Mathematical Regularity Research Articles

Mathematical competencies with applications of mirror classes in regular basic education

<span lang="EN-US">The problem about learning in mathematics lies in the lack of application of teaching strategies for the resolution of the calculation in mathematical problems, problems of movement, mathematical regularity, equivalence, and uncertainty; in populations with difficulties to learn collaboratively. Here the application of mirror classes in populations with interactive problems is demonstrated, thus contributing to strengthening their knowledge from cooperative information management, the use of analysis skills based on co-evaluation. In this sense, the purpose of the study was to evaluate the mirror class, as a pedagogical strategy, in order to optimize the competence of solution of quantity problems in basic school students of two educational institutions in Lima, Peru. The study was conducted under the action research approach where the diagnostic and exit test, question guide and field diary were the instruments used for data collection. It was concluded that the mirror class as a pedagogical strategy favors the optimization of competition and solves quantity problems in basic education students. So, they also developed concrete knowledge, to assign them in cognition more enduringly as a form of social learning.</span>

A hierarchical methodology for vessel traffic flow prediction using Bayesian tensor decomposition and similarity grouping

Accurate vessel traffic flow (VTF) prediction can enhance navigation safety and economic efficiency. To address the challenge of the inherently complex and dynamic growth of the VTF time series, a new hierarchical methodology for VTF prediction is proposed. Firstly, the original VTF data is reconfigured as a three-dimensional tensor by a modified Bayesian Gaussian CANDECOMP/PARAFAC (BGCP) tensor decomposition model. Secondly, the VTF matrix (hour ✕ day) of each week is decomposed into high- and low-frequency matrices using a Bidimensional Empirical Mode Decomposition (BEMD) model to address the non-stationary signals affecting prediction results. Thirdly, the self-similarities between VTF matrices of each week within the high-frequency tensor are utilised to rearrange the matrices as different one-dimensional time series to solve the weak mathematical regularity in the high-frequency matrix. Then, a Dynamic Time Warping (DTW) model is employed to identify grouped segments with high similarities to generate more suitable high-frequency tensors. The experimental results verify that the proposed methodology outperforms the state-of-the-art VTF prediction methods using real Automatic Identification System (AIS) datasets collected from two areas. The methodology can potentially optimise relation operations and manage vessel traffic, benefiting stakeholders such as port authorities, ship operators, and freight forwarders.

Droplet Collection Efficiency Regularity of NACA0012 Airfoil Based on the Eulerian Method

Obtaining droplet collection efficiency (DCE) is vital for icing numerical simulations. A droplet impact model based on the Eulerian two-phase flow model was established in this work to analyze the influence of different incoming flow parameters on DCE. Then, the mathematical regularity of the DCE distribution was explored using the parametric description, and the functional relation of the regularity between the incoming condition and the DCE distribution was accomplished. The results showed that the calculated DCE of NACA0012 and the two-dimensional cylinder matched well with the test data. The incoming flow velocity and droplet size, rather than the liquid water content (LWC) of the incoming flow, affected the collection efficiency significantly. The DCE distribution under different conditions was normalized to the same mathematical form with the peak collection efficiency and maximum position. The mathematical form had a highly normal distribution, which was expressed with good regularity of the Reynolds number and droplet diameter. Regularity can greatly reduce the amount of calculation and improve the calculation accuracy, which plays a positive role in the numerical prediction of the icing problem.

Radius theorems for subregularity in infinite dimensions

The paper continues our previous work (Dontchev et al. in Set-Valued Var Anal 28:451–473, 2020) on the radius of subregularity that was initiated by Asen Dontchev. We extend the results of (Dontchev et al. in Set-Valued Var Anal 28:451–473, 2020) to general Banach/Asplund spaces and to other classes of perturbations, and sharpen the coderivative tools used in the analysis of the robustness of well-posedness of mathematical problems and related regularity properties of mappings involved in the statements. We also expand the selection of classes of perturbations, for which the formula for the radius of strong subregularity is valid.

