The theorem about the transformer excitation current waveform mapping into the dynamic hysteresis loop branch for the sinusoidal magnetic flux case by Petrović Nenad, Pjevalica Velibor, Vujičić Vladimir

“…This paper analyses aspects of the approximation theory application on the certain subsets of the measured samples of the transformer excitation current and the sinusoidal magnetic flux. …”
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How Much We Gain by Surplus-Dependent Premiums—Asymptotic Analysis of Ruin Probability by Jing Wang, Zbigniew Palmowski, Corina Constantinescu

“…In this paper, we generate boundary value problems for ruin probabilities of surplus-dependent premium risk processes, under a renewal case scenario, Erlang (2) claim arrivals, and a hypoexponential claims scenario, Erlang (2) claim sizes. Applying the approximation theory of solutions of linear ordinary differential equations, we derive the asymptotics of the ruin probabilities when the initial reserve tends to infinity. …”
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First-order localization and quantum phase transition induced by quasicrystal imaginary domain by Xianqi Tong, Su-Peng Kou

“…To characterize the wave functions in these distinct phases, we introduce a low-energy approximation theory and an effective two-chain model. Additionally, we uncover a first-order quantum phase transition induced by quasicrystal domains. …”
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Rényi Entropies of Multidimensional Oscillator and Hydrogenic Systems with Applications to Highly Excited Rydberg States by Jesús S. Dehesa

“…Powerful asymptotic approaches of approximation theory have been used when the polynomial’s degree or the weight-function parameter(s) of the Hermite, Laguerre, and Gegenbauer polynomials have large values. …”
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Stochastic Resonance of Asymmetric Joint Potential System and Its Application in Weak Signal Detection by Yuan Liu, Shao Juan Ma, Xiao Yan Ma

“…Secondly, the analytical expression of signal-to-noise ratio (SNR) is derived based on two-state theory and adiabatic approximation theory. Meanwhile, the influence of system parameters on SNR is discussed theoretically. …”
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Eigenproblem Versus the Load-Carrying Capacity of Hybrid Thin-Walled Columns with Open Cross-Sections in the Elastic Range by Zbigniew Kolakowski, Andrzej Teter

“…Nonlinear buckling problems were solved within Koiter’s approximation theory. A multimodal approach was assumed to investigate an effect of symmetrical and anti-symmetrical buckling modes on the ultimate load-carrying capacity. …”
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How Many Subpopulations Is Too Many? Exponential Lower Bounds for Inferring Population Histories by Kim, Younhun, Koehler, Frederic, Moitra, Ankur, Mossel, Elchanan, Ramnarayan, Govind

“…Using a variety of tools from information theory, the theory of extremal polynomials, and approximation theory, we prove new sharp information-theoretic lower bounds on the problem of reconstructing population structure - the history of multiple subpopulations that merge, split, and change sizes over time. …”
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Lanczos method for spatio‐temporal graph convolutional networks to forecast expressway flow by Zhumei Gou, Yonggang Shen, Shuifu Chen

“…To address these limitations, the authors propose the Lanczos method for Spatio‐Temporal Graph Convolutional Networks (LSTGCN); this approach uses the low‐rank approximation theory to drive pre‐defined graphs to collect important information and eliminate spatial redundancy. …”
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A NEW FRAMEWORK FOR ACCURACY ASSESSMENT OF LIDAR-DERIVED DIGITAL ELEVATION MODELS by X. Liu

“…For DEM’s vertical accuracy, approximation theory from numerical analysis is used to quantify the total error at each DEM point as well as its three error components – sensor error, ground error, and interpolation error. …”
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Virtual Work Principle for Piezoelectric Semiconductors and Its Application on Extension and Bending of ZnO Nanowires by Jingbo Chen, Gongye Zhang, Dongbo Li, Yilin Qu

