Dynamic Analysis of a Delayed Reaction-Diffusion Predator-Prey System with Modified Holling-Tanner Functional Response by Xinhong Pan, Min Zhao, Chuanjun Dai, Yapei Wang

“…In addition, the direction of the Hopf bifurcation and the stability of bifurcated periodic solutions are also studied, and an explicit algorithm is obtained by applying normal form theory and the center manifold theorem. …”
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The <i>n^th</i> Prime Exponentially by Matt Visser

“…</mo></mrow></semantics></math></inline-formula> These bounds provide a modern, and very clean and explicit, version of the celebrated prime number theorem. …”
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The Solution of Embedding Problems in the Framework of GAPs with Applications on Nonlinear PDEs by Reinhard Starkl

“…It is shown that these embedding problems are solvable and explicit solutions are given. Not only are the solutions new but also the mathematical framework of their construction which is defined by a nonstandard function theory built over nonstandard algebraical structures, denoted as “GAPs”. …”
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Revisiting single inclusive jet production: timelike factorization and reciprocity by Kyle Lee, Ian Moult, Xiaoyuan Zhang

“…However, the non-trivial structure of convolutions in the factorization theorem implies that the jet functions exhibit a modified evolution. …”
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TEOREMA FUNGSI INVERS DAN APLIKASINYA DALAM ESTIMASI VOLATILITAS MODEL STOKASTIK by NILMA SARI, FAIHATUZ ZUHAIROH

“…The Inverse Function Theorem plays a fundamental role in various areas of applied mathematics, particularly in stochastic analysis and financial modeling. …”
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Flavor factorization at two-loops by Andrew J. Larkoski

“…We validate the factorization theorem through explicit calculation at two-loop order, and in the process extract all anomalous dimensions and renormalization factors for any ultraviolet-to-infrared flavor transition at this order. …”
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Pontryagin’s Maximum Principle for Optimal Control of Stochastic SEIR Models by Ruimin Xu, Rongwei Guo

“…We also establish a sufficient condition which is called verification theorem for the stochastic SEIR model.…”
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Optimal Control of Investment-Reinsurance Problem for an Insurer with Jump-Diffusion Risk Process: Independence of Brownian Motions by De-Lei Sheng, Ximin Rong, Hui Zhao

“…It aims at obtaining the explicit optimal control strategy and the optimal value function. …”
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Exponential optimization of adiabatic quantum-state preparation by Davide Cugini, Davide Nigro, Mattia Bruno, Dario Gerace

“…The preparation of a given quantum state on a quantum computing register is a typically demanding operation, requiring a number of elementary gates that scales exponentially with the size of the problem. Using the adiabatic theorem for state preparation, whose error decreases exponentially as a function of the preparation time, we derive an explicit analytic expression for the dependence of the characteristic time on the Hamiltonian used in the adiabatic evolution. …”
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Bootstrapping conformal defect operators on a line by Parijat Dey, Kausik Ghosh

“…We also compute the defect g-function for this setup and demonstrate that this is in agreement with the g-theorem, which states that the g-function is monotonic under the renormalisation group flow along the defect. …”
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Adaptive predefined-time precise anti-unwinding attitude control for a spacecraft with inertia uncertainty by Bojun Liu, Xiangkun Fu, Zhanpeng Zhang, Yingmin Yi

“…The novelty of the proposed algorithm lies in that the spacecraft attitude error is regulated to exact zero after a predefined settling time, which is an explicit parameter in the control algorithm. A time mapping function containing the predefined settling time is introduced, thus transforming the time scale of the original attitude control system. …”
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Stability of Fluid Flow through a Channel with Flexible Walls by Marianna A. Shubov, Madeline M. Edwards

“…Stability of fluid flow, the main focus of the research, is obtained by solving the initial boundary value problem for the stream function. The main findings of the paper are the following: (i) rigorous formulation of the initial boundary problem for the stream function, ψx,y,t, induced by the fluid-structure interaction model, which takes into account the axisymmetric pattern of the flow and “no-slip” condition near the channel walls; (ii) application of a double integral transformation (the Fourier transformation and Laplace transformation) to both the equation and boundary and initial conditions, which reduces the original partial differential equation to a parameter-dependent ordinary differential equation; (iii) derivation of the explicit formula for the Fourier transform of the stream function, ψ˜k,y,t; (iv) evaluation of the inverse Fourier transform of ψ˜k,y,t and proving that reconstruction of ψx,y,t can be obtained through a limiting process in the complex k-plane, which allows us to use the Residue theorem and represent the solution in the form of an infinite series of residues. …”
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Mann iterates of directionally nonexpansive mappings in hyperbolic spaces by Ulrich Kohlenbach, Laurentiu Leustean

“…In a previous paper, the first author derived an explicit quantitative version of a theorem due to Borwein, Reich, and Shafrir on the asymptotic behaviour of Mann iterations of nonexpansive mappings of convex sets C in normed linear spaces. …”
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On a class of polynomials associated with the Cliques in a graph and its applications by E. J. Farrell

“…The clique polynomial of a graph is defined. An explicit formula is then derived for the clique polynomial of the complete graph. …”
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A POSSIBILISTIC APPROACH TO CALCULATING THE INTERNAL RATE OF RETURN FOR INVESTMENT PROJECTS WITH FUZZY CASH FLOWS by E. S. Volkova, V. B. Gisin

“…Under the standard addition of fuzzy numbers we give explicit formulas for the membership function of the IRR. …”
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Continuous Mixture of Uniforms Framework for Modeling Residual Lifetime Distribution by Felipe A. Cruz-Perez, Sandra Lirio Castellanos-Lopez, Genaro Hernandez-Valdez, Mario Eduardo Rivero-Angeles

“…Through an alternative and intuitively comprehensible mathematical analysis, both the mixing distribution and the Residual Lifetime Theorem as a function of the Lifetime distribution are derived, providing a novel perspective compared to existing literature. …”
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A Riemannian-Geometry Approach for Modeling and Control of Dynamics of Object Manipulation under Constraints by Suguru Arimoto, Morio Yoshida, Masahiro Sekimoto, Kenji Tahara

“…An extension of Dirichlet-Lagrange's stability theorem to redundant systems under constraints is suggested by introducing a Morse-Lyapunov function.…”
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Stability and Hopf Bifurcation Analysis of a Plant Virus Propagation Model with Two Delays by Junli Liu, Tailei Zhang

“…Using the normal form theory and center manifold theorem, the explicit formulae which determine the stability, direction, and other properties of bifurcating periodic solutions are derived. …”
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THE CONSTRUCTION OF SOLUTIONS OF PIECEWISE-LINEAR PHASE SYSTEMS by A. F. Gribov, B. I. Shakhtarin

“…The article considers the construction of solutions of phase systems on the example of phase-locked frequency of arbitrary dimension with piecewise linear approximation of the nonlinear function. This approximation allowed to use an explicit form of solutions in the linearity and to obtain analytical conditions for the existence of various types of system behavior. …”
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Resonant Soliton and Soliton-Cnoidal Wave Solutions for a (3+1)-Dimensional Korteweg-de Vries-Like Equation by Zheng-Yi Ma, Jin-Xi Fei, Jun-Chao Chen, Quan-Yong Zhu

“…Finally, with the aid of the link between the consistent tanh expansion (CTE) method and the truncated Painlevé expansion, the explicit soliton-cnoidal wave interaction solution containing three kinds of Jacobian elliptic functions for this equation is derived.…”
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