inscribed Rectangle in a certain shape. The problem is studied for convex and non-convex polygons. Another criterion is the direction of the Rectangle: axis aligned or general. In this paper a heuristic algorithm is presented for  nding the largest axis aligned inscribed Rectangle in a general polygon. Comparing with stare of the art, the Rectangles resulted from our algorithm have bigger area. We also proposed an approach to use the algorithm for  finding a Rectangle with general direction.

Generally, intakes are used for conveying and diverting the flow within main channels and rivers. In this study, a flow field was simulated using FLOW-3D software. In addition, the flow free-surface variations were predicted using the Volume of Fluid (VOF) scheme. The flow turbulence was estimated by standard k-ε and RNG k-ε turbulence models. For instance, the MAE values for standard k-ε and RNG k-ε models to simulate the free surface profile were computed 0. 166 and 0. 201, respectively. The modeling results showed that the numerical model simulated the flow field with an acceptable accuracy. For example, the RMSE, MAE and R values for the simulated flow free-surface variations were calculated 0. 164, 0. 158 and 0. 997 percent, respectively. Then, the effects of four flow division angles (30, 45, 75 and 90 degrees) on flow field pattern were considered. Regarding the modeling results, the highest depth-averaged velocity was obtained for the model with 45-degree. Among the models with division angles of 30, 45 and 75 degrees, the maximum shear stress was predicted for the model with 45-degree.

One of the machine learning tasks is supervised learning. In supervised learning we infer a function from labeled training data. The goal of supervised learning algorithms is learning a good hypothesis that minimizes the sum of the errors. A wide range of supervised algorithms is available such as decision tress, SVM, and KNN methods. In this paper we focus on decision tree algorithms. When we use the decision tree algorithms, the data is partitioned by axis- aligned hyper planes. The geometric concept of decision tree algorithms is relative to separability problems in computational geometry. One of the famous problems in separability concept is computing the maximum bichromatic discrepancy problem. There exists an -time algorithm to compute the maximum bichromatic discrepancy in d dimensions. This problem is closely relative to decision trees in machine learning. We implement this problem in 1, 2, 3 and d dimension. Also, we implement the C4.5 algorithm. The experiments showed that results of this algorithm and C4.5 algorithm are comparable.

The volume of fluid (VOF) model together with the continuum surface stress (CSS) model is proposed to simulate the core annular of non-Newtonian oil and water flow through the Rectangle return bends (II-bends). A comprehensive investigation is conducted to generate the profiles of volume fraction, pressure and velocity. The influences of oil properties, flow direction, and bend geometric parameters on hydrodynamic of non- Newtonian oil and water core annular flow in II-bends are discussed. Through computational simulations the proper bend geometric parameters were identified, these results are useful for designing and optimizing the pipefitting system.

Shortest path problem is among the most interesting problems in the field of graph and network theory. There are many efficient matrices-based algorithms for detecting of shortest path and distance between all pairs of this problem in the literature of research. In this paper, a new exact algorithm, named the Cascade Rectangle Algorithm, is presented by using the main structure of previous exact algorithms and developing some new techniques. In cascade Rectangle algorithm, all mathematical calculations and operations execute in multiRectangle structure. This algorithm is an efficient exact algorithm with simple procedure and fast running time. Furthermore, a new matrix on the basis of route matrix, called the Transposition Matrix, is defined to apply the sensitivity analysis and reoptimization of the all pairs shortest path networks. Finally, one illustrative example is also solved in a step by step procedure to show the details of the cascade Rectangle algorithm, floyd-warshall algorithm, revised matrix algorithm, and Transposition Matrix.

