Quintic Research Articles

Mathematical Model on Distributed Denial of Service Attack in the Computer Network

In this paper, an electronic- epidemic two-folded mathematical model is formulated with help of non-linear ordinary differential equations. Distributed Denial of Service (DDoS) attacks in the computer network are studied. The modeling of both attacking nodes and targeting nodes is performed. Botnet based malicious devices and their threats on computer networks are addressed using appropriate parameters. The basic reproduction numbers for both the attacking and the targeting population are calculated and interpreted. Local and global stability analysis is carried out for the infection-free and endemic equilibrium points. Differential equations are solved with the help of the Runge-Kutta 4th order numerical method and graphs are analyzed using MATLAB software. Simulation shows that the success or failure depends on the number of initially infected computers in the attacking group. The proposed model exhibits the phenomenon of backward bifurcation for different values of transmission parameters. This model gives the theoretical base for controlling and predicting the DDoS attack. This shows the way to minimize the attack in the network. This study will be helpful to identify the botnet devices and run the latest version of antivirus in the network to protect against DDoS attacks from attacking sources. The application of this study is to ascertain online crime and locate the attacking nodes in the field of online transactions of real-life problems that involve the internet and computer networking systems. Moreover, our model can play an important role in policy-making against the distributed attack.

Developing stem taper of Shorea robusta in the far-western Terai of Nepal

Tree taper functions expressed in terms of height and diameter at breast height (BDH) can provide accurate and timely information on current growing stock. Taper equations are very important for calculation of growing stock in forest inventories, however, in the context of Nepal, these are still unavailable at the required level. The study aimed to develop taper equations, so that those can be used to predict the diameter anywhere along the stem, and estimate tree volumes at desired sections. The input data was a destructive sampling method of 81 sample trees of Shorea robusta distributed in ten locations of the far western Terai of Nepal (Kailali and Kanchanpur districts).
 Using two independent B-Spline and 5th-degree polynomial taper models, the upper stem diameters were imputed. Both models were applied on the whole dataset, irrespective of DBH size, to get common fitted taper models. Later, the same models were tested for three different DBH classes to compare and evaluate the best-fit model. 
 Taper models, developed under the B-spline polynomial model of 3rd degree, were found to be highly dependent on the tree (DBH) sizes. Thus, better models could be developed by classifying the whole dataset based on different DBH classes. On the other hand, developed models under the 5th degree polynomial taper model did not exhibit their dependency on the tree (DBH) sizes and a better model was found for the unclassified datasets, i.e. for all DBH sizes.

Vibration-polynomial-based optimal trajectory planning for mobile concrete pumping equipment with state constraints

To improve the operating stabilities of the flexible hydraulic manipulator in concrete pumping equipment, a trajectory planning method based on optimal vibration energy is presented. First, predefined trajectories are generated by the quintic polynomial method, and kinematic inversions are established by unifying the velocity and angle constraints into the velocity level. Then, relationships between the boom vibration and the vibration energy are solved in modal space. Specifically, hydraulic actuators are regarded as spring-damping systems to calculate generalized forces into the vibration equation. The vibration equation can solve the modal coordinate and vibration model function, such that the elastic potential energy to cause vibration is completely described. Next, floating values are captured by a genetic algorithm to minimize vibration energy, and then introduced to the predefined trajectory to weaken the boom vibration. Last, the proposed trajectory planning method is verified by a concrete pumping spreader with a 13 m hydraulic manipulator.

Entropy generation in free convective micropolar couple stress regime in vertical channel

The study reports an application of homotopy perturbation method to investigate entropy generation in the steady micropolar couple stress fluidics inside a vertical porous medium channel. The channel is composed of two isothermal parallel walls maintained at different temperatures. The governing equations are framed in the Cartesian system. The boundary value problem depicting the thermofluidic configuration is treated by the homotopy perturbation method (HPM) and for its validation, the 4th-order Runge-Kutta scheme is also invoked. The quantities of interest, viz. skin friction, wall couple stress, Nusselt number computed by HPM, and 4th order R-K method are found to be in good agreement. After getting the velocity, temperature, and microrotation regime, the entropy involved with the thermodynamic process was modeled to facilitate future thermodynamic optimizations.

