Gradient method for designing cascaded DOEs focusing radiation of different wavelengths by G.A. Motz, D.V. Soshikov, L.L. Doskolovich, E.V. Byzov, E.A. Bezus, D.A. Bykov

“…Explicit expressions are obtained for the derivatives of the functional, and on this basis, a gradient method for designing cascaded DOEs is formulated. …”
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Optimization of Shift Strategy Based on Vehicle Mass and Road Gradient Estimation by Huijun Yue, Haobo Jing, Zhenkun Dai, Jinyu Lin, Zihan Ma, Changtong Zhao, Pan Zhang

“…For electrically driven commercial vehicles equipped with three-speed automatic mechanical transmission (AMT), the transmission control unit (TCU) without vehicle mass and road gradient estimation function will lead to frequent shifting and insufficient power during vehicle full-load or grade climbing. …”
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On Solving of Constrained Convex Minimize Problem Using Gradient Projection Method by Taksaporn Sirirut, Pattanapong Tianchai

“…Let C and Q be closed convex subsets of real Hilbert spaces H1 and H2, respectively, and let g:C→R be a strictly real-valued convex function such that the gradient ∇g is an 1/L-ism with a constant L>0. …”
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The Impact of Plasma Density Gradients on Lower Band Chorus Wave Propagation by D. P. Hartley, L. Chen, W. Gu, I. W. Christopher, O. Santolik

“…Here, for the first time, this relationship is investigated more generally by considering the wave normal angle, θk, as a function of the magnitude of all observed density gradients. …”
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Boundedness of Global Solutions for a Heat Equation with Exponential Gradient Source by Zhengce Zhang, Yanyan Li

“…To do so, we explicitly compute a nontrivial Lyapunov's functional by carrying out the method of Zelenyak.…”
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Evolution of Reynolds Stresses in Turbulent Wake-Flows with Longitudinal Pressure Gradient by J.W. Elsner, J. Wilczyński

“…Special importance has also been attached to the analysis of energy spectrum functions and their dependence on longitudonal pressure gradient, The spectral coefficient of double correlation between turbulent velocity components has been found to be an increasing function of , which may be treated as a tendency of accelerated flows to a more intensive stabilization of isotropic structure. …”
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New conjugacy condition with pair-conjugate gradient methods for unconstrained optimization by Abbas Al-Bayati, Huda Ahmed

“…Conjugate gradient methods are wildly used for unconstrained optimization especially when the dimension is large. …”
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Optimization method for variable fractional delay filters based on gradient descent by ZHUANG Ling, HAO Hanjie

“…Firstly, the matrix form of the objective function and gradient expressions were derived, and an exponential moving average was used to adjust the step size based on historical and current gradient information. …”
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The impact of gradient variable temperature fermentation on the quality of cigar tobacco leaves by Qianying Zhang, Qianying Zhang, Yang Huang, Yang Huang, Hongyue An, Hongyue An, Shuanghong Yang, Shuanghong Yang, Jinshan Lei, Jinshan Lei, Yue Wang, Yue Wang, Pinhe Li, Pinhe Li, Hongfei Zhang, Wen Cai, Wen Cai, Wen Cai, Yun Jia, Yun Jia, Yongqiang Pang, Dongliang Li, Dongliang Li

“…Changes in sensory evaluation, chemical composition, and bacterial absolute quantitative structure and function were examined throughout the process of gradient variable temperature fermentation.ResultsCompared to constant temperature fermentation, gradient variable temperature fermentation improved the sensory quality of CTLs, reduced total sugar and cembrane degradation products, and increased the amino acid contents. …”
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Improving the Accuracy of Neural Network Pattern Recognition by Fractional Gradient Descent by Ruslan I. Abdulkadirov, Pavel A. Lyakhov, Valentina A. Baboshina, Nikolay N. Nagornov

