Provincial responsibility for carbon emissions in China under different principles

International Nuclear Information System (INIS)

Zhang, Youguo

2015-01-01

By applying a multi-regional input–output model, the study compares the provincial responsibility for carbon emissions and provincial carbon multipliers in China under seven responsibility-allocating principles, including three basic principles, the production, income and consumption principles, and four shared responsibility principles, the income-weighted, consumption weighted, comprehensive, and weighted comprehensive principles. Empirical results indicate that carbon multipliers of provinces under these principles are significantly different from one another. The carbon multipliers of provinces with higher ratios of carbon intensive sectors in their outputs are also larger. At the same time, the carbon multipliers of the same sector in the provinces are significantly different from one another. Changing the principle causes significant changes in the responsibility for carbon emissions of some provinces, but only slight changes in the responsibilities of some other provinces. However, the responsibilities of provinces with large economic sizes (output) are always the largest, whereas provinces with the smallest economic sizes are always the smallest regardless of the principles. Further, this study proposes a series of regional policies for carbon mitigation according to provincial carbon multipliers and responsibility allocation features under the different principles. - Highlights: • We link regional environmental responsibility to seven benefit principles. • We analyze provincial responsibility for carbon emissions in China. • We also report provincial carbon multipliers under different principles. • We compare the seven principles from the regional perspective. • Policy implications of the study are discussed.

Risk measurement with equivalent utility principles

NARCIS (Netherlands)

Denuit, M.; Dhaene, J.; Goovaerts, M.; Kaas, R.; Laeven, R.

2006-01-01

Risk measures have been studied for several decades in the actuarial literature, where they appeared under the guise of premium calculation principles. Risk measures and properties that risk measures should satisfy have recently received considerable attention in the financial mathematics

Using Coevolution Genetic Algorithm with Pareto Principles to Solve Project Scheduling Problem under Duration and Cost Constraints

Directory of Open Access Journals (Sweden)

Alexandr Victorovich Budylskiy

2014-06-01

Full Text Available This article considers the multicriteria optimization approach using the modified genetic algorithm to solve the project-scheduling problem under duration and cost constraints. The work contains the list of choices for solving this problem. The multicriteria optimization approach is justified here. The study describes the Pareto principles, which are used in the modified genetic algorithm. We identify the mathematical model of the project-scheduling problem. We introduced the modified genetic algorithm, the ranking strategies, the elitism approaches. The article includes the example.

Organizing principles underlying microorganism's growth-robustness trade-off.

Science.gov (United States)

Bolli, Alessandro; Salvador, Armindo

2014-10-01

Growth Robustness Reciprocity (GRR) is an intriguing microbial manifestation: the impairment of microorganism's growth enhances their ability to resist acute stresses, and vice-versa. This is caused by regulatory interactions that determine higher expression of protection mechanisms in response to low growth rates. But because such regulatory mechanisms are species-specific, GRR must result from convergent evolution. Why does natural selection favor such an outcome? We used mathematical models of optimal cellular resource allocation to identify the general principles underlying GRR. Non-linear optimization allowed to predict allocation patterns of biosynthetic resources (ribosomes devoted to the synthesis of each cell component) that maximize growth. These models predict the down-regulation of stress defenses under high substrate availabilities and low stress levels. Under these conditions, stress tolerance ensues from growth-related damage dilution: the higher the substrate availability, the fastest the dilution of damaged proteins by newly synthesized proteins, the lower the accumulation of damaged components into the cell. In turn, under low substrate availability growth is too slow for effective damage dilution, and the expression of the defenses up to some optimal level then increases growth. As a consequence, slow-growing cells are pre-adapted to withstand acute stresses. Therefore, the observed negative correlation between growth and stress tolerance can be explained as a consequence of optimal resource allocation for maximal growth. We acknowledge fellowship SFRH/BPD/90065/2012 and grants PEst-C/SAU/LA0001/2013-2014 and FCOMP-01-0124-FEDER-020978 financed by FEDER through the "Programa Operacional Factores de Competitividade, COMPETE" and by national funds through "FCT, Fundação para a Ciência e a Tecnologia" (project PTDC/QUI-BIQ/119657/2010). Copyright © 2014. Published by Elsevier Inc.

On the mathematics of fuzziness

International Nuclear Information System (INIS)

Kerre, E.

1994-01-01

During the past twenty-five years, the scientific community has been working very extensively on the development of reliable models for the representation and manipulation of impreciseness and uncertainty that pervade the real world. Fuzzy set theory is one of the most popular theories able to treat incomplete information. In this paper, the basic mathematical principles underlying fuzzy set theory are outlined. Special attention is paid to the way that set theory has influenced the development of mathematics in a positive way

On the mathematics of fuzziness

Energy Technology Data Exchange (ETDEWEB)

Kerre, E. [Ghent Univ. (Belgium)

1994-12-31

During the past twenty-five years, the scientific community has been working very extensively on the development of reliable models for the representation and manipulation of impreciseness and uncertainty that pervade the real world. Fuzzy set theory is one of the most popular theories able to treat incomplete information. In this paper, the basic mathematical principles underlying fuzzy set theory are outlined. Special attention is paid to the way that set theory has influenced the development of mathematics in a positive way.

The Principle of the Fermionic Projector: An Approach for Quantum Gravity?

Science.gov (United States)

Finster, Felix

In this short article we introduce the mathematical framework of the principle of the fermionic projector and set up a variational principle in discrete space-time. The underlying physical principles are discussed. We outline the connection to the continuum theory and state recent results. In the last two sections, we speculate on how it might be possible to describe quantum gravity within this framework.

Investigating Underlying Principles to Guide Health Impact Assessment

Directory of Open Access Journals (Sweden)

Ali Fakhri

2014-06-01

Full Text Available Background Many countries conduct Health Impact Assessment (HIA of their projects and policies to predict their positive and negative health impacts. In recent years many guides have been developed to inform HIA practice, largely reflecting local developments in HIA. These guides have often been designed for specific contexts and specific need, making the choice between guides difficult. The objective of the current study is to identify underlying principles in order to guide HIA practice in Iran. Methods This study was conducted in three stages: 1 Studies comparing HIA guidelines were reviewed to identify criteria used for comparison seeking emphasized principles. 2 The HIA characteristics extracted from published papers were categorized in order to determine the principles that could guide HIA practice. 3 Finally, these principles were agreed by experts using nominal group technique. Results The review of the studies comparing HIA guides demonstrated there are no clear comparison criteria for reviewing HIA guides and no study mentioned HIA principles. Investigating the HIA principles from peer-reviewed papers, we found 14 issues. These were, considering of general features in planning and conducting HIAs such as HIA stream, level, timing and type, considering of the wider socio-political and economic context, considering of economic, technical and legal aspects of HIA and capacities for HIA, rationality and comprehensiveness, using appropriate evidence, elaborating on HIA relation to other forms of Impact Assessment, considering of equity, and encouraging intersectoral and interdisciplinary cooperation, involvement of stakeholders and transparency as underlying principles to guide HIA practice. The results emphasize how critical these technical as well as tactical considerations are in the early scoping step of an HIA which plans the conduct of the HIA in reponse to local contextual issues. Conclusion Determining the principles of HIA from

Investigating underlying principles to guide health impact assessment.

Science.gov (United States)

Fakhri, Ali; Maleki, Mohammadreza; Gohari, Mahmoodreza; Harris, Patrick

2014-06-01

Many countries conduct Health Impact Assessment (HIA) of their projects and policies to predict their positive and negative health impacts. In recent years many guides have been developed to inform HIA practice, largely reflecting local developments in HIA. These guides have often been designed for specific contexts and specific need, making the choice between guides difficult. The objective of the current study is to identify underlying principles in order to guide HIA practice in Iran. This study was conducted in three stages: 1) Studies comparing HIA guidelines were reviewed to identify criteria used for comparison seeking emphasized principles. 2) The HIA characteristics extracted from published papers were categorized in order to determine the principles that could guide HIA practice. 3) Finally, these principles were agreed by experts using nominal group technique. The review of the studies comparing HIA guides demonstrated there are no clear comparison criteria for reviewing HIA guides and no study mentioned HIA principles. Investigating the HIA principles from peer-reviewed papers, we found 14 issues. These were, considering of general features in planning and conducting HIAs such as HIA stream, level, timing and type, considering of the wider socio-political and economic context, considering of economic, technical and legal aspects of HIA and capacities for HIA, rationality and comprehensiveness, using appropriate evidence, elaborating on HIA relation to other forms of Impact Assessment, considering of equity, and encouraging intersectoral and interdisciplinary cooperation, involvement of stakeholders and transparency as underlying principles to guide HIA practice. The results emphasize how critical these technical as well as tactical considerations are in the early scoping step of an HIA which plans the conduct of the HIA in reponse to local contextual issues. Determining the principles of HIA from peer-reviewed papers provides an opportunity for guiding

Some algorithms for reordering a sequence of objects, with application to E. Sparre Andersen's principle of equivalence in mathematical statistics

NARCIS (Netherlands)

Bruijn, de N.G.

1972-01-01

Recently A. W. Joseph described an algorithm providing combinatorial insight into E. Sparre Andersen's so-called Principle of Equivalence in mathematical statistics. In the present paper such algorithms are discussed systematically.

PROJECTING PRINCIPLES OF «MATHEMATICAL AND PHYSICAL BASICS IN INFORMATICS» MODULE AS PART OF A UNIVERSAL BACCALAUREATE PROGRAM

Directory of Open Access Journals (Sweden)

E. K. Samerkhanova

2016-01-01

Full Text Available This article is a presentation of “Mathematical and Physical Basics in Informatics” Module projected as part of universal baccalaureate model realized in Minin State Pedagogical University, Nizhny Novgorod, within the educational program for an extended group of qualifications “Informatics and Calculating Machines”. Module authors defined a strategy for baccalaureates preparation in the field of informational technology, which is realized due to a bunch of principles: education fundamentalization, learning systematization, activity, integration and student-centration. The principle of education fundamentalization requires consolidation of scientific and methodological preparation of students. The principle of learning systematization guarantees formation of students’ holistic ideology. The principle of integration is directed onto qualitative interdisciplinary conversion based on mutual enrichment of knowledge and skills. The principle of activity considers student personality, its formation and growth with respect to practical activity as a special form of psychical activity. The principle of student-centration is displayed as social-humanistic purpose of the educational process.

Teaching mathematics using excel

OpenAIRE

Bonello, Mary Rose; Camilleri, Silvana

2004-01-01

'Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning.' (Principles and Standards for School Mathematics-NCTM April 2000)

Modeling Clinic for Industrial Mathematics: A Collaborative Project Under Erasmus+ Program

DEFF Research Database (Denmark)

Jurlewicz, Agnieszka; Nunes, Claudia; Russo, Giovanni

2018-01-01

Modeling Clinic for Industrial Mathematics (MODCLIM) is a Strategic Partnership for the Development of Training Workshops and Modeling Clinic for Industrial Mathematics, funded through the European Commission under the Erasmus Plus Program, Key Action 2: Cooperation for innovation and the exchang...

Design Principles for Serious Video Games in Mathematics Education: From Theory to Practice

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Konstantinos Chorianopoulos

2014-09-01

Full Text Available There is growing interest in the employment of serious video games in science education, but there are no clear design principles. After surveying previous work in serious video game design, we highlighted the following design principles: 1 engage the students with narrative (hero, story, 2 employ familiar gameplay mechanics from popular video games, 3 engage students into constructive trial and error game-play and 4 situate collaborative learning. As illustrated examples we designed two math video games targeted to primary education students. The gameplay of the math video games embeds addition operations in a seamless way, which has been inspired by that of classic platform games. In this way, the students are adding numbers as part of popular gameplay mechanics and as a means to reach the video game objective, rather than as an end in itself. The employment of well-defined principles in the design of math video games should facilitate the evaluation of learning effectiveness by researchers. Moreover, educators can deploy alternative versions of the games in order to engage students with diverse learning styles. For example, some students might be motived and benefited by narrative, while others by collaboration, because it is unlikely that one type of serious video game might fit all learning styles. The proposed principles are not meant to be an exhaustive list, but a starting point for extending the list and applying them in other cases of serious video games beyond mathematics and learning.

Under Threes' Mathematical Learning

Science.gov (United States)

Franzén, Karin

2015-01-01

The article focuses on mathematics for toddlers in preschool, with the aim of challenging a strong learning discourse that mainly focuses on cognitive learning. By devoting more attention to other perspectives on learning, the hope is to better promote children's early mathematical development. Sweden is one of few countries to have a curriculum…

Humanist Principles Underlying Philosophy of Argument

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George Boger

2008-02-01

Full Text Available This discussion reviews the thinking of some prominent philosophers of argument to extract principles common to their thinking. It shows that a growing concern with dialogical pragmatics is better appreciated as a part of applied ethics than of applied epistemology. The discussion concludes by indicating a possible consequence for philosophy of argument and invites further discussion by asking whether argumentation philosophy has an implicit, underlying moral, or even political, posture.

