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In this paper, the analytical solution to the problem of heat transfer and fluid flow was obtained by using the quadruple Laplace transform method. Temperature distribution and fluid flow distribution were shown, temperature and fluid flow increase when the value of z increases, as well as the effect of the radiation parameter shown, it was concluded that the temperature increase with the increase in the value of the radiation coefficient . Matlab was used to plot the results.

In this paper three-dimensional heat conduction equation in cartesian coordinate has been solved in two different methods one of which depends on the separation of variables and the other depends on the integral transform .The results are got and plotted by using Matlab. And the results obtained showed the difference between the two methods that were used in the solution . That difference is evident in the illustrations . According to the results it was concluded that the integral transform method is the best because it has fewer steps to reached to the solution

Giving a high level modification story problems with multistep routine and non-routine problems in cartesian coordinate learning is an effort to achieve optimal learning and also important because it has good effect for students. Less than optimal learning of cartesian coordinates for eight grade it was usually represented by the frequent of student errors occurrence on an ongoing basis in solving on mathematical problems in assignments and daily tests. This research purpose was to reveal the dominant factor were caused eighth grade student errors in solving on cartesian coordinate multistep routine and non-routine modification story problems. This research is a descriptive qualitative in type. Research data collection based on survey, interview, test and documentation. The research subjects in this research were eight grade students of SMPN 4 Wonosobo. In this research 18 students of eight grade students SMPN 4 Wonosobo as the research sample. The sampling technique it was used in this research is purposive sampling. The results of this research indicate the dominant factor were caused eighth grade student errors in solving on cartesian coordinate multistep routine and non-routine modification story problems is students difficulties. Students difficulties such as compiling steps to solve problems in the form of multistep story problems, understanding the position conception of starting point with a certain point, understanding the conception of a perpendicular lines and a parallel lines to the X and Y axis, determining the distance of a point to certain point. The implication of this research is can obtain information about the dominant factor were caused student errors in solving on cartesian coordinate multistep routine and non-routine modification story problems as the relation to the current idealization of mathematics learning optimization and can be able for planing another appropriate and solution steps for the implementation of mathematics learning in an effort to minimize student errors.

Students experience problems while working in Math, with full of difficulties. They made mistakes in the process of solving questions. The error process that occurred in students leads to the low achievement of the learning outcomes. This research aimed to investigate the mistakes made by MTs students in working on the questions of the Cartesian coordinate integrated with Malay cultural nuances in Riau Province. The study was conducted at MTs in the odd semester of the 2019/2020 academic year. A descriptive approach was used as a research method with a purposive sampling technique. This technique used a test and interview to collect research data. The results of the study described that the errors faced by MTS NurulBilad students included: (1) 55% of misconceptions because students did not understand the concept in the material of Cartesian coordinate (2) procedural errors that 76% of students did not match the stages or steps in the process of drawing on the Cartesian coordinate. Based on the findings, it was hoped that the teacher emphasized more understanding about the concept of Cartesian coordinate.

Current shallow granular flow models suited to arbitrary topography can be divided into two types, those formulated in bed-fitted curvilinear coordinates and those formulated in global Cartesian coordinates. The shallow granular flow model of Denlinger and Iverson (J. Geophys. Res. 109, F01014, 2004) and the Boussinesq-type shallow granular flow theory of Castro-Orgaz et al. (2014) are formulated in a Cartesian coordinate system (with z vertical), and both account for the effect of nonzero vertical acceleration on depth-averaged momentum fluxes and stress states. In this paper, we first reformulate the vertical normal stress of Castro-Orgaz et al. (2014) in a quadratic polynomial in the relative elevation η. This form allows for analytical depth integration of the vertical normal stress. We then calculate the basal normal stress based on the basal friction law and scaling analysis. These calculations, plus certain constitutive relations, lead to a refined full non-hydrostatic shallow granular flow model, which is further rewritten in a form of Boussinesq-type water wave equations for future numerical studies. In the present numerical study, we apply the open-source code TITAN2D for numerical solution of a low-order version of the full model involving only a mean vertical acceleration correction term. To cure the numerical instability related with discretization of the enhanced gravity, we propose an approximate formula for the enhanced gravity by utilizing the hydrostatic pressure assumption in the bed normal direction. Numerical calculations are conducted for several test cases involving steep slopes. Comparison with a bed-fitted model shows that even the simplified non-hydrostatic Cartesian model can be used to simulate shallow granular flows over arbitrary topography. [ABSTRACT FROM AUTHOR]

