Application of the Time Method for Studying Linear Reproducing Systems for Assessing the Dynamic Accuracy of Devices Based on Magnetoelectric Systems by Oleksandr Sytnik, Miraziz Sagatov, Konstantin Klyuchka, Sergey Protasov

“…At the same time, frequency methods have a number of limitations, in particular, due to the finiteness of the number of terms of the Fourier series in the analysis of periodic functions of time, as well as some other limitations when using the Fourier integral for non-periodic functions. …”
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RobPer: An R Package to Calculate Periodograms for Light Curves Based on Robust Regression by Anita M. Thieler, Roland Fried, Jonathan Rathjens

“…Hence, methods to fit periodic functions using weighted regression were developed in the past to calculate periodograms. …”
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Theoretical examination and simulations of two nonlinear evolution equations along with stability analysis by Muhammad Abdaal Bin Iqbal, Ejaz Hussain, Syed Asif Ali Shah, Zhao Li, Muhammd Zubair Raza, Adham E. Ragab, Emad A. Az-Zo’bi, Mohamed R. Ali

“…The solutions obtained comprise periodic functions, mixed periodic functions, rational solutions, and exponential solutions.…”
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Novel solutions to the coupled KdV equations and the coupled system of variant Boussinesq equations by Shao-Wen Yao, Asim Zafar, Aalia Urooj, Benish Tariq, Muhammad Shakeel, Mustafa Inc

“…The simple ansatz approach produces a variety of novel solutions in terms of hyperbolic and periodic functions. Graphical representation of solutions are also presented.…”
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On estimates of the order of the best M–term approximations of functions of several variables in the anisotropic Lorentz – Zygmund space by Akishev, Gabdolla

“…The article considers the anisotropic  Lorentz – Karamata space of periodic functions of several variables and the Nikol'skii – Besov class in this space. …”
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Fredholm property of nonlocal problems for integro-differential hyperbolic systems by Irina Kmit, Roman Klyuchnyk

“…Under natural regularity assumptions on the data, it is shown that the problems display completely non-resonant behavior and satisfy the Fredholm alternative in the spaces of continuous and time-periodic functions.…”
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The use of the isometry of function spaces with different numbers of variables in the theory of approximation of functions by D.M. Bushev, F.G. Abdullayev, I.V. Kal'chuk, M. Imashkyzy

“…In the work, we found integral representations for function spaces that are isometric to spaces of entire functions of exponential type, which are necessary for giving examples of equality of approximation characteristics in function spaces isometric to spaces of non-periodic functions. Sufficient conditions are obtained for the nonnegativity of the delta-like kernels used to construct isometric function spaces with various numbers of variables.…”
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PERIODIC TWISTS OF $\operatorname{GL}_{3}$-AUTOMORPHIC FORMS by EMMANUEL KOWALSKI, YONGXIAO LIN, PHILIPPE MICHEL, WILL SAWIN

“…We prove that sums of length about $q^{3/2}$ of Hecke eigenvalues of automorphic forms on $\operatorname{SL}_{3}(\mathbf{Z})$ do not correlate with $q$-periodic functions with bounded Fourier transform. This generalizes the earlier results of Munshi and Holowinsky–Nelson, corresponding to multiplicative Dirichlet characters, and applies, in particular, to trace functions of small conductor modulo primes.…”
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Next-Generation Dried Blood Spot Samplers for Protein Analysis: Describing Trypsin-Modified Smart Sampling Paper by Eleonora Pizzi, Trine Grønhaug Halvorsen, Christian J. Koehler, Léon Reubsaet

“…Trypsin immobilized on potassium-periodate-functionalized discs exhibits the highest trypsin activity when using cytochrome C as substrate. …”
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Collision Forgery Attack on the AES-OTR Algorithm under Quantum Computing by Lipeng Chang, Yuechuan Wei, Xiangru Wang, Xiaozhong Pan