Hipatia: a hypermedia learning environment in mathematics

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Marisol Cueli

2016-01-01

Full Text Available Literature revealed the benefits of different instruments for the development of mathematical competence, problem solving, self-regulated learning, affective-motivational aspects and intervention in students with specific difficulties in mathematics. However, no one tool combined all these variables. The aim of this study is to present and describe the design and development of a hypermedia tool, Hipatia. Hypermedia environments are, by definición, adaptive learning systems, which are usually a web-based application program that provide a personalized learning environment. This paper describes the principles on which Hipatia is based as well as a review of available technologies developed in different academic subjects. Hipatia was created to boost self-regulated learning, develop specific math skills, and promote effective problem solving. It was targeted toward fifth and sixth grade students with and without learning difficulties in mathematics. After the development of the tool, we concluded that it aligned well with the logic underlying the principles of self-regulated learning. Future research is needed to test the efficacy of Hipatia with an empirical methodology.

The mathematics of soap films

CERN Document Server

Oprea, John

2000-01-01

Nature tries to minimize the surface area of a soap film through the action of surface tension. The process can be understood mathematically by using differential geometry, complex analysis, and the calculus of variations. This book employs ingredients from each of these subjects to tell the mathematical story of soap films. The text is fully self-contained, bringing together a mixture of types of mathematics along with a bit of the physics that underlies the subject. The development is primarily from first principles, requiring no advanced background material from either mathematics or physics. Through the Maple® applications, the reader is given tools for creating the shapes that are being studied. Thus, you can "see" a fluid rising up an inclined plane, create minimal surfaces from complex variables data, and investigate the "true" shape of a balloon. Oprea also includes descriptions of experiments and photographs that let you see real soap films on wire frames. The theory of minimal surfaces is a beautif...

Middle School Mathematics Teachers Panel Perspectives of Instructional Practicess

Science.gov (United States)

Ziegler, Cindy

2017-01-01

In a local middle school, students were not meeting standards on the state mathematics tests. The purpose of this qualitative study was to explore mathematics teachers' perspectives on effective mathematics instruction vis-a-vis the principles of the National Council of Teachers of Mathematics (NCTM). Within this framework, the 6 principles in the…

Scattered Radiation Emission Imaging: Principles and Applications

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M. K. Nguyen

2011-01-01

Full Text Available Imaging processes built on the Compton scattering effect have been under continuing investigation since it was first suggested in the 50s. However, despite many innovative contributions, there are still formidable theoretical and technical challenges to overcome. In this paper, we review the state-of-the-art principles of the so-called scattered radiation emission imaging. Basically, it consists of using the cleverly collected scattered radiation from a radiating object to reconstruct its inner structure. Image formation is based on the mathematical concept of compounded conical projection. It entails a Radon transform defined on circular cone surfaces in order to express the scattered radiation flux density on a detecting pixel. We discuss in particular invertible cases of such conical Radon transforms which form a mathematical basis for image reconstruction methods. Numerical simulations performed in two and three space dimensions speak in favor of the viability of this imaging principle and its potential applications in various fields.

The Collective Black and "Principles to Actions"

Science.gov (United States)

Martin, Danny Bernard

2015-01-01

In this commentary, Danny Martin describes five key take-aways and two sets of questions that arose from his reading of "Principles to Actions: Ensuring Mathematics Success for All (National Council of Teachers of Mathematics [NCTM], 2014). Martin begins by noting that "Principles to Actions" is clearly a political document that…

Essential concepts and underlying theories from physics, chemistry, and mathematics for "biochemistry and molecular biology" majors.

Science.gov (United States)

Wright, Ann; Provost, Joseph; Roecklein-Canfield, Jennifer A; Bell, Ellis

2013-01-01

Over the past two years, through an NSF RCN UBE grant, the ASBMB has held regional workshops for faculty members from around the country. The workshops have focused on developing lists of Core Principles or Foundational Concepts in Biochemistry and Molecular Biology, a list of foundational skills, and foundational concepts from Physics, Chemistry, and Mathematics that all Biochemistry or Molecular Biology majors must understand to complete their major coursework. The allied fields working group created a survey to validate foundational concepts from Physics, Chemistry, and Mathematics identified from participant feedback at various workshops. One-hundred twenty participants responded to the survey and 68% of the respondents answered yes to the question: "We have identified the following as the core concepts and underlying theories from Physics, Chemistry, and Mathematics that Biochemistry majors or Molecular Biology majors need to understand after they complete their major courses: 1) mechanical concepts from Physics, 2) energy and thermodynamic concepts from Physics, 3) critical concepts of structure from chemistry, 4) critical concepts of reactions from Chemistry, and 5) essential Mathematics. In your opinion, is the above list complete?" Respondents also delineated subcategories they felt should be included in these broad categories. From the results of the survey and this analysis the allied fields working group constructed a consensus list of allied fields concepts, which will help inform Biochemistry and Molecular Biology educators when considering the ASBMB recommended curriculum for Biochemistry or Molecular Biology majors and in the development of appropriate assessment tools to gauge student understanding of how these concepts relate to biochemistry and molecular biology. © 2013 by The International Union of Biochemistry and Molecular Biology.

The principle of the Fermionic projector

CERN Document Server

Finster, Felix

2006-01-01

The "principle of the fermionic projector" provides a new mathematical framework for the formulation of physical theories and is a promising approach for physics beyond the standard model. This book begins with a brief review of relativity, relativistic quantum mechanics, and classical gauge theories, emphasizing the basic physical concepts and mathematical foundations. The external field problem and Klein's paradox are discussed and then resolved by introducing the fermionic projector, a global object in space-time that generalizes the notion of the Dirac sea. At the mathematical core of the book is a precise definition of the fermionic projector and the use of methods of hyperbolic differential equations for detailed analysis. The fermionic projector makes it possible to formulate a new type of variational principle in space-time. The mathematical tools are developed for the analysis of the corresponding Euler-Lagrange equations. A particular variational principle is proposed that gives rise to an effective...

The Obstacle Version of the Geometric Dynamic Programming Principle: Application to the Pricing of American Options Under Constraints

International Nuclear Information System (INIS)

Bouchard, Bruno; Vu, Thanh Nam

2010-01-01

We provide an obstacle version of the Geometric Dynamic Programming Principle of Soner and Touzi (J. Eur. Math. Soc. 4:201-236, 2002) for stochastic target problems. This opens the doors to a wide range of applications, particularly in risk control in finance and insurance, in which a controlled stochastic process has to be maintained in a given set on a time interval [0,T]. As an example of application, we show how it can be used to provide a viscosity characterization of the super-hedging cost of American options under portfolio constraints, without appealing to the standard dual formulation from mathematical finance. In particular, we allow for a degenerate volatility, a case which does not seem to have been studied so far in this context.

PRINCIPLES OF DEVELOPMENT MATHEMATICAL MODEL FOR RESEARCHING OF NONPULSATILE FLOW PUMP AND CARDIAC SYSTEM

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I. V. Bykov

2013-01-01

Full Text Available Aim. The presented research uncovers the using of mathematical modeling methods for cardio-vascular system and axial blood pump interaction analysis under heart failure with combined valve pathology. The research will pro- vide data for automated pump control algorithm synthesis. Materials and methods. Mathematical model is build up by using experiments results from mock cardio-vascular circulation loop and mathematical representation of Newtonian fluid dynamics in pulsing circulation loop. The model implemented in modeling environment Simulink (Matlab. Results. Authors implemented mathematical model which describe cardio-vascular system and left-ven- tricular assistive device interaction for intact conditions. Values of parameters for intact conditions were acquired in the experiments on animals with implanted axial pump, experiments were conducted in FRCTAO. The model was verified by comparison of instantaneous blood flowrate values in experiments and in model. Conclusion. The paper present implemented mathematical model of cardio-vascular system and axial pump interaction for intact conditions, where the pump connected between left ventricle and aorta. In the next part of research authors will use the presented model to evaluate using the biotechnical system in conditions of heart failure and valve pathology. 

Facilitating Mathematical Practices through Visual Representations

Science.gov (United States)

Murata, Aki; Stewart, Chana

2017-01-01

Effective use of mathematical representation is key to supporting student learning. In "Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014), "use and connect mathematical representations" is one of the effective Mathematics Teaching Practices. By using different representations, students examine concepts…

Applied Mathematics Should Be Taught Mixed.

Science.gov (United States)

Brown, Gary I.

1994-01-01

Discusses the differences between applied and pure mathematics and provides extensive history of mixed mathematics. Argues that applied mathematics should be taught allowing for speculative mathematics, which involves breaking down a given problem into simpler parts until one arrives at first principles. (ASK)

Principles underlying the design of "The Number Race", an adaptive computer game for remediation of dyscalculia

Directory of Open Access Journals (Sweden)

Cohen Laurent

2006-05-01

Full Text Available Abstract Background Adaptive game software has been successful in remediation of dyslexia. Here we describe the cognitive and algorithmic principles underlying the development of similar software for dyscalculia. Our software is based on current understanding of the cerebral representation of number and the hypotheses that dyscalculia is due to a "core deficit" in number sense or in the link between number sense and symbolic number representations. Methods "The Number Race" software trains children on an entertaining numerical comparison task, by presenting problems adapted to the performance level of the individual child. We report full mathematical specifications of the algorithm used, which relies on an internal model of the child's knowledge in a multidimensional "learning space" consisting of three difficulty dimensions: numerical distance, response deadline, and conceptual complexity (from non-symbolic numerosity processing to increasingly complex symbolic operations. Results The performance of the software was evaluated both by mathematical simulations and by five weeks of use by nine children with mathematical learning difficulties. The results indicate that the software adapts well to varying levels of initial knowledge and learning speeds. Feedback from children, parents and teachers was positive. A companion article 1 describes the evolution of number sense and arithmetic scores before and after training. Conclusion The software, open-source and freely available online, is designed for learning disabled children aged 5–8, and may also be useful for general instruction of normal preschool children. The learning algorithm reported is highly general, and may be applied in other domains.

Perceived mathematical ability under challenge: a longitudinal perspective on sex segregation among STEM degree fields.

Science.gov (United States)

Nix, Samantha; Perez-Felkner, Lara; Thomas, Kirby

2015-01-01

Students' perceptions of their mathematics ability vary by gender and seem to influence science, technology, engineering, and mathematics (STEM) degree choice. Related, students' perceptions during academic difficulty are increasingly studied in educational psychology, suggesting a link between such perceptions and task persistence. Despite interest in examining the gender disparities in STEM, these concepts have not been considered in tandem. In this manuscript, we investigate how perceived ability under challenge-in particular in mathematics domains-influences entry into the most sex-segregated and mathematics-intensive undergraduate degrees: physics, engineering, mathematics, and computer science (PEMC). Using nationally representative Education Longitudinal Study of 2002 (ELS) data, we estimate the influence of perceived ability under challenging conditions on advanced high school science course taking, selection of an intended STEM major, and specific major type 2 years after high school. Demonstrating the importance of specificity when discussing how gender influences STEM career pathways, the intersecting effects of gender and perceived ability under mathematics challenge were distinct for each scientific major category. Perceived ability under challenge in secondary school varied by gender, and was highly predictive of selecting PEMC and health sciences majors. Notably, women's 12th grade perceptions of their ability under mathematics challenge increased their probability of selecting PEMC majors over and above biology. In addition, gender moderated the effect of growth mindset on students' selection of health science majors. Perceptions of ability under challenge in general and verbal domains also influenced retention in and declaration of certain STEM majors. The implications of these results are discussed, with particular attention to access to advanced scientific coursework in high school and interventions aimed at enhancing young women's perceptions of

Perceived mathematical ability under challenge: a longitudinal perspective on sex segregation among STEM degree fields

Science.gov (United States)

Nix, Samantha; Perez-Felkner, Lara; Thomas, Kirby

2015-01-01

Students' perceptions of their mathematics ability vary by gender and seem to influence science, technology, engineering, and mathematics (STEM) degree choice. Related, students' perceptions during academic difficulty are increasingly studied in educational psychology, suggesting a link between such perceptions and task persistence. Despite interest in examining the gender disparities in STEM, these concepts have not been considered in tandem. In this manuscript, we investigate how perceived ability under challenge—in particular in mathematics domains—influences entry into the most sex-segregated and mathematics-intensive undergraduate degrees: physics, engineering, mathematics, and computer science (PEMC). Using nationally representative Education Longitudinal Study of 2002 (ELS) data, we estimate the influence of perceived ability under challenging conditions on advanced high school science course taking, selection of an intended STEM major, and specific major type 2 years after high school. Demonstrating the importance of specificity when discussing how gender influences STEM career pathways, the intersecting effects of gender and perceived ability under mathematics challenge were distinct for each scientific major category. Perceived ability under challenge in secondary school varied by gender, and was highly predictive of selecting PEMC and health sciences majors. Notably, women's 12th grade perceptions of their ability under mathematics challenge increased their probability of selecting PEMC majors over and above biology. In addition, gender moderated the effect of growth mindset on students' selection of health science majors. Perceptions of ability under challenge in general and verbal domains also influenced retention in and declaration of certain STEM majors. The implications of these results are discussed, with particular attention to access to advanced scientific coursework in high school and interventions aimed at enhancing young women

On the Dirichlet's Box Principle

Science.gov (United States)

Poon, Kin-Keung; Shiu, Wai-Chee

2008-01-01

In this note, we will focus on several applications on the Dirichlet's box principle in Discrete Mathematics lesson and number theory lesson. In addition, the main result is an innovative game on a triangular board developed by the authors. The game has been used in teaching and learning mathematics in Discrete Mathematics and some high schools in…

STEM Gives Meaning to Mathematics

Science.gov (United States)

Hefty, Lukas J.