Compared with the original backprojection (BP) algorithm, the fast factorized BP algorithm accelerates enormously. As it is known to all, 2-D image interpolations are always utilized to raise the accuracy, yet leadings to the tradeoff with the efficiency. In this paper, a novel factorized BP algorithm based on Cartesian coordinate without interpolation, is proposed for high-resolution spotlight SAR with much better efficiency and accuracy. The innovative idea is achieved by establishing two spectrum compressing filters to decrease the cross-range Nyquist sampling rate enormously, thus avoid spectrum aliasing. The proposed algorithm, termed as the Cartesian factorized BP (CFBP) algorithm, can produce images with the similar quality as the BP does, but is better than FFBP, where the interpolations accumulate errors to some extent. The CFBP is designed for spotlight mode working in both the linear and curved trajectories. Simulation results and real-data processing validate the superiorities of CFBP by the comparisons with FFBP and the original BP individually. [ABSTRACT FROM PUBLISHER]

Incompatible modes with parametric coordinates are widely used in finite element method to develop low-order elements with high accuracy. But it leads to unstable results and must be used along with the constant Jacobian matrix technique to assure convergence. The incompatible modes with Cartesian coordinates are proposed as an alternative. The advantage is that the present method can improve the accuracy, assure the convergence of the elements without additional correction technique and greatly reduce the amount of calculation. With this method, a new quadrilateral element IMQ6 is formulated within the quasi-conforming scheme. Both theoretical and numerical analyses are conducted and it is proved that the present incompatible modes improve the element's performance in both precision and efficiency. [ABSTRACT FROM AUTHOR]

SUMMARY A nonhydrostatic finite volume model is presented to simulate free surface flow in a two-dimensional vertical plane. The algorithm is based on a projection method including the solution of the pressure Poisson equation (PPE). The model is developed in a Cartesian grid in which the size of all the cells in the computational domain, excluding those of the top layer, is constant in time. To simulate the variable water surface, the heights of the top layer cells are variable and proportional to the local water elevation. Taking the layout of the grid system into consideration, a new method is proposed to solve the PPE derived in Cartesian coordinates. In this method, the system of pressure equations is divided into two subsystems, namely a subsystem for the upper layer cells and another for the remaining cells. The coefficient matrix of the former is variable with respect to time, whereas that of the latter remains constant. Therefore, the coefficient matrix of the latter subsystem can be inversed once and saved throughout the simulation. The application of this procedure reduces the computational cost compared with other PPE solvers in certain conditions. The model is applied to simulate a series of numerical tests including strong vertical accelerations and is verified against analytical and experimental results, demonstrating satisfactory performance. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents some fresh aspects of studies that integrate geometry, algebra, trigonometry and calculus in some PNG cultural features such as traditional house wall patterns and PNG stamps through the use of Microsoft Excel. In order to represent these features visually in Excel, we generate the (x,y) coordinates of mathematical functions in Excel such as cosine and sine and use the XY scatter graph feature to generate curves to display the geometrical features that are discussed in this paper. The traditional houses or huts which still exist today in all native villages of the country are built mostly by using bush materials. The woven house walls display basic geometrical shapes such as diamonds, squares and triangles. The stamps are depict aspects of PNG culture such as flowers, clay pots, village houses, birds, butterflies and others. The paper concludes with a discussion of the method used and suggestions for future improvements and extensions in the use of the creative mathematics employed in the examples that we illustrate in Excel. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents analytical solutions for the stress and displacement field in elastic layered geo-materials induced by an arbitrary point load in the Cartesian coordinate system. The point load solutions can be obtained by referring to the integral transform and the transfer matrix technique. However, former solutions usually exist in the cylindrical coordinate system subjected to axisymmetric loading. Based on the proposed solutions in the Cartesian coordinate, it is very easy to solve asymmetric problems and consider the condition with internal loads in multi-layered geo-materials. Moreover, point load solutions can be used to construct solutions for analytical examination of elastic problems and incorporated into numerical schemes such as boundary element methods. The results discussed in this paper indicate that there is no problem in the evaluation of the point load solutions with high accuracy and efficiency, and that the material non-homogeneity has a significant effect on the elastic field due to adjacent loading. [Copyright &y& Elsevier]

Abstract: In this paper, a mathematical model describing the process of heat transfer in biological tissues for different coordinate system during thermal therapy by electromagnetic radiation is studied. The boundary value problem governing this process has been solved using Galerkin’s method taking B-polynomial as basis function. The system of ordinary differential equation in unknown time variable, thus obtained, is solved by homotopy perturbation method. The effect of thermal conductivity, antenna power constant, surface temperature, and blood perfusion rate on temperature for different coordinates are discussed. It has been observed that the process is faster in spherical symmetric coordinates in comparison to axisymmetric coordinate and faster in axisymmetric in comparison to Cartesian coordinate. [ABSTRACT FROM AUTHOR]