Современные подходы к хирургии катаракт с высокой остротой зрения на основании анализа волнового фронта

Relevance. Until recently, visual acuity was the main criterion for determining the timing of surgery, but already in the early stages of cataract development, patients may suffer from reduced image quality, which affects the quality of life (“night” myopia, light scattering, blurring). Deterioration in visual function in these patients may be explained by refractive errors. Analysis of internal higher-order aberrations resulting from slight opacification of the lens is important for determining the effect of media opacity on wavefront aberrations (WF) and for determining the indications and timing of surgical treatment, especially in patients with high visual acuity. Purpose. Evaluate the optical system of the eye with initial cataracts and high visual acuity. Evaluate the wavefront and its aberrations, contrast sensitivity and Shtrel coefficient. Material and methods. The study included 111 eyes with cataracts and 42 eyes without signs of cataracts (control group). Patients aged on average 57±5.3 years. Wavefront analysis was performed using an iTrace ray tracing aberrometer (Tracey Tech., USA) in a dark room under maximum drug-induced mydriasis. In each group, total, corneal, and internal wavefront aberrations were measured at a pupil diameter of 6.0 mm. Higher order aberrations were analyzed using Zernike polynomials (3rd to 5th order). The modulation transfer function (MTF) at different spatial frequencies (0–30 c/deg) and the Strehl coefficient in patients in the study groups were also assessed. Results. Total and internal higher-order wavefront aberrations were significant in different cataract groups compared with control patients, while higher-order corneal aberrations were not statistically different. We noted a higher level of total and internal aberrations in the group of patients with posterior subcapsular cataract. In this regard, patients with posterior subcapsular cataract require surgical treatment at an earlier stage, despite high visual acuity. Conclusion. We recommend assessing the optical quality of vision and wavefront aberrations when observing early cataracts in order to decide whether to perform surgery at an earlier date. Key words: initial cataract, quality of vision, higher order aberrations, internal wavefront aberrations

Automation of the Formation of a Mathematical Formulation of Kinetics for Multistage Chemical Reactions and Numerical Solution to a Direct Problem

Introduction. The basis for research, analysis and mathematical optimization of any chemical process is an adequate mathematical model that takes into account the kinetics of the object. Kinetic analysis is a challenge in chemical technology, since it allows for optimizing synthesis processes and predicting their efficiency. Numerous chemical processes involve several stage reactions. For successful design and optimization, a mathematical model that describes each stage is needed. Creating such a model manually can be time-consuming and costly, since it requires processing a large amount of information. The modern level of automation makes it possible to accelerate the obtaining of a mathematical formulation of the kinetics of multistage reactions. In this case, working with data is greatly simplified, and the probability of making mistakes is reduced. The resulting mathematical model can be applied for further analysis and optimization of the process. The paper considers the industrial reaction of catalytic reforming of gasoline, which occupies an important place in the modern scheme of oil refining, since it is a source of high-octane components of commercial gasolines and individual aromatic hydrocarbons. This process is characterized by the participation of a large number (up to 300) of various hydrocarbons, a change in the number of moles, and non-isothermality in it. Mathematical modeling of such processes involves detailing the stages to the required level. The detailing of up to 173 stages is considered. In this setting, automation of the formation of a mathematical formulation of kinetics for catalytic reforming of gasoline has not been carried out before. Therefore, the presented work aimed at implementing effective numerical methods and algorithms for automating the building of a mathematical model taking into account kinetics, thermodynamics, and changes in the number of moles.Materials and Methods. The mathematical formulation of the kinetics of multistage reactions was developed on the basis of the mass action law. The kinetic parameters values were taken from literary sources. The direct kinetics problem was solved using algorithms: the Gear method, the Runge-Kutta method of the 4th order, and the scipy.odeint() method of the Python language. The automation concept was implemented using the IDEF0 methodology. The software was written in the Python programming language.Results. A new software was created to automate the process of forming a mathematical model, taking into account the kinetics, thermodynamics, and the volume of the reaction mixture. The program results were presented by the example of catalytic reforming of gasoline. The model implemented the possibility of taking into account the intermediate heating of the mixture in the reactor cascade. Numerical values of temperature changes corresponding to industrial data were obtained.Discussion and Conclusion. The results obtained through modeling chemical transformations in the cascade of gasoline catalytic reforming reactors confirmed the exothermic nature of the reaction. The developed software product provides displaying changes in the concentrations of reactants, as well as temperature variations in the reactor, and it can be used in scientific research organizations for the analysis of multistage catalytic processes. The results of the reaction kinetics modeling will be used in the subsequent optimization of the process conditions in production.

