The Limits of Computer Science. Weizsäcker’s Argument by Olszewski Adam

“…We base the critique on two well-known results: the theorem of the unsolvability of the halting problem and Gödel’s first incompleteness theorem, and we formulate two objections interpreted without adopting Church’s thesis. …”
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Dynamical Analysis of SIR Epidemic Model with Nonlinear Pulse Vaccination and Lifelong Immunity by Wencai Zhao, Juan Li, Xinzhu Meng

“…Firstly, by using stroboscopic map and fixed point theory of difference equations, the existence of disease-free periodic solution is discussed, and the globally asymptotical stability of disease-free periodic solution is proven by using Floquet multiplier theory and differential impulsive comparison theorem. Moreover, by using the bifurcation theorem, sufficient condition for the existence of positive periodic solution is obtained by choosing impulsive vaccination period as a bifurcation parameter. …”
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Fuzzy Triple Controlled Metric Spaces and Related Fixed Point Results by Salman Furqan, Hüseyin Işık, Naeem Saleem

“…We prove Banach fixed point theorem in the settings of fuzzy triple controlled metric space that generalizes Banach fixed point theorem for aforementioned spaces. …”
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Koopmans' Analysis of Chemical Hardness with Spectral-Like Resolution by Mihai V. Putz

“…Three approximation levels of Koopmans' theorem are explored and applied: the first referring to the inner quantum behavior of the orbitalic energies that depart from the genuine ones in Fock space when the wave-functions' Hilbert-Banach basis set is specified to solve the many-electronic spectra of spin-orbitals' eigenstates; it is the most subtle issue regarding Koopmans' theorem as it brings many critics and refutation in the last decades, yet it is shown here as an irrefutable “observational” effect through computation, specific to any in silico spectra of an eigenproblem; the second level assumes the “frozen spin-orbitals” approximation during the extracting or adding of electrons to the frontier of the chemical system through the ionization and affinity processes, respectively; this approximation is nevertheless workable for great deal of chemical compounds, especially organic systems, and is justified for chemical reactivity and aromaticity hierarchies in an homologue series; the third and the most severe approximation regards the extension of the second one to superior orders of ionization and affinities, here studied at the level of chemical hardness compact-finite expressions up to spectral-like resolution for a paradigmatic set of aromatic carbohydrates.…”
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A New Class of Contact Pseudo Framed Manifolds with Applications by K. L. Duggal

“…We prove in our main Theorem 2 that M admits a closed 2-form Ω if λ is constant. …”
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The Study for Synchronization between Two Coupled FitzHugh-Nagumo Neurons Based on the Laplace Transform and the Adomian Decomposition Method by Bin Zhen, Zigen Song

“…Different from other researches, the synchronization error system is expressed as sets of Volterra integral equations based on the convolution theorem in the Laplace transform. Then, it is easy to analytically obtain the conditions that synchronization errors disappear based on the successive approximation method in integral equation theorem, the correctness of which is verified by numerical simulations. …”
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Discussion on Reciprocity, Unitary Matrix, and Lossless Multiple Beam Forming Networks by Nelson Jorge G. Fonseca

“…The Lorentz reciprocity theorem enables us to establish that the transmitting and receiving patterns of any antenna are identical, provided some hypotheses on this antenna and the surrounding medium are satisfied. …”
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Porous-elastic system with boundary dissipation of fractional derivative type by Oliveira Wilson, Cordeiro Sebastião, Raposo Carlos, Campelo Anderson

“…The existence and uniqueness of the solution are obtained by applying the well-known Lumer-Phillips Theorem. We present two results for the asymptotic behavior: Strong stability of the C0-semigroup associated with the system using Arendt-Batty and Lyubich-V~u's general criterion and polynomial stability applying Borichev-Tomilov's Theorem.…”
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The Existence of Solutions to a System of Discrete Fractional Boundary Value Problems by Yuanyuan Pan, Zhenlai Han, Shurong Sun, Yige Zhao

