Order Formula Research Articles

Mathematical Model of FWE Branching Type with Effect on Energy

: Mathematical modeling is one of the most important topics in teaching mathematics and converting real world problems into mathematical formulas in order to solve them. In this research we will take the behavior of lateral branching, tib-tib anostomosis with its effect on the energy of the growth of fungi. We will use the system of equations (PDEs) to solve a mathematical model and we will use mathematical techniques in order to reach the solution using non-dimensionality, stability, traveling wave, and numerical solution and use computer programs to facilitate the solution, including the Maple program, the MATLAB program, use Pdep code and the pplane7 code.

Spatially and temporally high-order dynamic nonlinear variational multiscale methods for generalized Newtonian flows

Non-Newtonian fluids are of interest in industrial sectors, biological problems and other natural phenomena. This work proposes rheologically-dependent, spatially and temporally high-order non-residual stabilized finite element formulations. The accuracy of the methods is assessed by tackling highly-convective time-dependent power-law flows. The spatial approximation uses Lagrangian finite elements up to fourth order. The temporal integration is done via backward differentiation formulas of order one, two and three. A key aspect of our work is using a non-residual orthogonal variational multiscale (VMS) formulation to stabilize dominant convection and to allow equal-order interpolation of velocity and pressure. Our VMS method uses dynamic nonlinear subscales, which have not been tested so far for generalized Newtonian fluids. In this work, the use of high-order temporal discretizations for the subscale components is systematically evaluated. Numerical experiments consider the flow over a confined cylinder for Reynolds numbers between 40 and 400 and power-law indices between 0.4 and 1.8. Numerical testing demonstrates the method to be stable in all combinations of spatial and temporal orders. Our results show that using high-order spatial discretizations more accurately approximates boundary layers and viscosity fields. Moreover, higher temporal orders allow using larger time steps while still capturing highly dynamic behaviors with better resolution in frequency spectra.

An unconditionally stable numerical scheme for solving nonlinear Fisher equation

Abstract In this study, novel numerical methods are presented for solving nonlinear Fisher equations. These equations have a wide range of applications in various scientific and engineering fields, particularly in the biomedical sciences for determining the size of brain tumors. The challenges posed by the nonlinearity of the equations are effectively addressed through the development of numerical techniques. The nonlinearity is tackled using a combination of the method of lines and backward differentiation formulas of varied orders. This method is unconditionally stable, and its accuracy is evaluated using error norms. The methods are successfully validated against test problems with known solutions, demonstrating their superiority through comparative analyses with existing methodologies in the literature.

Effectiveness of vibro-impact nonlinear energy sinks for vibration suppression of beams under traveling loads

Effective control of traveling-load-induced vibrations is a challenging issue of special significance in various engineering fields such as railways, bridges, cable systems, etc. Traditional passive strategies that rely on tuned mass dampers are effective over only a narrow traveling velocity range, thus cannot meet the broadband requirement for such problems. In this paper, a nonlinear device termed as vibro-impact nonlinear energy sink (VINES), that including a light-weight mass moving in-between the clearance of the primary structure, is proposed as a mean for the broadband control of vibrations induced by traveling loads. To do this, we considered a coupled system consisting of a beam as a host structure under traveling loads, and coupled to a set of VINESs. The system is modeled in a dimensionless formula in order to gain generalized results, and the vibro-impact dynamics is solved from a measure differential complementarity problem that is given by Signorini’s contact law. Comprehensive analyses are then conducted to investigate the vibration reduction potential of the VINES regarding the underlying nonlinear mechanisms, parametric effects, as well as robustness concerns. It is found that effective vibration reduction could be achieved by adding a simple VINES with a total mass around 10% of the host beam. Moreover, such a simple strategy shows an excellent broadband property to suppress multiple peaks, as well as a desirable robustness to perform well under excitation uncertainty and different traveling conditions.

Proposal for New Method for Calculating Sedimentation Process Efficiency in Water Treatment Plants.

