The Frankensteinian Nature of Mathematics

Frankenstein is a story about a scientist who creates a sapient creature that gets out of control and horrifies its creator by its unexpected behavior. In this note, we show that this type of undesirable behavior can reflect a part of the nature of mathematics, and that its origin is related to the ontological question of whether mathematics is invented or discovered. Based on a review of the relationship be- tween discovery and invention, we demonstrate that mathematics has similarities and differences with both discovery and invention. In the natural sciences, new instruments have to be invented to discover new goals. We want to stress that the same relation holds in mathematics. The special point about mathematics is that both the instruments and the goals are mathematics. The first mathemat- ics, usually including definitions and notations, is invented by mathematicians; the second, including lemmas, theorems and results, is accordingly discovered. The point we want to make about the chain of concepts invented and discovered in mathematics is that some of the new beings (created or discovered) can get out of the control of mathematicians, and that this reveals an important aspect of the nature of mathematical science, which we call the Frankensteinian nature of mathematics

On Mathematical Conjectures and Counterexamples

This article provides an overview of the limitations of checking out a few cases to prove conjectures in mathematics. To that end, I present a purposeful collection of number-theoretic conjectures where extensive checking of cases has found counterexamples, with emphasis on the historical backgrounds. Historical examples of long-term attempts to prove or disprove such conjectures could help individuals to realize more deeply that a limited number of observations does not guarantee the correctness of a conjecture, even though there may be many examples in its favor

Sensitivity and Uncertainty Analysis in a Circulating Fluidized Bed Reactor Modeling

As in many real applications, in the world of fine powders and small particles, there are uncertainties and vagueness in the parameters such as particle size, sphericity, initial solid void fraction, envelope density, etc. In some cases, there are different methods to measure a parameter, such as a particle size that depends on the method (based on length, weight, and volume); the measured values may be significantly different from each other. Therefore, there is no crisp or exactly known parameter in many cases because of the fine powders' inherent uncertain nature. On the other hand, being characteristic of the dynamic systems, physical parameters such as temperature and pressure fluctuate but can be kept in an acceptable range, affecting the main design parameters such as fluid density and dynamic viscosity. The most traditional tools and methods for simulating, modeling, and reasoning are crisp, deterministic, and precise, but these values are estimated or changing (randomly or stochastically). Several approaches can describe this phenomenon. Moreover, when it comes to uncertainties, mathematical tools are probably the best solutions. With the fuzzy set theory method, linguistic variables or ranges can be converted to mathematical expressions, and consequently, instead of crisp values, these can be applied to the equations. The uncertainty analysis can be more important when the model is susceptible to one parameter. A preliminary sensitivity analysis on a fluidized bed application has shown that the solid void fraction has the highest, and the fluid density has the lowest sensitivity to its operation. The theoretical approach has been validated by CPFD simulation using Barracuda v20.1.0.publishedVersio

Students’ Equation Understanding and Solving in Iran

The purpose of the present article is to investigate how 15 year old Iranian students interpret the concept of equation, its solution, and studying the relation between the students’ equation understanding and solving. Data from two equation-solving exercises are reported. Data analysis shows that there is a significant relationship between understanding and solving equation. The results indicate that students’ understanding of equation has, basically, been shaped by their experiences in arithmetic and students usually have not any perception of equations and real world problems. Moreover, the study shows that students rarely paid any attention to the equality sign and the use of operators in both sides of the equation

The Effect of Impurities on γ-Alumina Chlorination in a Fluidized Bed Reactor: A CPFD Study

Alumina is one of the most widely used materials today, with a total annual production of millions of tonnes of highly pure alumina. A large portion of this is used to make metal aluminum. Apart from that, a growing amount of alumina is used in ceramics, refractories, catalysts, and various other products. In nature, alumina can be found in different phases. These phases can be transformed into each other in different temperatures. Among these, γ-alumina is used in the chlorination process in the aluminum production industry because of the higher reaction rates. Previously, the chlorination of pure γ-alumina has been considered in the CPFD simulations. Extending previous researches, the present study investigates the effect of seven percent α-alumina impurity on the overall chlorination reaction, bed hydrodynamics, and composition of the outflow of the reactor. Commercial CPFD software Barracuda® v20.1.0 is used for the simulations. The results are compared with the pure γ-alumina simulations, and the results show that the impurity has no considerable effect on the chlorine concentration at the outlet. However, the mass balance of the bed shows an unfavorable accumulation of α-alumina in the fluidized bed reactor.publishedVersio

The association of personality dimensions, perceived stress and emotion regulation to driving anger among taxi drivers in Iran

The purpose of the present study was to determine the associations of personality dimensions, perceived stress and emotion regulation to driving anger among taxi drivers in Iran. Using a convenience sampling procedure, a number of 120 taxi drivers were recruited for the study. Data were collected using a sociodemographic data sheet, the HEXACO personality inventory, the perceived stress scale, the cognitive emotion regulation questionnaire and the driving anger scale. The data were analyzed using Pearson’s correlation coefficients and multiple regression analysis. Findings revealed that 5% to 20% of taxi drivers experience high levels of anger while driving. Most taxi drivers agree that slow driving and traffic obstructions as frustrating and anger-provoking. The drivers reported experiencing stress frequently. The personality dimensions of extroversion, agreeableness and honesty/humility were found to be associated with anger specifically related to the presence of police. Among the cognitive emotion regulation strategies, only catastrophizing and positive refocusing were found to be associated with driving anger from the involvement of police. Perception of stress, extroversion and conscientiousness and positive refocusing together explained 19.1% of the variance associated with anger elicited by driving situations, with the personality traits making the largest contribution

