Effect of the Presence of Semi-circular Cylinders on Heat Transfer From Heat Sources Placed in Two Dimensional Channel by Ahmed W. Mustafa, Adil A. Mohamed Saied, Hajer A. Sadiq

“…The laminar flow field is analyzed numerically by solving the steady forms of the two-dimensional incompressible Navier- Stokes and energy equations. The Cartesian velocity components and pressure on a collocated (non-staggered) grid are used as dependent variables in the momentum equations, which discretized by finite volume method, body fitted coordinates are used to represent the complex channel geometry accurately, and grid generation technique based on elliptic partial differential equations is employed. …”
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Natural Convection from Discrete Heat Sources Placed in Wavy Enclosure by Ahmad W. Mustafa, Mustafa Z. Abood

“…The two heat sources constant and high temperature, length of each heat source (10%) from the total length of bottom surface, the distances that do not contain heat source on the bottom surface thermally insulated, temperature of verticals walls and upper surface low and constant. corrugating upper surface was change the dimensional corrugation amplitude between (0.1-0.3), for number of corrugations (3), the dimensional distances between the two heat sources were change between (0.2-0.8), the Rayleigh numbers ranged between (103 ≤ Ra ≤ 105), the fluid inside the enclosure was air Prandtl number for it (0.7). were analyzed flow and temperature fields inside the enclosure numerically by solving Navier Stokes and Energy Equations, have been used Cartesian velocity components and pressure on a collocated grid are used as dependent variables in the momentum equations which discretized by finite volume method, body fitted coordinates are used to represent the geometry shape of the problem accurately, were grid generated technique based on elliptic partial differential equations, SIMPLE algorithm is used to adjust the velocity field to satisfy the conservation of mass. …”
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Recent studies on the super edge-magic deficiency of graphs by Rikio Ichishima, Susana C. Lopez, Francesc Muntaner, Yukio Takahashi

“…Imran, Baig, and Fe\u{n}ov\u{c}\'{i}kov\'{a} established that for integers $n$ with $n\equiv 0\pmod{4}$, $ \mu_{s}\left(D_{n}\right) \leq 3n/2-1$, where $D_{n}$ is the cartesian product of the cycle $C_{n}$ of order $n$ and the complete graph $K_{2}$ of order $2$. …”
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Realistic Dynamic Numerical Phantom for MRI of the Upper Vocal Tract by Joe Martin, Matthieu Ruthven, Redha Boubertakh, Marc E. Miquel

“…The phantom was used to: (1) test different k-space sampling schemes (Cartesian, radial and spiral); (2) create lower frame rate acquisitions by simulating segmented k-space acquisitions; (3) simulate parallel imaging reconstructions (SENSE and GRAPPA). …”
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محاكاة لاقط القطع المكافئ المركب الشمسي ذو مستقبل أنبوبي(CPC) باستخدام تقنية تتبع الشعاع by رامي جورج, رامي جبل

“…The equations were evaluated using analytical geometry for calculating the Cartesian coordinates of the reflecting surface, then the falling and reflected rays on the detector were calculated. …”
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Synthesis of the Inverse Kinematic Model of Non-Redundant Open-Chain Robotic Systems Using Groebner Basis Theory by José Guzmán-Giménez, Ángel Valera Fernández, Vicente Mata Amela, Miguel Ángel Díaz-Rodríguez

“…The developed procedure can be applied to all Cartesian robotic systems, SCARA robots, all the non-redundant robotic manipulators that satisfy the in-line wrist condition, and any non-redundant open-chain robot whose IKM should only solve the positioning problem, such as multi-legged walking robots.…”
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q-Rung Orthopair fuzzy time series forecasting technique: Prediction based decision making by Shahzaib Ashraf, Muhammad Shakir Chohan, Sameh Askar, Noman Jabbar

“…We also used numerous algebraic components for the q-Rung orthopair fuzzy time series, which has a union, max-min composition, cartesian product, and algorithm that are useful to calculate the method of data forecasting. …”
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HARA-GAN: Hybrid Attention and Relative Average Discriminator Based Generative Adversarial Network for MR Image Reconstruction by Lencho Desalegn, Worku Jifara

“…The zero filling image was generated using 12.5% under sampling rates for cartesian, and 10% under sampling rates for both radial and spiral under sampling masks. …”
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Philosophical Epistemological Study of Human–Machine Collaborative Technology in Intelligent Manufacturing by Qu Haoxiang, Xu Jiang, Sun Shouqian