An important aspect of water treatment is removing fine-grain materials from water. Due to the properties of fine-grain materials, they are difficult to remove from water. During the sedimentation process, which takes place in settling tanks, such materials are removed. The sedimentation process is often accompanied by coagulation and flocculation processes, which form aggregates of particles (flocs) from the fine-grained material particles in a suspension (non-grainy suspension). This kind of suspension (consisting of aggregates of particles or flocs) shows a different behaviour when falling compared with classic grainy suspensions. The main goal and novelty of this article are to propose (and test) a modification of the often used Stokes' formula with the addition of fractal geometry into the calculation of the terminal velocity of free-falling particles in order to overcome Stokes' formula's limitation, thus obtaining the sedimentation process efficiency. Because of this fractal modification, it is possible to use the simple and elegant Stokes' formula in order to calculate better the terminal velocity of non-grainy particles-aggregates or flocs-and thus obtain the sedimentation efficiency for the whole range of suspensions, both non-grainy and grainy. The results obtained in this article show that the sedimentation process efficiency calculated by using the modified formula based on the fractal geometry morphology of particles (the proposed fractal method) describes and agrees more with the data from the experiment than the sedimentation efficiency calculated only based on particle size (classic method).

Transparent boundary condition and its effectively local approximation for the Schrödinger equation on a rectangular computational domain

The transparent boundary condition for the free Schrödinger equation on a rectangular computational domain requires implementation of an operator of the form ∂t−i△Γ where △Γ is the Laplace-Beltrami operator. It is known that this operator is nonlocal in time as well as space which poses a significant challenge in developing an efficient numerical method of solution. The computational complexity of the existing methods scale with the number of time-steps which can be attributed to the nonlocal nature of the boundary operator. In this work, we report an effectively local approximation for the boundary operator such that the resulting complexity remains independent of number of time-steps. At the heart of this algorithm is a Padé approximant based rational approximation of certain fractional operators that handles corners of the domain adequately. For the spatial discretization, we use a Legendre-Galerkin spectral method with a new boundary adapted basis which ensures that the resulting linear system is banded. A compatible boundary-lifting procedure is also presented which accommodates the segments as well as the corners on the boundary. The proposed novel scheme can be implemented within the framework of any one-step time marching schemes. In particular, we demonstrate these ideas for two one-step methods, namely, the backward-differentiation formula of order 1 (BDF1) and the trapezoidal rule (TR). For the sake of comparison, we also present a convolution quadrature based scheme conforming to the one-step methods which is computationally expensive but serves as a golden standard. Finally, several numerical tests are presented to demonstrate the effectiveness of our novel method as well as to verify the order of convergence empirically.

RBF–based IMEX finite difference schemes for pricing option under liquidity switching

In this work, we introduce two accurate and efficient finite difference methods based on radial basis functions (RBF–FD) for pricing European and American options under liquidity shocks. The problem is formulated as the semi-linear complementarity and PDE systems for American and European options, respectively. In the context of temporal semi-discretization, we provide two backward difference formulas of order one and two (BDF1 & BDF2). Furthermore, we discuss the stability and convergence properties of the proposed methods. For the American option, to solve the semi-linear system of complementarity problems (LCPs), we combine the RBF-FD approaches with an operator splitting (OS) method. To illustrate the efficiency and accuracy of the suggested methods, we provide numerical examples for both European and American call options and verify them with the existing work in the literature. In numerical discussion, we show the Greeks (Delta & Gamma) plots for the American options.

