Mathematical Validation Research Articles

Pengembangan Perangkat Pembelajaran Menggunakan Model Problem Posing Berorientasi Kemampuan Pemecahan Masalah Matematis

This study aims to describe the level of validity of mathematics learning tools using the Problem Posing model oriented to mathematical problem solving abilities on statistics which has been tested valid. The development model in this study uses the Plomp model which has three stage, namely the Preliminary Research Phase, the Prototype Phase, the Assessment Phase. The data collection techniques used were the validation of learning tools. The data collection instrument used was a validation sheet. The data analysis technique used is descriptive statiscal analysis technique. The result of the research validation analysis by three validators obtained an average validation every RPP of each validator was 100% for aspect of indicator one as measured by guttman scale of which are very valid criteria and 80,36% for aspect of indicator two to seven as measured by likert scale of which are valid criteria, and for the average validation every LKPD of each validator was 93,33% for aspect of indicator one as measured by guttman scale of which are very valid criteria and 75% aspect of indicator two to three as measured by likert scale of which are valid criteria. Based on the results of this study it can be concluded that the development of learning tools using the Problem Posing model oriented to the mathematical problem solving abilities has been tested for its validity.Keywords: LKPD, RPP, Problem Posing

An improved method to localize simultaneously close and coherent sources based on symmetric-Toeplitz covariance matrix

There is a need to develop better algorithms for resolving multiple sound sources which are close or coherent. The Multiple Signal Classification method works satisfactorily in such situations when used along with spatial smoothing only when the SNR is high and array size is large. The MUSIC-Group Delay (MGD) method when used in conjunction with spatial smoothing works even for low SNR signals coming from close and coherent sources. However, it is computationally expensive and needs large arrays. To address these limitations, we propose the Improved MGD (IMGD) method which uses a symmetric-Toeplitz matrix derived from covariance matrices of regular sensor data and their conjugates for calculating the direction of arrival of sound sources. Such a method will work for close sources as we have shown that noise subspaces of conventional and symmetric-Toeplitz covariance matrices as well as phase characteristics of MUSIC spectra derived from these matrices are equivalent. Such a method will also work for coherent sources as we have shown that the spatially smoothened symmetric-Toeplitz covariance matrix, very much like the ordinary covariance matrix used for non-coherent sources, is positive semi-definite. In this way we have established the mathematical validity of the IMGD method. Next, we conducted several simulations to compare the efficacy of the proposed method relative to the MGD method. Our results show that the proposed method markedly performs better in terms of accuracy, and resolution capability. Finally, we also conducted experiments to validate the proposed method. Our experimental data show that the IMGD method is better than MGD in all aspects significantly.

Numerical and experimental study on fluid compressibility in a two-stage reciprocating pump-compressor

• Liquid piston velocity decreases with increasing pressure due to liquid compressibility. • Liquid piston brings the compression process closer to thermodynamically efficient. • Liquid expansion leads to a decrease of the pump volumetric efficiency. • Pressure ratio has the greatest impact on a decrease of liquid layer height and velocity. Currently, multistage (two and three-stage) reciprocating compressors are used to compress the gas to medium and high pressures. One of the promising operating principles of such machines is a preliminary compression in a single-stage piston compressor and a final gas compression in a working cavity with a liquid piston. The main advantages of a compressor using a liquid piston are intensive cooling of the compressed gas and the absence of leaks and leakages in the cylinder-piston group. This makes it possible to increase the indicated isothermal efficiency and actual volumetric efficiency. The article considered the effect of liquid compressibility in the two-stage piston hybrid positive-displacement machine with a liquid piston. We developed a calculus methodology for the liquid compressibility during gas compression in the second stage of the compression section based on the volume conservation equation and Hooke's law. Numerical simulation showed that the degree of pressure ratio had the greatest impact on the relative decrease in the height and velocity of the liquid layer. We found that the relative decrease in the liquid layer height was within 1%. The relative decrease in the liquid piston velocity was within 5%. We carried out the experiment and validation of the results with a numerical simulation, which reflected the mathematical model validity. The model worked correctly based on an estimated experimental error. The parametric analysis of the test model showed the influence of the main working cavity parameters. The discrepancy in determining the dynamic pressure in the machine cavities conducting theoretical and experimental studies is within 10–15%. The paper analysed the liquid piston compressibility influence on the thermodynamic efficiency of the compression process and compressor performance.