2015-01-01

The National Council of Teachers of Mathematics' (NCTM's) "Principles and Standards for School Mathematics" (2000) outlines fi ve Process Standards that are essential for developing deep understanding of mathematics: (1) Problem Solving; (2) Reasoning and Proof; (3) Communication; (4) Connections; and (5) Representation. The Common Core…

Mathematics Teaching as Problem Solving: A Framework for Studying Teacher Metacognition Underlying Instructional Practice in Mathematics.

Science.gov (United States)

Artzt, Alice F.; Armour-Thomas, Eleanor

1998-01-01

Uses a "teaching as problem solving" perspective to examine the components of metacognition underlying the instructional practice of seven experienced and seven beginning secondary-school mathematics teachers. Data analysis of observations, lesson plans, videotapes, and audiotapes of structured interviews suggests that the metacognition of…

Mathematical foundations of biomechanics.

Science.gov (United States)

Niederer, Peter F

2010-01-01

The aim of biomechanics is the analysis of the structure and function of humans, animals, and plants by means of the methods of mechanics. Its foundations are in particular embedded in mathematics, physics, and informatics. Due to the inherent multidisciplinary character deriving from its aim, biomechanics has numerous connections and overlapping areas with biology, biochemistry, physiology, and pathophysiology, along with clinical medicine, so its range is enormously wide. This treatise is mainly meant to serve as an introduction and overview for readers and students who intend to acquire a basic understanding of the mathematical principles and mechanics that constitute the foundation of biomechanics; accordingly, its contents are limited to basic theoretical principles of general validity and long-range significance. Selected examples are included that are representative for the problems treated in biomechanics. Although ultimate mathematical generality is not in the foreground, an attempt is made to derive the theory from basic principles. A concise and systematic formulation is thereby intended with the aim that the reader is provided with a working knowledge. It is assumed that he or she is familiar with the principles of calculus, vector analysis, and linear algebra.

Unified reduction principle for the evolution of mutation, migration, and recombination

Science.gov (United States)

Altenberg, Lee; Liberman, Uri; Feldman, Marcus W.

2017-01-01

Modifier-gene models for the evolution of genetic information transmission between generations of organisms exhibit the reduction principle: Selection favors reduction in the rate of variation production in populations near equilibrium under a balance of constant viability selection and variation production. Whereas this outcome has been proven for a variety of genetic models, it has not been proven in general for multiallelic genetic models of mutation, migration, and recombination modification with arbitrary linkage between the modifier and major genes under viability selection. We show that the reduction principle holds for all of these cases by developing a unifying mathematical framework that characterizes all of these evolutionary models. PMID:28265103

Design principles and developmental mechanisms underlying retinal mosaics.

Science.gov (United States)

Reese, Benjamin E; Keeley, Patrick W

2015-08-01

Most structures within the central nervous system (CNS) are composed of different types of neuron that vary in both number and morphology, but relatively little is known about the interplay between these two features, i.e. about the population dynamics of a given cell type. How such arrays of neurons are distributed within a structure, and how they differentiate their dendrites relative to each other, are issues that have recently drawn attention in the invertebrate nervous system, where the genetic and molecular underpinnings of these organizing principles are being revealed in exquisite detail. The retina is one of the few locations where these principles have been extensively studied in the vertebrate CNS, indeed, where the design principles of 'mosaic regularity' and 'uniformity of coverage' were first explicitly defined, quantified, and related to each other. Recent studies have revealed a number of genes that influence the formation of these histotypical features in the retina, including homologues of those invertebrate genes, although close inspection reveals that they do not always mediate comparable developmental processes nor elucidate fundamental design principles. The present review considers just how pervasive these features of 'mosaic regularity' and 'uniform dendritic coverage' are within the mammalian retina, discussing the means by which such features can be assessed in the mature and developing nervous system and examining the limitations associated with those assessments. We then address the extent to which these two design principles co-exist within different populations of neurons, and how they are achieved during development. Finally, we consider the neural phenotypes obtained in mutant nervous systems, to address whether a prospective gene of interest underlies those very design principles. © 2014 The Authors. Biological Reviews © 2014 Cambridge Philosophical Society.

Mathematical Optimization Algorithm for Minimizing the Cost Function of GHG Emission in AS/RS Using Positive Selection Based Clonal Selection Principle

Science.gov (United States)

Mahalakshmi; Murugesan, R.

2018-04-01

This paper regards with the minimization of total cost of Greenhouse Gas (GHG) efficiency in Automated Storage and Retrieval System (AS/RS). A mathematical model is constructed based on tax cost, penalty cost and discount cost of GHG emission of AS/RS. A two stage algorithm namely positive selection based clonal selection principle (PSBCSP) is used to find the optimal solution of the constructed model. In the first stage positive selection principle is used to reduce the search space of the optimal solution by fixing a threshold value. In the later stage clonal selection principle is used to generate best solutions. The obtained results are compared with other existing algorithms in the literature, which shows that the proposed algorithm yields a better result compared to others.

Extremum principles for irreversible processes

International Nuclear Information System (INIS)

Hillert, M.; Agren, J.

2006-01-01

Hamilton's extremum principle is a powerful mathematical tool in classical mechanics. Onsager's extremum principle may play a similar role in irreversible thermodynamics and may also become a valuable tool. His principle may formally be regarded as a principle of maximum rate of entropy production but does not have a clear physical interpretation. Prigogine's principle of minimum rate of entropy production has a physical interpretation when it applies, but is not strictly valid except for a very special case

Mathematical principles of signal processing Fourier and wavelet analysis

CERN Document Server

Brémaud, Pierre

2002-01-01

Fourier analysis is one of the most useful tools in many applied sciences. The recent developments of wavelet analysis indicates that in spite of its long history and well-established applications, the field is still one of active research. This text bridges the gap between engineering and mathematics, providing a rigorously mathematical introduction of Fourier analysis, wavelet analysis and related mathematical methods, while emphasizing their uses in signal processing and other applications in communications engineering. The interplay between Fourier series and Fourier transforms is at the heart of signal processing, which is couched most naturally in terms of the Dirac delta function and Lebesgue integrals. The exposition is organized into four parts. The first is a discussion of one-dimensional Fourier theory, including the classical results on convergence and the Poisson sum formula. The second part is devoted to the mathematical foundations of signal processing - sampling, filtering, digital signal proc...

The development of mathematics

CERN Document Server

Bell, Eric Temple

1945-01-01

""This important book . . . presents a broad account of the part played by mathematics in the evolution of civilization, describing clearly the main principles, methods, and theories of mathematics that have survived from about 4000 BC to 1940.""― BooklistIn this time-honored study, one of the 20th century's foremost scholars and interpreters of the history and meaning of mathematics masterfully outlines the development of its leading ideas, and clearly explains the mathematics involved in each. According to the author, a professor of mathematics at the California Institute of Technology from

Mathematics for the environment

CERN Document Server

Walter, Martin

2011-01-01

MATHEMATICS IS CONNECTED TO EVERYTHING ELSEEarth's Climate and Some Basic Principles One of the Greatest Crimes of the 20th Century Feedback Edison's Algorithm: Listening to Nature's Feedback Fuzzy Logic, Filters, the Bigger Picture Principle Consequences of the Crime: Suburbia's Topology A Toxic Consequence of the Crime Hubbert's Peak and the End of Cheap Oil Resource Wars: Oil and Water The CO2 Greenhouse Law of Svante ArrheniusEconomic Instability: Ongoing Causes Necessary Conditions for Economic Success The Mathematical Structure of Ponzi Schemes Dishonest Assessment of Risk One Reason Why

Perceived Mathematical Ability under Challenge: A Longitudinal Perspective on Sex Segregation among STEM Degree Fields

Directory of Open Access Journals (Sweden)

Samantha eNix

2015-06-01

Full Text Available Students’ perceptions of their mathematics ability vary by gender and seem to influence science, technology, engineering, and math (STEM degree choice. Related, students’ perceptions during academic difficulty are increasingly studied in educational psychology, suggesting a link between such perceptions and task persistence. Despite interest in examining the gender disparities in STEM, these concepts have not been considered in tandem. We investigate how perceived ability under challenge – in particular in mathematics domains – influences entry into the most sex-segregated and mathematics-intensive undergraduate degrees: physics, engineering, mathematics, and computer science (PEMC. Using nationally representative Education Longitudinal Study of 2002 (ELS data, we estimate the influence of perceived ability under challenging conditions on advanced high school science course taking, selection of an intended STEM major, and specific major type two years after high school. Demonstrating the importance of specificity when discussing how gender influences STEM career pathways, the intersecting effects of gender and perceived ability under mathematics challenge were distinct for each scientific major category. Perceived ability under challenge in secondary school varied by gender, and was highly predictive of selecting PEMC and health sciences majors. Notably, women’s 12th grade perceptions of their ability under mathematics challenge increased the probability that they would select PEMC majors, increasing women's probability of selecting PEMC over and above biology. In addition, gender moderated the effect of growth mindset on students’ selection of health science majors. The implications of these results are discussed, with particular attention to access to advanced scientific coursework in high school and interventions aimed at enhancing young women’s perceptions of their ability to facilitate their pathways to scientific degrees.

Success and failure in school mathematics: effects of instruction and school environment.

Science.gov (United States)

Reusser, K

2000-01-01

Given the stubborn phenomenon of many children's serious difficulties and failure in mathematical learning, the hypothesis of developmental delay, or neurocognitively based deficiency should be complemented by further explanantions of children's weaknesses and substandard performance in mathematics. One obvious explanantion is that schooling and instruction for low ability children and for children with special needs is often inadequate. The present contribution examines selected research on mathematics learning under a cognitive instructional (didactical) perspective. Constructivist learning theory, the rooting of meaningful learning in concrete modeling activities, the balancing of understanding and practice in mathematics instruction, diagnostic and adaptive teaching, computer-assisted instruction, and the role of nonmathematical stumbling-blocks are discussed as principles and factors of effective mathematics learning and teaching.

A software complex intended for constructing applied models and meta-models on the basis of mathematical programming principles

Directory of Open Access Journals (Sweden)

Михаил Юрьевич Чернышов

2013-12-01

Full Text Available A software complex (SC elaborated by the authors on the basis of the language LMPL and representing a software tool intended for synthesis of applied software models and meta-models constructed on the basis of mathematical programming (MP principles is described. LMPL provides for an explicit form of declarative representation of MP-models, presumes automatic constructing and transformation of models and the capability of adding external software packages. The following software versions of the SC have been implemented: 1 a SC intended for representing the process of choosing an optimal hydroelectric power plant model (on the principles of meta-modeling and 2 a SC intended for representing the logic-sense relations between the models of a set of discourse formations in the discourse meta-model.

Discrete Mathematics

DEFF Research Database (Denmark)

Sørensen, John Aasted

2011-01-01

; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics...... to new problems. Relations and functions: Define a product set; define and apply equivalence relations; construct and apply functions. Apply these concepts to new problems. Natural numbers and induction: Define the natural numbers; apply the principle of induction to verify a selection of properties...

Towards a simple mathematical theory of citation distributions.

