Mathematical Features Research Articles

A Variational Approach to Scripts.

This paper proposes a formal reconstruction of the script construct by leveraging the active inference framework, a behavioral modeling framework that casts action, perception, emotions, and attention as processes of (Bayesian or variational) inference. We propose a first principles account of the script construct that integrates its different uses in the behavioral and social sciences. We begin by reviewing the recent literature that uses the script construct. We then examine the main mathematical and computational features of active inference. Finally, we leverage the resources of active inference to offer a formal model of scripts. Our integrative model accounts for the dual nature of scripts (as internal, psychological schema used by agents to make sense of event types and as constitutive behavioral categories that make up the social order) and also for the stronger and weaker conceptions of the construct (which do and do not relate to explicit action sequences, respectively).

JUNIOR HIGH SCHOOL MATHEMATICS TEACHERS’ PROFESSIONAL AND PERSONAL CHARACTERISTICS

ABSTRACT
 
 This study sought to determine the Junior High School Mathematics teachers’ level of professional and personal characteristics in Maguindanao Division I. Specifically, it determined the Junior High School Mathematics Teachers’ level of Professional and personal characteristics; the Junior High School Students’ level of academic performance in Mathematics; and the significant relationships of the teachers’ level of Professional and personal characteristics and their Junior High students’ level of performance in Mathematics. The study used the descriptive-correlational survey method. It determined the level of teaching practices of twelve (12) Junior High School Mathematics teachers of Maguindanao Division I in terms of professional and personal characteristics. Pearson’s Product - Moment Correlation Coefficient was used to determine the significant relationship of the level of professional and personal characteristics of the junior high Mathematics teachers to the students’ level of academic performance. Based on the findings of the study, it is concluded that Junior High School Mathematics teachers’ professional and personal characteristics is very satisfactory. It is further concluded that the outstanding professional and personal characteristics of the teachers have no bearing on the academic achievement of the students. The students must work hard to get higher grades and the teacher must develop professional and personal characteristics to perform tasks exceedingly.
 
 Keywords: Professional and Personal Characteristics, Junior High School Mathematics Teachers, Level of Academic Performance

Social constructivism in mathematics? The promise and shortcomings of Julian Cole\u2019s institutional account

The core idea of social constructivism in mathematics is that mathematical entities are social constructs that exist in virtue of social practices, similar to more familiar social entities like institutions and money. Julian C. Cole has presented an institutional version of social constructivism about mathematics based on John Searle’s theory of the construction of the social reality. In this paper, I consider what merits social constructivism has and examine how well Cole’s institutional account meets the challenge of accounting for the characteristic features of mathematics, especially objectivity and applicability. I propose that in general social constructivism shows promise as an ontology of mathematics, because the view can agree with mathematical practice and it offers a way of understanding how mathematical entities can be real without conflicting with a scientific picture of reality. However, I argue that Cole’s specific theory does not provide an adequate social constructivist account of mathematics. His institutional account fails to sufficiently explain the objectivity and applicability of mathematics, because the explanations are weakened and limited by the three-level theoretical model underlying Cole’s account of the construction of mathematical reality and by the use of the Searlean institutional framework. The shortcomings of Cole’s theory give reason to suspect that the Searlean framework is not an optimal way to defend the view that mathematical reality is socially constructed.

Supporting cost-effective watershed management strategies for Chesapeake Bay using a modeling and optimization framework

Extensive efforts to adaptively manage nutrient pollution rely on Chesapeake Bay Program's (Phase 6) Watershed Model, called Chesapeake Assessment Scenario Tool (CAST), which helps decision-makers plan and track implementation of Best Management Practices (BMPs). We describe mathematical characteristics of CAST and develop a constrained nonlinear BMP-subset model, software, and visualization framework. This represents the first publicly available optimization framework for exploring least-cost strategies of pollutant load control for the United States' largest estuary. The optimization identifies implementation options for a BMP subset modeled with load reduction effectiveness factors, and the web interface facilitates interactive exploration of >30,000 solutions organized by objective, nutrient control level, and for ~200 counties. We assess framework performance and demonstrate modeled cost improvements when comparing optimization-suggested proposals with proposals inspired by jurisdiction plans. Stakeholder feedback highlights the framework's current utility for investigating cost-effective tradeoffs and its usefulness as a foundation for future analysis of restoration strategies.