“…This paper investigates the security of AES-OTR, one of the third-round algorithms in the CAESAR competition, under the Q2 model. The periodic functions of the associated data were constructed by forging the associated data according to the parallel and serial structure characteristics of the AES-OTR algorithm in processing the associated data, and the periodic functions of the associated data were constructed multiple times based on the Simon quantum algorithm. …”
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Weyl almost anti-periodic solution to a neutral functional semilinear differential equation by Weiwei Qi, Yongkun Li

“…In this work, we first propose a concept of Weyl almost anti-periodic functions. Then, we make use of the contraction mapping principle and analysis techniques to research the existence of a unique Weyl almost anti-periodic solution to a neutral functional semilinear abstract differential equation. …”
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Global asymptotic stability of pseudo almost periodic solutions to a Lasota-Wazewska model with distributed delays by Zhiwen Long

“…In this paper, we study a class of Lasota-Wazewska model with distributed delays, new criteria for the existence and global asymptotic stability of positive pseudo almost periodic solutions are established by using the fixed point method and the properties of pseudo almost periodic functions, together with constructing suitable Lyapunov function. …”
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GROUP CLASSIFICATION OF THE ELEMENTS AND D.I. MENDELEEV'S PERIODIC LAW by A. L. Gourski, L. I. Hurski

“…It is noted that in mathematics, one relate to the periodic functions those which values do not change by addition of the definite but not equal to zero number to the argument. …”
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Mittag-Leffler Stability and Attractiveness of Pseudo Almost Periodic Solutions for Delayed Cellular Neural Networks by Zahra Eidinejad, Reza Saadati, Dušan D. Repovš

“…Using general measure theory and the Mittag-Leffler function, we obtain the existence of unique solutions for cellular neural equations and investigate the Mittag-Leffler stability and attractiveness of pseudo almost periodic functions. We also present numerical examples to illustrate the application of our results.…”
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Various dynamic behaviors to the (2+1)-dimensional Nizhnik–Novikov–Veselov equations in incompressible fluids by Mei Yang, Jian-Guo Liu

“…Furthermore, the interaction solutions of the lump and periodic waves are investigated by a special function consist of the quadratic polynomial functions and periodic functions. At the same time, we also choose some specific examples to illustrate the dynamic behaviors of nonlinear waves.…”
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New traveling wave exact solutions to the coupled Klein–Gordon system of equations by Subin P. Joseph

“…A rational ansatz form is assumed to derive the required exact solutions in terms of the doubly periodic functions. We derive all the possible real solutions having this ansatz form and which are functions of Jacobi elliptic functions. …”
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Estimations of the best M-term approximations of functions in the Lorentz space with constructive methods by G. Akishev

“… This paper considers the Lorentz space of periodic functions of many variables with the anisotropic norm, of functional Nikol’skii-Besov’s class and of the best M -term approximation of function. …”
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Ground states for a class of asymptotically periodic Schrödinger–Poisson systems with critical growth by Da-Bin Wang, Hua-Fei Xie, Wen Guan

“…The purpose of this paper is to study the existence of ground state solution for the Schr\"{o}dinger–Poisson systems: \[\begin{cases} -\Delta u+V(x)u+K(x)\phi u=Q(x)|u|^{4}u+f(x,u),&x\in\mathbb{R}^{3},\\ -\Delta\phi=K(x)u^{2},&x\in\mathbb{R}^{3}, \end{cases} \] where $V(x)$, $K(x)$, $Q(x)$ and $f(x,u)$ are asymptotically periodic functions in $x$.…”
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Two Analytical Techniques for Fractional Differential Equations with Harmonic Terms via the Riemann–Liouville Definition by Ragwa S. E. Alatwi, Abdulrahman F. Aljohani, Abdelhalim Ebaid, Hind K. Al-Jeaid

“…The second approach avoids the LT and expresses the solution in terms of exponential and periodic functions which is analytic in the whole domain. …”
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Improved algorithm for periodic steady-state analysis in nonlinear electromagnetic devices by T.J. Sobczyk, M. Radzik

“…A novel differential operator is developed for periodic functions and the iterative algorithm determining periodic steady-state solutions in a selected set of time instants is identified. …”
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