Scanning steel junctions using eddy current probe

The aim of this research is the process of developing a miniature probe for studying electrical steel. The issue of safety when using the products made of this type of steel, assessment and forecast of their quality make this topic relevant. We have found it possible to study the characteristics of steel at different depths by changing the signal amplitude generated by the eddy current probe. The novelty of this research is due to the use of a superminiature eddy current probe of a transformer type that can perform point measurements (0.05 mm sections) of ferromagnetic materials using the eddy current method and is based on the study of conductivity of electrical steel. A hardware and software package is designed based on the developed probe. It can test steel at its boundary with a dielectric. A system that can automatically move the probe over a controlled object at a preset speed has been developed. The study consisted of continuous and discrete measurements that were made by moving the probe over a ferromagnetic and dielectric material at a given speed and scanning the object in 0.1 mm increments. The results of the test performed on samples at different measurements and at different frequencies from 2000 to 20000 Hz are indicated. The study showed that the magnetic field lines of steel, which occur as a result of the impact of the eddy current probe on the ferromagnetic material, have a strong effect on the signal received by the eddy current probe after it is removed from the controlled object at a distance of 1 mm. The signal frequency on the exciting coil of the eddy current probe has a significant influence on this process. The conducted tests have demonstrated the nonlinear nature of the dependency of the probe response when it passes through the steel-dielectric boundary; the mathematical regularity of this dependency is revealed. The effect of the gap between the eddy current probe and the object of study is also analyzed.

The phyllotaxis of the aortic valve.

Biological systems ubiquitously and inevitably exhibit stochasticity in traits from the molecular level to the multicellular and morphological level. However, there are several examples of natural events that might be described in mathematical terms. Plants grow in a structured and geometric way to maximize their sun exposure for photosynthesis while reducing the stress. The 'Fibonacci sequence' and its 'golden ratio' are considered a mathematical regularity and model that is one of the corner-stone of the 'phyllotaxis', the part of the botany that studies how plants branch. Nevertheless, we currently do not know if such mathematical model can be applied to humans. Different authors have hypothesized that 'fractal' might be identified along with the 'golden-ratio' in the human body (coronary artery, heart valves etc.). The aortic valve and the aortic root might represent an interesting model of human fractal geometry, where the phyllotactic rules can be reasonably applied, and where deviation from normality might results in dysfunction. However, in the absence of scientific validations, such report represents only the authors' perceptions of a beautiful shape.

Limitations of regenerative medicine and cell therapy in cancer therapy

In this paper, the mathematical regularity of the formation of cancer is deduced by the theory of the change and stability of gravitational wave field. The relationship between cancer and DNA information changes is presented. The cancer record of the cell DNA, which does not have a sudden mutation, needs to go through a long smooth evolutionary process.

What They Did Not Tell You about Algebraic (Non-) Existence, Mathematical (IR-)Regularity and (Non-) Asymptotic Properties of the Full BEKK Dynamic Conditional Covariance Model

Persistently high negative covariances between risky assets and hedging instruments are intended to mitigate against risk and subsequent financial losses. In the event of having more than one hedging instrument, multivariate covariances need to be calculated. Optimal hedge ratios are unlikely to remain constant using high frequency data, so it is essential to specify dynamic covariance models. These values can either be determined analytically or numerically on the basis of highly advanced computer simulations. Analytical developments are occasionally promulgated for multivariate conditional volatility models. The primary purpose of the paper is to analyze purported analytical developments for the most widely-used multivariate dynamic conditional covariance model to have been developed to date, namely the Full BEKK model, named for Baba, Engle, Kraft and Kroner. Dynamic models are not straightforward (or even possible) to translate in terms of the algebraic existence, underlying stochastic processes, specification, mathematical regularity conditions, and asymptotic properties of consistency and asymptotic normality, or the lack thereof. The paper presents a critical analysis, discussion, evaluation and presentation of caveats relating to the Full BEKK model, and an emphasis on the numerous dos and don’ts in implementing the Full BEKK and related non-Diagonal BEKK models, such as Triangular BEKK and Hadamard BEKK, in practice.

