Implementation of Special Function Unit for Vertex Shader Processor Using Hybrid Number System by Avni Agarwal, P. Harsha, Swati Vasishta, S. Sivanantham

“…A prime feature of this standard is a special function unit (SFU), which performs all the required mathematical computations on the vertex information corresponding to the image. …”
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Sliding Mode Output Feedback Control of a Flexible Rotor Supported by Magnetic Bearings by A. S. Lewis, A. Sinha, K. W. Wang

“…It is assumed that the number of states is greater than the number of sensors. A mathematical model of the rotor]magnetic bearing system is presented in terms of partial differential equations. …”
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The Spectrophotometric Multicomponent Analysis of a Ternary Mixture of Paracetamol, Aspirin, and Caffeine by the Double Divisor-Ratio Spectra Derivative Method by Reza Hajian, Ahmad Soltaninezhad

“…All of the solutions adjusted to pH 11 before recording the spectra in the range of 220 to 320 nm. Also, the mathematical explanation of the procedure is illustrated. …”
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Analysis of the Instability Phenomena Caused by Steam in High-Pressure Turbines by Paolo Pennacchi, Andrea Vania

“…As a consequence, the eigenvalues and eigenmodes of the mathematical model of the machine change. The real part of the eigenvalue associated with the first flexural normal mode of the turbine shaft may become positive causing the conditions for unstable vibrations. …”
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Modeling the dynamics of two-factor socio-economic states through mappings close to extension by V. V. Egorov

“…A new way of developing a mathematical model of the dynamics of the factors forming the considered social, political, economic, ecological or other space of life activity of society, depending on local changes in parameters affecting these factors, is presented. …”
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Higher-order topology for collective motions by Zijie Sun, Tianjiang Hu

“…Abstract Collective motions are prevalent in various natural groups, such as ant colonies, bird flocks, fish schools and mammal herds. Physical or mathematical models have been developed to formalize and/or regularize these collective behaviors. …”
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New Active Control Method Based on Using Multiactuators and Sensors Considering Uncertainty of Parameters by Babak Karimpour, Ali Keyhani, Javad Alamatian

“…This subject is achieved by simple mathematical formulation. The proposed method does not depend on the type of dynamic load and it could be applied to control structures with multidegrees of freedom. …”
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Similarities and differences between working processes of Ranque effect and Hartmann–Sprenger tube by V. I. Kuznetsov, V. V. Makarov, A. Yu. Shander

“…The physical and mathematical models of the processes occurring in the vortex tubes (Ranque effect) and Hartmann–Sprenger tube. …”
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Control of Limit Cycle Oscillation in a Three Degrees of Freedom Airfoil Section Using Fuzzy Takagi-Sugeno Modeling by Douglas Domingues Bueno, Luiz Carlos Sandoval Góes, Paulo José Paupitz Gonçalves

“…The proposed methodology is developed for the three degrees of freedom typical section airfoil considering aerodynamic forces from Theodorsen’s theory. The mathematical model is written in the state space representation using rational function approximation to write the aerodynamic forces in time domain. …”
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A Novel Ultrasound Thermometry Method Based on Thermal Strain and Short and Constant Acoustic Bursts: Preliminary Study in Phantoms by Omar Gachouch, Bruno Giammarinaro, Teymour Kangot, Caterina Monini, Rémi Souchon

“…Under the assumption that the acoustic attenuation does not change significantly with temperature, the thermal strain induced by such bursts presents a linear relation with temperature. A mathematical demonstration is given in the introduction. …”
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A Lattice-Theoretic Approach to Multigranulation Approximation Space by Xiaoli He, Yanhong She

“…The obtained results help us gain more insights into the mathematical structure of multigranulation approximation spaces.…”
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The surface of non-linear rotation by K. L. Panchuk, T. M. Myasoyedova

“…The paper considers a geometric scheme, a mathematical model and an algorithm for shaping a non-linear rotation surface. …”
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Intelligent Management of Air Traffic Flow Based on Intelligent Motion Coordinate Data Model by Junhao Liu, Qing Cheng, Yuanji Wang, Changqi Yang, Rui Zhou, Xinping Zhu, Di Yao, Junjie Zhou, Yaqian Du, Shanshan Yang

“…To adapt to the intelligent management of traffic flow in modern aviation, this study improves the algorithm according to the data exercise method and establishes the mathematical model and vector model of intelligent motion coordinates. …”
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Power Balance Optimization Technology of Microgrid Based on Full-Bridge Converter by Shuailong Dai, Bin Cao, Rui Liu, Liyang Zhu, Mengfan Li

“…First, the working structure and mathematical model are analyzed, and the power model is then established. …”
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Diffusion models for super-resolution microscopy: a tutorial by Harshith Bachimanchi, Giovanni Volpe

“…We provide the necessary theoretical background, the essential mathematical derivations, and a detailed Python code implementation using PyTorch. …”
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Solving “Antenna Array Thinning Problem” Using Genetic Algorithm by Rajashree Jain, G. S. Mani

“…It is required to find a strategic subset of antenna elements for thinning so as to have its optimum performance. From a mathematical perspective this is a nonlinear, multidimensional problem with multiple objectives and many constraints. …”
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Optimization kinematic synthesis of four-link linkage mechanism in two preset positions by E. S. Gebel, E. A. Chigrinova

“…The widespread use of flat articulated four-link mechanisms in various automatic devices and devices requires the further development of automated kinematic synthesis methods, which, based on modern mathematical approaches, will reduce the required amount of a priori information and obtain an exact solution. …”
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The Use of Big Data to Improve Human Health: How Experience From other Industries Will Shape the Future by Timothy E Hewett, Greg Olsen, Mark Atkinson

“…‘Data science’ represents a set of mathematical and software development related techniques that are applied across a wide range of problems and industries. …”
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Dynamic Modeling and Simulation of a Super-High-Speed Circumferential-Flux Hysteresis Motor by A. Halvaei Niasar, M. Zare, H. Moghbelli

“…This paper presents the dynamic performance characteristics of hysteresis motors using a Matlab/Simulink software. A nonlinear mathematical model based on a d-q axis theory in the rotor reference frame is applied to study the starting and synchronization processes of a hysteresis machine with a circumferential-flux-type rotor. …”
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Analysis of the Thermal Characteristics of Surrounding Rock in Deep Underground Space by Liu Chen, Jiangbo Li, Fei Han, Yu Zhang, Lang Liu, Bo Zhang

“…The high temperature of deep underground space is essentially influenced by the thermal characteristics of the surrounding rock. According to the mathematical model of heat transfer of the surrounding rock in deep underground space, similar criteria numbers are established. …”
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