Chaotic Vibration Prediction of a Free-Floating Flexible Redundant Space Manipulator by Congqing Wang, Linfeng Wu

“…The chaotic time series prediction scheme for the space manipulator is presented based on the theory of phase space reconstruction under Takens’ embedding theorem. The trajectories of phase space can be reconstructed in embedding space, which are equivalent to the original space manipulator in dynamics. …”
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Optimal quinary cyclic codes with minimum distance four by Ye TIAN, Yu-qing ZHANG, Yu-pu HU

“…Cyclic codes are an extremely important subclass of linear codes.They are widely used in the communication systems and data storage systems because they have efficient encoding and decoding algorithm.Until now,how to construct the optimal ternary cyclic codes has received a lot of attention and much progress has been made.However,there is less research about the optimal quinary cyclic codes.Firstly,an efficient method to determine if cyclic codes C_(1,e,t)were optimal codes was obtained.Secondly,based on the proposed method,when the equation e=5_k+1 or e=5_m−2hold,the theorem that the cyclic codes C_(1,e,t)were optimal quinary cyclic codes was proved.In addition,perfect nonlinear monomials were used to construct optimal quinary cyclic codes with parameters[5_m−1,5_m−2m−2,4]optimal quinary cyclic codes over <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML"> <msub> <mi>F</mi> <mrow> <msup> <mn>5</mn> <mi>m</mi> </msup> </mrow> </msub> </math></inline-formula>.…”
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Positivity of Fundamental Matrix and Exponential Stability of Delay Differential System by Alexander Domoshnitsky, Roman Shklyar, Mikhail Gitman, Valery Stolbov

“…The classical Wazewski theorem established that nonpositivity of all nondiagonal elements pij  (i≠j,  i,j=1,…,n) is necessary and sufficient for nonnegativity of the fundamental (Cauchy) matrix and consequently for applicability of the Chaplygin approach of approximate integration for system of linear ordinary differential equations xi′t+∑j=1n‍pijtxjt=fit,   i=1,…,n. …”
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Investigating Some Diatomic Molecules Bounded by the Two-Dimensional Isotropic Oscillator plus Inverse Quadratic Potential in an External Magnetic Field by O. J. Oluwadare, E. O. Ilesanmi, T. O. Abiola, O. Olubosede, E. A. Odo, S. O. Ajibade, K. J. Oyewumi

“…The expectation values square of the position r2, square of the momentum p2, kinetic energy T, and potential energy V are obtained by applying the Hellmann-Feynman theorem, and an expression for the diamagnetic susceptibility X is also derived. …”
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Global bifurcation of positive solutions for a superlinear $p$-Laplacian system by Lijuan Yang, Ruyun Ma

“…We obtain the principal eigenvalue of $(P)$ by using a nonlinear Krein–Rutman theorem and the unbounded branch of positive solutions for $(Q)$ via bifurcation technology.…”
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Scattering, absorption and emission of highly excited strings by M. Firrotta, E. Kiritsis, V. Niarchos

“…We obtain new exact compact formulae for heavy-heavy-light-light scattering amplitudes in open or closed bosonic string theories, and derive explicit exact expressions for the absorption cross-sections, and corresponding emission rates, of highly excited string states using the optical theorem and time reversal symmetry. We show that these expressions are independent of the microscopic structure of the excited string states without averaging. …”
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Online Coregularization for Multiview Semisupervised Learning by Boliang Sun, Guohui Li, Li Jia, Kuihua Huang

“…Using the weak duality theorem, we reduce the online coregularization to the task of increasing the dual function. …”
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On a Memristor-Based Hyperchaotic Circuit in the Context of Nonlocal and Nonsingular Kernel Fractional Operator by Shahram Rezapour, Chernet Tuge Deressa, Sina Etemad

“…The Banach fixed point theorem and contraction principle are utilized to verify the existence and uniqueness of the solution of the five-dimensional system. …”
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Adaptive control of uncertain non-linear fractional-order systems in the presence of actuator failures and input constraints by Masood Bagherzadeh

“…Stability analysis is conducted using the Mittag-Lefler stability theorem, and numerical simulations are performed to validate the proposed method.Findings: The simulation results demonstrate the effectiveness of the proposed method in compensating actuator failures and input constraints while achieving closed-loop system stability and output tracking.Originality/Value: This research offers an innovative contribution to the field of control systems by employing adaptive control for actuator failure compensation in non-linear fractional-order systems and presenting a comprehensive theoretical framework, addressing both practical and theoretical challenges.…”
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Multiplicity of Solutions for a Class of Elliptic Problem of p-Laplacian Type with a p-Gradient Term by Zakariya Chaouai, Soufiane Maatouk