Приложение биоинспирированных алгоритмов глобальной оптимизации в задаче подбора коэффициентов модели усталостной деградации жесткости композиционного материала

<p>The problem of finding the fatigue characteristics of a material based on the test results of a composite material is considered. The initial data are the properties of the material, load parameters and the tabulated dependence of the elastic modulus on the number of tests performed. A differential mathematical model has been formed that describes the change in the elastic modulus with increasing number of loading cycles. Its parameters are found by approximating the rate of change of the elastic modulus using numerical differentiation formulas of various orders and solving the parametric identification problem. The model coefficients are determined by using a method that simulates the behavior of a swarm of moths, related to bio–inspired global optimization algorithms. A solution to the problem for a specific composite material is given.</p>

A new robust dynamic state estimation approach for power systems with non-Gaussian noise

The Gaussian noise distribution is typically used in dynamic state estimation (DSE) but it is not always true in practice because of abnormal system inputs, impulsive noise and measurement outliers. In this paper, a new robust DSE approach based on a new robust Lp norm based estimator and the cubature Kalman filter (CKF) is developed for power systems with non-Gaussian noise statistics. The Lp norm based estimator is derived from the Lp norm formula and the quadratic formula in order to alleviate the impacts from bad data and outliers. The proposed Lp-CKF DSE approach exhibits good accuracy because a new estimation error covariance is obtained by using the influence function. The robustness of the proposed Lp-CKF DSE approach is verified by performing simulations on a generator in the IEEE 39-bus system.

PPSZ is better than you think

PPSZ, for long time the fastest known algorithm for $k$-SAT, works by going through the variables of the input formula in random order; each variable is then set randomly to $0$ or $1$, unless the correct value can be inferred by an efficiently implementable rule (like small-width resolution; or being implied by a small set of clauses). We show that PPSZ performs exponentially better than previously known, for all $k \geq 3$. For Unique-$3$-SAT we bound its running time by $O(1.306973^{n})$, which is somewhat better than the algorithm of Hansen, Kaplan, Zamir, and Zwick, which runs in time $O(1.306995^n)$. Before that, the best known upper bound for Unique-$3$-SAT was $O(1.3070319^n)$. All improvements are achieved without changing the original PPSZ. The core idea is to pretend that PPSZ does not process the variables in uniformly random order, but according to a carefully designed distribution. We write "pretend" since this can be done without any actual change to the algorithm.

On Perturbation of Operators and Rayleigh-Schrödinger Coefficients

Let A and E be self-adjoint matrices or operators on ℓ2(N)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell ^2({{\\mathbb {N}}})$$\\end{document}, where A is fixed and E is a small perturbation. We study how the eigenvalues of A+E\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A+E$$\\end{document} depend on E, with the aim of obtaining second order formulas that are explicitly computable in terms of the spectral decomposition of A and a certain block decomposition of E. In particular we extend the classical Rayleigh-Schrödinger formulas for the one-parameter perturbation A+tE\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A+tE$$\\end{document} where t∈R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t\\in {{\\mathbb {R}}}$$\\end{document} varies and E is held fixed, by dropping t and considering E as the variable.

Hubungan Komunikasi Orang Tua dalam Keluarga dengan Prestasi Belajar Siswa di SMP N 30 Padang

This research was motivated by the author's observations at State Junior High School 30 Padang. From the observations made, it appears that there are still many students who get low test scores. This research aims to obtain data and information regarding the relationship between parental communication in the family and student learning achievement at State Junior High School 30 Padang. The population in this study was 39 students and the research sample was 31 students. The sampling method applied by researchers was Stratified Proportional Random Sampling. The instrument used is a questionnaire with a Likert scale model. The data was analyzed using the rank order formula. The results show that there is a very significant relationship between parental communication in the family and student learning achievement at State Junior High School 30 Padang.

Logical generation of groups

A group G is called logically generated by a subset S, if every element of G can be defined by a first order formula with parameters from S. We consider the case where G is a direct product of finite nilpotent groups with mutually coprime orders and we show that logical and algebraic generations are equivalent in G. We also prove that in the case when G is a free non-abelian group, if S logically generates G then either it generates G algebraically or 〈 S 〉 is not a free factor of G.

