Quaternion Fractional Fourier Transform: Bridging Signal Processing and Probability Theory by Muhammad Adnan Samad, Yuanqing Xia, Saima Siddiqui, Muhammad Younus Bhat, Didar Urynbassarova, Altyn Urynbassarova

“…This paper presents a rigorous theoretical foundation for the 1DQFRFT, examining essential properties such as linearity, the Plancherel theorem, conjugate symmetry, convolution, and a generalized Parseval’s theorem that collectively demonstrate the transform’s analytical power. …”
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Dynamics Analysis of an Avian Influenza A (H7N9) Epidemic Model with Vaccination and Seasonality by Juping Zhang, Yun Li, Zhen Jin, Huaiping Zhu

“…The global stability of the disease-free equilibrium and the existence of positive periodic solution are proved by the comparison theorem and the asymptotic autonomous system theorem. …”
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Fast Hybrid Method for the Study on Monostatic Scattering from Plasma-Coated Target above a Rough Surface by Rui Wang, Shui-Rong Chai, Li-Xin Guo

“…A fast hybrid method combining the reciprocity theorem with high frequency approximation algorithm is presented to deal with the problem of the monostatic scattering from a two-dimensional (2D) plasma-coated target above a one-dimensional (1D) Gaussian rough surface illuminated by the tapered incident wave. …”
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Fractional Grassi–Miller Map Based on the Caputo h-Difference Operator: Linear Methods for Chaos Control and Synchronization by Ibtissem Talbi, Adel Ouannas, Giuseppe Grassi, Amina-Aicha Khennaoui, Viet-Thanh Pham, Dumitru Baleanu

“…By exploiting the Caputo h-difference operator, at first, the chaotic dynamics of the map are analyzed via bifurcation diagrams and phase plots. Then, a novel theorem is proved in order to stabilize the dynamics of the map at the origin by linear control laws. …”
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Periodic orbits and gravitational wave radiation in short hair black hole spacetimes for an extreme mass ratio system by Lai Zhao, Meirong Tang, Zhaoyi Xu

“…Abstract For a short hair black hole(BH) that bypasses the “no-short-hair” theorem, its hair parameters have a significant impact near the event horizon and may thus carry the internal information of the BH. …”
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The Existence of Positive Solutions for Boundary Value Problem of the Fractional Sturm-Liouville Functional Differential Equation by Yanan Li, Shurong Sun, Zhenlai Han, Hongling Lu

“…By means of the Guo-Krasnoselskii fixed point theorem and the fixed point index theorem, some positive solutions are obtained, respectively. …”
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Rogue Wave and Multiple Lump Solutions of the (2+1)-Dimensional Benjamin-Ono Equation in Fluid Mechanics by Zhonglong Zhao, Lingchao He, Yubin Gao

“…Four kinds of rogue wave solutions are obtained by means of Theorem 1. In Theorem 2, three polynomial functions are used to derive multiple lump wave solutions. …”
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Set-Word Embeddings and Semantic Indices: A New Contextual Model for Empirical Language Analysis by Pedro Fernández de Córdoba, Carlos A. Reyes Pérez, Claudia Sánchez Arnau, Enrique A. Sánchez Pérez

“…We formally define all necessary elements and prove the main results about the model, including a compatibility theorem for estimating the representability of semantically meaningful external terms in the model (which are written as real Lipschitz functions in the metric space), proving the relation between the semantic index and the metric of the space (Theorem 1). …”
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Flow of electrorheological fluid under conditions of slip on the boundary

“…<p>We study a mathematical model describing flows of electrorheological fluids. A theorem of existence of a weak solution is proved. …”
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Compatible mappings and common fixed points revisited by Gerald Jungck

“…A fixed point theorem involving a Meir-Keeler type contraction principle is refined by diminishing continuity requirements.…”
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On Dirichlet convolution method by Indulata Sukla

“…In this paper we have proved limitation theorem for (D,h(n)) summability methods and have shown that it is best possible.…”
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Bifurcation Analysis and Chaos Control in a Discrete Epidemic System by Wei Tan, Jianguo Gao, Wenjun Fan

“…By using the center manifold theorem and bifurcation theorem in the interior R+2, the specific conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation have been derived. …”
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Tauberian-Cardy formula with spin by Sridip Pal, Zhengdi Sun

“…Abstract We prove a 2 dimensional Tauberian theorem in context of 2 dimensional conformal field theory. …”
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Noether symmetries, solutions and conserved quantities of a new (3+1)-dimensional Painlevé integrable fifth-order equation with third-order temporal dispersion: Multi-analytical ap... by Oke Davies Adeyemo

“…The well-celebrated Noether's theorem is engaged to comprehensively construct conserved vectors of the underlying equation. …”
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Lie and Riccati Linearization of a Class of Liénard Type Equations by A. G. Johnpillai, C. M. Khalique, F. M. Mahomed

“…Since the class of equations also admits an eight-parameter Lie group of point transformations, we utilize the Lie-Tresse linearization theorem to obtain linearizing point transformations as well. …”
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Compressive narrowband interference detection and parameter estimation in direct sequence spread spectrum communication by Zengkai Shi, Yongshun Zhang, Zhaoyong Qian, Xiaoshuang Sun, Xiangtai Ma

“…Abstract The Shannon‐Nyquist sampling theorem that is based on narrowband interference (NBI) detection and parameter estimation methods in direct sequence spread spectrum (DSSS) communication is limited by the high sampling rate. …”
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Finite-Time Projective Synchronization of Fractional-Order Memristive Neural Networks with Mixed Time-Varying Delays by Meng Hui, Chen Wei, Jiao Zhang, Herbert Ho-Ching Iu, Ni Luo, Rui Yao, Lin Bai

“…In addition to the traditional Lyapunov function with 1-norm form in Theorem 1, a more general and flexible Lyapunov function based on p-norm is constructed in Theorem 2 to analyze the finite-time projective synchronization problem, and the estimation of settling time has been verified less conservative than previous results. …”
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On the 75th birth anniversary of Marat Mirzaevich Arslanov by I.Sh. Kalimullin, V.L. Selivanov

“…Numerous generalizations and unexpected applications of this theorem have been found by many authors in various areas of mathematics and computer science. …”
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A characterization of random approximations by Ismat Beg

“…By using Hahn-Banach theorem, a characterization of random approximations is obtained.…”
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