Topology of 3-dimensional manifolds by Eaman Eftekhary

“…Starting with the work of Poincare in the last years of 19th century and first few years of 20th century, we review the major steps in putting 3-manifolds and their algebraic topology in a solid mathematical framework, and the important theorems which strengthened the understanding of 3-manifolds, including the prime decomposition theorem and JSJ decomposition of 3-manifolds. …”
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On Nonlinear Neutral Fractional Integrodifferential Inclusions with Infinite Delay by Fang Li, Ti-Jun Xiao, Hong-Kun Xu

“…Of concern is a class of nonlinear neutral fractional integrodifferential inclusions with infinite delay in Banach spaces. A theorem about the existence of mild solutions to the fractional integrodifferential inclusions is obtained based on Martelli’s fixed point theorem. …”
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Some Reduction and Exact Solutions of a Higher-Dimensional Equation by Guangming Wang, Zhong Han

“…The conservation laws of the (3+1)-dimensional Zakharov-Kuznetsov equation were obtained using Noether’s theorem after an interesting substitution u=vx to the equation. …”
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Robustness design of templates for logic OR operation CNN in gray-scale images by Qun ZHANG, Le-quan MIN

“…The theorem provided parameter inequalities for determining parameter intervals to implement the corresponding tasks. …”
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Derived equivalences of upper-triangular ring spectra via lax limits by Jasso, Gustavo

“…We extend a theorem of Ladkani concerning derived equivalences between upper-triangular matrix rings to ring spectra. …”
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Fractional Langevin Equations with Nonseparated Integral Boundary Conditions by Khalid Hilal, Lahcen Ibnelazyz, Karim Guida, Said Melliani

“…The Banach fixed point theorem and Krasnoselskii fixed point theorem are applied to establish the results. …”
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W-Stability of Multistable Nonlinear Discrete-Time Systems by Zhishuai Ding, Guifang Cheng, Xiaowu Mu

“…Efimov, the estimates of solution and the Lyapunov stability theorem and converse theorem are proposed for multi-stable discrete-time nonlinear systems.…”
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Existence of Generalized Homoclinic Solutions of Lotka-Volterra System under a Small Perturbation by Yuzhen Mi

“…By the Fourier series expansion technique method, the fixed point theorem, the perturbation theorem, and the reversibility, we prove that near μ=0 the system has a generalized homoclinic solution exponentially approaching a periodic solution.…”
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Dynamics of Stochastic Coral Reefs Model with Multiplicative Nonlinear Noise by Zaitang Huang

“…This paper is devoted to discern asymptotic behavior dynamics through the stochastic coral reefs model with multiplicative nonlinear noise. By support theorem and Hörmander theorem, the Markov semigroup corresponding to the solutions is to prove the Foguel alternative. …”
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Uniformly Primal Submodule over Noncommutative Ring by Lamis J. M. Abulebda

“…Also, we generalize the prime avoidance theorem for modules over noncommutative rings to the uniformly primal avoidance theorem for modules.…”
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Density by Moduli and Statistical Boundedness by Vinod K. Bhardwaj, Shweta Dhawan, Sandeep Gupta

“…It is shown that bounded sequences are precisely those sequences which are f-statistically bounded for every unbounded modulus f. A decomposition theorem for f-statistical convergence for vector valued sequences and a structure theorem for f-statistical boundedness have also been established.…”
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Multiplicity Results of Solutions to the Fractional <i>p</i>-Laplacian Problems of the Kirchhoff–Schrödinger–Hardy Type by Yun-Ho Kim

“…To demonstrate the multiplicity results, we exploit the fountain theorem and the dual fountain theorem as the main tools, respectively.…”
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Point-Symmetric Multivariate Density Function and Its Decomposition by Kiyotaka Iki, Sadao Tomizawa

“…The theorem is illustrated for the multivariate normal density function.…”
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An Alternative Method for the Study of Impulsive Differential Equations of Fractional Orders in a Banach Space by Asma Bouzaroura, Saïd Mazouzi

“…The derived results are based on Banach's contraction theorem as well as Schaefer's fixed point theorem.…”
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Cohen Positive Strongly p-Summing and p-Dominated m-Homogeneous Polynomials by Halima Hamdi, Samuel García-Hernández, Amar Belacel, Djamel Ouchenane, Sulima Ahmed Zubair

“…The version of Pietsch’s domination theorem for the first class among other results and a Bu-type theorem is proved, as well as some inclusions with other known spaces. …”
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A Generalization of Arrow’s Lemma on Extending a Binary Relation by Athanasios Andrikopoulos

“…By examining whether the individualistic assumptions used in social choice could be used in the aggregation of individual preferences, Arrow proved a key lemma that generalizes the famous Szpilrajn’s extension theorem and used it to demonstrate the impossibility theorem. …”
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Some Properties and Applications of a New General Triple Integral Transform “Gamar Transform’’ by Abdelilah Kamal H. Sedeeg

“…We outline its essential properties and prove some important results, including linearity property, existence theorem, triple convolution theorem, and derivatives properties. …”
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Analisis Kesalahan dalam Pembuktian Teorema Bilangan Bulat pada Mahasiswa IKIP Budi Utomo Malang by Nok Izatul Yazidah, Yunis Sulistyorini, Era Dewi Kartika

“…This research is motivated by problems related to the proof of the integer theorem. The purpose of this study was to find out what errors were made by students in proving the integer theorem. …”
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Notes on the Hermitian Positive Definite Solutions of a Matrix Equation by Jing Li, Yuhai Zhang

“…The nonlinear matrix equation, X-∑i=1mAi*XδiAi=Q, with -1≤δi<0 is investigated. A fixed point theorem in partially ordered sets is proved. And then, by means of this fixed point theorem, the existence of a unique Hermitian positive definite solution for the matrix equation is derived. …”
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Non-interference trusted model based on processes by ZHANG Xing1, CHEN You-lei2, SHEN Chang-xiang2

“…A novel abstract model for the design of trusted computing platform system was proposed.By using the basic idea of non-interference theory as reference and introduces the reasoning method of process algebra, thus abstracting the system as processes, actions, states and outputs, and giving the formal definition of the trusted of process running.Process isolation trusted theorem was verified formally.Furthermore, by associating process with system state, the definition and the theorem of system running trusted was proposed.The model was established by logic reasoning and independent of special security mechanism and enforcement.The trust of the running system can be realized by any method which satisfies the conditions of the model.…”
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