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Huge data over the cloud computing and big data are processed over the network. The data may be stored, send, altered and communicated over the network between the source and destination. Once data send by source to destination, before reaching the destination data may be attacked by any intruders over the network. The network has numerous routers and devices to connect to internet. Intruders may attack any were in the network and breaks the original data, secrets. Detection of attack in the network became interesting task for many researchers. There are many intrusion detection feature selection algorithm has been suggested which lags on performance and accuracy. In our article we propose new IDS feature selection algorithm with higher accuracy and performance in detecting the intruders. The combination of wrapper filtering method using Pearson correlation with recursion function is used to eliminate the unwanted features. This feature extraction process clearly extracts the attacked data. Then the deep neural network is used for detecting intruders attack over the data in the network. This hybrid machine learning algorithm in feature extraction process helps to find attacked information using recursive function. Performance of proposed method is compared with existing solution. The traditional feature selection in IDS such as differential equation (DE), Gain ratio (GR), symmetrical uncertainty (SU) and artificial bee colony (ABC) has less accuracy than proposed PCRFE. The experimented results are shown that our proposed PCRFE-CDNN gives 99% of accuracy in IDS feature selection process and 98% in sensitivity. [ABSTRACT FROM AUTHOR]

It is well-known that the Lotka–Volterra predator-prey model has a family of periodic orbits, but does not possess limit cycles and therefore the model is said to be structurally unstable. The Lotka–Volterra model is a special case of a much larger group namely the quadratic population models and it can be shown that none of them can produce limit cycles. The surprising finding is that by combining two quadratic models a quadratic population model with two limit cycles is uncovered. Although the model looks simple at first glance it provides a rich source of dynamics and deserves attention. In this paper, we revisit a model that has its origin in the work of Dubois and Closset. A set of two quadratic population models interact as piecewise defined differential equations. The model has been discussed by Ren Yongtai and Han Li, cryptically written and showing some linguistic and typographical errors, but providing an excellent vehicle for developing skills in mathematical modelling, differential equations and technology for the young researcher. We explore the model in clearer detail and supplement the theory with rich graphical illustration. The paper has the purpose of providing an example of how a young researcher, such as a postgraduate student in biomathematics, can expand on an existing model by making use of current technology. [ABSTRACT FROM AUTHOR]

In this paper, the compliance of interface between fixture elements and workpiece is theoretically and experimentally investigated. The proposed theoretical model allows modelling of the behaviour of all kinds of interfaces between fixture elements and workpiece, under arbitrary dynamic loads. Workpiece displacement relative to fixture element was determined by analytical solution of the Lagrange differential equations of motion. Interface stiffness and damping coefficient were determined experimentally. The results of experimental investigation confirm the claims of theoretical model. [ABSTRACT FROM AUTHOR]

In this article, the problem of pricing discrete double barrier options which only monitored at specific times is investigated. According to the Black-Scholes framework, the option price would be obtained from recursively solving the Black-Sholes partial differential equations on the monitoring intervals. In this way, the sine-cosine wavelet approach is applied in approximating the yielded analytical expression. Finally, an operational matrix form is derived which is highly comparable with other methods. According to the method of the present paper, the computational time is nearly fixed against increases in the number of monitoring dates. [ABSTRACT FROM AUTHOR]

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This paper discusses the existence of solutions for fractional differential equations with nonlocal boundary conditions (NFDEs) under essential assumptions. The boundary conditions incorporate a point 0 ≤ c < d and fixed points at the end of the interval [0, d]. For i = 0, 1, the boundary conditions are as follows: ai, bi > 0, a0p(c) = -b0p(d), a1p'(c) = -b1p'(d). Furthermore, the research aims to expand the usability and comprehension of these results to encompass not just NFDEs but also classical fractional differential equations (FDEs) by using the Krasnoselskii fixedpoint theorem and the contraction principle to improve the completeness and usefulness of the results in a wider context of fractional differential equations. We offer examples to demonstrate the results we have achieved. [ABSTRACT FROM AUTHOR]