What They Did Not Tell You about Algebraic (Non-) Existence, Mathematical (IR-)Regularity, and (Non-) Asymptotic Properties of the Dynamic Conditional Correlation (DCC) Model

In order to hedge efficiently, persistently high negative covariances or, equivalently, correlations, between risky assets and the hedging instruments are intended to mitigate against financial risk and subsequent losses. If there is more than one hedging instrument, multivariate covariances and correlations have to be calculated. As optimal hedge ratios are unlikely to remain constant using high frequency data, it is essential to specify dynamic time-varying models of covariances and correlations. These values can either be determined analytically or numerically on the basis of highly advanced computer simulations. Analytical developments are occasionally promulgated for multivariate conditional volatility models. The primary purpose of this paper is to analyze purported analytical developments for the only multivariate dynamic conditional correlation model to have been developed to date, namely the widely used Dynamic Conditional Correlation (DCC) model. Dynamic models are not straightforward (or even possible) to translate in terms of the algebraic existence, underlying stochastic processes, specification, mathematical regularity conditions, and asymptotic properties of consistency and asymptotic normality, or the lack thereof. This paper presents a critical analysis, discussion, evaluation, and presentation of caveats relating to the DCC model, with an emphasis on the numerous dos and don’ts in implementing the DCC model, as well as a related model, in practice.

Similarity Grouping-Guided Neural Network Modeling for Maritime Time Series Prediction

Reliable and accurate prediction of time series plays a crucial role in maritime industry, such as economic investment, transportation planning, port planning and design, etc. The dynamic growth of maritime time series has the predominantly complex, nonlinear and non-stationary properties. To guarantee high-quality prediction performance, we propose to first adopt the empirical mode decomposition (EMD) and ensemble EMD (EEMD) methods to decompose the original time series into high- and low-frequency components. The low-frequency components can be easily predicted directly through traditional neural network (NN) methods. It is more difficult to predict high-frequency components due to their properties of weak mathematical regularity. To take advantage of the inherent self-similarities within high-frequency components, these components will be divided into several continuous small (overlapping) segments. The grouped segments with high similarities are then selected to form more proper training datasets for traditional NN methods. This regrouping strategy can assist in enhancing the prediction accuracy of high-frequency components. The final prediction result is obtained by integrating the predicted high- and low-frequency components. Our proposed three-step prediction frameworks benefit from the time series decomposition and similar segments grouping. Experiments on both port cargo throughput and vessel traffic flow have illustrated its superior performance in terms of prediction accuracy and robustness.

Electrical resistivity of steel fiber reinforced concrete

Electrical resistivity is one of the key electro-physical characteristics describing the steel fiber reinforced concrete's ability to conduct electric current. The experiments were carried out to test the hypothesis for the occurrence of a short-circuit effect in steel-fiber concrete structures for the method of electrode heating. Further studies were made to determine the electrical resistivity for various compositions of steel fiber reinforced concrete. The mathematical regularity was found to determine the change of specific electrical resistance subject to the water-cement ratio, the percentage of fiber, the modulus of the fiber surface, and the size of the aggregates. Graphic nomograms (a group of line charts) were made to determine the value of the electrical resistivity for steel fiber reinforced concrete and choose the parameters of electrical heating and the appropriate operating mode of technological equipment.

Electrical resistivity of steel fiber reinforced concrete

Electrical resistivity is one of the key electro-physical characteristics describing the steel fiber reinforced concrete’s ability to conduct electric current. The experiments were carried out to test the hypothesis for the occurrence of a short-circuit effect in steel-fiber concrete structures for the method of electrode heating. Further studies were made to determine the electrical resistivity for various compositions of steel fiber reinforced concrete. The mathematical regularity was found to determine the change of specific electrical resistance subject to the water-cement ratio, the percentage of fiber, the modulus of the fiber surface, and the size of the aggregates. Graphic nomograms (a group of line charts) were made to determine the value of the electrical resistivity for steel fiber reinforced concrete and choose the parameters of electrical heating and the appropriate operating mode of technological equipment.