Development of a Mathematical Model and Validation for Methane Production Using Cow Dung as Substrate in the Underground Biogas Digester

South Africa is highly dependent on conventional fuels from non-renewable energy sources such as coal and fossil fuels. The methane from biogas is a renewable energy source for generating electricity using a combined heat and power plant. Therefore, the aim of the study is to develop and validate a mathematical model for predicting methane production in an underground biogas digester. The developed model was able to predict the production of methane gas as separate entity differing from other models. A total of 286 datasets were used as a trained dataset for the model development, and 144 datasets served as test data for the validation of the model, making a total of 430 measured datasets of all the predictors. The determination coefficient (R2) and the p-value of the predicted and calculated methane yield were 0.962 and 0.920, respectively. The high R2 in the present study confirms a good correlation between the model and experimental value. Hence, the model is of significance because it is applicable in predicting the performance of methane production of systems of the same design used in different locations, thereby arriving at the same constant values. From the study, the ambient weather factors (ambient temperature, relative humidity, and global horizontal irradiance) affected the methane production. Additionally, the indoor parameters (pH, gas temperature, slurry bottom and slurry top temperature) impacted on the yield of the methane production because the scaling factors associated with these quantities are non-zero real numbers. Hence, the scope of the study did not consider the volume of the biogas digester as an input parameter to the response.

A framework for rapid virtual prototyping: a case study with the Gunnerus research vessel

ABSTRACT Virtual prototypes (VPs) are digital models that mock-up existing or conceptual systems' behaviour. In offshore operations, VPs find usages in design, proof of concept for new equipment or method, control system testing, procedure planning, and expert crew training. Moreover, VP can be used in full mission simulators with crews of maritime and offshore engineers, in which case they integrate with control systems such as handles and dynamic positioning systems. Putting the human in the loop sets high requirements for the fidelity of the visual 3D-models and the mathematical models' validity. VPs are thus time-consuming to create and difficult to validate, even based on an existing offshore system. This paper presents an innovative framework for rapid virtual prototyping of ships for hardware and human in the loop simulations and validates the results with data gathered in a sea trial performed on a research vessel, with satisfying results for position keeping. Abbreviations: CLI, Command line interpreter; DP, Dynamic positioning system: ship equipment used to maintain position and heading; DM, Damping matrix; Force FBK, Force Feedback Thruster1; HIL, Hardware in the loop; HITL, Human in the loop; JNI, Java native interface; LC, Loading condition; RAO, Response amplitude operator; RPM, Revolutions per minute; RPM FBK, RPM Feedback Thruster2/3 (Main/Azimuth); SCM, Source code management system; SOG, Speed over ground; VP, Virtual prototyping/prototype; VST, Virtual sea trial; sea trial performed in a simulation

Predictive model for the risk of cardiovascular disease and type 2 diabetes in obese people

In this article, we study a predictive model of the risk of cardiovascular disease (CVD) and type 2 diabetes mellitus (T2DM) in obese populations and investigate its impact on the evolution of their health, terms related to lifestyle and risk factors are also incorporated. This model represented mathematically by a nonlinear temporal system of ordinary differential equations. An analysis of the stability of stationary solutions is also obtained to theoretically confirm the mathematical validity. Numerical simulations presented to explain the usefulness of the developed model; they show the role of a healthy lifestyle (diet, regular exercise, smoking, and increasing alcohol consumption above moderate levels) in alleviating the burden of cardiovascular disease (CVD) and can significantly reduce the risk to develop type 2 diabetes mellitus (T2DM). On the other hand, risk factors management of obesity with complications greatly decreases the risk of developing other complications.