Engineering the Optical Vacuum: Arbitrary Magnitude, Sign, and Order of Dispersion in Free Space Using Space–Time Wave Packets

Spatial structuring of an optical pulse can lead in some cases upon free propagation to changes in its temporal profile. For example, introducing conventional angular dispersion into the field results in the pulse encountering group-velocity dispersion in free space. However, only limited control is accessible via this strategy. Here we show that precise and versatile control can be exercised in free space over the dispersion profile of so-called `space-time' wave packets: a class of pulsed beams undergirded by non-differentiable angular dispersion. This abstract mathematical feature allows us to tune the magnitude and sign of the different dispersion orders without introducing losses, thereby realizing arbitrary dispersion profiles, and achieving dispersion values unattainable in optical materials away from resonance. Unlike optical materials and photonic structures in which the values of the different dispersion orders are not independent of each other, these orders are addressable separately using our strategy. These results demonstrate the versatility of space-time wave packets as a platform for structured light and point towards their utility in nonlinear and quantum optics.

HAMBATAN SISWA DALAM BELAJAR MATEMATIKA DIKAJI DARI KEPERCAYAAN MATEMATIS

The purpose of this study was to find out the learning obstacles in linear program assessed by mathematical beliefs at the Mujahidin Senior High School. The form of research used in this study is a case study. The data source used in this study was the students of class XI MIPA 1 in Pontianak Mujahidin High School, the data of which were the results of students' mathematical belief questionnaires and the answers of research subjects on the given test. Students learning obstacles in linear program material revealed in this study were assessed from mathematical beliefs including: students with mathematical beliefs in believing about mathematical characteristics have obstacles in the form of not being able to determine the mathematical model of linear program because he not understand teacher explanations, students with mathematical belief in believing about self abilitiy have an obstacles like not being able to mention the benefits of a linear program, students with mathematical beliefs in believing about teaching mathematics experience obstacles like not being able to make mathematical models correctly and the last is students with mathematical beliefs in believing about the usefulness of mathematics experiencing obstacles like not being able to make mathematical models because forget..

Calculation Method of Spatial Equilibrium Coefficient for Land Expansion of High Density Building Complex

The existing calculation methods have the problem of fuzzy characteristics of equilibrium coefficient, which leads to too many iterations in the calculation process. Combined with the normal force climbing effect, the shear stress of the rise and fall angle of the high density building group is obtained. Extract the mathematical characteristics of the equilibrium coefficient based on the space sharing theory, quantify the index data, calculate the equilibrium coefficient of the high density building group, and realize the calculation method design. Experimental results: under the same experimental conditions, the approximate number of iterations of this design method and the existing two calculation methods is 10 ~ 25 times less than the other two calculation methods, which proves that the performance of this design method is better.

Mathematical Study of the Verhulst and Gompertz Growth Functions and Their Contemporary Applications

This study examines the mathematical characteristics of the logistic, the generalized logistic and the Gompertz growth function used in human population analysis. When a population growth is mathematically modeled, it starts with differential equations considered as a preliminary study. Then, a general solution equation is derived. This is the method followed by the mathematicians who developed these models. To prepare for the study, I used the framework of the objectives and adhered to the resources and approaches outlined by mathematicians who developed the growth function. In addition, I wanted to evaluate the methodologies that remain valid in contemporary applications using the current perspectives. Mathematician and actuary Benjamin Gompertz developed the first survivors’ function in 1825 which was used later as a population growth function while systematizing life tables. In his three published articles, the mathematician Pierre-François Verhulst developed a logistic human population growth function based on his economic analysis. In addition, he searched for test opportunities using the limited population statistics of France, Belgium, England, the USA, and Russia. Contemporary authors Richards and, ‘Ricketts and Head’ made very invaluable contributions to logistic growth function.

Photoplethysmographic characteristics of the efficiency of the calf muscle-venous pump in norm and in patients with cvd of various clinical classes according to CEAP

