An Extension of the Carathéodory Differentiability to Set-Valued Maps by Pedro Hurtado, Alexander Leones, M. Martelo, J. B. Moreno

“…This paper uses the generalization of the Hukuhara difference for compact convex set to extend the classical notions of Carathéodory differentiability to multifunctions (set-valued maps). …”
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Introductory remarks on complex multiplication by Harvey Cohn

“…In its advanced form it is a unifying motivation of classical mathematics from elliptic integrals to number theory; and it is still of active interest. …”
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The dirichlet boundary conditions and related natural boundary conditions in strengthened sobolev spaces for discretized parabolic problems by E. D'Yakonov

“…Correctness of initial boundary value problems and their discretizations are analyzed under unusual second-order boundary conditions, which can be considered as natural boundary conditions in strengthened Sobolev spaces and as improvements (in some cases) of the classical Dirichlet boundary conditions. Special attention is paid to optimal perturbation estimates for new variants of the penalty method with respect to the Dirichlet conditions.…”
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Anterior Palatal Fistula Formation after Le Fort I Osteotomy in Conventional Orthognathic Surgery by Saeed Nezafati, Tannaz Pourlak

“…The present study investigated a case of anterior palatal fistula following the classic Le Fort I osteotomy.…”
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Computation of Channel Capacity Based on Self-Concordant Functions by Da-gang Tian, Yi-qun Huang

“…The computation of channel capacity is a classical issue in information theory. We prove that algorithms based on self-concordant functions can be used to deal with such issues, especially when constrains are included. …”
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PHILOSOPHY OF SCIENCE IN ENGINEERING EDUCATION: A PRACTICE!ORIENTED APPROACH by Natalya I. Martishina

“…The key theme of the article is the necessity of the classical course of the philosophy of science for training of a future researcher and engineer. …”
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On the numerical solving of one minimization problem by Raimondas Čiegis, Violeta Pakenienė

“…We propose the numerical algorithm determination of the optimal iterative parameters. Using it we solve classical minimization 2D and 3D problems and modificate 2D and 3D minimization problems and analyse the convergence rate dependence on the matrix spectral characteristics. …”
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About Stabilization of the Controlled Inverted Pendulum Under Stochastic Perturbations of the Type of Poisson’s Jumps by Leonid Shaikhet

“…The classical problem of stabilization of the controlled inverted pendulum is considered in the case of stochastic perturbations of the type of Poisson’s jumps. …”
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Localization and summability of multiple Hermite series by G. E. Karadzhov, E. E. El-Adad

“…More precisely, localization theorems for some classes of functions are proved and sharp sufficient conditions are given. Thus the classical Szegö results are extended to the n-dimensional case. …”
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Dissipative measure-valued solutions to the magnetohydrodynamic equations by Jianwei Yang, Huimin Wang, Qihong Shi

“… In this paper, we study the dissipative measure-valued solution to the magnetohydrodynamic equations of 3D compressible isentropic flows with the adiabatic exponent γ > 1 and prove that a dissipative measure-valued solution is the same as the standard smooth classical solution as long as the latter exists, provided they emanate from the same initial data (weak–strong) uniqueness principle. …”
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Notes on stability of the generalized gamma functional equation by Gwang Hui Kim, Bing Xu, Weinian Zhang

“…In this note, those conditions are simplified to be checked easily and more interesting examples other than the classical gamma functional equation are displayed.…”
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HyQ2: A Hybrid Quantum Neural Network for NextG Vulnerability Detection by Yifeng Peng, Xinyi Li, Zhiding Liang, Ying Wang

“…We address the limitations of classical machine learning models in processing the intrinsic linkage relationships of high-dimensional data. …”
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Forecasting the Number of the Wounded after an Earthquake Disaster Based on the Continuous Interval Grey Discrete Verhulst Model by Jun Zhang, Tongyuan Wang, Jianpeng Chang, Yan Gou

“…It can effectively overcome the systematic errors caused by the discrete form equation for parameter estimation and continuous form equation for simulation and prediction in classical grey Verhulst model, so as to improve the prediction accuracy. …”
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Evaluation of the Hair Cell Regeneration in Zebrafish Larvae by Measuring and Quantifying the Startle Responses by Changquan Wang, Zhenmin Zhong, Peng Sun, Hanbing Zhong, Hongzhe Li, Fangyi Chen

“…The results show a similar trend to the classical hair cell staining method. The startle response was reduced with drug treatment and recovered after removal of the drug. …”
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Parameter constraints on a black hole with Minkowski core through quasiperiodic oscillations by Ming-Yu Guo, Meng-He Wu, Xiao-Mei Kuang, Hong Guo

“…In particular, since the parameter g describes the degree of deviation from the classical Schwarzschild black hole, our studies suggest that, within a certain level of confidence, the black holes in the current model can deviate from the classical singularity structure of Schwarzschild black holes, and exhibit quantum corrections near the core.…”
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Multi-objective assessment of hydrological model performances using Nash–Sutcliffe and Kling–Gupta efficiencies on a worldwide large sample of watersheds by Mathevet, Thibault, Le Moine, Nicolas, Andréassian, Vazken, Gupta, Hoshin, Oudin, Ludovic

“…We also illustrate the negative impacts of classical mathematical transformations (square root) applied to streamflow when employing NSE and KGE as metrics for model calibration.…”
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Nearly AdS2 holography in quantum CGHS model by Shinji Hirano, Yang Lei

“…In distinction to the classical model, the quantum-corrected CGHS model has an AdS2 vacuum with a constant dilaton. …”
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Evaluation of the PANS method for the prediction of the fluid flow in a cyclone separator by Bitar, Zaher, Uystepruyst, David, Beaubert, François, Méresse, Damien, Morin, Céline

“…The proposed model offers a better cost to quality ratio compared to the classic RANS approach.…”
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Influence of Surface Energy Effects on Elastic Fields of a Layered Elastic Medium under Surface Loading by Supakorn Tirapat, Teerapong Senjuntichai, Jaroon Rungamornrat

“…In addition, unlike the classical elasticity solution, size-dependent behavior of elastic fields is noted. …”
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Logarithmic Generalization of the Lambert W Function and Its Applications to Adiabatic Thermostatistics of the Three-Parameter Entropy by Cristina B. Corcino, Roberto B. Corcino

“…A generalization of the Lambert W function called the logarithmic Lambert function is introduced and is found to be a solution to the thermostatistics of the three-parameter entropy of classical ideal gas in adiabatic ensembles. The derivative, integral, Taylor series, approximation formula, and branches of the function are obtained. …”
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