Science.gov (United States)

Katchanov, Yurij L

2015-01-01

The paper is written with the assumption that the purpose of a mathematical theory of citation is to explain bibliometric regularities at the level of mathematical formalism. A mathematical formalism is proposed for the appearance of power law distributions in social citation systems. The principal contributions of this paper are an axiomatic characterization of citation distributions in terms of the Ekeland variational principle and a mathematical exploration of the power law nature of citation distributions. Apart from its inherent value in providing a better understanding of the mathematical underpinnings of bibliometric models, such an approach can be used to derive a citation distribution from first principles.

Gauge theories under incorporation of a generalized uncertainty principle

International Nuclear Information System (INIS)

Kober, Martin

2010-01-01

There is considered an extension of gauge theories according to the assumption of a generalized uncertainty principle which implies a minimal length scale. A modification of the usual uncertainty principle implies an extended shape of matter field equations like the Dirac equation. If there is postulated invariance of such a generalized field equation under local gauge transformations, the usual covariant derivative containing the gauge potential has to be replaced by a generalized covariant derivative. This leads to a generalized interaction between the matter field and the gauge field as well as to an additional self-interaction of the gauge field. Since the existence of a minimal length scale seems to be a necessary assumption of any consistent quantum theory of gravity, the gauge principle is a constitutive ingredient of the standard model, and even gravity can be described as gauge theory of local translations or Lorentz transformations, the presented extension of gauge theories appears as a very important consideration.

Demand of Insurance under the Cost-of-Capital Premium Calculation Principle

Directory of Open Access Journals (Sweden)

Michael Merz

2014-06-01

Full Text Available We study the optimal insurance design problem. This is a risk sharing problem between an insured and an insurer. The main novelty in this paper is that we study this optimization problem under a risk-adjusted premium calculation principle for the insurance cover. This risk-adjusted premium calculation principle uses the cost-of-capital approach as it is suggested (and used by the regulator and the insurance industry.

Using Mathematical Model in Audit of Compliance with the Principle of Continuity of Company Activities

Directory of Open Access Journals (Sweden)

S. V.

2017-05-01

Full Text Available The article’s objective is to study and systematize the existing methods to assess the risk of termination of company activities, and to develop a methodology for applications of factor models in assessment of this risk. Criteria to be met by the method selected for audit are highlighted. The extensive review of the most widespread methods for predicting the financial performance at company level is made: computation of current ratio, computation of acid text ratio, Beaver model, two-factor model of Altman, five-factor model of Altman, Springate model. The study aimed at further development and adaptation of the existing mathematical models for audit of compliance with the principle of continuity of company activities is made. The review of the above mentioned methods and analysis of their applications in the procedures involved in assessing the risk of inadequate use of the assumption on the continuity of company activities in preparing financial reports by company managers allows for the conclusion that the best way to obtain auditor evidence based on mathematical coefficients reflecting the declining economic performance of a company is to apply the methods for computation of current ratio and acid text ratio, and Springate model.

Exploring mathematics problem-solving and proof

CERN Document Server

Grieser, Daniel

2018-01-01

Have you ever faced a mathematical problem and had no idea how to approach it? Or perhaps you had an idea but got stuck halfway through? This book guides you in developing your creativity, as it takes you on a voyage of discovery into mathematics. Readers will not only learn strategies for solving problems and logical reasoning, but they will also learn about the importance of proofs and various proof techniques. Other topics covered include recursion, mathematical induction, graphs, counting, elementary number theory, and the pigeonhole, extremal and invariance principles. Designed to help students make the transition from secondary school to university level, this book provides readers with a refreshing look at mathematics and deep insights into universal principles that are valuable far beyond the scope of this book. Aimed especially at undergraduate and secondary school students as well as teachers, this book will appeal to anyone interested in mathematics. Only basic secondary school mathematics is requi...

CULTUROLOGICAL APPROACH AS METHODOLOGICAL BASIS OF MATHEMATICAL EDUCATION

Directory of Open Access Journals (Sweden)

Ye. A. Perminov

2017-01-01

Full Text Available Introduction. Today, in the era of a mathematization of science and total expansion of digital technologies, mass mathematical education becomes a necessary part of culture of every person. However, there are some serious obstacles to formation and development of general mathematical culture: insufficient understanding of its importance by society and the state; fragmentary-clipconsciousness, emerging among representatives of the younger generation under the influence of the Internet, and preventing formation of a complete picture of the modern world; traditional system of disjointed subjects and courses in school, secondary vocational and high school mathematics education; non-cognitive (automatic transferring of the approaches, principles, technologies and techniques into training which are not specific in order to master a course. Development of sociological, axiological and especially culturological aspects of mathematical methodology is required for the solution of the urgent problems of methodology in mathematical education.The aim of the publication is to discuss methodological aspects of culturological approach realization in mathematical education.Methodology and research methods. The theoretical scientific methods of the present article involve analysis and synthesis of the content of philosophical, mathematical, pedagogical, methodological literature and normative documents; comparative, culturological and logical types of analysis of mathematical education; systematic, competence-based, practice-oriented and personal-activity metho-dological approaches were used to understand the concept of mathematical education.Results and scientific novelty. The practicability and leading role of culturological approach to promoting mathematical knowledge is proved from historical, philosophical and pedagogical positions. It is stated that objective conceptualization of progressive ideas and new methods of mathematical science and mathematical

Higher engineering mathematics

CERN Document Server

John Bird

2014-01-01

A practical introduction to the core mathematics principles required at higher engineering levelJohn Bird's approach to mathematics, based on numerous worked examples and interactive problems, is ideal for vocational students that require an advanced textbook.Theory is kept to a minimum, with the emphasis firmly placed on problem-solving skills, making this a thoroughly practical introduction to the advanced mathematics engineering that students need to master. The extensive and thorough topic coverage makes this an ideal text for upper level vocational courses. Now in

Mathematical modeling

CERN Document Server

Eck, Christof; Knabner, Peter

2017-01-01

Mathematical models are the decisive tool to explain and predict phenomena in the natural and engineering sciences. With this book readers will learn to derive mathematical models which help to understand real world phenomena. At the same time a wealth of important examples for the abstract concepts treated in the curriculum of mathematics degrees are given. An essential feature of this book is that mathematical structures are used as an ordering principle and not the fields of application. Methods from linear algebra, analysis and the theory of ordinary and partial differential equations are thoroughly introduced and applied in the modeling process. Examples of applications in the fields electrical networks, chemical reaction dynamics, population dynamics, fluid dynamics, elasticity theory and crystal growth are treated comprehensively.

Middle-School Mathematics Teachers' Beliefs in NCTM's Vision

Science.gov (United States)

Perrin, John Robert

2012-01-01

This study examined the extent to which seventh- and eighth-grade mathematics teachers are aware of National Council of Teachers of Mathematics (NCTM) standards documents, Curriculum and Evaluation Standards for School Mathematics and Principles and Standards for School Mathematics and agree with NCTM's vision of school mathematics as expressed in…

Mathematical card magic fifty-two new effects

CERN Document Server

Mulcahy, Colm

2013-01-01

Mathematical card effects offer both beginning and experienced magicians an opportunity to entertain with a minimum of props. Featuring mostly original creations, Mathematical Card Magic: Fifty-Two New Effects presents an entertaining look at new mathematically based card tricks. Each chapter contains four card effects, generally starting with simple applications of a particular mathematical principle and ending with more complex ones. Practice a handful of the introductory effects and, in no time, you'll establish your reputation as a "mathemagician." Delve a little deeper into each chapter and the mathematics gets more interesting. The author explains the mathematics as needed in an easy-to-follow way. He also provides additional details, background, and suggestions for further explorations.Suitable for recreational math buffs and amateur card lovers or as a text in a first-year seminar, this color book offers a diverse collection of new mathemagic principles and effects.

"Take Me to the Mathematical Circle!"

OpenAIRE

Veilande, Ingrida

2012-01-01

Preparing the students for various mathematical contests are the key goals of mathematical circles in Latvian schools. The reason why mathematical circles for students of primary schools are organised rather seldom is that problem sets of Olympiads are mainly created for students of 5th to 12th grades. The young participants of circles have to be introduced with the basic principles of Olimpiads mathematics too.

Mathematics revealed

CERN Document Server

Berman, Elizabeth

1979-01-01

Mathematics Revealed focuses on the principles, processes, operations, and exercises in mathematics.The book first offers information on whole numbers, fractions, and decimals and percents. Discussions focus on measuring length, percent, decimals, numbers as products, addition and subtraction of fractions, mixed numbers and ratios, division of fractions, addition, subtraction, multiplication, and division. The text then examines positive and negative numbers and powers and computation. Topics include division and averages, multiplication, ratios, and measurements, scientific notation and estim

Mathematical logic foundations for information science

CERN Document Server

Li, Wei

2010-01-01

This book presents the basic principles and formal calculus of mathematical logic. It covers core contents, extensions and developments of classical mathematical logic, and it offers formal proofs and concrete examples for all theoretical results.

A new computing principle

International Nuclear Information System (INIS)

Fatmi, H.A.; Resconi, G.

1988-01-01

In 1954 while reviewing the theory of communication and cybernetics the late Professor Dennis Gabor presented a new mathematical principle for the design of advanced computers. During our work on these computers it was found that the Gabor formulation can be further advanced to include more recent developments in Lie algebras and geometric probability, giving rise to a new computing principle

Magical mathematics the mathematical ideas that animate great magic tricks

CERN Document Server

Diaconis, Persi

2012-01-01

Magical Mathematics reveals the secrets of amazing, fun-to-perform card tricks--and the profound mathematical ideas behind them--that will astound even the most accomplished magician. Persi Diaconis and Ron Graham provide easy, step-by-step instructions for each trick, explaining how to set up the effect and offering tips on what to say and do while performing it. Each card trick introduces a new mathematical idea, and varying the tricks in turn takes readers to the very threshold of today's mathematical knowledge. For example, the Gilbreath Principle--a fantastic effect where the cards remain in control despite being shuffled--is found to share an intimate connection with the Mandelbrot set. Other card tricks link to the mathematical secrets of combinatorics, graph theory, number theory, topology, the Riemann hypothesis, and even Fermat's last theorem.

Minimalism as a Guiding Principle: Linking Mathematical Learning to Everyday Knowledge

Science.gov (United States)

Inoue, Noriyuki

2008-01-01

Studies report that students often fail to consider familiar aspects of reality in solving mathematical word problems. This study explored how different features of mathematical problems influence the way that undergraduate students employ realistic considerations in mathematical problem solving. Incorporating familiar contents in the word…

The Constructivist Mathematics Classroom

Science.gov (United States)

Jones, Karrie; Jones, Jennifer L.; Vermette, Paul J.

2010-01-01

By examining how people learn, the educational theories of Dewey, Piaget, Vygotsky and Bruner can be synthesized to give this set of core Constructivist principles. Principles of effective mathematics teaching: (1) allows learning that is "active" and "reflective". Students are required to transfer key concepts to new situations; (2) allows…

Hobbes on natural philosophy as "True Physics" and mixed mathematics.

Science.gov (United States)

Adams, Marcus P

2016-04-01

In this paper, I offer an alternative account of the relationship of Hobbesian geometry to natural philosophy by arguing that mixed mathematics provided Hobbes with a model for thinking about it. In mixed mathematics, one may borrow causal principles from one science and use them in another science without there being a deductive relationship between those two sciences. Natural philosophy for Hobbes is mixed because an explanation may combine observations from experience (the 'that') with causal principles from geometry (the 'why'). My argument shows that Hobbesian natural philosophy relies upon suppositions that bodies plausibly behave according to these borrowed causal principles from geometry, acknowledging that bodies in the world may not actually behave this way. First, I consider Hobbes's relation to Aristotelian mixed mathematics and to Isaac Barrow's broadening of mixed mathematics in Mathematical Lectures (1683). I show that for Hobbes maker's knowledge from geometry provides the 'why' in mixed-mathematical explanations. Next, I examine two explanations from De corpore Part IV: (1) the explanation of sense in De corpore 25.1-2; and (2) the explanation of the swelling of parts of the body when they become warm in De corpore 27.3. In both explanations, I show Hobbes borrowing and citing geometrical principles and mixing these principles with appeals to experience. Copyright © 2015 Elsevier Ltd. All rights reserved.