“…For this purpose, we use the Mountain Pass theorem, on an equivalent problem to (P) with variational structure. …”
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First-order analysis of slip flow for micro and nanoscale applications by Duncan A. Lockerby

“…The technique, which exploits the reciprocal theorem, can generate first-order predictions of the impact of Navier or Maxwell slip boundary conditions on surface moments of the traction force (e.g. on drag and torque). …”
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An Analytical Solution to the Electromagnetic Performance of an Ultra-High-Speed PM Motor by Wenjie Cheng, Zhikai Deng, Ling Xiao, Bin Zhong, Yanhua Sun

“…Aiming for this type of PMSM, two methods, namely, the Poynting theorem and the Maxwell stress tensor, were used to deduce the analytic expression of the electromagnetic driving torque. …”
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Mathematical model for managing vector-borne pathogen outbreaks in chickens using impulsive vaccination and drug treatment by Kamonchat Trachoo, Din Prathumwan, Darunee Padasee, Supatcha Paopan, Inthira Chaiya

“…We find that the periodic solution of the disease-free equilibrium is locally asymptotically stable under specific conditions outlined in the proposed theorem. This highlights the effectiveness of impulsive vaccination strategies in controlling disease transmission.…”
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A Dual-Controller of Quadrotor UAV Elastic Hanging Model Based on Event-Triggered Mechanism and Its Control Design by Sen Yang, Hang Guo, Jigang Tong, Tian Xie, Jingyi Yan

“…The former is designed based on the robust sliding mode control, and the latter is designed based on the energy analysis method, and the stability analysis of the designed system and the control law is carried out using the Lyapunov method and the Russell&#x2019;s invariant theorem. A group of simulation results is presented to illustrate the effectiveness of the algorithms.…”
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Geometric quantum machine learning with horizontal quantum gates by Roeland Wiersema, Alexander F. Kemper, Bojko N. Bakalov, Nathan Killoran

“…Moreover, for a particular subclass of horizontal gates based on symmetric spaces, we can obtain efficient circuit decompositions for our gates through the KAK theorem. Finally, we highlight a particular class of horizontal quantum gates that behave similarly to general SU(4) gates, while achieving a quadratic reduction in the number of parameters for a generic problem.…”
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Impact of media coverage on the transmission dynamics of TB with vaccines and treatment. by Kumneger Tadesse Mulugeta, Mohammed Yiha Dawed, Shewafera Wondimagegnhu Teklu

“…In the qualitative analysis of the proposed model we proved the existence, uniqueness, positivity, and boundedness of the model solutions, investigated both the disease-free and endemic equilibrium points, computed the basic and effective reproduction numbers using next generation matrix approach, analyzed the stability analysis of the equilibrium points, the backward bifurcation using the Castillo-Chavez and Song theorem and we re-formulated the corresponding optimal control problem and analyzed by applying the Pontryagin's Minimum Principle. …”
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On the uniqueness of linear convection–diffusion equations with integral boundary conditions by Lee, Chiun-Chang, Mizuno, Masashi, Moon, Sang-Hyuck

“…This approach has the advantage of transforming the integral boundary conditions into new Dirichlet boundary conditions so that we can obtain refined estimates, and the comparison theorem can be applied to the equations. Furthermore, we show a domain such that under different boundary data, the equation in this domain can have infinitely numerous solutions or no solution. …”
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The Gauge Integral Theory in HOL4 by Zhiping Shi, Weiqing Gu, Xiaojuan Li, Yong Guan, Shiwei Ye, Jie Zhang, Hongxing Wei

“…The formalized theorem library has been accepted by the HOL4 authority and will appear in HOL4 Kananaskis-9.…”
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Wind Turbine Aerodynamic Performance by Lifting Line Method by Horia Dumitrescu, Vladimir Cardos

“…Performance parameters are calculated by application of the Biot-Savart law along with the Kutta-Joukowski theorem. Predictions are, shown to compare favorably with existing numerical data from more involved free wake methods, but require less computational effort. …”
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Zip and weak zip algebras in a congruence-modular variety by George Georgescu

“…Using the reticulation and a Hochster's theorem we prove that  a neo-commutative algebra $A\in \mathcal{V}$ is a weak zip algebra if and only if the minimal prime spectrum $Min(A)$ of $A$ is a finite space.…”
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