A Dynamic Intrusion Detection System Based on Multivariate Hotelling’s T2 Statistics Approach for Network Environments by Aneetha Avalappampatty Sivasamy, Bose Sundan

“…With a threshold range obtained using the central limit theorem, observed traffic profiles have been classified either as normal or attack types. …”
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Approximate Solution of a Reduced-Type Index-k Hessenberg Differential-Algebraic Control System by Ghazwa F. Abd, Radhi A. Zaboon

“…The implicit function theorem is first applied to solve the algebraic constraints of having unknown state differential variables to form a reduced state-space representation of an ordinary differential (control) system defined on smooth manifold with consistent initial conditions. …”
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Local uniform convexity and Kadec-Klee type properties in K-interpolation spaces I: General Theory by Peter G. Dodds, Theresa K. Dodds, Alexander A. Sedaev, Fyodor A. Sukochev

“…A central motivation for our study lies in the observation that classical renorming theorems of Kadec and of Davis, Ghoussoub and Lindenstrauss have an interpolation nature. …”
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Moments of von mises and fisher distributions and applications by Thomas Hillen, Kevin J. Painter, Amanda C. Swan, Albert D. Murtha

“…Here we present a new method to compute the moments of spherical distributions, based on the divergence theorem. This method allows a clear derivation of the second moments and can be easily generalized to higher dimensions. …”
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Modelling and Simulation of The Spread of HBV Disease. by Niyirora, Ignatius

“…It was guided by specific objectives that were to find out the disease free equilibrium of the spread of Hepatitis B Virus, to determine sensitivity analysis on Ro to ascertain which parameter that is most sensitive and that should be targeted by way of intervention and to examine the local stability of the model equation using the modified implicit function theorem. The first result of our simulations confirms that the disease free equilibrium is globally asymptotically stable when Ro< 1. …”
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Structured Dynamics in the Algorithmic Agent by Giulio Ruffini, Francesca Castaldo, Jakub Vohryzek

“…Then, adopting a generic neural network as a proxy for the agent dynamical system and drawing parallels to Noether’s theorem in physics, we demonstrate that data tracking forces the agent to mirror the symmetry properties of the generative world model. …”
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Finite-Time Synchronization of Fractional-Order Complex-Valued Multi-Layer Network via Adaptive Quantized Control Under Deceptive Attacks by Lulu Xu, Juan Yu, Cheng Hu, Kailong Xiong, Tingting Shi

“…According to the finite-time theorem, Lyapunov function, and graph theory methods, some sufficient criteria for realizing finite-time synchronization in complex-valued fractional-order multi-layer networks have been obtained. …”
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The approximate lag and anticipating synchronization between two unidirectionally coupled Hindmarsh-Rose neurons with uncertain parameters by Bin Zhen, Ya-Lan Li, Li-Jun Pei, Li-Jun Ouyang

“…The precise condition for lag synchronization is deduced analytically, utilizing the Laplace transform and convolution theorem, alongside the iterative approach within the framework of Volterra integral equations theory. …”
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PREDICTION AND CONTROL OF THINNING RATE OF DEFORMATION ZONE THICKNESS IN METAL SHEET SINGLE POINT INCREMENTAL FORMING PROCESS by FAN Yuan, LI Yan, YANG MingShun, YAO ZiMeng, BAI Lang

“…The results showed that the thinness value calculated by fitted formula to predict the deformation zone thickness is more close to the experimental data than by sine theorem. Thinning rate of deformation zone thickness increases with the increase of tool diameter,forming angle and sheet thickness and the decreases of step size,the feeding speed had no significant effect on the thinning rate. …”
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Some Existence, Uniqueness, and Stability Results for a Class of <i>ϑ</i>-Fractional Stochastic Integral Equations by Fahad Alsharari, Raouf Fakhfakh, Omar Kahouli, Abdellatif Ben Makhlouf

“…This paper focuses on the existence and uniqueness of solutions for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϑ</mi></semantics></math></inline-formula>-fractional stochastic integral equations (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϑ</mi></semantics></math></inline-formula>-FSIEs) using the Banach fixed point theorem (BFPT). We explore the Ulam–Hyers stability (UHS) of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϑ</mi></semantics></math></inline-formula>-FSIEs through traditional methods of stochastic calculus and the BFPT. …”
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Definition and Properties of the Libera Operator on Mixed Norm Spaces by Miroslav Pavlovic