ANALISIS KETERATURAN MATEMATIS PADA BUDAYA BANTEN

This research is motivated by the searching of banten cultural information which is viewed from mathematics aspect is still unfocus, whereas the culture contains the elements of mathematics, mathematics is the construction of the culture. The search for mathematical regularity in Banten culture can be a study that can be integrated in mathematics learning on transformation material. The research use descriptive qualitative research. Based on the results of research, on the object of Banten gate, Banten Great Mosque, Banten Tower, Banten traditional roof contains elements of reflection, dilatation, translation, symmetry, rotation. In Banten gate appears regularity of reflection, dilation, translation. At the grand mosque of Banten it appears the regularity of rotation, reflection, dilation. In the tower of Banten there is regularity of rotation, dilation, reflection. On the roof of the house Banten has the regularity of reflection, dilation, rotation. With the study of banten culture in terms of the concept of transformation, it can be used by teachers in learning mathematics on the transformation materials in schools, so that students are expected not only to achieve the knowledge competence related to transformation material, but also as a form of strengthening character education at nationalist value by having attitude competence love of its own culture can grow and be owned by students as national identity

The correct regularity condition and interpretation of asymmetry in EGARCH

In the class of univariate conditional volatility models, the three most popular are the generalized autoregressive conditional heteroskedasticity (GARCH) model of Engle (1982) and Bollerslev (1986), the GJR (or threshold GARCH) model of Glosten et al. (1992), and the exponential GARCH (or EGARCH) model of Nelson (1990, 1991). For purposes of deriving the mathematical regularity properties, including invertibility that relates the standardized residuals to the returns shocks, to determine the likelihood function for estimation, and the statistical conditions to establish asymptotic properties, it is essential to understand the stochastic properties underlying the three univariate models. The random coefficient autoregressive process was used to obtain GARCH by Tsay (1987), an extension of which was used by McAleer (2014) to obtain GJR. A random coefficient complex nonlinear moving average process was used by McAleer and Hafner (2014) to obtain EGARCH. These models can be used to capture asymmetry, which denotes the different impacts on conditional volatility of positive and negative shocks of equal magnitude, and possibly also leverage, which is the negative correlation between returns shocks and subsequent shocks to volatility (see Black 1976). McAleer (2014) showed that asymmetry was possible for GJR, but not leverage. McAleer and Hafner (2014) showed that leverage was not possible for EGARCH. Surprisingly, the condition for asymmetry in EGARCH seem to have been ignored in the literature, or has concentrated on the incorrect parametric condition, with no clear explanation, and hence with associated unclear and misleading interpretations. The purpose of the paper is to derive the regularity condition for asymmetry in EGARCH, and to provide the correct interpretation. It is shown that, in practice, EGARCH always displays asymmetry, though not leverage.

The Correct Regularity Condition and Interpretation of Asymmetry in EGARCH

In the class of univariate conditional volatility models, the three most popular are the generalized autoregressive conditional heteroskedasticity (GARCH) model of Engle (1982) and Bollerslev (1986), the GJR (or threshold GARCH) model of Glosten, Jagannathan and Runkle (1992), and the exponential GARCH (or EGARCH) model of Nelson (1990, 1991). For purposes of deriving the mathematical regularity properties, including invertibility, to determine the likelihood function for estimation, and the statistical conditions to establish asymptotic properties, it is convenient to understand the stochastic properties underlying the three univariate models. The random coefficient autoregressive process was used to obtain GARCH by Tsay (1987), an extension of which was used by McAleer (2004) to obtain GJR. A random coefficient complex nonlinear moving average process was used by McAleer and Hafner (2014) to obtain EGARCH. These models can be used to capture asymmetry, which denotes the different effects on conditional volatility of positive and negative effects of equal magnitude, and possibly also leverage, which is the negative correlation between returns shocks and subsequent shocks to volatility (see Black 1979). McAleer (2014) showed that asymmetry was possible for GJR, but not leverage. McAleer and Hafner showed that leverage was not possible for EGARCH. Surprisingly, the conditions for asymmetry in EGARCH seem to have been ignored in the literature, or have concentrated on the incorrect conditions, with no clear explanation, and hence with associated misleading interpretations. The purpose of the paper is to derive the regularity condition for asymmetry in EGARCH to provide the correct interpretation. It is shown that, in practice, EGARCH always displays asymmetry, though not leverage.

