Results on Uniqueness of Solution of Nonhomogeneous Impulsive Retarded Equation Using the Generalized Ordinary Differential Equation by D. K. Igobi, U. Abasiekwere

“…The fundamental matrix theorem is employed to derive the integral equivalent of the equation which is Lebesgue integrable. …”
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Design and Analysis of Flexible Hinge Using in Optoelectronics Packaging Platform by Zheng Jiamain, 2Zhou Haibo, 2Huang Kai

“…In the six degrees of freedom flexible parallel platform using in optoelectronics packaging,the performance of the flexible hinge is an important influence factor on moving platform workspace and precision.According to Castigliano’s theorem and Lobatto quadrature formula,the mechanical model of the corner- filleted is established and the compliance matrix of flexible hinge is deduced. …”
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UC secure one-time signature based broadcast authentication by ZHANG Jun-wei, MA Jian-feng, YANG Li

“…The provable security of one-time signature based broadcast authentication protocols was investigated.In the UC framework,a one-time signature based broadcast authentication model was proposed.Firstly,the one-time signature ideal functionality FOTS and the broadcast authentication ideal functionality FBAUTH were formally defined in the model.Then,one-time signature protocol HORS+ was proposed.At the same time,a broadcast authentication scheme πBAUTH was designed in the（FOTS,FREG）-hybrid model.Finally,based on the scheme πBAUTH,a new broadcast authentication protocol was then obtained by the combined use of HORS+.The result shows that HORS+ securely realizes the ideal func-tionality FOTS,and πBAUTH also realizes the ideal functionality FBAUTH.According to the composition theorem in the UC framework,the composed broadcast authentication protocol is UC secure and can be applied to broadcast the authenticated message in the resource-limited networks.…”
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Performance analysis of IRS aided downlink NOMA short-packet communication with hardware impairment by Lei YUAN, Jing XU, Mingxiu MO, Yan LEI

“…Impact of hardware impairment on the performance of intelligent reflecting surface (IRS) aided downlink two-user short-packet communication (SPC) systems using non-orthogonal multiple access over Rician channels was analyzed.Phase adjustments at the IRS were based on statistical channel state information.Firstly, the analytical expressions for average block error rates of two users were derived by using central limit theorem, moment matching method, SPC related theory, and Gaussian-Chebyshev quadrature method.Secondly, to minimize the transmission latency under the reliability constraints of two users, the optimal power allocation scheme for the considered system was given by using the proposed bisection search algorithm and one-dimensional search algorithm.Finally, simulation results verified the correctness of the theoretical analysis and showed that, compared to long-packet communication, hardware impairments have a greater impact on SPC.…”
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Analysis of an SEIR Epidemic Model with Saturated Incidence and Saturated Treatment Function by Jinhong Zhang, Jianwen Jia, Xinyu Song

“…We also discuss the global asymptotical stability of the endemic equilibrium by autonomous convergence theorem. The study indicates that we should improve the efficiency and enlarge the capacity of the treatment to control the spread of disease. …”
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On the emergence of the Quanta Prime sequence by Moustafa Ibrahim

“…This paper presents the Quanta Prime Sequence (QPS) and its foundational theorem, showcasing a unique class of polynomials with substantial implications. …”
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Turbulent Flow Analysis with Banach and Sobolev Spaces in the LES Method Incorporating the Smagorinsky Subgrid-Scale Model by Rômulo Damasclin Chaves dos Santos, Jorge Henrique Oliveira Sales

“…In this context, this investigation marks a significant step forward in the advancement of the Smagorinsky model coupled with the LES methodology, resulting, based on the Banach and Sobolev Spaces, a new theorem that points the way to the construction of an anisotropic viscosity model (not yet discussed in the present work). …”
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Robust Adaptive Switching Control for Markovian Jump Nonlinear Systems via Backstepping Technique by Jin Zhu, Hongsheng Xi, Qiang Ling, Wanqing Xie

“…By using backstepping technique and stochastic small-gain theorem, a switching controller is designed such that stochastic stability is ensured. …”
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Single index regression for locally stationary functional time series by Breix Michael Agua, Salim Bouzebda

“…Additionally, we provided a central limit theorem for the NW estimator. Finally, the theory was supported by a comprehensive simulation study to investigate the finite-sample performance of our proposed method.…”
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Global Hopf Bifurcation Analysis for an Avian Influenza Virus Propagation Model with Nonlinear Incidence Rate and Delay by Yanhui Zhai, Ying Xiong, Xiaona Ma, Haiyun Bai