The Relationship Between Social Support from Peers and Learning Outcomes of Trainees at LPK Smart College Padang

This research was motivated by the low learning outcomes of training participants at LPK Smart College Padang, this was caused by a lack of communication between training participants. This research aims to: 1) determine the description of the social support of trainee participants at LPK Smart College, 2) determine the description of the learning outcomes of trainees at LPK Smart College, 3) see the relationship between peer social support and the learning outcomes of trainees at LPK Smart College. This research uses a quantitative approach with a correlational type. The population of this research is all 20 registered and active training participants in training in 2023 at LPK Smart College. The sampling technique uses saturated sampling, namely the entire population is taken as a sample. The data collection technique uses a questionnaire and the data collection tool uses a questionnaire which contains a list of statements. The data analysis technique in this research uses percentage and rank order formulas. The results of this research show that: 1) the peer social support received by trainees at LPK Smart College is categorized as quite low, 2) the learning outcomes of trainees at LPK Smart College Padang are categorized as low, 3) there is a significant relationship between peer social support with the learning outcomes of training participants at LPK Smart College.

A NEW MULTI-STEP BDF ENERGY STABLE TECHNIQUE FOR THE EXTENDED FISHER-KOLMOGOROV EQUATION

The multi-step backward difference formulas of order k (BDF-k) for 3 ≤ k ≤ 5 are proposed for solving the extended Fisher–Kolmogorov equation. Based upon the careful discrete gradient structures of the BDF-k formulas, the suggested numerical schemes are proved to preserve the energy dissipation laws at the discrete levels. The maximum norm priori estimate of the numerical solution is established by means of the energy stable property. With the help of discrete orthogonal convolution kernels techniques, the L2 norm error estimates of the implicit BDF-k schemes are established. Several numerical experiments are included to illustrate our theoretical results.

A Sparse Differential Algebraic Equation (DAE) and Stiff Ordinary Differential Equation (ODE) Solver in Maple

This paper implements efficient numerical methods in Maple to solve index-1 nonlinear Differential Algebraic Equations (DAEs) and stiff Ordinary Differential Equations (ODEs) systems. Single-step methods (like Trapezoid (TR), Implicit-mid point (IMP), Euler-backward (EB), Radau IIA (Rad) methods, TRBDF2, TRX2) and backward-difference formula of order 2 are implemented with adaptive time-stepping methods in Maple to solve index-1 nonlinear DAEs. Maple’s robust and efficient ability to search within a list/set is exploited to identify the sparsity pattern and automatically calculate the analytic Jacobian. The algorithm and implementation are robust and efficient for index-1 DAE problems and scale well for finite difference/finite element discretization of two-dimensional models with system size up to 10,000 nonlinear DAEs and solve the same in a few seconds. The computational efficiency of the proposed algorithm (provided as an open-access code) compares favorably with the commercial solver gPROMs, one of the most commonly used sparse DAE solvers in the industry.

A generalized mixture fraction formulation for nonpremixed ammonia–hydrogen flames

For nonpremixed combustion, the mixture fraction variables are widely used as a conserved scalar to map out the flame structure in a unified manner. For ammonia–hydrogen flames, however, a proper definition of the mixture fraction variable is difficult due to the presence of fuel-bound nitrogen in ammonia. This work proposes a revised mathematical definition of the mixture fraction as a modified form of the Bilger’s formula in order to describe the characteristics of nonpremixed ammonia–hydrogen blend flames at general fuel mixture ratios. The newly defined mixture fraction properly accounts for differential diffusion effects in the presence of hydrogen, and thus serves as a convenient invariant coordinate for the flame manifolds. Counterflow nonpremixed flames with different ammonia–hydrogen ratios were computed and the validity of the new formulation is demonstrated. The analysis of the flame structure revealed the presence of double reaction zones, one dominated by the hydrogen oxidation and the other by ammonia oxidation. The role of differential diffusion is crucial in determining the existence of double reactive layers and its impact is evaluated by varying the strain rate. Detailed reaction analysis revealed that the hydrogen flame is related to HO2 reactions, while the ammonia flame to N, NH2 and NH3 reaction groups. As the strain rate is increased, OH reactions are responsible for shifting dominant heat release rate from the hydrogen flame to the ammonia flames. The scalar dissipation rate profile shows two distinct peaks, suggesting that a different functional description is needed in the flamelet modeling framework.