Reliability of protection and apparatus selection of the electrical power systems depend on the correct and accurate calculation of short-circuit currents. The simulation of the electrical power systems is one of the methods that is used for the determination of the short-circuit currents. In this paper, the model of the electrical power system has been represented by a system of differential equations for current determination. These differential equations have been expressed in Cartesian system of coordinates that decreased the number of the equations by one-third. This paper compares two approaches of short-circuit simulation in electrical power systems and evaluates the error in the calculated short-circuit current during both transient and steady-state conditions. These approaches are as follows: first, the replacement of the load parameters by zero and second, the introduction of fault simulation switch. A fault has been simulated in a study electrical power system and the factors on which the error depends have been determined. In this paper, the envelope of the short-circuit current has been considered as a comparative criterion. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This brief proposes a new Cartesian-to-polar coordinate conversion technique based on the radix-4 SRT division. The coarse quotient is used to derive the magnitude and the coarse phase by referring to tables, while the fine quotient is applied to linearly interpolate the fine phase to be added to the coarse phase. Compared to the CORDIC-based techniques, the proposed conversion requires less internal word-length and provides parallelism between internal stages, resulting in reduced computation latency and small chip area. A prototype chip designed using 0.25-μm CMOS technology occupies 0.203 mm2, and post-layout simulations show maximum frequency of 400 MHz and power consumption of 170 mW at 2.5 V. [ABSTRACT FROM AUTHOR]

This paper presented a simple technique to derive the stiffness and mass matrices of a horizontally circular curved beam element so that the possibility of practical applications of the presented property matrices should be greater than that of the existing ones. Where the element stiffness matrix was derived from the force–displacement equations and the element consistent mass matrix was derived from the kinetic energy equations. The effect of rotary inertias due to both bending and torsional vibrations and the effect of shear deformation were considered in the formulation. Since all element property matrices of the curved beam element were derived based on the local polar coordinate system (rather than the local Cartesian one), their coefficients were invariant for any curved beam element with constant radius of curvature and subtended angle. For this reason, one did not need to transform the property matrices of each curved beam element from the local coordinate system to the global one to achieve the overall property matrices of the entire curved beam before they were assembled. However, the simple transformation matrices between the local polar coordinate system and the global Cartesian coordinate system were also presented so that the element property matrices of the curved beam elements can be assembled with those of the conventional straight beam elements (or the other curved beam elements with different radii of curvatures and/or subtended angles) to achieve the overall property matrices of the entire “hybrid” structural system. The good accuracy of the presented approach has been verified by both the existing analytical (exact) solutions for the continuum curved beam and the numerical (approximate) solutions for the discretized curved beam composed of the conventional straight beam elements using either the consistent mass model or the lumped mass model. [Copyright &y& Elsevier]

A brief survey of fractional calculus and fractional differential forms was firstly given. The fractional exterior transition to curvilinear coordinate at the origin were discussed and the two coordinate transformations for the fractional differentials for three-dimensional Cartesian coordinates to spherical and cylindrical coordinates are obtained, respectively. In particular, for v=m=1, the usual exterior transformations, between the spherical coordinate and Cartesian coordinate, as well as the cylindrical coordinate and Cartesian coordinate, are found respectively, from fractional exterior transformation. [ABSTRACT FROM AUTHOR]

Cartesian coordinates are discussed in the finding of target position from radar signals. The Cartesian coordinates are used for the tracking algorithm of radar signal under the cluttering condition by PDA (Probabilistic Data Association) method. The possibility of transforming some dimensions of PDA using one Cartesian coordinate to the other Cartesian coordinate has not as yet been reported. Dimensions are the estimated values of position, velocity, and some other variables of movement of the target, and the covariance matrix as the evaluation of their errors in estimation. The Cartesian coordinate system which takes the true north as the first coordinate, or the one which takes the vector toward the target position as the first coordinate have been proposed in order to find the coordinate system of the best tracking ability. In this paper, it is proved that PDA of one Cartesian coordinate can be transformed to the other by the mathematical reduction method of sampling time, and also the range of target estimation and correlation probabilities between target and observed vector is the same under any Cartesian coordinate. Then, it is not necessary to make mutual comparisons of performance and evaluation of PDA in different Cartesian coordinates. Furthermore, transformation formulas are derived for dimensions of target movement, covariance matrices of errors, and gain matrices in these coordinates. © 1998 Scripta Technica, Electron Comm Jpn Pt 1, 81(9): 47–57, 1998 [ABSTRACT FROM AUTHOR]