“…An explicit algorithm for determining the direction of the Hopf bifurcations and stability of the bifurcation periodic solutions is derived by applying the normal form theory and center manifold theorem. What is more, the global existence of periodic solutions is established by using a global Hopf bifurcation result.…”
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Dynamical Models for Infectious Diseases with Varying Population Size and Vaccinations by Peilin Shi, Lingzhen Dong

“…By a useful bifurcation theorem, we acquire the existence of the endemic periodic solutions when the disease-related deaths do not occur. …”
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Unique gating strategy identifier based on the Prime Population System and Gödel Numbers by Antonio Cosma

“…The unique identifiers hold since according to the fundamental theorem of arithmetic, every natural number other than one either is a prime or is a product of prime numbers, and every nonprime number can be factored into a product of prime in only one way. …”
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New classes of rearrangement-invariant spaces appearing in extreme cases of weak interpolation by Evgeniy Pustylnik, Teresa Signes

“…,E are not “too close” to the endpoint spaces of interpolation (in the sense of Boyd), the optimal interpolation theorem was stated in [13]. The case of “too close” spaces was studied in [15] with results which are optimal, but only among ultrasymmetric spaces. …”
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Continuité des racines d’après Rabinoff by Marie, Emeryck

“…The content of this paper is a generalization of a theorem by Joseph Rabinoff: if $\mathscr{P}$ is a finite family of pointed and rational polyhedra in $N_\mathbb{R}$ such that there exists a fan in $N_\mathbb{R}$ that contains all the recession cones of the polyhedra of $\mathscr{P}$, if $k$ is a complete non-archimedean field, if $S$ is a connected and regular $k$-analytic space (in the sense of Berkovich) and $Y$ is a closed $k$-analytic subset of $U_{\mathscr{P}} \times _k S$ which is relative complete intersection and contained in the relative interior of $U_{\mathscr{P}} \times _k S$ over $S$, then the quasifiniteness of $\pi : Y \rightarrow S$ implies its flatness and finiteness; moreover, all the finite fibers of $\pi $ have the same length. …”
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Comment comprendre les « communs » : Elinor Ostrom, la propriété et la nouvelle économie institutionnelle by Olivier Weinstein

“…To do this, we first consider her original and important analysis of rules and norms, and its conception of economic behavior, then we explore her theory of property rights and of the conditions of selection of forms of property and institutions, with the prospect of a confrontation with the idea of a “generalized Coase theorem”. This leads us, finally, to questioning Elinor Ostrom’s views on institutions and the commons, and possible ways to go beyond these conceptions.…”
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Chaos and bifurcation analysis of tumor-immune controlled system with time delay by Danni Wang, Hongli Yang, Liangui Yang

“…The Flip bifurcation and Neimark–Sacker bifurcation of system are proved by the normal form method, central manifold theorem, and bifurcation theory. The Gram–Schmidt orthonormalization (GSO) method is used to interpret the attractor properties of uncontrolled and controlled systems, it is revealed that the attractors of controlled systems are smaller than those of uncontrolled systems, and the theoretical and numerical results are consistent. …”
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Traveling Waves for Delayed Cellular Neural Networks with Nonmonotonic Output Functions by Zhi-Xian Yu, Rong Yuan, Cheng-Hsiung Hsu, Ming-Shu Peng

“…Then we construct a suitable wave profiles set and derive the existence of traveling wave solutions by using Schauder's fixed point theorem.…”
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The NSVZ β-function for theories regularized by higher covariant derivatives: the all-loop sum of matter and ghost singularities by K. V. Stepanyantz

“…It coincides with the corresponding part of the new form of the NSVZ equation, which can be reduced to the original one with the help of the non-renormalization theorem for the triple gauge-ghost vertices.…”
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Existence Results for a Nonlocal Coupled System of Sequential Fractional Differential Equations Involving ψ-Hilfer Fractional Derivatives by Athasit Wongcharoen, Sotiris K. Ntouyas, Phollakrit Wongsantisuk, Jessada Tariboon

“…We make use of Banach’s fixed point theorem to obtain the uniqueness result and the Leray-Schauder alternative to obtain the existence result. …”
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An essay on the foundations of variational methods: Exploring Sobolev Spaces for boundary integral equations by Rômulo Damasclin Chaves dos Santos, Jorge Henrique de Oliveira Sales

“…By leveraging Sobolev spaces, particularly fractional Sobolev spaces , and the properties of the Slobodetskii norm, we develop a robust theoretical framework. Our main theorem demonstrates that, under suitable conditions, has a unique solution in , and this solution inherits the regularity properties from the function . …”
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