Neutron fission chain behavior for modern 235U multiplicity data

The use of modern analog Monte Carlo software to perform space-time kinetics and probability of extinction (POE) calculations in support of nuclear design and safety studies can be hampered by appreciable execution times and code crashes attributable to lengthy finite and divergent prompt-neutron fission chains. To estimate chain behavior for modern 235U fission-multiplicity data and constant reactivity conditions, static point POE discrete-step stochastic models of unrestricted and restricted prompt-neutron fission chains are developed and solved analytically. These models are used in a simple expression which gives the estimated chain length LMAX required to calculate a POE to a prescribed accuracy. The analytical procedure entails solving a quintic polynomial, the roots of which are POE candidates. Methods including Galois theory are used to analyze the POE quintic. Analytical techniques are used to show that only a single POE exists for any state of criticality. Ingenious mathematics from the late 1800's, as updated in the early 1990's by King, are used to obtain the algebraic roots. The analytical models give valuable insights into fission chain behavior, and should be of use in providing chain control guidance for mainstream analog Monte Carlo code simulations of nuclear systems.

Effective decoupling method for derivation of eigenfunctions for closed cylindrical shell

By expansion into Fourier series along the circumferential coordinate, the problem for elastic thin-walled closed cylindrical shell is reduced to 8th order differential equation with respect to axial coordinate. In spite that the general structure of eigenvalues for this equation was known starting from 60-s of last century, they were derived only to some simplified versions of the shell theory. So, the main goal of paper consists in development of the general procedure for determination of the eigenvalues. The idea is based on that the theory of shell is actually formed by two much simple problems: the plane task of elasticity and the plate problem, each of them is reduced to much easily treated biquadratic equation. So, we start from either of two problems (main problem) while not taking into account the impact from another (auxiliary) problem. After computing its eigenfunctions, we gradually introduce the influence of auxiliary problem by presenting its functions as linear combination of functions for main problem. The results of calculation show the perfect accuracy of the method for any desired number of significant digits in eigenvalues. The comparison with known results for concentrated radial force shows the perfect ability to solve any boundary problem with any desirable accuracy.

The Determination of Dawn Time through Image Processing Camera

Determining the early time prayer is very fundamental for Muslims as it directly relates to the legal requirements of prayer. Prayers are not performed whenever we want, but rather there is a determination of the beginning and end of the prayer time as a guideline for Muslims to carry it out. The Indonesia government sets standards for Muslims to perform the dawn prayer service, by precisely determining the degree of the emergence of the dawn of Sadiq by -200. This study aims to compare the determination of the government's dawn time using different sensors, specifically drone cameras as image sensors. Drones were chosen due to their several advantages. The data generated by the drone is in the form of photos, which are subsequently processed using digital image processing software, called image-J. The data obtained are in the form of mean and standard deviation. All data collected in 1 day is recorded using Excel to form a graph of data which is then carried out by a polynomial approach to find out the cutoff point as the beginning of the dawn of Sadiq which indicates the start of dawn. The method used in this research is using the 4th order polynomial approach and the Sarrus method and the data obtained is the mean value and standard deviation. The conclusions obtained in the image analysis research are that the government's dawn time is 15 minutes too fast, the standard obtained in this study is -14.98° and unlike 2D SQM data, 3D drone data results in more accurate data analysis.

Analytic Solutions of 2D Cubic Quintic Complex Ginzburg-Landau Equation

The dynamical behaviour of traveling waves in a class of two-dimensional system whose amplitude obeys the two-dimensional complex cubic-quintic Ginzburg-Landau equation is deeply studied as a function of parameters near a subcritical bifurcation. Then, the bifurcation method is used to predict the nature of solutions of the considered wave equation. It is applied to reduce the two-dimensional complex cubic-quintic Ginzburg-Landau equation to the quintic nonlinear ordinary differential equation, easily solvable. Under some constraints of parameters, equilibrium points are obtained and phase portraits have been plotted. The particularity of these phase portraits obtained for new ordinary differential equation is the existence of homoclinic or heteroclinic orbits depending on the nature of equilibrium points. For some parameters, one has the orbits starting to one fixed point and passing through another fixed point before returning to the same fixed point, predicting then the existence of the combination of a pair of pulse-dark soliton. One has also for other parameters, the orbits linking three equilibrium points predicting the existence of a dark soliton pair. These results are very important and can predict the same solutions in many domains, particularly in wave phenomena, mechanical systems, or laterally heated fluid layers. Moreover, depending on the values of parameter systems, the analytical expression of the solutions predicted is found. The three-dimensional graphs of these solutions are plotted as well as their 2D plots in the propagation direction.