The aim of this paper is to numerically solve the Fokker-Planck-Kolmogorov fractional-time differential equations using the Legendre wavelet. Also, we analyzed the convergence of function approximation using Legendre wavelets. Introduced the absolute value between the exact answer and the approximate answer obtained by the given numerical methods, and analyzed the error of the numerical method. This method has the advantage of being simple to solve. The results revealed that the suggested numerical method is highly accurate and effective. The results for some numerical examples are documented in table and graph form to elaborate on the efficiency and precision of the suggested method. The simulation was carried out using MATLAB software. In this paper and for the first time, the authors presented results on the numerical simulation for classes of time-fractional differential equations. The authors applied the reproducing Legendre wavelet method for the numerical solutions of nonlinear Fokker-Planck-Kolmogorov time-fractional differential equation. The method presented in the present study can be used by programmers, engineers, and other researchers in this field. [ABSTRACT FROM AUTHOR]

The inconsistency between the whitening differential equation and the grey basic form of the non-homogeneous continuous grey model CFNGM(1,1,k,c) will result in internal errors. Thus this paper proposes a CFNGMA(1,1,k,c) model with adjustable parameters, which improves the accuracy of the CFNGM(1,1,k,c). This paper first elucidates reasons for the internal errors generated by the continuous grey model CFNGM(1,1,k,c), and explains the classic method, the discrete grey forecasting model, of eliminating internal errors. On the basis of an in-depth analysis of the modeling mechanism of CFNGM(1,1,k,c) model, a new parameter adjustable grey forecasting model is proposed by introducing parameter adjustment factors to modify model's parameters. Finally, the new model is applied to explore the gross regional product of Chengdu and Deyang in the Chengdu metropolitan area. The calculation results indicate that the newly proposed model can obtain more accurate results. [ABSTRACT FROM AUTHOR]

The dynamic analysis of the out-of-plane response of masonry walls, with different reinforcing systems and hit by sequences of pulses alternating in sign, representative of the seismic action, is the aim of the paper. The analysis is done in the context of the Heyman model of the no tension masonry structures. We consider the wall of the last story of a simple masonry house, commonly reinforced at its head by a ring beam, usually in a reinforced concrete. It has also been considered the retrofitting of the wall by applying, on both its sides, vertical bands in FRP, or similar. The dynamics of the wall, activated by sequences of pulses, is analyzed in detail, considering the change of geometry occurring in the mechanism during the motion. The corresponding differential equation is integrated in a closed form. It is shown that, under the alternating sequence of shocks, the dynamical collapse of the wall takes place immediately after the occurrence of an accumulation of out-of-plane deformation of the wall that drags it into the configuration of zero strength, where any resistance, due to the weight, has been lost. The collapse takes place right after when the subsequent incoming pulse pushes the wall to go further beyond this configuration. The check of the seismic safety of the masonry wall concludes the paper. The smallest limit static strength of the wall required in order the wall, having pulsation p, could be able to sustain, at the limit of the dynamical collapse, the action of the asymptotic pulse sequence with acceleration intensity PGA and specific duration p TE/2 of the expected earthquake. It is shown that the wall, reinforced by a top ring beam, with the addition of vertical bands of glass or similar, of suitable length, pasted with lime mortar, can reach the required level of seismic safety. [ABSTRACT FROM AUTHOR]

This paper introduces a new approach for analyzing the dynamics of DC–DC converters. Currently, the primary widely accepted method for examining dynamic processes is the Small Signal Analysis technique. However, when applied to modern complex converters, this method poses additional challenges in formulating and solving systems of differential equations. The method proposed in this paper is based on its application to the analysis of dynamic modes of energy functions—Lagrangians. These functions make it possible to define simple criteria to describe the course of dynamic processes, and in the end define an equivalent (approximating) conventional converter identical to the original one with respect to the course of dynamics. If the magnetic and electrical energies in the Lagrangians of both the converters are equal, the outcome is practically identical transient processes. These findings were confirmed by both theoretical analysis and experimentally modelling the dynamics of the initial converter and an equivalent to it in the Matlab–Simscape program. An additional possibility of using the transfer functions of a conventional boost converter for the theoretical analysis of the converters of much greater orders is also discussed. The authors' experiments confirm the correctness of their theoretical conclusions. [ABSTRACT FROM AUTHOR]