In this article, an attempt has been made to estimate the amount of sound transmission loss in a flat oval channel by applying the approach of statistical energy analysis. Correct estimation of sound transmission loss in an air conditioning channel is of great importance due to the harmful effects of noise pollution in the environment on human health. Simulation with the statistical energy analysis method is a powerful approach to estimate sound and vibration in problems in which we deal with complex and multi-part systems; is considered. In this method, first, a system is divided into several subsystems, and then by writing a matrix equation that includes the energy exchanges between subsystems and energy loss coefficients; It is investigated from the perspective of vibration and sound estimation.On average, the model presented in this research is able to estimate the sound transmission loss in different dimensions of the air conditioning channels according to the experimental results in the accuracy range of ± 2.5 dB. Considering that it seems that the results obtained from modeling with this method are in good agreement with the experimental data; The results of this research can be used as an efficient approach to estimate noise in oval shaped channels stretched in different lengths.

A novel Halbach permanent magnet array with Rectangle section and trapezoid section is proposed and optimized in this paper. The analytical model of the premanent magnet segment is established based on the surface current method, which is numerically efficient and can be utilized to evaluate the magnetic field closely with the premanent magnet segment’s configurations. The analytical model of the Halbach array is acquired based on the superposition principle and coordinate transformation. The fundamental component of the magnetic flux density and the sinusoidal distortion rate are chosen as the optimization object. And the optimization is executed on the Halbach array with one specific set of dimensions by the genetic algorithm in global scale. The effectiveness of the optimization is validated by the finite element analysis. Compared to the traditional Halbach array with Rectangle section, the magnetic field created by the optimized proposed Halbach array in this paper owns better performance.

Rectangle array is widely used in resistivity and induced polarization (IP) studies. The purpose of this array is to restrict the wide areas especially in the exploration of sulfide minerals. On the contrary to the wide application of this array, less attention has been paid to the results of modelling and true estimates. The interpretations are normally qualitative.A 3D resistivity and IP model was developed for the geoelectric surveys with a Rectangle array. We used the COMSOL environment to solve the DC-resistivity and Maxwell’s equations by the finite element method. Codes were programmed in Matlab language.A common geometry of the model space was used for both resistivity and IP modelling. In the Rectangle array, two current electrodes were located in a large distance and different potentials were measured on the profiles parallel to the current electrodes. Our model was formed by a homogeneous half space (a large block with dimensions 800×800×500m3, with a resistivity of 400 ohm.m). Two current electrodes with a 200-m distance were located on the surface. Non-polarizing electrodes were located in a 5-m distance. The two measuring electrodes were moved on the profiles (parallel to the current electrode direction). Nine parallel profiles were located symmetrically on each side of the current electrode direction. Each profile had a 40-m length. The distance between the profiles was 5 m. The electrode configuration could be changed in the model. IP and resistivity anomalies could be created from different blocked locations in the subsurface (into the half space). The blocks near the potential profiles had small dimensions. The block sizes increased as the depth increased. We calculated the geometrical factor for the half-space. Apparent resistivity for each dual potential electrode was calculated from different potentials measured during the code execution and its geometry factors.We compared the results from different anomalies by sensitivity Dpa/Dpi, where Dpa is the difference between the apparent resistivity of the anomaly and the homogeneous half-space (400 ohm.m) and Dpi is the difference between the resistivity value of the half-space and the anomaly in block number i.Frequency domain IP was calculated directly from Maxwell's equations. Block scheme of the model done in the modelling space resistivity were used here. There was a resistivity value for each subsurface block in the resistivity model while there were a resistivity and a dielectric value for each block in an IP model. Resistivity and dielectric values of each block are functions of the frequency. We used the Cole-Cole model in order to calculate the resistivity and dielectric values in each frequency. Four intrinsic Cole-Cole parameters (DC-resistivity, chargeability, time constant and frequency relaxation) were considered for each block. During the frequency changes, these parameters were constant. Finally, apparent resistivity and percentage frequency effect (PFE) maps were calculated in a frequency range of 0.1 to 12000 Hz.In this research, we studied the effect of size, depth and overburden thickness of the subsurface anomalies. The geoelectrical effects of vertical and horizontal anomalies were investigated. The impact of the potential electrode separation was also verified. The results showed that the qualitative interpretation using the apparent resistivity and appearent percentage frequency effect (PFE) maps was correct when anomaly had remarkable dimensions, a small depth and a high conductivity. The apparent-resistivity map reflected the effect of conductive and polarisable anomalies better than the PFE map.