Introduction. A literature review on the use of plethysmographic methods for studying the features of venous blood flow in lower extremities under physiological conditions and for global assessment of venous hemodynamics in chronic venous diseases urges to conduct further studies.The aim of the study was to carrying off a detailed statistical analysis of the value of the refilling time (RT) obtained during a photoplethysmographic study (PPG) to evaluate the degree of effectiveness of the calf muscle-venous pump in normal and in patients of different clinical classes according to CEAR.Materials and methods. For the period from 2002 to 2012, 116 healthy individuals with no symptoms of chronic venous diseases and 530 patients with CVD were examined with the use of PPG, with their distribution in accordance with the CEAR international classification as follows: C0-C1 – 140 people (26.42%), C2-C3 – 218 people (41.13%) and 172 persons (32.45%) had trophic disorders, that is, they belonged to the C4-C6 clinical classes. The analysis of the statistical significance of the obtained mathematical characteristics in groups by conducting a t-test for two independent samples calculated by the program and the student’s criterion Z-statistics, to conduct a correlation analysis.Results and discussion. Statistical comparative analysis of the RT value as a result of the t-test at the significance level p < 0,05 showed statistically significant differences between С0-С1, С2-С3 and С4-С6 groups with test with (or no) compression cuff. A stable correlation of average strength was observed between the groups in all cases. The differences were not statistically significant between the Norm and C0-C1 groups. The testing hypotheses for adequacy using linear regression methods allowed us to conclude that conducting a photoplethysmographic examination of patients with CVD of different clinical classes as part of the venous reflux test can provide objective information about the effectiveness of the calf muscle - venous pump. A comparative analysis in groups using the criteria RT > 20 sec and 10 < RT < 20 sec showed that there was no correlation between many groups.Conclusion. PPG is not a universal tool for diagnosing disorders of venous hemodynamics in the lower extremities. The value of RT > 20 seconds can be used as a criterion for evaluating the effectiveness of the calf muscle-venous pump, since more than 70% of cases occur in norm and in patients with C0-C1 clinical classes.

A generalized equation approach for hyoid bone displacement and penetration\u2013aspiration scale analysis

Swallowing physiology includes numerous biomechanical events including displacement of the hyoid bone, which is a crucial component of airway protection and opening of the proximal esophagus. The objective of this study was to evaluate the potential relations between the trajectory of hyoid bone movement and the risk of airway penetration and aspiration during a videofluoroscopic swallowing study. Two hundred sixty-five patients were involved in this study, producing a total of 1433 swallows of various volumes consisting of thin liquid, nectar-thick liquid, and solids during a fluoroscopic exam. The anterior and posterior landmarks of the body of the hyoid bone were manually marked in each frame of each fluoroscopic video. Generalized estimation equations were applied to evaluate the relationship between penetration–aspiration scores and mathematical features extracted from the hyoid bone trajectories, while also considering the influence of other independent variables such as age, bolus volume, and viscosity. Our results indicated that penetration–aspiration scores showed a significant relation to age. The maximum anterior (horizontal) displacement of the anterior hyoid bone landmark was significantly associated with the penetration–aspiration scores. Differences in the displacement of the hyoid bone are useful observations in airway protection.Article highlightsIn this work, the potential relations between the trajectory of hyoid bone movement and the risk of airway penetration and aspiration during a videofluoroscopic swallowing study were evaluated.We extracted features from the hyoid bone trajectories and applied generalized estimation equations to investigate their relationship to penetration–aspiration scales.The results showed that the maximum anterior (horizontal) displacement of the anterior hyoid bone landmark was significantly associated with the penetration–aspiration scales.

A Study on Mathematical characteristics in Indian Carnatic Musicians

Background/Objectives: The main aim of this research is to observe the mathematical skills in Indian Carnatic musicians. Math and Music seem to be completely different fields of study, but there are a few similar cognitive abilities needed to learn mathematics as well as music. Any mathematical theory works on given premises, set of rules, assumptions and given constraints. The same way “Music” in-particular Indian Carnatic Music also needs a methodic way to learn and perform. Mathematics if rightly viewed not only possesses the truth but also beauty like music. Being good in one of them may enhance abilities in the other. Methods and Statistical Analysis: The data is collected from a sample of 153 respondents which is collected through a structured questionnaire using Microsoft forms based on random sampling method. The data have been analysed and hypotheses have been tested by using valid statistical tools that is descriptive statistics, chi square test using IBM SPSS version 25. Findings: Most of the hypotheses developed in this study were positively confirmed. This study observes the aptitude of the Carnatic musicians to be associated with mathematics up to considerable level of their education. It also reveals the impact of mathematics in understanding the observational skills to identify “Sruthi” one of the basic concepts Carnatic Music. Novelty: All the stake holders of Education can observe that learning of mathematics is not just as only practicing the high -level concepts but also to develop the logical and reasoning skills which are really needed for the excellence in other art forms like Music. Also, these types of quantitative measures can be used to scale the learning quality of any musician since excellence in Carnatic music may not be considered only by performance. Keywords Mathematical skills, Indian Carnatic Music, Sruthi, Rhythm

Enhanced Image Segmentation: Merging Fuzzy K-Means and Fuzzy C-Means Clustering Algorithms for Medical Applications