“…This optimizer searches the global minimum of the loss function considering the fractional gradient directions achieved by Riemann-Liouville, Caputo, and Grunwald-Letnikov derivatives. …”
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Adaptive Multi-Gradient Guidance with Conflict Resolution for Limited-Sample Regression by Yu Lin, Jiaxiang Lin, Keju Zhang, Qin Zheng, Liqiang Lin, Qianqian Chen

“…Recent studies report that gradient guidance extracted from a single-reference model can improve Limited-Sample regression. …”
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A Gradient-Based Reinforcement Learning Algorithm for Multiple Cooperative Agents by Zhen Zhang, Dongqing Wang, Dongbin Zhao, Qiaoni Han, Tingting Song

“…Furthermore, we apply the Q-value function to estimate the gradient and derive the probability of maximal reward based on estimated gradient ascent (PMR-EGA) algorithm. …”
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Variable-Parameter Impedance Control of Manipulator Based on RBFNN and Gradient Descent by Linshen Li, Fan Wang, Huilin Tang, Yanbing Liang

“…To address the computationally intensive nature of current hybrid force/position control methods, a variable-parameter impedance control method for manipulators, utilizing a gradient descent method and Radial Basis Function Neural Network (RBFNN), is proposed. …”
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Specificity and tunability of efflux pumps: A new role for the proton gradient? by Matthew Gerry, Duncan Kirby, Boian S Alexandrov, Dvira Segal, Anton Zilman

“…These results highlight the unexpected effects of thermodynamic driving forces out of equilibrium and illustrate how efflux pump structure and function are conducive to the emergence of multidrug resistance.…”
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Formation and Evolution Simulations of Saturn, Including Composition Gradients and Helium Immiscibility by Peter Bodenheimer, David J. Stevenson, Jack J. Lissauer, Gennaro D’Angelo

“…Models of the distribution of heavy elements as a function of radius are compared with those derived to fit the observations of the Cassini mission, with rough qualitative agreement. …”
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Stochastic Zeroth-Order Multi-Gradient Algorithm for Multi-Objective Optimization by Zhihao Li, Qingtao Wu, Moli Zhang, Lin Wang, Youming Ge, Guoyong Wang

“…Nowadays, many MOO algorithms assume that gradient information is easily available and use this information to optimize functions. …”
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Estimates of the Hyperbolic Radius Gradient and Schwarz–Pick Inequalities for the Eccentric Annulus by D.Kh. Giniyatova

“…By A(Ω, Π) we shall designate the class of functions f which are holomorphic or meromorphic in Ω and such that f(Ω) ϲ Π. …”
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Importance of gradients in membrane properties and electrical coupling in sinoatrial node pacing. by Shin Inada, Henggui Zhang, James O Tellez, Nitaro Shibata, Kazuo Nakazawa, Kaichiro Kamiya, Itsuo Kodama, Kazuyuki Mitsui, Halina Dobrzynski, Mark R Boyett, Haruo Honjo

“…Normal functioning of the SAN (in terms of cycle length, position of leading pacemaker site, conduction times, activation and repolarization sequences and space constants) was observed when, from the centre to the periphery, (i) cell characteristics (cell size and ionic current densities) were changed in a gradient fashion from a central-type (lacking INa) to a peripheral-type (possessing INa) and (ii) coupling conductance was increased in a gradient fashion. …”
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New Scaled Proposed formulas For Conjugate Gradient Methods in Unconstrained Optimization by Abbas Al-Bayati, Marwan Jameel

“…In this paper, three efficient Scaled Nonlinear Conjugate Gradient (CG) methods for solving unconstrained optimization problems are proposed. …”
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New Scale Dai-Yaun Conjugate Gradient Method for Unconstrained Optimization by Hamsa Chilmerane

“…In this paper, we suggest a modified Dai-Yuan conjucay coefficient of conjugate gradient algorithm and propose new spectral form three-term conjugate gradient algorithm. …”
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