“…As an application of the PVW, a one-dimensional (1D) approximation theory for the extension and bending of PS nanowires is established by directly applying the PVW and Bernoulli–Euler beam theory with the aid of the second-order approximation of electrostatic potential. …”
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Theoretical Simulation of the High–Order Harmonic Generated from Neon Atom Irradiated by the Intense Laser Pulse by Siqi Wei, Yun Pan, Yue Qiao, Shushan Zhou, Haiying Yuan, Jun Wang, Fuming Guo, Yujun Yang

“…Based on the strong field approximation theory and numerical solution of Maxwell’s propagation equations, the high–order harmonic is generated from a neon (Ne) atom irradiated by a high–intensity laser pulse whose central wavelength is 800 nm. …”
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Quality Assessment of Fruits and Vegetables Based on Spatially Resolved Spectroscopy: A Review by Wan Si, Jie Xiong, Yuping Huang, Xuesong Jiang, Dong Hu

“…The principle of light transfer in biological tissues, diffusion approximation theory and methodologies are introduced, and different configuration designs for spatially resolved spectroscopy are compared and analyzed. …”
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A theta-scheme approximation of basic reproduction number for an age-structured epidemic system in a finite horizon by Wenjuan Guo, Ming Ye, Xining Li, Anke Meyer-Baese, Qimin Zhang

“…Using the spectral approximation theory, we obtain that $\mathcal{R}_{0, n}\rightarrow\mathcal{R}_0$ as $n\rightarrow+\infty$. …”
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Rheology of peristaltic flow in couple stress fluid in an inclined tube: Heat and mass transfer analysis by Z Abbas, A Shakeel, MY Rafiq, S Khaliq, J Hasnain, A Nadeem

“…The lubrication approximation theory is utilized to simplify the normalized equations. …”
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Tunneling Current Variations in Small-Sized Devices Based on a Compact Threshold Voltage Model by Zhichao Zhao, Tiefeng Wu, Chunyu Zhou, Miao Wang, Yunfang Xi, Qiuxia Feng

“…By solving a Poisson equation, in this paper, we demonstrate a comprehensive physical model for the threshold voltage of strained Si NMOSFETs using the gradual channel approximation theory and a quasi-two-dimensional analysis. …”
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A Priori-Based Subarray Selection Algorithm for DOA Estimation by Linghao Zeng, Guanghua Zhang, Chongzhao Han

“…Thus, according to the low-rank matrix approximation theory, an optimal low-rank approximate matrix is obtained and an algorithm is proposed to select the elements of the original array according to right singular vectors of the approximate matrix. …”
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Multiobjective Hyperparameter Optimization of Artificial Neural Networks for Optimal Feedforward Torque Control of Synchronous Machines by Niklas Monzen, Florian Stroebl, Herbert Palm, Christoph M. Hackl

“…Finally, based on the most recent results from ANN approximation theory, guidelines for Pareto optimal ANN-based OFTC design and implementation are provided.…”
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Multi-Time Scale Smoothed Functional With Nesterov’s Acceleration by Abhinav Sharma, K. Lakshmanan, Ruchir Gupta, Atul Gupta

“…The main contribution of our work is to prove the convergence of this algorithm using the stochastic approximation theory. We propose a novel Lyapunov function to show the associated second-order ordinary differential equations’ (o.d.e.) stability for a non-autonomous system. …”
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The characteristic analysis of stochastic resonance in a time polo-delayed tristable system and its application by Gang Zhang, Pan Xie, Tianqi Zhang

“…Then, by adiabatic approximation theory, the signal-to-noise ratio (SNR) is derived. …”
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A Bayesian regularization network approach to thermal distortion control in 3D printing by Xie, Yuxi, Li, Boyuan, Wang, Chao, Zhou, Kun, Wu, C. T., Li, Shaofan

“…Inspired by points registration in computer vision and function approximation theory, the Bayesian regularization network method is used to quantify thermal distortion in 3D printed products. …”
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