Order Formula Research Articles

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.

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.

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

The Relationship Between The Use Of Media and The Learning Activities of Training Participants at Uptd BLK Padang Pariaman

This research was motivated by the active learning of training participants in the learning process at UPTD BLK Padang Pariaman, which was thought to be because the instructor used learning media that was less than optimal. This research aims to see a description of the use of media used by instructors in the learning process. The learning activity of trainees in the learning process and the relationship between the use of media and the learning activity of trainees at UPTD BLK Padang Pariaman. This type of research uses a correlational quantitative approach. The population in this study was all training participants at UPTD BLK Padang Pariaman, totaling 32 people. Meanwhile, samples were taken using the cluster random sampling technique as much as 75% of the population of 32 people so that the sample taken was 24 people. Data collection techniques use a questionnaire which will be distributed via Google Form. Meanwhile, the data analysis technique uses a percentage formula and to look for relationships using the rank order formula. The results of this research indicate that instructors have not used media optimally in the learning process so that the trainees' active learning in the learning process is low. There is a significant relationship between media use and the active learning of training participants at UPTD BLK Padang Pariaman.Keywords: use of media, learning activity

The Relationship Between Students' Understanding of PIR-R Organization With its Activity at Sma N 1 Koto XI Tarusan

This research was motivated by student activity in the PIK-R organization at SMA N 1 Koto This research aims to see a picture of students' understanding of the PIK-R organization, see a picture of students' activity in the PIK-R organization, and see the relationship between students' understanding of the PIK-R organization and their activity at SMA N 1 Koto XI Tarusan. This research uses a quantitative, correlational type approach. The population of this research is all students who are members of PIK-R at SMA N 1 Koto XI Tarusan, totaling 24 respondents. Meanwhile, samples were taken using a total sampling technique, namely 100% (24) and trials were carried out at other schools that had the same characteristics. Data collection techniques using tests and questionnaires distributed directly to respondents. Meanwhile, the data analysis technique uses percentage formulas and rank order formulas. The research results show that students' understanding of the PIK-R organization is still relatively low. Students in organizations have low activity, and there is a significant relationship between students' understanding of the PIK-R organization and their activity. This means that the higher the student's understanding of the PIK-R organization, the more active the student is in the organization, but conversely, the lower the student's understanding of the PIK-R organization, the lower the student's activeness.                                                                                           Keywords : Understanding, PIK-R organization, activeness

THE RELATIONSHIP BETWEEN THE APPLICATION OF THE PROBLEM METHOD BASED LEARNING WITH PARTICIPANT LEARNING OUTCOMES COMPUTER COURSE AT SMART COLLEGE PADANG

This research was motivated by the low learning outcomes of computer course participants at LKP Smart College Padang. This is thought to be due to the poor application of problem based learning methods so that the learning outcomes of course participants are low. The research objectives are: 1) To find out the description of the application of the Problem Based Learning method to the learning outcomes of computer course participants at LKP Smart College Padang, 2) To find out the description of the learning outcomes of computer course participants at LKPSmart College Padang, 3) To find out the relationship between the application of the Problem Based Learning method to learning outcomes of computer course participants at LKP Smart College Padang.This type of research is correlational, with a quantitative approach. The population in this study was 30 people and a sample of 21 people whose sample was determined using the Simple Random Sampling method. Then a questionnaire is used to collect data. As well as data analysis techniques using percentage and rank order formulas.                The results of the research show that: 1) The description of the application of the Problem Based Learning method among computer course participants at Smart College Padang is categorized as low; 2) A description of the learning outcomes of computer course participants at LKP Smart College Padang is categorized as low. 3) A description of the significant relationship between the application of the problem based learning method and the learning outcomes of computer course participants at LKP Smart College Padang.The research suggestions are: 1) It is hoped that instructors can innovate regarding learning methods so that they can become good and appropriate learning methods for course participants to learn. 2) It is hoped that course participants will be able to learn and adapt learning methods so that they can maximize learning outcomes. 3) It is hoped that future researchers will innovate and research new variables to add variables and complete them.Keywords: Problem Based Learning, Learning Outcomes.