A Low-Power 30MHz ,6th Order Band-pass Differential Gm-C Filter on Chip Using Floating Current Source

A 30MHz center frequency, 6th order Butterworth and elliptic band-pass filter using a leap-frog Gm-C structure in this work. A continuous time differential voltage mode Gm-C biquad and its adjoin voltage - mode version are described, employing FCS (Floating Current Source) circuits as building blocks. The improved current source structure is simple and includes fewer transistors. This provides an effective use of the chip area and brings simplicity to the design of circuits. The proposed filter structure does not contain the resistor which is very important for integration. All capacitors in proposed filter are grounded which reduces the parasitic effects. The proposed filter has been successfully implemented by TSMC 0.18μm CMOS process. Simulation results are given to confirm the theoretical analysis.

Improved assessment sensitivity of time-varying cavitation events based on wavelet analysis

Ultrasonic cavitation, characterized by the oscillation or abrupt collapse of cavitation nuclei in response to ultrasound stimulation, plays a significant role in various applications within both industrial and biomedical sectors. In particular, inertial cavitation (IC) has garnered considerable attention due to the resulting mechanical, chemical, and thermal effects. Passive cavitation detection (PCD) has emerged as a valuable technique for monitoring this procedure. While the fast Fourier transform (FFT) is a widely used algorithm to analyze IC-induced broadband noise detected by PCD system, it may not adequately capture the time-varying instability of cavitation due to potential nuclei collapse during ultrasound irradiation. In contrast, the continuous wavelet transform offers a more flexible approach, enabling more sensitive analysis of signals with varying frequencies over time. In this study, nanodiamond (ND) and its derivative, nitro-doped nanodiamond (N-AND), known to possess cavitation potential from previous research, were chosen as the source of cavitation nuclei. The cavitation signals detected by PCD were subjected to both FFT and wavelet analyses, with their results comprehensively compared. This research showcased the feasibility of employing wavelet analysis for effective inertial cavitation evaluation. It provided the advantage of monitoring the temporal evolution of cavitation events in real-time, enhancing sensitivity to weak and unstable cavitation signals, especially those in higher order components (3rd and 4th order). Additionally, it yielded a higher level of precision in determining IC thresholds and doses. Furthermore, the inclusion of time information through wavelet analysis offered insights into the limitations of low-cycle ultrasound in inducing IC. This study introduces a novel perspective for more sensitive and precise cavitation assessment, leveraging time and frequency data from wavelet analysis, and holds promise for effective utilization of cavitation effects while minimizing losses and damages resulting from unintended cavitation events.

Practical considerations for HIL simulations of power converters using different numerical methods

The use of Hardware-In-the-Loop systems implemented in FPGAs is constantly growing due to their performance. However, hardware implementation of numerical methods to solve differential equations presents some challenges when applied to power converters. This paper shows a comparison of several numerical methods: Euler, Heun, Midpoint and 4th order Runge-Kutta, taking into account the accuracy of the methods and how they can be applied to power converters, where the equations change depending on the status of the switches. Results show that the speed in the solution of the numerical method is the main variable that affects the accuracy of the simulation, so in order to keep a fast resolution speed numerical method with low resources should be used.

Numerical computational approach for 6th order boundary value problems

This study introduces numerical computational methods that employ fourth-kind Chebyshev polynomials as basis functions to solve sixth-order boundary value problems. The approach transforms the BVPs into a system of linear algebraic equations, expressed as unknown Chebyshev coefficients, which are subsequently solved through matrix inversion. Numerical experiments were conducted to validate the accuracy and efficiency of the technique, demonstrating its simplicity and superiority over existing solutions. The graphical representation of the method's solution is also presented.

A High-Order Immersed Moving Boundary Method Using Ghost Points and Characteristics for Acoustics

Realistic acoustic problems often involve interactions between arbitrary-shaped moving objects at the interface with a fluid domain. The present work aims at developing numerical methods to take into account moving boundaries for acoustic problems, with a high order of convergence. The reference problem considered in this work is the solution of the non-linear Euler equations by a finite-difference time-domain method, describing the formation of one-dimensional waves created by a moving piston. The most suitable class of methods to solve this type of problem in the case of complex moving boundaries is the ghost-point method for sharp interface with 4th order reconstruction. 1 In order to accurately formulate the immersed boundaries with ghost points, the boundary conditions are formulated in terms of characteristic waves of the non-linear equations. The proposed approach is also extended to represent moving boundaries with a prescribed acoustic impedance. This is achieved by coupling a time-domain acoustic impedance model to the immersed boundary technique. The method is also applied to a two-dimensional example, where an acoustic pulse is reflected by a moving wall.