“…As an application of 3∘ we have a generalization of Bernstein’s theorem on absolute convergence of power series that belong to a Hölder class.…”
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Supporting Characteristics of Soldier Piles for Foundation Pits under Rainfall Infiltration by Changxi Huang, Xinghua Wang, Min Zhang, Hao Zhou, Yan Liang

“…Based on the Richards seepage equation and earth pressure theory considering the effect of intermediate principal stress of unsaturated soil, the approximate solution of permeability coefficient in unsaturated soil is developed using the Laplace integral transform and residue theorem. The transition of the boundary condition from flux boundary to head boundary is taken into account, and the rationality of the solution is verified. …”
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New Jensen–Shannon divergence measures for intuitionistic fuzzy sets with the construction of a parametric intuitionistic fuzzy TOPSIS by Xinxing Wu, Qian Liu, Lantian Liu, Miin-Shen Yang, Xu Zhang

“…Abstract In this paper, we first give an example to show that Theorem 1 in Hung and Yang (Inf Sci 178(6):1641–1650, 2008) does not hold, implying that the J-divergence introduced by Hung and Yang does not satisfy the axiomatic definition of intuitionistic fuzzy divergence measure. …”
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On Pro-$p$ Cappitt Groups with finite exponent by Porto, Anderson, Lima, Igor

“…These results are pro-$p$ versions of the generalized Dedekind groups studied by Cappitt (see Theorem 1 and Lemma 7 in [1]).…”
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Three Positive Periodic Solutions to Nonlinear Neutral Functional Differential Equations with Parameters on Variable Time Scales by Yongkun Li, Chao Wang

“…Using two successive reductions: B-equivalence of the system on a variable time scale to a system on a time scale and a reduction to an impulsive differential equation and by Leggett-Williams fixed point theorem, we investigate the existence of three positive periodic solutions to the nonlinear neutral functional differential equation on variable time scales with a transition condition between two consecutive parts of the scale (d/dt)(x(t)+c(t)x(t-α))=a(t)g(x(t))x(t)-∑j=1nλjfj(t,x(t-vj(t))), (t,x)∈T0(x),Δt|(t,x)∈S2i=Πi1(t,x)-t, Δx|(t,x)∈S2i=Πi2(t,x)-x, where Πi1(t,x)=t2i+1+τ2i+1(Πi2(t,x)) and Πi2(t,x)=Bix+Ji(x)+x,  i=1,2,….  …”
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Discrete Derivative Nonlinear Schrödinger Equations by Dirk Hennig, Jesús Cuevas-Maraver

“…In fact, we prove the existence of solitary TWs, facilitating Schauder’s fixed-point theorem. For the damped forward expansive ddNLS we demonstrate that there exists such a balance of dissipation so that solitary stationary modes exist.…”
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Approximation-Based Fixed-Time Adaptive Tracking Control for a Class of Uncertain Nonlinear Pure-Feedback Systems by Cheng He, Jian Wu, Jiyang Dai, Zhe Zhang, Libin Xu, Pinwei Li

“…Radial basis function neural networks are introduced to approximate unknown functions for solving the fixed-time control problem of unknown nonlinear pure-feedback systems, and the mean value theorem is used to solve the problem of nonaffine structure in nonlinear pure-feedback systems. …”
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Sufficient statistics for the Pareto distribution parameter by I. S. Pulkin, A. V. Tatarintsev

“…Also, on the basis of the Rao–Blackwell–Kolmogorov theorem, effective estimates of the Pareto distribution parameter are constructed. …”
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Fractional order slide mode droop control for simultaneous voltage and frequency regulation of AC microgrid by Mohamad Issa Ibraheem, Mehdi Edrisi, Hassan Haes Alhelou, Mehdi Gholipour

“…Design parameters were chosen using the Lyapunov stability theorem. The validation of the proposed method using Simulink‐MATLAB confirms its effectiveness in enhancing level power sharing, regulating frequency, and maintaining voltage stability across the system.…”
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Selective learning for sensing using shift-invariant spectrally stable undersampled networks by Ankur Verma, Ayush Goyal, Sanjay Sarma, Soundar Kumara

“…Abstract The amount of data collected for sensing tasks in scientific computing is based on the Shannon-Nyquist sampling theorem proposed in the 1940s. Sensor data generation will surpass 73 trillion GB by 2025 as we increase the high-fidelity digitization of the physical world. …”
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