The Efficiency Comparison and Application of Proposed Rhombus Ranked Set Sampling

A new scheme ‘Rhombus Ranked Set Sampling’ (RRSS) is developed in this research together with its properties for estimating the population means. Mathematical validation along with the simulation evaluation is presented. The proposed method is an addition to the family of different sampling methods and generalization of ‘Folded Ranked Set Sampling’ (FRSS). For the simulation process, nine probability distributions are considered for the efficiency comparison of proposed scheme from which four are symmetric and rest are asymmetric among which Weibull and beta distributions which are used twice, unlike parametric values. (Al-Naseer, 2007 and Bani-Mustafa, 2011). Through simulation processes, it is observed that RRSS is competent and more reliable relative to simple random sampling (SRS), ranked set sampling (RSS) and folded ranked set sampling (FRSS). It is noted that for all the underlying distributions, an increase in the efficiency of Rhombus Ranked Set Sampling (RRSS) is achieved via increasing the size of the sample ‘p’. Besides the efficiency comparison, consistency of the proposed method is also valued by using Co-efficient of Variation (CV). Secondary data on zinc (Zn) concentration and lead (Pb) contamination in different parts and tissues of freshwater fish was collected to illustrate the evaluation of RRSS against SRS, RSS, FRSS and ERSS (extreme ranked set sampling). The results obtained through real life illustration defend the simulation study and hence indicates that the RRSS estimator is efficient substitute for existing methods (Al-Omari, 2011).

On the emerging asymptotic patterns of the Winfree model with frustrations

We study the emergence of asymptotic patterns in Winfree ensemble such as the partial/complete phase-locking and bump states under the effect of heterogeneous frustrations. Although the Winfree model is the first model for the synchronization of limit-cycle oscillators, there is little literature on the mathematical validity of asymptotic patterns compared to the vast literature of the well-studied Kuramoto model. Recently, it has received a renewed attention in nonlinear dynamics and statistical physics communities due to its diverse asymptotic patterns that it can generate. In particular, we provide a rigorous result on the existence of bump states in a homogeneous ensemble with the same natural frequency. Our provided results exhibit the robustness of emerging asymptotic patterns with respect to frustrations. We derive several sufficient frameworks for the unique existence of an equilibrium state, bump states and uniform stability with respect to initial data.

Model predictive control optimisation using the metaheuristic optimisation for blood pressure control

Given the importance of high blood pressure, it is important to control and maintain a constant blood pressure level in the normal state. The main aim of this article is to design a model predictive controller with a genetic algorithm (GA) for the regulation of arterial blood pressure. The present study is an applied cross‐sectional study. In order to do this research, studies related to designing mathematical models for blood pressure regulation and mechanical models for heart muscle and pressure sensors are investigated. Then, a model predictive controller with GA is designed for blood pressure control. All control and design operations are performed in the MATLAB software. According to the viscoelasticity of blood, transducer, and injection set, we can assume the mechanical model as Mass, Spring, and Damper. Initially, the patient's blood pressure is lower than normal, and after controlling, the patient's blood pressure returned to normal. By using a GA‐based model predictive control (MPC), mathematical validation, and mechanical model, the patient's blood pressure can be adjusted and maintained. The simulation result shows that the GA‐based MPC offers acceptable response and speed of operation and the proposed controller can achieve good tracking and disturbance rejection.

