ANALYSIS OF ELEMENTARY SCHOOL STUDENTS DIFFICULTIES’ IN SOLVING INTEGER WORD PROBLEMS

This type of research is descriptive qualitative with a case study approach. This study aimed to identify forms of students’ conceptual and principle difficulties in solving integer story problems. The research participants were 34 fifth-grade elementary students. The purposive sampling technique was used to select research subjects based on the minimum completeness criteria value. Methods of data collection using tests and interviews. Data analysis techniques include data reduction, data presentation, and drawing conclusions. The results showed that there were two types of difficulties for elementary school students in solving integer story problems, namely, conceptual difficulties and principle difficulties. The form of conceptual difficulties experienced by students is the difficulty in converting story problems into mathematical form. Besides that, students tend not to write down the steps according to solving story problems, and the principal difficulties experienced by students include errors in performing mathematical calculations. This can be minimized by increasing practice questions in the form of story problems.

Analisis Kemampuan Pemecahan Masalah Matematika ditinjau dari Tipe Kepribadian Siswa Madrasah Tsanawiyah

This study aims to describe the mathematical problem solving abilities in terms of students personality types of grade VIII at MTs Al-Ma’arif NU Qamarul Huda Narmada academic year 2020/2021. This type of research is a qualitative descriptive with a quantitative approach. The sampling technique used saturated sampling and each 2 students were selected to represent each personality types. The data collection technique used are personality type questionnaires, mathematical problem solving ability tests, and interviews. The data analysis techniques used quantitative data analysis and qualitative data analysis that are data reduction, data presentation and conclusions. The result of this study are students with introvert and extrovert personality types are not able to write down the stage of understanding the problem, do the stage of making a plan by writing them into mathematical form, able to write down the problem solving systemtatically but there are some errors, write the conclusion of the answer though it’s not quite right. While students with ambivert personality types are able to do the stage of understanding the problem by writing down even though it’s incomplete, write a plan for solving the problem by directly writing it into mathematical form, are able to write the solution of the problem according to the plan even though there are some missteps, re-examine and write down the conclusion even though there are error in the results.

Analysis of entropy generation and Joule heating on curvilinear flow of thermally radiative viscous fluid due to an oscillation of curved Riga surface

This paper investigates the phenomena of heat transfer and entropy generation on time-dependent electro-magnetohydrodynamic boundary layer flow of viscous fluid past a curved oscillatory stretchable Riga surface. Also, the impacts of thermal radiation and Joule heating are accounted for in the energy equation. To develop the flow model in mathematical form, curvilinear coordinates system is followed. The series solution of the governing nonlinear partial differential equations is attained with the help of the homotopy analysis method (HAM). The impacts of various involved parameters like dimensionless radius of curvature, modified magnetic parameter, the proportion of frequency of oscillation of the sheet to its stretchable rate parameter, magnetic parameter, Prandtl number, Eckert number, radiation parameter and Brinkman number on entropy generation, Bejan number, temperature and flow equations are comprehensively examined and results are displayed through graphs. Numerical variation in the magnitude of surface drag force and local Nusselt number under the influence of aforesaid parameters are presented through the tables. Entropy generation is enhanced with an enhancement in a radius of curvature and Brinkman number, while the Bejan number shows opposite behavior for both parameters. The amplitude of velocity distribution shows growing behavior with modified magnetic parameter.

Mathematical Modeling of Integral Characteristics of Repair Process under Maintenance Contracts

The repair rate is a very important parameter for system maintainability and can be defined as a frequency of successfully performed repair actions on a failed component per unit of time. This paper analyzes the integral characteristics of a stochastic repair rate for corresponding values of availability in a system operating under maintenance contracts. The probability density function (PDF) of the repair rate has been studied extensively and it was concluded that it is not a symmetric function so its mean value does not correspond to its maximum. Based on that, the equation for the envelope line of the PDF maximums of the repair rate has been provided. Namely, instead of repair rate PDF equations, we can use envelope line parameters for certain calculations, which are expressed in a simpler mathematical form. That will reduce time required for calculations and prediction and enhance reactions in failure events. Further, for the analytical and numerical evaluation of a system performance, the annual repair rate PDFs are analyzed, such as particular solutions of corresponding differential equation, while the existence of a singular solution is considered and analyzed under different conditions. Moreover, we derived optimal values of availability for which the PDF maximums have been obtained. Finally, in order to generalize the behavior of the repair process, a partial differential equation, as a function of the repair rate process and availability parameter, has been formed.