Separating an image into regions according to some criterion is called image segmentation. This paper presents an algorithm that combines the fuzzy k-means (FKM) and fuzzy c-means (FCM) clustering strategies. The proposed algorithm combines the FKM and the FCM algorithms mathematical features, which is referred to as (CFKCM). The FKM and FCM clustering algorithms are adopted to compare the performance and hence evaluate the proposed clustering algorithm. Tests are conducted, and performance parameters are calculated for validation. The comparison and assessment analysis are based on metrics related to the image clustering process, such as the Segmentation Accuracy (SA), Clustering Fitness (CF), and cluster Validity function (V_pc and V_pe). A dataset of MR images is used by this research for the application, test, and evaluation of the image clustering. The results for clustering backbone MRI images show that CFKCM algorithm is featured by being more effective, and comparatively independent of the noise, where it can process the

Simulation of the Potential Distribution of the Glacier Based on Maximum Entropy Model in the Tianshan Mountains, China

Under the background of global climate change, the variation in the spatial distribution and ice volume of mountain glaciers have a profound influence on regional economic development and ecological security. The development of glaciers is like biological succession; when climate change approaches or exceeds the threshold of suitable conditions for glacier development, it will lead to changes in potential distribution pattern. Therefore, from the perspective of the "biological" characteristics of glaciers, it is a beneficial exploration and attempt in the field of glaciology to explore its potential distribution law with the help of the niche model. The maximum entropy model (MaxEnt) can explain the environmental conditions suitable for the survival of things by analyzing the mathematical characteristics and distribution laws of samples in space. According to glacier samples and the geographical environment data screened by correlation analysis and iterative calculation, the potential distribution pattern of Tianshan glaciers in China in reference years (1970–2000) was simulated by MaxEnt. This paper describes the contribution of geographical environmental factors to distribution of glaciers in Tianshan Mountains, quantifies the threshold range of factors affecting the suitable habitat of glaciers, and predicts the area variation and distribution pattern of glaciers under different climate scenarios (SSP1-2.6, SSP5-8.5) in the future (2040–2060, 2080–2100). The results show that the MaxEnt model has good adaptability to simulate the distribution of glaciers. The spatial heterogeneity of potential distribution of glaciers is caused by the spatio-temporal differences of hydrothermal combination and topographic conditions. Among the environmental variables, precipitation during the wettest month, altitude, annual mean temperature, and temperature seasonality have more significant effects on the potential distribution of glaciers. There is significant spatial heterogeneity in the potential distribution of glaciers in different watersheds, altitudes, and aspects. From the forecast results of glacier in various climatic scenarios in the future, about 18.16–27.62% of the total reference year glacier area are in an alternating change of melting and accumulation, among which few glaciers are increasing, but this has not changed the overall retreat trend of glaciers in the study area. Under the low emission scenario, the glacier area of the Tianshan Mountains in China decreased by 18.18% and 23.73% respectively in the middle and end of the 21st century compared with the reference years and decreased by 20.04% and 27.63%, respectively, under the high emission scenario, which showed that the extent of glacier retreat is more intense under the high emission scenario. Our study offers momentous theoretical value and practical significance for enriching and expanding the theories and analytical methods of the glacier change.

The Cosmological Semiclassical Einstein Equation as an Infinite-Dimensional Dynamical System

We develop a comprehensive framework in which the existence of solutions to the semiclassical Einstein equation (SCE) in cosmological spacetimes is shown. Different from previous work on this subject, we do not restrict to the conformally coupled scalar field and we admit the full renormalization freedom. Based on a regularization procedure, which utilizes homogeneous distributions and is equivalent to Hadamard point splitting, we obtain a reformulation of the evolution of the quantum state as an infinite-dimensional dynamical system with mathematical features that are distinct from the standard theory of infinite-dimensional dynamical systems (e.g., unbounded evolution operators). Nevertheless, applying methods closely related to Ovsyannikov’s method, we show existence of maximal/global solutions to the SCE for vacuum-like states and of local solutions for thermal-like states. Our equations do not show the instability of the Minkowski solution described by other authors.

Modeling Sustainable Economic Development Using Production Functions

The most popular two-factor production functions used in the process of modeling sustainable economic development are examined. Economic and mathematical characteristics of Cobb-Douglas production functions, CES-function, linear function, Leontief and Allen functions are considered, in particular, type of dependence of labour productivity in relation to capital-labour ratio of commodity production system within mentioned production functions. Their most important economic and mathematical characteristics are presented: factors average and marginal return, demand for production resources, factor substitution, factors marginal rate of technical substitution, output elasticity by factors, elasticity of factors technical substitution, optimal capital-labour ratio according to the criterion of maximum output. Comparative analysis is given to Cobb-Douglas and CES-functions, which are two production functions mostly required in practice.