Brain Shift in Neuronavigation of Brain Tumors: An Updated Review of Intra-Operative Ultrasound Applications

Neuronavigation using pre-operative imaging data for neurosurgical guidance is a ubiquitous tool for the planning and resection of oncologic brain disease. These systems are rendered unreliable when brain shift invalidates the patient-image registration. Our previous review in 2015, Brain shift in neuronavigation of brain tumours: A review offered a new taxonomy, classification system, and a historical perspective on the causes, measurement, and pre- and intra-operative compensation of this phenomenon. Here we present an updated review using the same taxonomy and framework, focused on the developments of intra-operative ultrasound-based brain shift research from 2015 to the present (2020). The review was performed using PubMed to identify articles since 2015 with the specific words and phrases: “Brain shift” AND “Ultrasound”. Since 2015, the rate of publication of intra-operative ultrasound based articles in the context of brain shift has increased from 2–3 per year to 8–10 per year. This efficient and low-cost technology and increasing comfort among clinicians and researchers have allowed unique avenues of development. Since 2015, there has been a trend towards more mathematical advancements in the field which is often validated on publicly available datasets from early intra-operative ultrasound research, and may not give a just representation to the intra-operative imaging landscape in modern image-guided neurosurgery. Focus on vessel-based registration and virtual and augmented reality paradigms have seen traction, offering new perspectives to overcome some of the different pitfalls of ultrasound based technologies. Unfortunately, clinical adaptation and evaluation has not seen as significant of a publication boost. Brain shift continues to be a highly prevalent pitfall in maintaining accuracy throughout oncologic neurosurgical intervention and continues to be an area of active research. Intra-operative ultrasound continues to show promise as an effective, efficient, and low-cost solution for intra-operative accuracy management. A major drawback of the current research landscape is that mathematical tool validation based on retrospective data outpaces prospective clinical evaluations decreasing the strength of the evidence. The need for newer and more publicly available clinical datasets will be instrumental in more reliable validation of these methods that reflect the modern intra-operative imaging in these procedures.

Stability of the boundary layer expansion for the 3D plane parallel MHD flow

In this paper, we establish the mathematical validity of the Prandtl boundary layer theory for a class of nonlinear plane parallel flows of viscous incompressible magnetohydrodynamic flow with the no-slip boundary condition of velocity and perfectly conducting walls for magnetic fields. The convergence is shown under various Sobolev norms, including the physically important space–time uniform norm L∞(H1). In addition, similar convergence results are also obtained under the case with uniform magnetic fields. This implies the stabilizing effects of magnetic fields. Besides, the higher-order expansion is also considered.

Development of Learning Modules Based on a Realistic Mathematical Approach with Autograph Software to Improve Creative Mathematical Thinking Ability Students of SMP Negeri 1 Blangkejeren

This study aims to analyze the practicality of the learning modules developed based on the Realistic Mathematical Approach with autograph software, to analyze the effectiveness of the learning modules developed based on the Realistic Mathematical Approach assisted by autograph software, and to describe the improvement of students' mathematical creative thinking abilities through learning modules developed based on the Mathematical Approach. Realistic assisted autograph software. The data were obtained through the learning module validity sheet consisting of the lesson plan validation sheet and the mathematical creative ab ility test validation sheet, student response questionnaires and teacher interview guidelines for the learning module and the learning module effectiveness instrument seen from the students' mathematical creative test results. Module development in this study uses the Thiagarajan, Semmel and Semmel development models, namely the 4-D model (define, design, develop, disseminate). The results of the research were students and teachers stated that the developed device was easy to use, the students' critical thinking ability obtained classical completeness with a percentage of 87.5%, the level of student activity met the ideal time tolerance criteria set, student responses to the components of learning devices and learning activities is positive. The increase in creative thinking skills in the first try was 77.9, an increase in the second try to 81.64.