Principles to Actions: Mathematics Programs as the Core for Student Learning

Science.gov (United States)

Brahier, Daniel; Leinwand, Steve; Huniker, DeAnn

2014-01-01

The National Council of Teachers of Mathematics (NCTM) launched the "standards-based" education movement in North America in 1989 with the release of "Curriculum and Evaluation Standards for School Mathematics," an unprecedented action to promote systemic improvement in mathematics education. Now, twenty-five years later, the…

Nonlinear optics principles and applications

CERN Document Server

Li, Chunfei

2017-01-01

This book reflects the latest advances in nonlinear optics. Besides the simple, strict mathematical deduction, it also discusses the experimental verification and possible future applications, such as the all-optical switches. It consistently uses the practical unit system throughout. It employs simple physical images, such as "light waves" and "photons" to systematically explain the main principles of nonlinear optical effects. It uses the first-order nonlinear wave equation in frequency domain under the condition of “slowly varying amplitude approximation" and the classical model of the interaction between the light and electric dipole. At the same time, it also uses the rate equations based on the energy-level transition of particle systems excited by photons and the energy and momentum conservation principles to explain the nonlinear optical phenomenon. The book is intended for researchers, engineers and graduate students in the field of the optics, optoelectronics, fiber communication, information tech...

A New Principle in Physics: the Principle 'Finiteness', and Some Consequences

International Nuclear Information System (INIS)

Sternlieb, Abraham

2010-01-01

In this paper I propose a new principle in physics: the principle of 'finiteness'. It stems from the definition of physics as a science that deals (among other things) with measurable dimensional physical quantities. Since measurement results, including their errors, are always finite, the principle of finiteness postulates that the mathematical formulation of 'legitimate' laws of physics should prevent exactly zero or infinite solutions. Some consequences of the principle of finiteness are discussed, in general, and then more specifically in the fields of special relativity, quantum mechanics, and quantum gravity. The consequences are derived independently of any other theory or principle in physics. I propose 'finiteness' as a postulate (like the constancy of the speed of light in vacuum, 'c'), as opposed to a notion whose validity has to be corroborated by, or derived theoretically or experimentally from other facts, theories, or principles.

MATHEMATICS TEACHER: MOVING KNOWLEDGE UNDER FORMATION

Directory of Open Access Journals (Sweden)

Roselaine Machado Albernaz

2010-07-01

Full Text Available This essay approaches the Mathematics teacher forming process from his/her experiences in the school system and the set of knowledge that hashistorical, philosophical and politically constituted him/her. This set of knowledge not only comprises academic knowledge, but also involves the subjective effects of knowledge it incorporates. Starting from a tale, the character, called ‘researcher-teacher’, conducts the text throughout questions about the forming processes of teachers of such a particular subject as Mathematics. The character seems to have an “interrogative something” which is peculiar to us, teachers, concerned about our disciplinary field. Having the objective of problematize the formation and knowledge of our character, her ways of being, thinking and perceiving, we intend to question, with and through her, the new requirements that have been demanded towards Mathematics teachers and the set of knowledge that constitute her, the way she is, her way of acting and taking  position in the school universe. The proposed essay seeks for an articulation between the fields of Art, Philosophy, Science and Education. It speaks about the intriguing school world, but not least, the ways we think to treat the forming process of Mathematics teachers from a set of logical, subjective and sensitive knowledge.  Key words: Forming process of teachers; mathematics; aesthetic experience; philosophy of difference.

Variational principles

CERN Document Server

Moiseiwitsch, B L

2004-01-01

This graduate-level text's primary objective is to demonstrate the expression of the equations of the various branches of mathematical physics in the succinct and elegant form of variational principles (and thereby illuminate their interrelationship). Its related intentions are to show how variational principles may be employed to determine the discrete eigenvalues for stationary state problems and to illustrate how to find the values of quantities (such as the phase shifts) that arise in the theory of scattering. Chapter-by-chapter treatment consists of analytical dynamics; optics, wave mecha

Under-Threes' Mathematical Learning--Teachers' Perspectives

Science.gov (United States)

Franzén, Karin

2014-01-01

This project highlights preschool teachers' views of toddlers' learning in mathematics. The Swedish national curriculum covers even the youngest children who are 1-3?years old. Interesting questions are thus: what should mathematics be for this age group and how should preschool teachers work with maths to achieve the curriculum objectives? Data…

Heisenberg's principle of uncertainty and the uncertainty relations

International Nuclear Information System (INIS)

Redei, Miklos

1987-01-01

The usual verbal form of the Heisenberg uncertainty principle and the usual mathematical formulation (the so-called uncertainty theorem) are not equivalent. The meaning of the concept 'uncertainty' is not unambiguous and different interpretations are used in the literature. Recently a renewed interest has appeared to reinterpret and reformulate the precise meaning of Heisenberg's principle and to find adequate mathematical form. The suggested new theorems are surveyed and critically analyzed. (D.Gy.) 20 refs

Vital directions for mathematics education research

CERN Document Server

Leatham, Keith R

2013-01-01

In this book, experts discuss vital issues in mathematics education and what they see as viable directions for research in mathematics education to address them. Their recommendations take the form of overarching principles and ideas that cut across the field.

Mathematical model for the technological system of working a thin coal bed

Energy Technology Data Exchange (ETDEWEB)

Isayev, V V

1979-01-01

The principle for constructing a mathematical model of working a thin coal bed using the adaptation criterion is examined. Intersecting parameters of the medium and the unit are presented. Based on these parameters, dependences are presented for the adaptation criterion and its maximization. A general mathematical model is presented for the technological system of unmanned extraction of a thin bed D/sub 5/ under conditions of the mine ''Dolinskaya'' of the Karaganda Basin. The work results can be used to plan technological systems for working thin coal beds.

Precautionary principles: a jurisdiction-free framework for decision-making under risk.

Science.gov (United States)

Ricci, Paolo F; Cox, Louis A; MacDonald, Thomas R

2004-12-01

Fundamental principles of precaution are legal maxims that ask for preventive actions, perhaps as contingent interim measures while relevant information about causality and harm remains unavailable, to minimize the societal impact of potentially severe or irreversible outcomes. Such principles do not explain how to make choices or how to identify what is protective when incomplete and inconsistent scientific evidence of causation characterizes the potential hazards. Rather, they entrust lower jurisdictions, such as agencies or authorities, to make current decisions while recognizing that future information can contradict the scientific basis that supported the initial decision. After reviewing and synthesizing national and international legal aspects of precautionary principles, this paper addresses the key question: How can society manage potentially severe, irreversible or serious environmental outcomes when variability, uncertainty, and limited causal knowledge characterize their decision-making? A decision-analytic solution is outlined that focuses on risky decisions and accounts for prior states of information and scientific beliefs that can be updated as subsequent information becomes available. As a practical and established approach to causal reasoning and decision-making under risk, inherent to precautionary decision-making, these (Bayesian) methods help decision-makers and stakeholders because they formally account for probabilistic outcomes, new information, and are consistent and replicable. Rational choice of an action from among various alternatives--defined as a choice that makes preferred consequences more likely--requires accounting for costs, benefits and the change in risks associated with each candidate action. Decisions under any form of the precautionary principle reviewed must account for the contingent nature of scientific information, creating a link to the decision-analytic principle of expected value of information (VOI), to show the

Principles of Uncertainty

CERN Document Server

Kadane, Joseph B

2011-01-01

An intuitive and mathematical introduction to subjective probability and Bayesian statistics. An accessible, comprehensive guide to the theory of Bayesian statistics, Principles of Uncertainty presents the subjective Bayesian approach, which has played a pivotal role in game theory, economics, and the recent boom in Markov Chain Monte Carlo methods. Both rigorous and friendly, the book contains: Introductory chapters examining each new concept or assumption Just-in-time mathematics -- the presentation of ideas just before they are applied Summary and exercises at the end of each chapter Discus

Elaboration of the recently proposed test of Pauli's principle under strong interactions

International Nuclear Information System (INIS)

Ktorides, C.N.; Myung, H.C.; Santilli, R.M.

1980-01-01

The primary objective of this paper is to stimulate the experimental verification of the validity or invalidity of Pauli's principle under strong interactions. We first outline the most relevant steps in the evolution of the notion of particle. The spin as well as other intrinsic characteristics of extended, massive, particles under electromagnetic interactions at large distances might be subjected to a mutation under additional strong interactions at distances smaller than their charge radius. These dynamical effects can apparently be conjectured to account for the nonpointlike nature of the particles, their necessary state of penetration to activate the strong interactions, and the consequential emergence of broader forces which imply the breaking of the SU(2)-spin symmetry. We study a characterization of the mutated value of the spin via the transition from the associative enveloping algebra of SU(2) to a nonassociative Lie-admissible form. The departure from the original associative product then becomes directly representative of the breaking of the SU(2)-spin symmetry, the presence of forces more general than those derivable from a potential, and the mutated value of the spin. In turn, such a departure of the spin from conventional quantum-mechanical values implies the inapplicability of Pauli's exclusion principle under strong interactions, because, according to this hypothesis, particles that are fermions under long-range electromagnetic interactions are no longer fermions under these broader, short-range, forces. In nuclear physics possible deviations from Pauli's exclusion principle can at most be very small. These experimental data establish that, for the nuclei considered, nucleons are in a partial state of penetration of their charge volumes although of small statistical character

La Meme Chose: How Mathematics Can Explain the Thinking of Children and the Thinking of Children Can Illuminate Mathematical Philosophy

Science.gov (United States)

Cable, John

2014-01-01

This article offers a new interpretation of Piaget's decanting experiments, employing the mathematical notion of equivalence instead of conservation. Some reference is made to Piaget's theories and to his educational legacy, but the focus in on certain of the experiments. The key to the new analysis is the abstraction principle, which has been formally enunciated in mathematical philosophy but has universal application. It becomes necessary to identity fluid objects (both configured and unconfigured) and configured and unconfigured sets-of-objects. Issues emerge regarding the conflict between philosophic realism and anti-realism, including constructivism. Questions are asked concerning mathematics and mathematical philosophy, particularly over the nature of sets, the wisdom of the axiomatic method and aspects of the abstraction principle itself.

A survey of variational principles

International Nuclear Information System (INIS)

Lewins, J.D.

1993-01-01

In this article survey of variational principles has been given. Variational principles play a significant role in mathematical theory with emphasis on the physical aspects. There are two principals used i.e. to represent the equation of the system in a succinct way and to enable a particular computation in the system to be carried out with greater accuracy. The survey of variational principles has ranged widely from its starting point in the Lagrange multiplier to optimisation principles. In an age of digital computation, these classic methods can be adapted to improve such calculations. We emphasize particularly the advantage of basic finite element methods on variational principles. (A.B.)

Pre-Service Teachers' Developing Conceptions about the Nature and Pedagogy of Mathematical Modeling in the Context of a Mathematical Modeling Course

Science.gov (United States)

Cetinkaya, Bulent; Kertil, Mahmut; Erbas, Ayhan Kursat; Korkmaz, Himmet; Alacaci, Cengiz; Cakiroglu, Erdinc

2016-01-01

Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers' developing conceptions about (a) the nature of mathematical modeling in simulations of "real life" problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike…

Mathematical Optimiation in Economics

CERN Document Server

De Finetti, Bruno

2011-01-01

Preface by B. de Finetti.- G.Th. Guilbaud: Les equilibres dans les modeles economiques.-H.W. Kuhn: Locational problems and mathematical programming.- M. Morishima: The multi-sectoral theory of economic growth.- B. Martos, J. Kornai: Experiments in Hungary with industry-wide and economy wide programming.- A. Prekopa: Probability distribution problems concerning stochastic programming problems.- R. Frisch: General principles and mathematical techniques of macroeconomic programming.

The Search for Underlying Principles of Health Impact Assessment: Progress and Prospects; Comment on “Investigating Underlying Principles to Guide Health Impact Assessment”

Directory of Open Access Journals (Sweden)

Mirko S. Winkler

2014-07-01

Full Text Available Health Impact Assessment (HIA is a relatively young field of endeavour, and hence, future progress will depend on the planning, implementation and rigorous evaluation of additional HIAs of projects, programmes and policies the world over. In the June 2014 issue of the International Journal of Health Policy and Management, Fakhri and colleagues investigated underlying principles of HIA through a comprehensive review of the literature and expert consultation. With an emphasis on the Islamic Republic of Iran, the authors identified multiple issues that are relevant for guiding HIA practice. At the same time, the study unravelled current shortcomings in the understanding and definition of HIA principles and best practice at national, regional, and global levels. In this commentary we scrutinise the research presented, highlight strengths and limitations, and discuss the findings in the context of other recent attempts to guide HIA.