The aim of this paper is to determine the eigenvalue intervals of μk; 1 < k < n for which an iterative systems of a class of fractional-order differential equations with parameterized integral boundary conditions (BCs) has at least one positive solution by means of standard fixed point theorem of cone type. To the best of our knowledge, this will be the first time that we attempt to reach such findings for the topic at hand in the literature. The obtained results in the paper are illustrated with an example for their feasibility. [ABSTRACT FROM AUTHOR]

In this paper, a semi-analytical technique based on Taylor's series method namely DTM has been used to solve the differential equation which governs the motion of three types of annular FGM plates. The differential equation has been obtained using Hamilton principle and classical plate theory. The mechanical properties of the plate (Young's modulus and density) are considered to be graded in thickness direction and vary following the power-law. The behaviour of volume fraction index and radii ratio has been investigated onto first three modes of frequency parameter for all three plates. Moreover, the novelty of this paper is the application of the versatile technique DTM to study the effect of radii ratio and volume fraction index on three different types of annular FGM plates. A comparison has been made between the obtained numerical results and the results are available in the literature. A good agreement of the results verifies the accuracy of the present technique. Three-dimensional mode shapes for all three plates are also presented. [ABSTRACT FROM AUTHOR]

This paper explores the existence and stability of implicit neutral Caputo fractional qdifference equations within four distinct classes, incorporating various delay types such as finite, infinite, and state-dependent delays. To establish the existence of solutions, we utilize the fixed point theorem of Krasnoselskii in Banach spaces. The concluding section provides illustrative examples that highlight the obtained results. [ABSTRACT FROM AUTHOR]

This paper delves into the asymptotic and oscillatory behavior of all classes of solutions of fourth-order nonlinear neutral delay differential equations in the noncanonical form with damping terms. This research aims to improve the relationships between the solutions of these equations and their corresponding functions and derivatives. By refining these relationships, we unveil new insights into the asymptotic properties governing these solutions. These insights lead to the establishment of improved conditions that ensure the nonexistence of any positive solutions to the studied equation, thus obtaining improved oscillation criteria. In light of the broader context, our findings extend and build upon the existing literature in the field of neutral differential equations. To emphasize the importance of the results and their applicability, this paper concludes with some examples. [ABSTRACT FROM AUTHOR]

Purpose: In order to solve the problem that the existing models can't accurately reproduce the mechanical properties of metallic plates under complex working conditions, and the accuracy and efficiency can't be satisfied at the same time. The analysis of metallic plates by different refined finite elements is presented in this paper. The working efficiency and accuracy of the higher-order model in engineering applications are studied. Methods: The refined plate elements are based on several series expansion, and applied to the modeling and analysis of plate structures. The Carrera unified formulation is introduced to express the plate displacement field, the theoretical model of plate thickness expansion is established by using Taylor series expansion and Lagrange series expansion. The governing differential equations of metallic plate are established by using the principle of virtual displacements, the mass matrix and stiffness matrix of plate elements are deduced simultaneously. Finally, the shear locking phenomenon of the plate models is considered, tensor component mixed interpolation (MITC4) is used to revise the model. The accuracy and the reliability of the refined plate models are verified by comparing several order models and solid models generated in the commercial software ANSYS. Results and Conclusion: In this paper, the higher-order model has very low degree of freedoms (DOFs) on the premise of ensuring accuracy. And this modeling method can be used not only for thin plate analysis, but also for medium-thick plate analysis. Meanwhile, the refined plate model has high working efficiency and wide application range, which provides a new modeling method for the research of metallic plates. [ABSTRACT FROM AUTHOR]