“…Therefore, this paper, through ontological reflection, proposes a Cartesian intelligent manufacturing technology development path based on the Internet of Things, Internet of Contents & Knowledge, and Internet of Bodies. …”
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Correcting attenuation effects caused by interactions in the forest canopy in full-waveform airborne laser scanner data by K. Richter, N. Stelling, H.-G. Maas

“…For this purpose, the differential backscatter cross sections have to be projected into a Cartesian voxel structure. Thereby the voxel entries represent amplitudes of the cross section and can be interpreted as a local measure for the amount of pulse reflecting matter. …”
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Weighted Total Least Squares (WTLS) Solutions for Straight Line Fitting to 3D Point Data by Georgios Malissiovas, Frank Neitzel, Sven Weisbrich, Svetozar Petrovic

“…In this contribution the fitting of a straight line to 3D point data is considered, with Cartesian coordinates <inline-formula><math display="inline"><semantics><msub><mi>x</mi><mi>i</mi></msub></semantics></math></inline-formula>, <inline-formula><math display="inline"><semantics><msub><mi>y</mi><mi>i</mi></msub></semantics></math></inline-formula>, <inline-formula><math display="inline"><semantics><msub><mi>z</mi><mi>i</mi></msub></semantics></math></inline-formula> as observations subject to random errors. …”
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Phenomenological and Dialogic Thinking in Spiritual Reading: Spiritual Paradigms of Selected Biblical Figures by Sheldon Tabile

“…Evanston, Northwestern University Press, 1973. ______., Cartesian Mediations, the Hague: Martinus Nijhoff, 1967. ______., Ideas pertaining to a pure phenomenology and to a phenomenological philosophy (1st book), The Hague -Boston-Lancaster: Springer, 1983. ______., The Crisis of European Sciences and Transcendental Phenomenology, Evanston: Northwestern University Press, 1970. …”
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REGRESIÓN Y CORRELACIÓN DE SUPERFICIES ÓPTICAS DE REVOLUCIÓN EN FORMA CANÓNICA CONOCIDOS LOS RADIOS DE CURVATURA REGRESSÃO E CORRELAÇÃO DE SUPERFÍCIES ÓPTICAS DE REVOLUÇÃO EM FORMA... by Juan Camilo Valencia, Álvaro Hernán Bedoya

“…<br>Three mathematical models are presented for the regression and correlation of a cloud of N points in R3 with Cartesian coordinates xj, yj as abscissas, with his respective ordinate ri as a radius of curvature of the axial or sagittal section, but not corresponding to the Gaussian curvature, with a paraboloid, ellipsoid, and hyperboloid of revolution in canonical form. …”
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The design and development of specialized design tools for manufacturing equipment by Kriebel, Andrew Turner

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Shock formation in solutions to the 2D compressible Euler equations in the presence of non-zero vorticity by Speck, Jared R.

“…Specifically, the vorticity remains uniformly bounded, while the vorticity divided by the density exhibits even more regular behavior: the ratio remains uniformly Lipschitz relative to the standard Cartesian coordinates. To control the vorticity, we rely on a coalition of new geometric and analytic insights that complement the ones used by Christodoulou in his groundbreaking, sharp proof of shock formation in vorticity-free regions. …”
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Efficient spherical surface integration of Gauss functions in three-dimensional spherical coordinates and the solution for the modified Bessel function of the first kind by Wang, Y, Kong, J

“…A computationally concise algorithm is proposed for obtaining the expansion coefficients of polynomial terms when the coordinate system is transformed from cartesian to spherical. The resulting expression for h(s, Q) includes a number of cases of elementary integrals, the most difficult of which is II(n,μ)=∫0πcosnθe-μcosθdθ, with a nonnegative integer n and positive μ. …”
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Performance enhancements for a generic conic interior point algorithm by Coey, Chris, Kapelevich, Lea, Vielma, Juan P.

“…Our extensible, open-source conic interior point solver, Hypatia, allows modeling and solving any conic problem over a Cartesian product of exotic cones. In this paper, we introduce Hypatia’s interior point algorithm, which generalizes that of Skajaa and Ye (Math. …”
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Model predictive control for formation flying spacecraft by Breger, Louis Scott, 1979-

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Control and Estimation for Cooperative Manipulator Tasks by Blackmore, Lars, Block, Steve

“…As with most manipulation problems, the inverse kinematics problem must be solved so that the desired endpoint location can be specified in Cartesian coordinates, rather than in the joint space of the manipulator. …”
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Influence modeling of complex stochastic processes by Dong, Wen

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