Mathematics for the liberal arts

CERN Document Server

Bindner, Donald; Hemmeter, Joe

2014-01-01

Presents a clear bridge between mathematics and the liberal arts Mathematics for the Liberal Arts provides a comprehensible and precise introduction to modern mathematics intertwined with the history of mathematical discoveries. The book discusses mathematical ideas in the context of the unfolding story of human thought and highlights the application of mathematics in everyday life. Divided into two parts, Mathematics for the Liberal Arts first traces the history of mathematics from the ancient world to the Middle Ages, then moves on to the Renaissance and finishes with the development of modern mathematics. In the second part, the book explores major topics of calculus and number theory, including problem-solving techniques and real-world applications. This book emphasizes learning through doing, presents a practical approach, and features: A detailed explanation of why mathematical principles are true and how the mathematical processes workNumerous figures and diagrams as well as hundreds of worked example...

There is more variation within than across domains: an interview with Paul A. Kirschner about applying cognitive psychology based instructional design principles in mathematics teaching and learning

NARCIS (Netherlands)

Kirschner, Paul A.; Verschaffel, Lieven; Star, Jon; Van Dooren, Wim

2018-01-01

In this interview we asked Paul A. Kirschner about his comments and reflections regarding the idea to apply cognitive psychology-based instructional design principles to mathematics education and some related issues. With a main focus on cognitive psychology, educational psychology, educational

Theory of group extension, Shubnikov-Curie principle and phase transformations

International Nuclear Information System (INIS)

Koptsik, V.A.; Talis, A.L.

1983-01-01

It is shown, that the generalized Curie principle (GCP) is the principle of nondecreasing abstract symmetry under structural transformations in (quasi) isolated physical systems. Asymmetry of such systems at any structural level is compensated by their symmetrization at another one, transformation of the old and appearance of qualitatively new symmetries. A corresponding situation is preserved also at the description level (mathematical simulation) of physical systems. Structural levels of substance arrangement and forms of connection between them, reflected by the Shubnikov-Curie (SCP) and GCP are inexhaustible. With the discovery of new structural levels and new forms of relations between them can be discovered and new forms of SCP, which can not be exhausted in the given work

Scattering theory in quantum mechanics. Physical principles and mathematical methods

International Nuclear Information System (INIS)

Amrein, W.O.; Jauch, J.M.; Sinha, K.B.

1977-01-01

A contemporary approach is given to the classical topics of physics. The purpose is to explain the basic physical concepts of quantum scattering theory, to develop the necessary mathematical tools for their description, to display the interrelation between the three methods (the Schroedinger equation solutions, stationary scattering theory, and time dependence) to derive the properties of various quantities of physical interest with mathematically rigorous methods

Connection of Scattering Principles: A Visual and Mathematical Tour

Science.gov (United States)

Broggini, Filippo; Snieder, Roel

2012-01-01

Inverse scattering, Green's function reconstruction, focusing, imaging and the optical theorem are subjects usually studied as separate problems in different research areas. We show a physical connection between the principles because the equations that rule these "scattering principles" have a similar functional form. We first lead the reader…

Complexity-Based Modeling of Scientific Capital: An Outline of Mathematical Theory

Directory of Open Access Journals (Sweden)

Yurij L. Katchanov

2014-01-01

measuring and assessing the accumulated recognition and the specific scientific power. The concept of scientific capital developed by Bourdieu is used in international social science research to explain a set of scholarly properties and practices. Mathematical modeling is applied as a lens through which the scientific capital is addressed. The principal contribution of this paper is an axiomatic characterization of scientific capital in terms of natural axioms. The application of the axiomatic method to scientific capital reveals novel insights into problem still not covered by mathematical modeling. Proposed model embraces the interrelations between separate sociological variables, providing a unified sociological view of science. Suggested microvariational principle is based upon postulate, which affirms that (under suitable conditions the observed state of the agent in scientific field maximizes scientific capital. Its value can be roughly imagined as a volume of social differences. According to the considered macrovariational principle, the actual state of scientific field makes so-called energy functional (which is associated with the distribution of scientific capital minimal.

The Mathematical Foundations of 3D Compton Scatter Emission Imaging

Directory of Open Access Journals (Sweden)

T. T. Truong

2007-01-01

Full Text Available The mathematical principles of tomographic imaging using detected (unscattered X- or gamma-rays are based on the two-dimensional Radon transform and many of its variants. In this paper, we show that two new generalizations, called conical Radon transforms, are related to three-dimensional imaging processes based on detected Compton scattered radiation. The first class of conical Radon transform has been introduced recently to support imaging principles of collimated detector systems. The second class is new and is closely related to the Compton camera imaging principles and invertible under special conditions. As they are poised to play a major role in future designs of biomedical imaging systems, we present an account of their most important properties which may be relevant for active researchers in the field.

COLLEGE STUDENTS’ PERCEPTIONS OF LEARNING MATHEMATICS AND USING COMPUTERS

OpenAIRE

Gok, Tolga

2016-01-01

Mathematics isthe key course to interpret the science and nature. A positive attitude shouldbe improved by learners to comprehend the logic of mathematics. However, mostof the research indicated that they were not interested in learning andstudying mathematics. Instead of understanding the basic principles, manystudents preferred to use sophisticated software packages or graphingcalculators for solving mathematics problems. Thus, these tools prevent theimprovement of their mathematical skills...

Mathematical physiology

CERN Document Server

Sneyd, James

2009-01-01

There has been a long history of interaction between mathematics and physiology. This book looks in detail at a wide selection of mathematical models in physiology, showing how physiological problems can be formulated and studied mathematically, and how such models give rise to interesting and challenging mathematical questions. With its coverage of many recent models it gives an overview of the field, while many older models are also discussed, to put the modern work in context. In this second edition the coverage of basic principles has been expanded to include such topics as stochastic differential equations, Markov models and Gibbs free energy, and the selection of models has also been expanded to include some of the basic models of fluid transport, respiration/perfusion, blood diseases, molecular motors, smooth muscle, neuroendrocine cells, the baroreceptor loop, turboglomerular oscillations, blood clotting and the retina. Owing to this extensive coverage, the second edition is published in two volumes. ...

Children's Understanding of the Addition/Subtraction Complement Principle

Science.gov (United States)

Torbeyns, Joke; Peters, Greet; De Smedt, Bert; Ghesquière, Pol; Verschaffel, Lieven

2016-01-01

Background: In the last decades, children's understanding of mathematical principles has become an important research topic. Different from the commutativity and inversion principles, only few studies have focused on children's understanding of the addition/subtraction complement principle (if a - b = c, then c + b = a), mainly relying on verbal…

Principles of electrodynamics

CERN Document Server

Schwartz, Melvin

1972-01-01

This advanced undergraduate- and graduate-level text by the 1988 Nobel Prize winner establishes the subject's mathematical background, reviews the principles of electrostatics, then introduces Einstein's special theory of relativity and applies it throughout the book in topics ranging from Gauss' theorem and Coulomb's law to electric and magnetic susceptibility.

Mathematical Modeling of Extinction of Inhomogeneous Populations

Science.gov (United States)

Karev, G.P.; Kareva, I.

2016-01-01

Mathematical models of population extinction have a variety of applications in such areas as ecology, paleontology and conservation biology. Here we propose and investigate two types of sub-exponential models of population extinction. Unlike the more traditional exponential models, the life duration of sub-exponential models is finite. In the first model, the population is assumed to be composed clones that are independent from each other. In the second model, we assume that the size of the population as a whole decreases according to the sub-exponential equation. We then investigate the “unobserved heterogeneity”, i.e. the underlying inhomogeneous population model, and calculate the distribution of frequencies of clones for both models. We show that the dynamics of frequencies in the first model is governed by the principle of minimum of Tsallis information loss. In the second model, the notion of “internal population time” is proposed; with respect to the internal time, the dynamics of frequencies is governed by the principle of minimum of Shannon information loss. The results of this analysis show that the principle of minimum of information loss is the underlying law for the evolution of a broad class of models of population extinction. Finally, we propose a possible application of this modeling framework to mechanisms underlying time perception. PMID:27090117

The principle of least action history and physics

CERN Document Server

Rojo, Alberto

2018-01-01

The principle of least action originates in the idea that, if nature has a purpose, it should follow a minimum or critical path. This simple principle, and its variants and generalizations, applies to optics, mechanics, electromagnetism, relativity, and quantum mechanics, and provides an essential guide to understanding the beauty of physics. This unique text provides an accessible introduction to the action principle across these various fields of physics, and examines its history and fundamental role in science. It includes - with varying levels of mathematical sophistication - explanations from historical sources, discussion of classic papers, and original worked examples. The result is a story that is understandable to those with a modest mathematical background, as well as to researchers and students in physics and the history of physics.

Principles of Fourier analysis

CERN Document Server

Howell, Kenneth B

2001-01-01

Fourier analysis is one of the most useful and widely employed sets of tools for the engineer, the scientist, and the applied mathematician. As such, students and practitioners in these disciplines need a practical and mathematically solid introduction to its principles. They need straightforward verifications of its results and formulas, and they need clear indications of the limitations of those results and formulas.Principles of Fourier Analysis furnishes all this and more. It provides a comprehensive overview of the mathematical theory of Fourier analysis, including the development of Fourier series, "classical" Fourier transforms, generalized Fourier transforms and analysis, and the discrete theory. Much of the author''s development is strikingly different from typical presentations. His approach to defining the classical Fourier transform results in a much cleaner, more coherent theory that leads naturally to a starting point for the generalized theory. He also introduces a new generalized theory based ...

Crossroads in the History of Mathematics and Mathematics Education. The Montana Mathematics Enthusiast: Monograph Series in Mathematics Education

Science.gov (United States)

Sriraman, Bharath, Ed.

2012-01-01

The interaction of the history of mathematics and mathematics education has long been construed as an esoteric area of inquiry. Much of the research done in this realm has been under the auspices of the history and pedagogy of mathematics group. However there is little systematization or consolidation of the existing literature aimed at…

Mathematics Teachers at Work: Connecting Curriculum Materials and Classroom Instruction. Studies in Mathematical Thinking and Learning Series

Science.gov (United States)

Remillard, Janine T., Ed.; Herbel-Eisenmann, Beth A., Ed.; Lloyd, Gwendolyn M., Ed.

2011-01-01

This book compiles and synthesizes existing research on teachers' use of mathematics curriculum materials and the impact of curriculum materials on teaching and teachers, with a particular emphasis on--but not restricted to--those materials developed in the 1990s in response to the NCTM's Principles and Standards for School Mathematics. Despite…

There Is More Variation "within" than "across" Domains: An Interview with Paul A. Kirschner about Applying Cognitive Psychology-Based Instructional Design Principles in Mathematics Teaching and Learning

Science.gov (United States)

Kirschner, Paul A.; Verschaffel, Lieven; Star, Jon; Van Dooren, Wim

2017-01-01

In this interview we asked Paul A. Kirschner about his comments and reflections regarding the idea to apply cognitive psychology-based instructional design principles to mathematics education and some related issues. With a main focus on cognitive psychology, educational psychology, educational technology and instructional design, this…

How Bob Barker Would (Probably) Teach Discrete Mathematics

Science.gov (United States)

Urness, Timothy

2010-01-01

This article proposes a discrete mathematics course in which games from "The Price Is Right" are used to engage students in a deeper, practical study of discrete mathematics. The games themselves are not the focus of the course; rather, the mathematical principles of the games give motivation for the concepts being taught. The game examples are…

A mathematical framework for modelling and evaluating natural gas pipeline networks under hydrogen injection

Energy Technology Data Exchange (ETDEWEB)

Tabkhi, F.; Azzaro-Pantel, C.; Pibouleau, L.; Domenech, S. [Laboratoire de Genie Chimique, UMR5503 CNRS/INP/UPS, 5 rue Paulin Talabot F-BP1301, 31106 Toulouse Cedex 1 (France)

2008-11-15

This article presents the framework of a mathematical formulation for modelling and evaluating natural gas pipeline networks under hydrogen injection. The model development is based on gas transport through pipelines and compressors which compensate for the pressure drops by implying mainly the mass and energy balances on the basic elements of the network. The model was initially implemented for natural gas transport and the principle of extension for hydrogen-natural gas mixtures is presented. The objective is the treatment of the classical fuel minimizing problem in compressor stations. The optimization procedure has been formulated by means of a nonlinear technique within the General Algebraic Modelling System (GAMS) environment. This work deals with the adaptation of the current transmission networks of natural gas to the transport of hydrogen-natural gas mixtures. More precisely, the quantitative amount of hydrogen that can be added to natural gas can be determined. The studied pipeline network, initially proposed in [1] is revisited here for the case of hydrogen-natural gas mixtures. Typical quantitative results are presented, showing that the addition of hydrogen to natural gas decreases significantly the transmitted power: the maximum fraction of hydrogen that can be added to natural gas is around 6 mass% for this example. (author)

Promoting Mathematical Connections Using Three-Dimensional Manipulatives

Science.gov (United States)

