Green’s Function and Positive Solutions for a Second-Order Singular Boundary Value Problem with Integral Boundary Conditions and a Delayed Argument by Xuemei Zhang, Meiqiang Feng

“…Furthermore, several new and more general results are obtained for the existence of positive solutions for the above problem by using Krasnosel’skii’s fixed point theorem. We discuss our problems with a delayed argument, which may concern optimization issues of some technical problems. …”
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On Multivalued Fuzzy Contractions in Extended b-Metric Spaces by Nayab Alamgir, Quanita Kiran, Hassen Aydi, Yaé Ulrich Gaba

“…Thereafter, we introduce the concept of multivalued fuzzy contraction mappings and prove related α-fuzzy fixed point theorems in the context of extended b-metric spaces that generalize Nadler’s fixed point theorem as well as many preexisting results in the literature. …”
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The Centrifugal State: In Search of an Explanation of Why Countries Decentralise by Rodríguez-Pose Andrés

“…Through the dual lenses of the efficiency-based decentralisation theorem and political economy analysis, I discuss how globalisation, technological upheaval, and innovations in governance have fundamentally reshaped the relationship between political centres and periphery within countries. …”
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Multistability and Instability of Competitive Neural Networks with Mexican-Hat-Type Activation Functions by Xiaobing Nie, Jinde Cao, Shumin Fei

“…By tracking the dynamics of each state component and applying fixed point theorem and analysis method, some sufficient conditions are presented to study the multistability and instability, including the total number of equilibria, their locations, and local stability and instability. …”
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Implications of Raychaudhuri equation and geodesic focusing in interacting two fluid systems by Madhukrishna Chakraborty, Subenoy Chakraborty

“…Abstract The present work analyses Raychaudhuri equation (RE) in Einstein gravity for two interacting fluids. Focusing theorem, a consequence of RE, is directly related to the singularity theorems of Penrose and Hawking. …”
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Spatial and Temporal Dynamics of a Viral Infection Model with Two Nonlocal Effects by Xiaoyan Wang, Yuming Chen, Junyuan Yang

“…Then we obtain the existence of endemic steady states by Shauder fixed point theorem. A threshold dynamics is established by the approach of Lyapunov functionals. …”
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Model Value of Taiji Curve Algorithm in Economic Geographic and Natural Game Management Information System by Chengqi Xu, Kegong Chen

“…In order to study the role of tai chi curve algorithm in economic geography and natural ecological management and explore the application value of tai chi curve algorithm and its model, this study discusses the principle of Chinese tai chi diagram, using mathematical model construction method by the previous tai chi map and Pythagoras theorem clever results, produced the tai chi graph s curve algorithm, and discusses the application value of tai chi curve algorithm and its model from different angles; this study takes Zhangye geography as an example, which provides an applied research direction for the future scientific research of Chinese economic geography and also provides a clever connection with ecological correlation and nature; finally, it is found that the Taiji graph s curve algorithm can calculate the corresponding Yin and Yang values according to the balance point and relative deviation amount of the attribute state, and the results have an extraordinary influence in economic geography, information management system, natural ecology, and other aspects.…”
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Existence Results for Fractional Difference Equations with Three-Point Fractional Sum Boundary Conditions by Thanin Sitthiwirattham, Jessada Tariboon, Sotiris K. Ntouyas

“…The existence of at least one solution is proved by using Krasnoselskii's fixed point theorem and Leray-Schauder's nonlinear alternative. …”
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Robust Command Filtered Adaptive Backstepping Control for a Quadrotor Aircraft by Yicheng Liu, Junhui Ma, Haiyan Tu

“…Stability and robust performance of the designed controller are verified by Lyapunov stability theorem. Simulations are provided to validate the proposed controller.…”
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Families of jets of arc type and higher (co)dimensional Du Val singularities by de Fernex, Tommaso, Wang, Shih-Hsin

“…In dimension two, the result partially recovers a theorem of Mourtada on the jet schemes of Du Val singularities. …”
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Sound Power Estimation by Laser Doppler Vibration Measurement Techniques by G.M. Revel, G. L. Rossi

“…The first is based on the method proposed in the Standard ISO/TR 7849, while the second is based on the superposition theorem. A laser-Doppler scanning vibrometer has been employed for vibration measurements. …”
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An Extension to the Owa-Srivastava Fractional Operator with Applications to Parabolic Starlike and Uniformly Convex Functions by Oqlah Al-Refai, Maslina Darus

“…These include subordination, characterization and inclusions, growth theorems, distortion theorems, and class-preserving operators. …”
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Negative Energy Solutions for a New Fractional px-Kirchhoff Problem without the (AR) Condition by Weichun Bu, Tianqing An, Guoju Ye, Said Taarabti

“…By using Ekeland’s variational principle and dual fountain theorem, we obtain some new existence and multiplicity of negative energy solutions for the above problem without the Ambrosetti-Rabinowitz ((AR) for short) condition.…”
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3D DC Resistivity Inversion with Topography Based on Regularized Conjugate Gradient Method by Jian-ke Qiang, Xue Han, Shi-kun Dai

“…The Fréchet derivative is assembled with the electric potential in order to speed up the inversion process based on the reciprocity theorem. In this study, we also analyzed the sensitivity of the electric potential on the earth’s surface to the conductivity in each cell underground and introduced an optimized weighting function to produce new sensitivity matrix. …”
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Finite-Time Robust Stabilization for Stochastic Neural Networks by Weixiong Jin, Xiaoyang Liu, Xiangjun Zhao, Nan Jiang, Zhengxin Wang

“…Based on the recent finite-time stability theorem of stochastic nonlinear systems, sufficient conditions are established for ensuring the finite-time stability of the dynamics of SNNs in probability. …”
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Iterative Analysis of the Unique Positive Solution for a Class of Singular Nonlinear Boundary Value Problems Involving Two Types of Fractional Derivatives with p-Laplacian Operator by Fang Wang, Lishan Liu, Yonghong Wu, Yumei Zou

“…Based on the method of reducing the order of fractional derivative, some properties of the corresponding Green’s function, and the fixed point theorem of mixed monotone operator, an interesting result on the iterative sequence of the uniqueness of positive solutions is obtained under the assumption that the nonlinear term may be singular in regard to both the time variable and space variables. …”
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Pinning Synchronization for Complex Networks with Interval Coupling Delay by Variable Subintervals Method and Finsler’s Lemma by Dawei Gong, Frank L. Lewis, Liping Wang, Dong Dai, Shuang Zhang

“…Finally, the stability of the networks is proved via Lyapunov’s stability theorem, and the simulation of the trajectory claims the practicality of the proposed pinning control.…”
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The Transmission Dynamics of Hepatitis B Virus via the Fractional-Order Epidemiological Model by Tahir Khan, Zi-Shan Qian, Roman Ullah, Basem Al Alwan, Gul Zaman, Qasem M. Al-Mdallal, Youssef El Khatib, Khaled Kheder

“…For the local and global analysis, we use linearization, mean value theorem, and fractional Barbalat’s lemma, respectively. …”
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Fixed Point Results for α-ψ-Contractive Mappings Including Almost Contractions and Applications by Gonca Durmaz, Gülhan Mınak, Ishak Altun

“…Vetro, and P. Vetro, Fixed point theorems for α-ψ-contractive type mappings, Nonlinear Analysis. …”
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General Iterative Algorithms for Hierarchical Fixed Points Approach to Variational Inequalities by Nopparat Wairojjana, Poom Kumam

“…Furthermore, we give an example which supports our main theorem in the last part.…”
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