General formulae for the periapsis shift of a quasi-circular orbit in static spherically symmetric spacetimes and the active gravitational mass density

We study the periapsis shift of a quasi-circular orbit in general static spherically symmetric spacetimes. We derive two formulae in full order with respect to the gravitational field, one in terms of the gravitational mass [Formula: see text] and the Einstein tensor and the other in terms of the orbital angular velocity and the Einstein tensor. These formulae reproduce the well-known ones for the forward shift in the Schwarzschild spacetime. In a general case, the shift deviates from that in the vacuum spacetime due to a particular combination of the components of the Einstein tensor at the radius [Formula: see text] of the orbit. The formulae give a backward shift due to the extended-mass effect in Newtonian gravity. In general relativity, in the weak-field and diffuse regime, the active gravitational mass density, [Formula: see text], plays an important role, where [Formula: see text], [Formula: see text] and [Formula: see text] are the energy density, the radial stress and the tangential stress of the matter field, respectively. We show that the shift is backward if [Formula: see text] is beyond a critical value [Formula: see text][Formula: see text]g/cm3[Formula: see text], while a forward shift greater than that in the vacuum spacetime instead implies [Formula: see text], i.e. the violation of the strong energy condition, and thereby provides evidence for dark energy. We obtain new observational constraints on [Formula: see text] in the Solar System and the Galactic Centre.

The Relationship of Parental Control with Children’s Digital Literacy Skills in Pesisir Selatan

The digital divide in Indonesia demands that digital literacy education be delivered through several knowledge transfer mechanisms. The purpose of this research is to look at the relationship between parental control and digital literacy skills in children in Pesisir Selatan. This type of research is quantitative correlational. Sources of data in this study are parents and children. The population in this study amounted to 30 parents and the sampling technique was Simple Random Sampling and 70% were taken, namely 21 children. The data collection method uses a questionnaire with a statement list format as a data collection tool, data analysis techniques use a percentage formula and to find correlations use the Rank Order formula. The results of the study found: 1) Parental control of this child was classified in the unfavorable category. 2) digital literacy skills in children are classified in the low category. 3) There is a significant relationship between parental control and digital literacy skills in children in Pesisir Selatan. Furthermore, some suggestions are: 1) According to the respondents' assessment, parental control over children is still much that has not been implemented, when viewed from the duties and responsibilities of parents, it is suggested to parents to better understand their duties and responsibilities so that they are able to protect children from the dangers of digital media. 2) It is necessary for children to be aware of how important it is to understand increasingly sophisticated digital media that can develop various potentials in children so that they have knowledge and experience. 3) It is hoped that other studies will be able to see several other factors that have not been studied in this study

Gauss diagram formulae for Vassiliev invariants from Kauffman polynomial

A state model for Kauffman polynomial of Dubrovnik-version is described using Gauss diagrams. Based on the state model, the Gauss diagram formulae for Vassiliev invariants are given from the coefficients of Kauffman polynomial following the method of Chmutov and Polyak. Some arrow diagram identities are given to simplify the Gauss diagram formulae of order 3, which give Polyak–Viro and Chmutov–Polyak formulae for the Vassiliev invariant of order 3. The models of Kauffman polynomial and HOMFLY-PT polynomial give different Gauss diagram expressions when specializing in Jones polynomial.

Sign balances and promotion order of Young-Fibonacci tableaux

In this paper we give two results on Young Fibonacci tableaux. First we establish identities about the sign balances of Young Fibonacci tableaux, analog to known results on standard Young tableaux. Then we investigate the promotion action on a Young Fibonacci tableau and determine the order of the action. In contrast with the fact that there is no general formula of the promotion order for a standard Young tableau, here we can determine the order completely.