Safi, Farshid; Desai, Siddhi

2017-01-01

"Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014) gives teachers access to an insightful, research-informed framework that outlines ways to promote reasoning and sense making. Specifically, as students transition on their mathematical journey through middle school and beyond, their knowledge and use of…

A course of higher mathematics

CERN Document Server

Smirnov, Vladimir Ivanovich; Lohwater, A J

1964-01-01

A Course of Higher Mathematics, I: Elementary Calculus is a five-volume course of higher mathematics used by mathematicians, physicists, and engineers in the U.S.S.R. This volume deals with calculus and principles of mathematical analysis including topics on functions of single and multiple variables. The functional relationships, theory of limits, and the concept of differentiation, whether as theories and applications, are discussed. This book also examines the applications of differential calculus to geometry. For example, the equations to determine the differential of arc or the parameter

VEDIC MATHEMATICS

Directory of Open Access Journals (Sweden)

Sead Rešić

2015-09-01

Full Text Available It is very difficult to motivate students when it comes to a school subject like Mathematics. Teachers spend a lot of time trying to find something that will arouse interest in students. It is particularly difficult to find materials that are motivating enough for students that they eagerly wait for the next lesson. One of the solutions may be found in Vedic Mathematics. Traditional methods of teaching Mathematics create fear of this otherwise interesting subject in the majority of students. Fear increases failure. Often the traditional, conventional mathematical methods consist of very long lessons which are difficult to understand. Vedic Mathematics is an ancient system that is very flexible and encourages the development of intuition and innovation. It is a mental calculating tool that does not require a calculator because the calculator is embedded in each of us. Starting from the above problems of fear and failure in Mathematics, the goal of this paper is to do research with the control and the experimental group and to compare the test results. Two tests should be done for each of the groups. The control group would do the tests in the conventional way. The experimental group would do the first test in a conventional manner and then be subjected to different treatment, that is to say, be taught on the basis of Vedic Mathematics. After that, the second group would do the second test according to the principles of Vedic Mathematics. Expectations are that after short lectures on Vedic mathematics results of the experimental group would improve and that students will show greater interest in Mathematics.

Methods and models in mathematical biology deterministic and stochastic approaches

CERN Document Server

Müller, Johannes

2015-01-01

This book developed from classes in mathematical biology taught by the authors over several years at the Technische Universität München. The main themes are modeling principles, mathematical principles for the analysis of these models, and model-based analysis of data. The key topics of modern biomathematics are covered: ecology, epidemiology, biochemistry, regulatory networks, neuronal networks, and population genetics. A variety of mathematical methods are introduced, ranging from ordinary and partial differential equations to stochastic graph theory and  branching processes. A special emphasis is placed on the interplay between stochastic and deterministic models.

Mathematical structures of natural intelligence

CERN Document Server

Neuman, Yair

2017-01-01

This book uncovers mathematical structures underlying natural intelligence and applies category theory as a modeling language for understanding human cognition, giving readers new insights into the nature of human thought. In this context, the book explores various topics and questions, such as the human representation of the number system, why our counting ability is different from that which is evident among non-human organisms, and why the idea of zero is so difficult to grasp. The book is organized into three parts: the first introduces the general reason for studying general structures underlying the human mind; the second part introduces category theory as a modeling language and use it for exposing the deep and fascinating structures underlying human cognition; and the third applies the general principles and ideas of the first two parts to reaching a better understanding of challenging aspects of the human mind such as our understanding of the number system, the metaphorical nature of our thinking and...

Mathematical foundations of thermodynamics

CERN Document Server

Giles, R; Stark, M; Ulam, S

2013-01-01

Mathematical Foundations of Thermodynamics details the core concepts of the mathematical principles employed in thermodynamics. The book discusses the topics in a way that physical meanings are assigned to the theoretical terms. The coverage of the text includes the mechanical systems and adiabatic processes; topological considerations; and equilibrium states and potentials. The book also covers Galilean thermodynamics; symmetry in thermodynamics; and special relativistic thermodynamics. The book will be of great interest to practitioners and researchers of disciplines that deal with thermodyn

Microgravity: A Teacher's Guide with Activities in Science, Mathematics, and Technology

Science.gov (United States)

Rogers, Melissa J.B.; Vogt, Gregory L.; Wargo, Michael J.

1997-01-01

Microgravity is the subject of this teacher's guide. This publication identifies the underlying mathematics, physics, and technology principles that apply to microgravity. The topics included in this publication are: 1) Microgravity Science Primer; 2) The Microgravity Environment of Orbiting Spacecraft; 3) Biotechnology; 4) Combustion Science; 5) Fluid Physics; 6) Fundamental Physics; and 7) Materials Science; 8) Microgravity Research and Exploration; and 9) Microgravity Science Space Flights. This publication also contains a glossary of selected terms.

What Makes Mathematics Manipulatives Effective? Lessons From Cognitive Science and Montessori Education

Directory of Open Access Journals (Sweden)

Elida V. Laski

2015-06-01

Full Text Available Manipulatives are ubiquitous in early childhood classrooms; yet, findings regarding their efficacy for learning mathematics concepts are inconsistent. In this article, we present four general principles that have emerged from cognitive science about ways to ensure that manipulatives promote learning when used with young children. We also describe how Montessori instruction offers a concrete example of the application of these principles in practice, which may, in turn, explain the high levels of mathematics achievement among children who attend Montessori programs during early childhood. The general principles and concrete examples presented in this article should help early childhood programs maximize the benefits of using manipulatives for developmentally appropriate mathematics instruction.

Cognitive Play and Mathematical Learning in Computer Microworlds.

Science.gov (United States)

Steffe, Leslie P.; Wiegel, Heide G.

1994-01-01

Uses the constructivist principle of active learning to explore the possibly essential elements in transforming a cognitive play activity into mathematical activity. Suggests that for such transformation to occur, cognitive play activity must involve operations of intelligence that, yield situations of mathematical schemes. Illustrates the…

Bridging CAGD knowledge into CAD/CG applications: Mathematical theories as stepping stones of innovations

Science.gov (United States)

Gobithaasan, R. U.; Miura, Kenjiro T.; Hassan, Mohamad Nor

2014-07-01

Computer Aided Geometric Design (CAGD) which surpasses the underlying theories of Computer Aided Design (CAD) and Computer Graphics (CG) has been taught in a number of Malaysian universities under the umbrella of Mathematical Sciences' faculty/department. On the other hand, CAD/CG is taught either under the Engineering or Computer Science Faculty. Even though CAGD researchers/educators/students (denoted as contributors) have been enriching this field of study by means of article/journal publication, many fail to convert the idea into constructive innovation due to the gap that occurs between CAGD contributors and practitioners (engineers/product/designers/architects/artists). This paper addresses this issue by advocating a number of technologies that can be used to transform CAGD contributors into innovators where immediate impact in terms of practical application can be experienced by the CAD/CG practitioners. The underlying principle of solving this issue is twofold. First would be to expose the CAGD contributors on ways to turn mathematical ideas into plug-ins and second is to impart relevant CAGD theories to CAD/CG to practitioners. Both cases are discussed in detail and the final section shows examples to illustrate the importance of turning mathematical knowledge into innovations.

On the constitutive laws of 1-D, two-fluid, two-phase flow models: possible mathematical forms, restrictions resulting from basic principles

International Nuclear Information System (INIS)

Boure, J.A.

1981-01-01

From both the theoretical and the practical points of view, the problem of constitutive laws is part and parcel of the modeling problem. In particular, the necessity to restore in the model, through topological laws, some of the information lost during the usual averaging process is emphasized. A new void fraction topological law is proposed. The limitations of the current assumption of uniform pressure within each phase in any cross section are also illustrated. The importance of proximity effects (neighborhood and history effects, related to characteristic lengths and times) is brought out. It results in the importance of the mathematical form of the constitutive laws. Possible mathematical forms for the transfer laws are reviewed. The last part of the paper is devoted to some restrictions, which are imposed on the transfer terms because of some basic principles: Indifference to Galilean changes of frame and to some changes of origins, second law of thermodynamics and hypothesis of local thermodynamic equilibrium, closure constraints. Practical recommendations are formulated

Mathematics, anxiety, and the brain.

Science.gov (United States)

Moustafa, Ahmed A; Tindle, Richard; Ansari, Zaheda; Doyle, Margery J; Hewedi, Doaa H; Eissa, Abeer

2017-05-24

Given that achievement in learning mathematics at school correlates with work and social achievements, it is important to understand the cognitive processes underlying abilities to learn mathematics efficiently as well as reasons underlying the occurrence of mathematics anxiety (i.e. feelings of tension and fear upon facing mathematical problems or numbers) among certain individuals. Over the last two decades, many studies have shown that learning mathematical and numerical concepts relies on many cognitive processes, including working memory, spatial skills, and linguistic abilities. In this review, we discuss the relationship between mathematical learning and cognitive processes as well as the neural substrates underlying successful mathematical learning and problem solving. More importantly, we also discuss the relationship between these cognitive processes, mathematics anxiety, and mathematics learning disabilities (dyscalculia). Our review shows that mathematical cognition relies on a complex brain network, and dysfunction to different segments of this network leads to varying manifestations of mathematical learning disabilities.

Quasi-static responses and variational principles in gradient plasticity

Science.gov (United States)

Nguyen, Quoc-Son

2016-12-01

Gradient models have been much discussed in the literature for the study of time-dependent or time-independent processes such as visco-plasticity, plasticity and damage. This paper is devoted to the theory of Standard Gradient Plasticity at small strain. A general and consistent mathematical description available for common time-independent behaviours is presented. Our attention is focussed on the derivation of general results such as the description of the governing equations for the global response and the derivation of related variational principles in terms of the energy and the dissipation potentials. It is shown that the quasi-static response under a loading path is a solution of an evolution variational inequality as in classical plasticity. The rate problem and the rate minimum principle are revisited. A time-discretization by the implicit scheme of the evolution equation leads to the increment problem. An increment of the response associated with a load increment is a solution of a variational inequality and satisfies also a minimum principle if the energy potential is convex. The increment minimum principle deals with stables solutions of the variational inequality. Some numerical methods are discussed in view of the numerical simulation of the quasi-static response.

On Weak Markov's Principle

DEFF Research Database (Denmark)

Kohlenbach, Ulrich Wilhelm

2002-01-01

We show that the so-called weak Markov's principle (WMP) which states that every pseudo-positive real number is positive is underivable in E-HA + AC. Since allows one to formalize (atl eastl arge parts of) Bishop's constructive mathematics, this makes it unlikely that WMP can be proved within...... the framework of Bishop-style mathematics (which has been open for about 20 years). The underivability even holds if the ine.ective schema of full comprehension (in all types) for negated formulas (in particular for -free formulas) is added, which allows one to derive the law of excluded middle...

The concept of training in community network for teaching algebraic structures that are aimed to create a methodical competence of a mathematics teacher

Directory of Open Access Journals (Sweden)

Ирина Викторовна Кузнецова

2012-12-01

Full Text Available The paper proposes the concept of learning activities in online communities for teaching algebraic structures of the future teachers of mathematics, including a set of theoretical and methodological positions, laws, principles, factors, and pedagogical conditions of its implementation. Work is executed with support of the Russian fund of basic researches under the initiative project № 11-07-00733 «The Hypertext information retrieval thesaurus» a science Meta language» (structure; mathematical, linguistic and program maintenance; sections linguistics, mathematics, economy».

Turbulence and the Stabilization Principle

Science.gov (United States)

Zak, Michail

2010-01-01

Further results of research, reported in several previous NASA Tech Briefs articles, were obtained on a mathematical formalism for postinstability motions of a dynamical system characterized by exponential divergences of trajectories leading to chaos (including turbulence). To recapitulate: Fictitious control forces are introduced to couple the dynamical equations with a Liouville equation that describes the evolution of the probability density of errors in initial conditions. These forces create a powerful terminal attractor in probability space that corresponds to occurrence of a target trajectory with probability one. The effect in ordinary perceived three-dimensional space is to suppress exponential divergences of neighboring trajectories without affecting the target trajectory. Con sequently, the postinstability motion is represented by a set of functions describing the evolution of such statistical quantities as expectations and higher moments, and this representation is stable. The previously reported findings are analyzed from the perspective of the authors Stabilization Principle, according to which (1) stability is recognized as an attribute of mathematical formalism rather than of underlying physics and (2) a dynamical system that appears unstable when modeled by differentiable functions only can be rendered stable by modifying the dynamical equations to incorporate intrinsic stochasticity.