Language Games and Meaning as Used in Student Encounters With Scientific Literacy Test Items

ABSTRACTPrevious research in science education has suggested that difficulties among students learning science relate to challenges in framing its discourse. This article examines the role that language plays in a scientific literacy test for which everyday life is an augmented aspect. Video‐recorded data was collected in four ninth‐grade science classes in a Swedish compulsory school as small groups of students discussed and collaboratively solved Programme for International Student Assessment (PISA) science test items. The theoretical framework assumes sociocultural perspectives as well as that of Wittgenstein's later works on language. The study involves an analysis of students’ meaning making of specific words that occur in the test and the various language games to which these words contribute. Specifically, we analyzed the students’ use of four different words: reference, constant, pattern, and factor. We found that the students use these words in everyday or mathematical language games; for example, understanding the word “pattern” as a mathematical regularity rather than a result of a scientific experiment. The results were analyzed in relation to the specific illustrations and wording that contextualize the items. We argue that a crucial part of being scientifically literate is privileging science content over other possible disciplines and contexts and ignoring the everyday perspective.

On the convergence and accuracy of the cardiovascular intrinsic frequency method.

In this paper, we analyse the convergence, accuracy and stability of the intrinsic frequency (IF) method. The IF method is a descendant of the sparse time frequency representation methods. These methods are designed for analysing nonlinear and non-stationary signals. Specifically, the IF method is created to address the cardiovascular system that by nature is a nonlinear and non-stationary dynamical system. The IF method is capable of handling specific nonlinear and non-stationary signals with less mathematical regularity. In previous works, we showed the clinical importance of the IF method. There, we showed that the IF method can be used to evaluate cardiovascular performance. In this article, we will present further details of the mathematical background of the IF method by discussing the convergence and the accuracy of the method with and without noise. It will be shown that the waveform fit extracted from the signal is accurate even in the presence of noise.

Biophysical optimality of the golden angle in phyllotaxis.

Plant leaves are arranged around a stem axis in a regular pattern characterized by common fractions, a phenomenon known as phyllotaxis or phyllotaxy. As plants grow, these fractions often transition according to simple rules related to Fibonacci sequences. This mathematical regularity originates from leaf primordia at the shoot tip (shoot apical meristem), which successively arise at fixed intervals of a divergence angle, typically the golden angle of 137.5°. Algebraic and numerical interpretations have been proposed to explain the golden angle observed in phyllotaxis. However, it remains unknown whether phyllotaxis has adaptive value, even though two centuries have passed since the phenomenon was discovered. Here, I propose a new adaptive mechanism explaining the presence of the golden angle. This angle is the optimal solution to minimize the energy cost of phyllotaxis transition. This model accounts for not only the high precision of the golden angle but also the occurrences of other angles observed in nature. The model also effectively explains the observed diversity of rational and irrational numbers in phyllotaxis.

The Magnetocaloric Performance of (Pr,Ca) Manganites Estimated by Magnetic Transition Entropies

The magnetocaloric applicability of the perovskite-structured (Pr,Ca) manganite family (PCMO) was estimated based on the magnetic transition entropies of polycrystalline bulk samples. Transitions in the temperature range from 5 to 400 K were investigated in external fields up to 5 T. Earlier results published on the matter were reproduced, extended to Ca concentrations below x = 0.2 and up to x = 1, and complemented by determining standardized refrigerant capacity estimates corresponding to the largest entropy changes detected in each sample. The quantitative agreement between the measured transition entropies and literature also served to verify a time-optimized data collection method based on quick temperature scans of magnetization at constant magnetic fields. Making use of the mathematical regularity of magnetization curves, improved time, and cryogen efficiency was arguably attained compared with a more traditional data collection method without significant loss of accuracy. The results of this paper convey a very graphical overview of the quite well established phase diagram of PCMO and promise a significant magnetocaloric effect below 150 K, possibly on par with that exhibited by Gd-based alloys around room temperature. However, little hope can be offered for the room temperature refrigeration applications of PCMO.

Predicting Competitive Effects from Prescription Drug Mergers: How Standard Economic Analysis Can Go Wrong

Key insights on the unilateral competitive effects of mergers derive from economic models built on behavioral assumptions and mathematical regularity conditions ensuring that merger effects are determined by the premerger margin of competition between products combined. But the usual behavioral assumptions and regularity conditions might not hold for prescription drugs, and the usual insights might not apply. Analysis of a simple model based on the facts of FTC v. Lundbeck shows that weak competition between two therapeutic substitute drugs plausibly results in monopoly prices, so merging them has no effect on their prices.