Mathematical validation of proposed machine learning classifier for heterogeneous traffic and anomaly detection

The modeling of an efficient classifier is a fundamental issue in automatic training involving a large volume of representative data. Hence, automatic classification is a major task that entails the use of training methods capable of assigning classes to data objects by using the input activities presented to learn classes. The recognition of new elements is possible based on predefined classes. Intrusion detection systems suffer from numerous vulnerabilities during analysis and classification of data activities. To overcome this problem, new analysis methods should be derived so as to implement a relevant system to monitor circulated traffic. The main objective of this study is to model and validate a heterogeneous traffic classifier capable of categorizing collected events within networks. The new model is based on a proposed machine learning algorithm that comprises an input layer, a hidden layer, and an output layer. A reliable training algorithm is proposed to optimize the weights, and a recognition algorithm is used to validate the model. Preprocessing is applied to the collected traffic prior to the analysis step. This work aims to describe the mathematical validation of a new machine learning classifier for heterogeneous traffic and anomaly detection.

The validity of inquiry-based mathematics learning tools using the Malay context of Rengat to improve mathematical reasoning skills

Students' low ability in mathematical reasoning is influenced by the learning model applied in the classroom. Such as the use of learning tools with a context that is closer to students' life. The purpose of this research is to produce inquiry-based learning tools with a Malay Rengat context that is valid in improving students' mathematical reasoning abilities. This development research uses the Plomp model which consists of three phases, namely preliminary research, prototyping, and the assessment phase. The validation of the tools was carried out by three mathematics education experts, one educational technology expert, and one Indonesian language expert. The average scores obtained from the validation are 3.57 for the validity of the lesson plans and 3.55 for the validity of the worksheet. With these results it can be concluded that the development of inquiry-based mathematics learning tools with the Malay Rengat context is valid.

Chemical Reaction Rate from a (Semiempirical) Dynamical Point of View

The aim of the present paper is to check - or better to confirm - the mathematical validity of chemical reaction rate, faced as a set of differential equations. Firstly one - way elementary reactions are considered, in the most general case. Secondly the same thing is done with two-way (opposing) elementary reactions. At this stage, we show that the two – way reaction, as we mean it, is compatible with the reduction of the total Gibbs energy as expected in every natural process. As an example of a two way elementary reaction of a completely solvable problem we give the hydrolysis of sucrose to glucose and fructose, where the “inversion” of sucrose is examined not only with the initial linear reaction of “Wilhelmy” (1850), but also with the two way nonlinear reaction introduced. Finally the validity of the mathematical model is checked for more complex cases such as the Michaelis-Menten mechanism or reactions in solution, where it is found that the two cases, apparently are four – dimensional while in reality are two – dimensional (after the “subtraction” of the constraints of “motion”) and naturally cannot exhibit chaotic behavior. In all cases the treatment is not one-hundred-percent mathematically austere but it has also arbitrary although reasonable hypotheses.

Multi-terrain Quadrupedal-wheeled Robot Mechanism: Design, Modeling, and Analysis

For a robot to navigate in terrains of rough and uneven topographies, its drives and controllers must generate and control large mechanical power with great precision. This paper is aimed at developing an autonomous robot with active-suspensions in form of a hybrid quadrupedal-wheel drive mechanism. This involves a computational approach to optimizing the development cost without compromising the system’s performance. Using the Solidworks CAD tool, auxiliary components were designed and integrated with the bed structure to form an actively suspended robot drive mechanism. Also, using the S-Math Computing tool, the robot’s suspension system was optimized, employing a four-bar mechanism. To enhance the compatibility of this design with the intended controller, some mathematical equations and numerical validations were formulated and solved. These included the modeling of tip-over stability and skid steering, the trendline equations for computing the angular positions of the suspension servomotors, and the computation of R2– values for determining the accuracy of these trendline equations. Using finite element analysis (FEA), we simulated the structural integrity of key sub-components of the final structure. The results show that our mechanical design is appropriate for developing an actively suspended robot that can efficiently navigate in different terrestrial sites and topographies.