This paper is devoted to electric arc furnace (EAF) modeling using a random differential equation based on the power balance equation. The proposed approach broadens and improves the model through the introduction of stochastic processes in place of existing coefficients. The paper presents a method which enables the estimation of EAF model coefficients with the help of measurement data - voltage and current waveforms recorded during the melting stage of an EAF work cycle. The estimation process is conducted with a Monte Carlo method and genetic algorithm, which is applied iteratively to each of the defined frames of the input signal. The estimated coefficients have been analyzed with respect to their time variability as well as the probability distributions of their values and increments. The results have been extensively visualized. Next, the identification of the stochastic processes representing the model coefficients has been carried out. Based on the previous results and autocorrelation functions, the density functions and parameters of discrete-time stochastic processes were identified. The paper presents solutions validated with statistical tests. [ABSTRACT FROM AUTHOR]

The authors of this paper examine uniformly asymptotically stability (UAS). uniformly boundedness (UB). ultimately uniformly boundedness (UUB) and existence of periodic solutions (EPSs) of certain nonlinear delay differential equations (DDEs) of third order with multiple constant delays. They prove two results and give a corollary on these properties of solutions. The main results of this paper have sufficient conditions and the technique of the proofs for these results is based on construction of a proper Lyapunov- KrasovskiT function (LKF). This paper has novel results to the theory of DDEs of third order and fills some gaps related to the mentioned concepts. [ABSTRACT FROM AUTHOR]

The year 2018 marked the 100th anniversary of the publication of paper "On the question of the biological basis of fisheries" by F.I. Baranov considered a cornerstone paper of modern fishery science. Baranov formalized population dynamics by describing changes in population abundance using differential equations, introducing the concept of instantaneous fishing and natural mortality rates, and developing his catch equation, which is the foundation of most modern age-structured stock assessment models. Baranov was the first to show the effect of fishing on population structure based on theoretical grounds. At the time of its publication, Baranov's paper did not receive much attention in Russia and was completely unknown to scientists in the West. The second publication (On the question of the dynamics of the fishing industry, 1925) received substantial criticism from many and sparked a furious debate between Baranov and his opponents that lasted for several decades. The history and content of those debates, expressed in multiple papers by Baranov, is still largely unknown. I describe the essence of arguments by Baranov and his opponents. The story of these scientific debates reveals how different philosophical concepts and dominant points of view evolved through time. [ABSTRACT FROM AUTHOR]

In this paper, abundant analytical solutions of the damped (2 + 1)‐dimensional nonlinear Schrödinger equation are achieved by taking advantage of the extended systematic method. By considering various values of parameters, dynamic behaviors of bright, dark soliton, period wave, and kink solitary solutions are displayed with different amplitudes and directions in 3D graphs, lines, contour maps, and time evolution plots. Further analysis of the obtained results is studied to show the efficient effect of the parameters on the propagation and configuration of waves. In addition, computer simulations are considered to show the correlation between parameters and velocity. Our results indicate that the extended systematic method for solving differential equations is more convenient and yields richer solutions. The other mathematical physics equations that appear in nonlinear science can also be investigated by the concept of this study. [ABSTRACT FROM AUTHOR]

This manuscript presents a comprehensive exploration of the nonlinear charged particle oscillation equation, employing the Laplace–Adomian decomposition method (LDM) to obtain approximate analytical solutions. The investigation leads to the formulation of five initial equations governing the oscillatory behavior of a charged particle, which are visually represented and analyzed with insightful interpretations. Notably, the existing literature lacks an exact solution to this problem. However, this paper fills this gap by presenting an approximate analytical solution utilizing the LDM. The solution is carefully studied and analyzed, contributing to a deeper understanding of the complex behavior of charged particle oscillation. [ABSTRACT FROM AUTHOR]