STUDY ON THE INITIAL BOUNDARY VALUE PROBLEM FOR AFRACTIONAL DIFFERENTIAL EQUATION WITH A FRACTIONALDERIVATIVE OF VARIABLE ORDER

This article studies the convergence of a numerical method for solving an initial-boundary value problem of a fractional differential equation with a variable order of the fractional derivative. In the generalized fractional differential filtration equation with a transitional filtration law in heterogeneous porous media, it is assumed that the order of the fractional derivative depends on the spatial variable. The main attention is paid to the development and theoretical justification of a method that provides high accuracy and efficiency of calculations with a variable order of the fractional derivative. For the numerical solution, an approximation was developed that combines the finite difference method for the time derivative and the finite element method for the spatial variable. The fractional derivative of variable order in the sense of Caputo is approximated by a formula of second order in time. The convergence of the constructed method is proven with order O(τ2+hk+1) for the case α(x)ϵ(0,1). The results of computational experiments for various functions of the order of the fractional derivative are presented, confirming the reliability of the theoretical analysis. The conclusions drawn emphasize the importance and relevance of the further development of numerical methods for fractional differential equations of variable order in modern mathematics and applied sciences, including the modeling of complex processes.

Adsorption Dye in Batik Wastewater using Biomass Adsorbent : a State of the Art Review

In this article, we study several research about optimizing the adsorption of harmful compounds contained in batik dye liquid waste using activated carbon. The employment of naphthalene as a chromogenic agent in the batik industry introduces a significant quandary by contributing to water pollution through effluent discharge. Noteworthy efforts have been made by certain industries, employing activated carbon to mitigate the presence of Pb and Cr attributable to naphthalene. The principal objective of this exposition is to consolidate insights into the sequestration of perilous dyes within batik industry effluents, leveraging various forms of natural activated carbon. The kinetics of the adsorption process will be quantified utilizing the appropriate kinetic order formula, while equilibrium data will be scrutinized through reaction isotherms employing diverse models.

The Relationship Between Emotional Intelligence and Learning Outcomes of Economic Subjects in The Package C Program at SKB 1 Tanah Datar

The background to this research is the low learning outcomes of students studying economics in the package C learning program at SKB 1 Tanah Datar. This is thought to be due to the low emotional intelligence of students studying. This research aims to: 1) describe the description of the emotional intelligence of students studying package C at SKB 1 Tanah Datar, 2) describe the description of the learning outcomes of students studying economics in the package C program at SKB 1 Tanah Datar, 3) to determine the relationship between emotional intelligence residents study with the results of studying economics subjects in the package C program at SKB 1 Tanah Datar. This research was carried out with a correlational quantitative approach which aims to test the relationship between emotional intelligence and learning outcomes in economics subjects in the package C program at SKB 1 Tanah Datar consisting of 39 students. The sampling technique was simple random sampling and 80% were taken. namely 30 people studied and as many as 20% were used as trials, namely 9 people. The data collection method uses a questionnaire with a statement list format as a data collection tool, the data analysis technique uses a percentage formula and to find correlations uses the Rank Order formula. The results of the research illustrate that: 1) the emotional intelligence of students studying in the package C program at SKB 1 Tanah Datar is categorized as low, 2) the learning outcomes for economic subjects in the package C program at SKB 1 Tanah Datar are categorized as low because many students' grades are below the KKM, and 3) there is a significant relationship between emotional intelligence and learning outcomes in economics subjects in the package C program at SKB 1 Tanah Datar. Keywords: Emotional Intelligence; Learning outcomes