Study of the Thermal Performance of Industrial Alumina Chlorination Reactor Based on CPFD Simulation

As a part of the new sustainable aluminum production process under study, alumina chlorination plays a crucial role. The relevant process is an exothermic reaction in a fluidized bed reactor. The solid alumina reacts with chlorine and carbon monoxide and produces aluminum chloride and carbon dioxide as the main products. Then carbon dioxide can be separated efficiently. The optimum temperature for the alumina chlorination is 700℃. The reactor’s temperature should be kept in the range of 650-850℃ (most preferably 700℃) because below that temperature range, the reaction rate drops, and above that range, the alumina (which usually is γ-alumina) transfers to other alumina types, which is not desirable for the purpose. Extending other simulation studies by authors on alumina chlorination in an isothermal condition, the CPFD method has been utilized to thermal study and simulate the overall heat transfer of the system, including convective fluid to the wall, fluid to particle, and radiation heat transfer. Radial and axial heat transfer coefficient profiles at different levels show that almost all the heat should be transferred in the lower half of the reactor, making the design more challenging. At the steady-state, the range for the fluid temperature inside the reactor has been recorded 700-780℃.publishedVersio

Modélisation de la relation entre les composantes de connaissances et les compétences d’élèves pour l’apprentissage de l’expression algébrique dans les écoles secondaires à l’aide de la méthode AHM

The purpose of this study is to apply the Attribute Hierarchy Method (AHM) in the cognitive domains of algebraic expressions to find cognitive inferences about students’ mathematical problem-solving skills. Initially, cognitive content techniques were developed to determine the knowledge and skills needed to solve mathematical assignments. Then, items were written specifically to assess skills in cognitive models. Finally, confirmatory psychometric analyses were used to evaluate students' response information by estimating the proportionality of the data model, attribute probabilities to report the diagnostic score and attribute validity. The first domain is concerned with the cognition and diagnosis of general polynomials and algebraic expressions and encompasses other areas. Therefore, the focus is on the precise definition of the basic concepts of the recognition of polynomials such as the polynomials and the number of very important terms and similar monomials and incorrect learning of algebra. Nevertheless, in the second domain, which focuses on simplification and related concepts, less emphasis has been placed on the seventh to ninth grades. The defect in the expression and practice of this field leads to weakness in solving and analyzing relevant mathematical problems. The third domain is related to the second domain and directly to the first domain. Factorization and distributive properties are often used without considering the rules of simplification by students. The weakness associated with the second domain causes the students not to be able to easily analyze and solve the problem in difficult polynomials in which the rules do not apply easily.L’objectif principal de cette étude est d’appliquer la méthode de hiérarchie d'attributs dans les domaines cognitifs d’expressions algébriques pour trouver d’inférences cognitives concernant les compétences d’élèves en résolution de problèmes mathématiques. Initialement, des techniques de contenu cognitif ont été développées pour déterminer les connaissances et les compétences nécessaires pour résoudre des problèmes de mathématiques. » Ensuite, l’on a écrit d’articles spécifiquement pour évaluer les compétences en modèles cognitifs. Enfin, des analyses psychométriques de confirmation ont été utilisées pour évaluer les informations sur la réponse d’étudiants en estimant la proportionnalité du modèle de données, les probabilités d’attributs pour rendre compte du résultat diagnostique et la validité d’attributs. » Le premier domaine concerne la connaissance et le diagnostic des polynômes généraux et des termes algébriques, et comprend d'autres domaines. Conséquemment, l’accent est mis sur la définition précise de concepts de base de la reconnaissance des polynômes tels que les polynômes et le nombre de termes très importants et de monômes similaires et l’apprentissage incorrect de l’algèbre. Cependant, dans le deuxième domaine, qui met l'accent sur simplification et concepts connexes, moins d'attention a été accordée aux septième à neuvième années. Le défaut dans l'expression et dans la pratique de ce domaine entraîne une faiblesse dans résolution et analyse de problèmes mathématiques pertinents. Le troisième domaine est lié au deuxième domaine et directement au premier domaine. La factorisation et les propriétés distributives sont souvent utilisées sans tenir compte des règles de simplification appliquées par les étudiants. La faiblesse du deuxième domaine empêche les étudiants d'analyser et de résoudre facilement le problème dans des polynômes difficiles dans lesquels les règles ne s'appliquent pas facilement

Management Development in Iranian Academic Libraries: Performances and Obstacles

This paper aims to investigate the current status of management development in academic libraries and it identifies the deterrent factors in administering management development programs. In order to fulfill the aim of the study, 268 managers from 73 academic libraries answered the questions on their need to management development and the current performance of their organizations. They also prioritized the organizational obstacles to their development. The results revealed that, in general, almost all academic library managers express the need for managerial development. In spite of that, in more than half of libraries no management development program has been held. As the results showed, the three most important obstacles to management development include “Not recognized as a need”, “Inappropriate appraisal system” and “Lack of suitable program” respectively