“…The existence of solutions to this problem is established by the Guo-Krasnosel'kii theorem and the Schauder fixed-point theorem, and some examples are given to illustrate the main results.…”
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Dynamical Behavior and Stability Analysis in a Stage-Structured Prey Predator Model with Discrete Delay and Distributed Delay by Chao Liu, Qingling Zhang

“…According to Hopf bifurcation theorem for functional differential equations, it can be found that model undergoes Hopf bifurcation around the interior equilibrium when local stability switch occurs and corresponding stable limit cycle is observed. …”
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Anatomy of the Higgs Boson Decay into Two Photons in the Unitary Gauge by Athanasios Dedes, Kristaq Suxho

“…The remaining ambiguity is then fixed by exploiting gauge invariance and the Goldstone Boson Equivalence Theorem. Our method is strictly realised in four dimensions. …”
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Stabilities of Cubic Mappings in Various Normed Spaces: Direct and Fixed Point Methods by H. Azadi Kenary, H. Rezaei, S. Talebzadeh, S. Jin Lee

“…In 1940 and 1964, Ulam proposed the general problem: “When is it true that by changing a little the hypotheses of a theorem one can still assert that the thesis of the theorem remains true or approximately true?”. …”
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Dynamic Processes, Fixed Points, Endpoints, Asymmetric Structures, and Investigations Related to Caristi, Nadler, and Banach in Uniform Spaces by Kazimierz Włodarczyk, Robert Plebaniak

“…One of the main key ideas in this paper is the application of our fixed point and endpoint version of Caristi type theorem for dissipative set-valued dynamic systems without lower semicontinuous entropies in uniform spaces with structures determined by J-families. …”
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An Approximation Algorithm for the Combination of <i>G</i>-Variational Inequalities and Fixed Point Problems by Araya Kheawborisut, Atid Kangtunyakarn

“…Under appropriate assumptions, we establish a strong convergence theorem within the framework of a Hilbert space endowed with graphs. …”
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Investigating modules with partial endomorphisms having μ-small kernels by Abderrahim El Moussaouy, Ali Reza Moniri Hamzekolaee, M hammed Ziane, Samira Asgari

“…Further, we prove a similar theorem to Hilbert's basis theorem for monoform, small monoform and $G-M$ modules.…”
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Inverse Fourier Transform in the Gamma Coordinate System by Yuchuan Wei, Hengyong Yu, Ge Wang

“…Then, we generate Orlov's theorem and a weighted Radon formula from the inverse Fourier transform in the new system. …”
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Rapid Measurements of Damaged Areas and Cavities Formed on Highways Caused by Heavy Rain Falls, Earthquakes or Similar Catastrophes by Bhattacharya Syama P., Ghosh Asis

“…However, in this study Bhattacharya’s theorem was applied for the measurement of an abnormal area with success. …”
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Applications of a New q-Difference Operator in Janowski-Type Meromorphic Convex Functions by Bakhtiar Ahmad, Muhammad Ghaffar Khan, Mohamed Kamal Aouf, Wali Khan Mashwani, Zabidin Salleh, Huo Tang

“…Furthermore, we discuss a number of useful geometric properties for the functions belonging to this class such as sufficiency criteria, coefficient estimates, distortion theorem, growth theorem, radius of starlikeness, and radius of convexity. …”
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Noether and partial Noether approach for the nonlinear (3+1)-dimensional elastic wave equations. by Akhtar Hussain, M Usman, Fiazuddin Zaman, Ahmed M Zidan, Jorge Herrera

“…For the conservation laws, we applied Noether's theorem to the nonlinear elastic wave equations owing to the availability of a classical Lagrangian. …”
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The homology groups of the Cartesian product $\Omega_{n_1}(m_1)\times \Omega_{n_2}(m_2)$ by A.M. Pasko

“…In order to find the homology groups of this Cartesian product the Kunneth theorem has been used. Using the Kunneth theorem and the fact that $\text{Tor}(A,B)=0$ if at least one of the group $A, B$ is free we presented the homology group of the Cartesian product $\Omega_{n_1}(m_1)\times \Omega_{n_2}(m_2)$ as the sum of the tensor products of the homology groups of this spaces. …”
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