Alpha Fractal Rational Quintic Spline with Shape Preserving Properties

The intent of this paper is to construct the alpha fractal rational quintic spline. We have considered C2 rational quintic function, which is of the rational form, where the numerator is a quintic polynomial and denominator is a linear polynomial having two shape parameters i.e. sm & tm and deduced the uniform error bound for alpha fractal rational quintic spline. Also constraints have been applied on shape parameters and scaling factors to drive the shape preserving properties.

An improved Fourier series solution for vibration analysis of elastically restrained beams in Rayleigh–Ritz method

A combination of Fourier cosines series and polynomials (4 terms, 4th order) in Rayleigh–Ritz method is proposed to solve the vibration problem of a generally restrained beam. The characteristics of auxiliary polynomials, which actually are determined by homogeneous boundary conditions of the beam under consideration, can directly change the convergence properties and numerical instabilities of vibration results significantly. Fast convergence and reliability of the proposed polynomials are illustrated with numerical examples in comparisons with available results.

Empirical Degradation Models of the Different Indexes of the Proton Exchange Membrane Fuel Cell Based on the Component Degradation

To describe the degradation of proton exchange membrane fuel cells (PEMFCs), empirical degradation models of different indexes of PEMFCs are established. Firstly, the simulation process and assumptions of PEMFC degradation are proposed. Secondly, the degradation simulation results including the performance and distribution indexes under the different degradation levels are conducted by AVL FIRE M. Finally, the empirical degradation models of performance and distribution indexes are established based on the above simulation results and experimental data. The results show that the relationship between the experimental and simulation results is established by the index of current density. The empirical degradation models of current density, average equilibrium potential on the cathode catalyst layer (CL), average membrane water content, average oxygen molar concentration on the cathode CL, and average hydrogen crossover flux are the linear function. The empirical degradation models of average exchange current density on the anode CL, average hydrogen molar concentration on the anode CL, and average oxygen crossover flux are the quadratic function. The empirical degradation model of average activation overpotential on the cathode CL is the quintic function.

Adverse effects of receiver clock bias and drift on NavIC user position coordinates and their mitigation

We investigated the effects of receiver clock bias and drift on NavIC receiver position coordinates at a low latitude station and proposed a mitigation technique. For this, Five weeks data of Accord IRNSS-GPS-SPS (AIGS) receiver are considered. Error in each position coordinates (X, Y and Z) is estimated and observed that the maximum error occurred in user position Z-coordinate. CEP for 2D position is analyzed and observed that the Circular Error Probability (CEP) values are high in Z coordinate of YZ and ZX planes. Further, it is noticed that the timing of sudden enhancement of both clock bias and drift parameters coincides with the periodic anomaly of the X, Y and Z coordinates. The error in individual position coordinates is minimized by applying 6th order Butterworth low pass filter resulting in improved position accuracy. If such errors are not mitigated, the position estimation of the receiver becomes highly erroneous.

Broadening of He 1083nm, 388.8 nm, 501.6 nm, 587.5 nm, 667.8 nm, 706.5 nm, 728.1 nm lines and of H(α), H(β) and O 777 nm lines in atmospheric pressure helium

Helium atoms in electronically excited states are produced in atmospheric pressure parallel plate DBD helium plasma. Pressure broadening coefficients of several helium lines and of O(777 nm), H(β) and H(α) lines are deduced from the analysis of the spectral profiles of those lines. Absorption spectroscopy on He(3S) metastable atoms with a diode laser is used for 1083 nm He line. The influence of the laser power density on recorded absorption spectral profile is analyzed. For the other lines, emission from the plasma is analyzed with a very high resolution 2 m focal length spectrometer, working in the 2nd, 3rd or 4th diffraction order of the 1200 g/mm grating. Instrumental width ΔI ranges between 2.2 and 9.8 pm, depending on the spectral line. Knowing with high precision ΔI and the Doppler widths of the lines and the fact that the resulting Gaussian width of each line remains, at least, 4 times smaller than its Lorentzian width, permits to deduce the pressure broadening coefficients of helium 388.8, 501.6, 587.5, 667.8, 706.5, 728.1 and 1083 nm lines and of 777 O line with less than 3 % uncertainty for most of them. Observation of the forbidden 2p 1P1 –4f 1F3 component in the blue wing of the allowed 492.19 nm He(2p 1P1 –4d 1D2) line, indicates the presence of a static electric field E ≈ 5 ± 1 kV/cm during the 0.4 µs light collection time from the DBD. It is concluded that in pulsed plasmas, like DBD and plasma-jet, before deducing the plasma density from the homogeneous widths of H(β) or H(α) lines, one should ascertain that the static E-field in the gas is small enough during the light collection period for not inducing significant splitting of these lines. This would induce an extra broadening of the line, leading to an overestimated electron density.