Computing indefinite integrals by difference equations

In teaching mathematics to first-year undergraduates, and thus in the appropriate calculus textbooks, the task of calculating an integral that satisfies a specific first-order or second-order recurrence relation often appears. These relations are obtained mainly by applying the method of integration by parts. Calculating such integrals is usually tedious, especially for an integer n > 2, time-consuming, and presents the possibility of making a large number of errors when computing involves multiple iterative steps. In [1], it is shown that in two cases (Theorems 2.1. and 2.3), the process of calculating integrals satisfying first-order recurrence relations can be performed quickly using easily memorised closed-form formulas for corresponding primitive functions. The question can rightly be asked whether there is a faster way to calculate other integrals of this type. In this paper, our goal is to give an affirmative answer to such a question, though without convering all situations. Since each recurrence relation is equivalent to a difference equation of the same order, the calculation of integrals mentioned above can be reduced to solving the corresponding difference equations. Since every first-order or second-order linear difference equation is solvable, it follows that for every integral which can be reduced to a first- order or second-order recurrence formula, it is possible to find corresponding primitive functions directly. Sometimes such a procedure is much faster than iterative solving of the integral. Closed-form formulas for the integrals discussed in the following sections are not unknown (see [2]). However, here our goal is to present the idea of computing indefinite integrals using difference equations. We will discuss it in more detail in Section 2. In Section 3, we discuss the application of the results obtained to calculate several improper integrals and the application of some of them in different sciences. An exciting example of such an application is the integral , which in the case n = 1 is used in the kinetic theory of gases, particularly in the Maxwell-Boltzmann distribution of gas molecules by energies (see Remark 4). Also, we compare the formulas obtained by the method of difference equations with the formulas obtained using Wolfram Alpha software (see Remark 5).

Human Energy Expenditure in High-Level Order Picking

Order picking is one of the most significant components of the warehouse management. More than 50% of the cost incurred in warehouses is due to the order picking process. Although this process has mostly been considered within the framework of economic objectives, in recent years the ergonomic perspective has become increasingly visible. Order picking studies regarding ergonomic objectives have mostly focused on low-level order picking systems, but the human factor has been ignored in high-level order picking. In order to fill this gap, this study focuses on the order picking process of a single block high-level warehouse with a special focus on human factor. For this purpose, a capacity-constrained mathematical model based on order batching and routing for the minimization of human energy expenditure is proposed. In this three-dimensional (3D) warehouse system, the distances and travel times between locations were first determined using Tchebychev formulas in order to calculate the human energy expenditure between order locations. Then, human energy matrices between order locations were created using human energy calculation formulas based on time and item weight. These matrices, which were created for three different randomly generated sample data sets, were used in the mathematical model solution and the optimum batches and routes were determined. In order to compare the results, First-come First-serve (FCFS) batching and S-shaped routing, which are simple and common batching and routing methods used in practice, were applied for the sample problem data sets and it was observed that the mathematical model gave better results.

Efektivitas Metode Index Card Match Dalam Meningkatkan Pemahaman Belajar Siswa Pada Mata Pelajaran Pendidikan Agama Islam (PAI) Di SMP Tahfidz Qur’an Al-Fatih Bengkalis

The researcher discusses the Index Card Match Method (looking for pairs of cards) which is a fun learning method used to repeat material previously provided. This type of research is field research with a quantitative approach, namely a research method based on the philosophy of positivism. Data collection uses a questionnaire, observation and interviews. After the data was collected, the researcher used the prodact moment formula in order to find out alternative success scores for learning using the index card match method. From the percentage results, the recapitulation of the results of the questionnaire respondents answered the effectiveness of the lecture method in increasing students' learning understanding in Islamic Religious Education (PAI) subjects. has a less good and less high value, because the alternative answers yes are fewer than the alternative no, the percentage result is 44.65. While the research results from the recapitulation of the questionnaire regarding the index card match method in increasing students' learning understanding in the subject of Islamic Religious Education has a value of 89%. This is included in the very good criteria, which means that H0 is rejected, thus the Alternative Hypothesis (Ha) is accepted