Experimental Research and Numerical Analysis of Flow Phenomena in Discharge Object with Siphon

This article presents results of the experimental research and numerical simulations of the flow in a pumping system’s discharge object with the welded siphon. The laboratory simplified model was used in the study. Two stationary flow regimes characterized by different volume flow rates and water level heights have been chosen. The study concentrates mainly on the regions below and behind the siphon outlet. The mathematical modelling using advanced turbulence models has been performed. The free-surface flow has been carried out by means of the volume-of-fluid method. The experimental results obtained by the particle image velocimetry method have been used for the mathematical model validation. The evolution and interactions of main flow structures are analyzed using visualizations and the spectral analysis. The presented results show a good agreement of the measured and calculated complex flow topology and give a deep insight into the flow structures below and behind the siphon outlet. The presented methodology and results can increase the applicability and reliability of the numerical tools used for the design of the pump and turbine stations and their optimization with respect to the efficiency, lifetime and environmental demands.

Comments on “Role of power-to-gas in an integrated gas and electricity system in Great Britain”, Int J Hydrogen Energ 40 (2015) 5763–5775

In the article published by Qadrdan et al. in INT J HYDROGEN ENERG 40 (2015) 5763–5775, the role of power-to-hydrogen in the GB's combined gas and electricity network (CGEN) was presented. The purpose of this comment is to point out the errors associated with the CGEN's unsteady-state gas model. No agreement can be found when one compares the proposed modelling approach with the governing (continuity and momentum) equations. The selected base-length, and initial/boundary conditions were not described by the authors. No mathematical proof and model validation (with available software packages) were presented for their proposed approach. In addition, the authors did not consider the change of hydrogen concentration along the pipes and its impact on the gas density and heating value.

Evaluación de un protocolo automatizado para la obtención de medidas morfométricas de huevos de aves a partir de fotografías digitales

Evaluation of a protocol for automated extraction of morphometric measurements from avian eggs using digital photography As many ecomorphological studies are limited by the time required to gather manual measurement data, automatizing the process is an important focus of methodological innovations. We developed, implemented and validated a protocol for the semi–automated extraction of a set of morphometric variables of egg size and shape from digital pictures. The protocol was implemented in R language as a web app called OvometriK. After binarizing and calibrating images, this protocol uses geometric and trigonometric functions to calculate eleven egg variables. We tested calculations in several ways, assuming contour continuity or using voxel counts. Application was validated with geometric shapes and 30 manually–measured chicken eggs. Mathematical validation with spheres showed that the algorithm provided high precision diameter measures, with a correlation of 99.9 %. Average estimation error was 1.4 %. The mathematical volume estimation was underestimated by 27 %, while voxels were underestimated by only 6 %. Differences between manual egg measurements of diameters and those obtained from images was less than 3 mm (4 %). Correlation between estimated volume and measured by silica gel filling was higher than 90 % using the voxel count method. Neither inclination angle or picture resolution had significant effects on precision (3.2 % maximum difference). Measures showed high repeatability and represent a significant saving in processing time. This new protocol represents an improvement on previous programs regarding limitations of platform, accessibility and number of variables. Furthermore, its flexibility and openness means it can be adapted to other specific applications.

Design acceptance criteria for operating open-pit slopes: An update

ABSTRACT Open-pit slope engineering involves balancing economic imperatives and risk, where an optimum pit slope design seeks to safely steepen the pit slope angles to minimize the mining of waste, therefore maximizing ore recovery. Open-pit Design Acceptance Criteria (DAC) had been proposed and adopted by industry, and the Guidelines for Open Pit Slope Design, published in 2009, finally provided a consistent set of guidelines. Since the publication of these guidelines, it has been the industry experience that practical DAC requires consideration of multiple levels of design confidence, ranging from highly uncertain greenfield sites to mature operations; the unique nature of consequences associated with open pit wall failures as opposed to other civil and mining structures; and differences between operators’ risk appetite. This article presents the state of practice for inter-ramp and overall open-pit slope design in the mining industry and develops flexible DAC for operating pits that addresses the considerations outlined. The criteria are rooted in robust risk tolerance principles, previously adopted criteria, a database of open-pit designs, and mathematical validation for criteria in terms of both Factor of Safety (FoS) and Probability of Failure (PoF).