A framework of safety analysis with temporal feature based on MBSA and case study for ACC system

The safety of automotive Adaptive Cruise Control (ACC) system is of great significance to prevent fatigue driving, improve driving comfort, reduce accident rate and promote the development of intelligent transportation and autonomous driving technology. However, the current safety analysis of ACC lacks consideration of the temporal dynamic property, so it is necessary to establish a set of safety analysis methods to consider the temporal characteristics. This paper proposes a new safety analysis method based on MBSA framework and introduces temporal features. Altarica3.0 is a high-level modeling language for safety analysis, and its basic mathematical form is Guardian Transformation System (GTS). In this paper we outline an analysis approach that converts failure behavioral models (GTS) to temporal fault trees (TFTs), which can be analyzed using Pandora a recent technique for introducing temporal logic to fault trees. However, like classical fault tree analysis, TFT analysis requires a lot of manual effort, which makes it time consuming and expensive. In order to improve the safety of the system, the proposal extends Bayesian Networks with Pandora and results to dependability analysis with temporal relationships to provide more reliable basis for safety design. As a typical case study, the safety analysis method proposed in this paper is applied to the safety analysis of adaptive cruise system, and the results show the effectiveness of the proposed method. Furthermore, it also provides new technologies for the automation and intelligence of safety analysis for Smart Internet of Vehicle.

Geometric Complexity and the Information-Theoretic Comparison of Functional-Response Models

The assessment of relative model performance using information criteria like AIC and BIC has become routine among functional-response studies, reflecting trends in the broader ecological literature. Such information criteria allow comparison across diverse models because they penalize each model's fit by its parametric complexity—in terms of their number of free parameters—which allows simpler models to outperform similarly fitting models of higher parametric complexity. However, criteria like AIC and BIC do not consider an additional form of model complexity, referred to as geometric complexity, which relates specifically to the mathematical form of the model. Models of equivalent parametric complexity can differ in their geometric complexity and thereby in their ability to flexibly fit data. Here we use the Fisher Information Approximation to compare, explain, and contextualize how geometric complexity varies across a large compilation of single-prey functional-response models—including prey-, ratio-, and predator-dependent formulations—reflecting varying apparent degrees and forms of non-linearity. Because a model's geometric complexity varies with the data's underlying experimental design, we also sought to determine which designs are best at leveling the playing field among functional-response models. Our analyses illustrate (1) the large differences in geometric complexity that exist among functional-response models, (2) there is no experimental design that can minimize these differences across all models, and (3) even the qualitative nature by which some models are more or less flexible than others is reversed by changes in experimental design. Failure to appreciate model flexibility in the empirical evaluation of functional-response models may therefore lead to biased inferences for predator–prey ecology, particularly at low experimental sample sizes where its impact is strongest. We conclude by discussing the statistical and epistemological challenges that model flexibility poses for the study of functional responses as it relates to the attainment of biological truth and predictive ability.

1. Time until Newton

‘Time until Newton’ begins by describing the historical origin of calendars and mathematical ways of representing time. It discusses the Aristotelian worldview, which formed the dominant understanding of the Universe in the West from the time of Aristotle until the 17th century when Newton proposed his theory of motion. This was the first physical theory in the mathematical form that we expect nowadays and by making space and time subjects of scientific investigation Newton forever changed the way that people studied space and time. After the publication of his theory, a debate about whether space and time were entities or systems of relations broke out between Newton and the philosopher Gottfried Wilhelm Leibniz. A series of letters between Leibniz and the philosopher Samuel Clarke focusing on this question introduced the mathematical tools of symmetry and invariance that would become important in subsequent study of the structure of space and time.

Preventive Control Strategy of Cascading Fault considering Safety and Economy

The operation and structure of the power system are becoming increasingly complex, and the probability of cascading fault increases. To this end, this paper proposes a cascading fault preventive control strategy that considers safety and the economy. First is to give a mathematical form to discriminate the cascading fault according to the action characteristics of the current-type backup protection. Second, the safety and economy of the system are evaluated in terms of power grid safety margin and generation operation cost, respectively, the initial faults are selected based on the power grid vulnerability and safety margin, and a cascading fault preventive control model is constructed for different initial faults’ scenarios. The model is a two-layer optimization mathematical model, with the inner model being solved by particle swarm optimization to minimize the power grid safety margin. The outer model is solved by the multiobjective algorithm to minimize generation cost and maximizing power grid safety margin. Finally, the calculated Pareto set is evaluated using fuzzy set theory to determine the optimal generator output strategy. The feasibility of the proposed method is verified by conducting a simulation study with the IEEE39 node system as an example.

Flow stress characterization of magnesium alloys at elevated temperatures: A review

The flow behaviors of magnesium alloys are too complicated to be simply formulated in a mathematical form. Most researches have based metallurgically or phenomenologically on specific functions with many constants, which could be applied only to the limited magnesium alloys under specific conditions. In this study, a review on the studies of flow stress characterization of magnesium alloys is conducted and the possibility of using the traditional piecewise C-m model and its extension to characterize the magnesium alloys is emphasized. The formulations of major flow models are given with three typical applications to magnesium alloy AZ80 and its characteristics are demonstrated through comparison of the fitted flow behaviors with their associated experiments and various flow stress models including Arrehenius model, four Ludwik family models (Johnson Cook, Modified Johnson-Cook, Hensel-Spittel, Sutton-Luo), two Voce family models (Ebrahimi et al., Razali et al.) and C-m models.