USING THE POTENTIAL OF A TOY BOOK IN THE PREPARATION OF BACHELOR STUDENTS IN THE FIELD OF MATHEMATICAL EDUCATION OF PRESCHOOL CHILDREN

The article outlines the problem of using the potential of toy books in preparing bachelor students for purposeful work on the formation of mathematical concepts in preschool children and suggests the idea of organizing the creative activity of students to design toy books with mathematical content.The article contains an overview of classifications of toy books, pedagogically characterized and methodically described examples-constructs of various types of toy books created by bachelor students. The pedagogical potential of these constructs allows us in this work to consider a toy book as a means of mathematical education for preschool children.The purpose of the study is a theoretical description and empirical understanding of the advantages of using the potential of a toy book with mathematical content in the educational activities of a university for the development of creative thinking of future preschool teachers. To achieve the goal, the following methods were used: theoretical analysis of literary sources, Internet resources, analysis of statistical data and a pedagogical experiment.The results of the study showed difficulties in mastering the method of designing a toy book with mathematical content, revealed the preferences of future educators-educators in choosing one or another type of toy book that dominates in its content a mathematical topic and methodological features of its implementation in the presented design form.The conducted research and analysis of the results allowed us to obtain data on the importance of including in the process of training future teachers-educators a creative technique - the design of toy books with mathematical content.

Systematic Review on Local Ancestor Inference From a Mathematical and Algorithmic Perspective.

Genotypic data provide deep insights into the population history and medical genetics. The local ancestry inference (LAI) (also termed local ancestry deconvolution) method uses the hidden Markov model (HMM) to solve the mathematical problem of ancestry reconstruction based on genomic data. HMM is combined with other statistical models and machine learning techniques for particular genetic tasks in a series of computer tools. In this article, we surveyed the mathematical structure, application characteristics, historical development, and benchmark analysis of the LAI method in detail, which will help researchers better understand and further develop LAI methods. Firstly, we extensively explore the mathematical structure of each model and its characteristic applications. Next, we use bibliometrics to show detailed model application fields and list articles to elaborate on the historical development. LAI publications had experienced a peak period during 2006–2016 and had kept on moving in the following years. The efficiency, accuracy, and stability of the existing models were evaluated by the benchmark. We find that phased data had higher accuracy in comparison with unphased data. We summarize these models with their distinct advantages and disadvantages. The Loter model uses dynamic programming to obtain a globally optimal solution with its parameter-free advantage. Aligned bases can be used directly in the Seqmix model if the genotype is hard to call. This research may help model developers to realize current challenges, develop more advanced models, and enable scholars to select appropriate models according to given populations and datasets.

Printed Arabic Text Recognition Algorithms.(Dept.E)

This paper presents three efficient and reliable algorithms for the automatic recognition of printed Arabic text. The first algorithm is based on mathematical features, the second uses structural and mathematical features, while the third uses structural features. The performance of each algorithm is experimentally tested under different conditions. Comparisons between the results are also made.

Principle and performance analysis for six‐pole hybrid magnetic bearing with a secondary air gap

In order to reduce the non-linearity of radial suspension forces of the three-pole hybrid magnetic bearing and further reduce the cost and power consumption, an AC six-pole hybrid magnetic bearing with secondary air gaps is proposed. First, the structure and working principle of the AC six-pole hybrid magnetic bearing with secondary air gaps are introduced, and the mathematical model of suspension forces are derived. Second, on the basis of the mathematical model, the linearity and coupling characteristics of the radial suspension forces are analysed, and then the suspension forces are simulated and verified by the finite element method (FEM). Then, the correlation performance indexes are compared with the six-pole hybrid magnetic bearing without secondary air gaps. Finally, an experimental platform is built, and suspension and disturbance tests are carried out. The research results show that the maximum bearing capacity of the six-pole hybrid magnetic bearing with secondary air gaps is 184% of the six-pole hybrid magnetic bearing without secondary air gaps.

A new generalization of Lehmann type-II distribution: Theory, simulation, and applications to survival and failure rate data

In this paper, a potentiated lifetime model that demonstrates the bathtub-shaped hazard rate function is developed. This proposed model is referred to as Kumaraswamy modified size-biased Lehmann Type-II (Kum–MSBL–II) distribution. Various mathematical and reliability characteristics are derived and discussed. The maximum likelihood estimation method is used to estimate the model parameters and its performance is discussed by following a simulation study. Three-lifetime sets of data are utilized to illustrate the flexibility of the proposed model and the results demonstrate that the proposed model can adequately fit the real-life datasets than the competitors.