Concepts of mathematical modeling

CERN Document Server

Meyer, Walter J

2004-01-01

Appropriate for undergraduate and graduate students, this text features independent sections that illustrate the most important principles of mathematical modeling, a variety of applications, and classic models. Students with a solid background in calculus and some knowledge of probability and matrix theory will find the material entirely accessible. The range of subjects includes topics from the physical, biological, and social sciences, as well as those of operations research. Discussions cover related mathematical tools and the historical eras from which the applications are drawn. Each sec

Microhydrodynamics principles and selected applications

CERN Document Server

Kim, Sangtae; Brenner, Howard

1991-01-01

Microhydrodynamics: Principles and Selected Applications presents analytical and numerical methods for describing motion of small particles suspended in viscous fluids. The text first covers the fundamental principles of low-Reynolds-number flow, including the governing equations and fundamental theorems; the dynamics of a single particle in a flow field; and hydrodynamic interactions between suspended particles. Next, the book deals with the advances in the mathematical and computational aspects of viscous particulate flows that point to innovations for large-scale simulations on parallel co

Aesthetics of interdisciplinarity art and mathematics

CERN Document Server

Lähdesmäki, Tuuli

2017-01-01

This anthology fosters an interdisciplinary dialogue between the mathematical and artistic approaches in the field where mathematical and artistic thinking and practice merge. The articles included highlight the most significant current ideas and phenomena, providing a multifaceted and extensive snapshot of the field and indicating how interdisciplinary approaches are applied in the research of various cultural and artistic phenomena. The discussions are related, for example, to the fields of aesthetics, anthropology, art history, art theory, artistic practice, cultural studies, ethno-mathematics, geometry, mathematics, new physics, philosophy, physics, study of visual illusions, and symmetry studies. Further, the book introduces a new concept: the interdisciplinary aesthetics of mathematical art, which the editors use to explain the manifold nature of the aesthetic principles intertwined in these discussions.

Discrete maximum principle for the P1 - P0 weak Galerkin finite element approximations

Science.gov (United States)

Wang, Junping; Ye, Xiu; Zhai, Qilong; Zhang, Ran

2018-06-01

This paper presents two discrete maximum principles (DMP) for the numerical solution of second order elliptic equations arising from the weak Galerkin finite element method. The results are established by assuming an h-acute angle condition for the underlying finite element triangulations. The mathematical theory is based on the well-known De Giorgi technique adapted in the finite element context. Some numerical results are reported to validate the theory of DMP.

Mathematical modeling a chemical engineer's perspective

CERN Document Server

Rutherford, Aris

1999-01-01

Mathematical modeling is the art and craft of building a system of equations that is both sufficiently complex to do justice to physical reality and sufficiently simple to give real insight into the situation. Mathematical Modeling: A Chemical Engineer's Perspective provides an elementary introduction to the craft by one of the century's most distinguished practitioners.Though the book is written from a chemical engineering viewpoint, the principles and pitfalls are common to all mathematical modeling of physical systems. Seventeen of the author's frequently cited papers are reprinted to illus

A Call for Mathematics Education Colleagues and Stakeholders to Collaboratively Engage with NCTM: In Response to Martin's Commentary

Science.gov (United States)

Briars, Diane J.; Larson, Matt; Strutchens, Marilyn E.; Barnes, David

2015-01-01

In his commentary "The Collective Black and 'Principles to Actions,'" Martin (2015) offers a thought-provoking critique of "Principles to Actions: Ensuring Mathematical Success for All" (National Council of Teachers of Mathematics [NCTM], 2014). Martin (2015) states that the mathematics education community, in general, and the…

XI. The Relation between Mathematics and Physic

Indian Academy of Sciences (India)

of mathematics in this scheme is to represent the laws of motion by equations, and to obtain solutions ... What makes the theory of relativity so acceptable to physicists in spite of its going against the principle of simplicity is its great mathematical peauty. This is a quality ... The difference may be expressed concisely, but in·a ...

Mathematical writing

CERN Document Server

Vivaldi, Franco

2014-01-01

This book teaches the art of writing mathematics, an essential -and difficult- skill for any mathematics student.   The book begins with an informal introduction on basic writing principles and a review of the essential dictionary for mathematics. Writing techniques are developed gradually, from the small to the large: words, phrases, sentences, paragraphs, to end with short compositions. These may represent the introduction of a concept, the abstract of a presentation or the proof of a theorem. Along the way the student will learn how to establish a coherent notation, mix words and symbols effectively, write neat formulae, and structure a definition.   Some elements of logic and all common methods of proofs are featured, including various versions of induction and existence proofs. The book concludes with advice on specific aspects of thesis writing (choosing of a title, composing an abstract, compiling a bibliography) illustrated by large number of real-life examples. Many exercises are included; over 150...

Expert systems - basic principles and possible applications in nuclear energy

International Nuclear Information System (INIS)

Cain, D.G.; Schmidt, F.

1987-01-01

One of the primary goals of the application of mathematical methods and computational techniques in reactor physics is the effective and accurate solution of the neutron diffusion equation under various conditions. To reach this goal still requires much skill, experience, knowledge and imagination as can be seen from various contributions at this and other conferences. Experts are necessary. Will expert systems replace them. We shall discuss this question by describing the basic principles of problem solving by expert systems as compared to problem solving by mathematical and computational methods. From this we shall identify areas of possible applications of the new techniques in nuclear energy and develop some thoughts on present limitations. As a result we conclude that expert systems will not be able to replace experts as long as the experts use the systems to improve their own expertise

Mathematical modelling of unglazed solar collectors under extreme operating conditions

DEFF Research Database (Denmark)

Bunea, M.; Perers, Bengt; Eicher, S.

2015-01-01

average temperature levels at the evaporator. Simulation of these systems requires a collector model that can take into account operation at very low temperatures (below freezing) and under various weather conditions, particularly operation without solar irradiation.A solar collector mathematical model......Combined heat pumps and solar collectors got a renewed interest on the heating system market worldwide. Connected to the heat pump evaporator, unglazed solar collectors can considerably increase their efficiency, but they also raise the coefficient of performance of the heat pump with higher...... was found due to the condensation phenomenon and up to 40% due to frost under no solar irradiation. This work also points out the influence of the operating conditions on the collector's characteristics.Based on experiments carried out at a test facility, every heat flux on the absorber was separately...

Quantum Duality in Mathematical Finance

OpenAIRE

McCloud, Paul

2017-01-01

Mathematical finance explores the consistency relationships between the prices of securities imposed by elementary economic principles. Commonplace among these are replicability and the absence of arbitrage, both essentially algebraic constraints on the valuation map from a security to its price. The discussion is framed in terms of observables, the securities, and states, the linear and positive maps from security to price. Founded on the principles of replicability and the absence of arbitr...

Teaching geometrical principles to design students

Directory of Open Access Journals (Sweden)

Christoph Bartneck

2009-12-01

Full Text Available We propose a new method of teaching the principles of geometry to design students. The students focus on a field of design in which geometry is the design: tessellation. We review different approaches to geometry and the field of tessellation before we discuss the setup of the course. Instead of employing 2D drawing tools, such as Adobe Illustrator, the students define their tessellation in mathematical formulas, using the Mathematica software. This procedure enables them to understand the mathematical principles on which graphical tools, such as Illustrator are built upon. But we do not stop at a digital representation of their tessellation design we continue to cut their tessellations in Perspex. It moves the abstract concepts of math into the real world, so that the students can experience them directly, which provides a tremendous reward to the students.

History of Mathematics

DEFF Research Database (Denmark)

Hansen, Vagn Lundsgaard; Gray, Jeremy

Volume 1 in Theme on "History of Mathematics", in "Encyclopedia of Life Support Systems (EOLSS), developed under the auspices of the UNESCO.......Volume 1 in Theme on "History of Mathematics", in "Encyclopedia of Life Support Systems (EOLSS), developed under the auspices of the UNESCO....

An Embalse nuclear power plant basic principles simulator

International Nuclear Information System (INIS)

Fernandez, Oscar; Galdoz, Erwin; Flury, Celso; Fontanini, Horacio

1989-01-01

A nuclear power plant basic principles simulator is a package of programs that numerically solve the dynamic equations of the simulated plant. This kind of tools is mainly used in the first step of training of operational personnel, to allow mental representation of physical phenomena governing the plant. They are also used for students or professional training, and experienced operators can also improve there performance under abnormal operation situations using the simulator. For the Embalse nuclear power plant, mainly the thermohydraulic behaviour, is simulated. The mathematical model was adapted from MANUVR, a code developed at the Electric Systems and Control Department of the National Atomic Energy Commission (CNEA). (Author) [es

The development of a professional development intervention for mathematical problem-solving pedagogy in a localised context

Directory of Open Access Journals (Sweden)

Brantina Chirinda

2017-06-01

Full Text Available This article reports on the design and findings of the first iteration of a classroom-based design research project which endeavours to design a professional development intervention for teachers’ mathematical problem-solving pedagogy. The major outcome of this study is the generation of design principles that can be used by other researchers developing a professional development (PD intervention for mathematical problem-solving pedagogy. This study contributes to the mathematical problem-solving pedagogy and PD body of knowledge by working with teachers in an under-researched environment (an informal settlement in Gauteng, South Africa. In this iteration, two experienced Grade 9 mathematics teachers and their learners at a public secondary school in Gauteng, South Africa, participated in a 6-month intervention. Findings from the data are discussed in light of their implications for the next cycle and other PD studies.

The mathematics behind biological invasions

CERN Document Server

Lewis, Mark A; Potts, Jonathan R

2016-01-01

This book investigates the mathematical analysis of biological invasions. Unlike purely qualitative treatments of ecology, it draws on mathematical theory and methods, equipping the reader with sharp tools and rigorous methodology. Subjects include invasion dynamics, species interactions, population spread, long-distance dispersal, stochastic effects, risk analysis, and optimal responses to invaders. While based on the theory of dynamical systems, including partial differential equations and integrodifference equations, the book also draws on information theory, machine learning, Monte Carlo methods, optimal control, statistics, and stochastic processes. Applications to real biological invasions are included throughout. Ultimately, the book imparts a powerful principle: that by bringing ecology and mathematics together, researchers can uncover new understanding of, and effective response strategies to, biological invasions. It is suitable for graduate students and established researchers in mathematical ecolo...

Mathematical principles of road congestion pricing | Pienaar | ORiON

African Journals Online (AJOL)

This paper briefly considers the objectives of road congestion pricing and identies prereq-uisites to the successful application of such a pricing scheme. The paper is divided into two sections. In the rst section, a mathematical analysis of the constituents of an optimal road congestion price is oered. The eliminated inefficiency ...

Mathematics in the K-8 Classroom and Library

Science.gov (United States)

McKinney, Sueanne; Hinton, KaaVonia

2010-01-01

Two experts on education offer a rich and diverse selection of children's literature and teaching strategies for the K-8 mathematics classroom. To date, a vast majority of classrooms continue to fall short in the implementation and direction of NCTM Principles and Standards for School Mathematics (PSSM), in part because most of these classrooms…

Modelling Mathematical Reasoning in Physics Education

Science.gov (United States)

Uhden, Olaf; Karam, Ricardo; Pietrocola, Maurício; Pospiech, Gesche

2012-04-01

Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a tool for calculation which hinders a conceptual understanding of physical principles. However, the role of mathematics cannot be reduced to this technical aspect. Hence, instead of putting mathematics away we delve into the nature of physical science to reveal the strong conceptual relationship between mathematics and physics. Moreover, we suggest that, for both prospective teaching and further research, a focus on deeply exploring such interdependency can significantly improve the understanding of physics. To provide a suitable basis, we develop a new model which can be used for analysing different levels of mathematical reasoning within physics. It is also a guideline for shifting the attention from technical to structural mathematical skills while teaching physics. We demonstrate its applicability for analysing physical-mathematical reasoning processes with an example.

NATURAL-SCIENCE EDUCATION: SCIENTIFIC AND RELIGIOUS KNOWLEDGE CORRELATION IN THE VIEW OF A SYMMETRY PRINCIPLE. PART I. THE CONTENT OF A SYMMETRY PRINCIPLE

Directory of Open Access Journals (Sweden)

Vitaly L. Gapontsev

2015-01-01

Full Text Available The aim of the investigation is to disclose the content of a symmetry principle; to show system hierarchy of its forms, developed in the course of evolution of scientific knowledge, a society and development of individual consciousness of the person. Methods. Based on the analysis of existing scientific sources, comparison, synthesis and generalisation of its content, the role of symmetry was found out in the course of historical formation of scientific disciplines, arrangement of an empirical set of the facts and its subsequent registration in the form of strict deductive systems. Results. It is proved that the concept «a symmetry principle» (V. I. Vernadsky was the first to coin this concept into the circulation objectifies now the highest level of scientific knowledge. Following E. Vigner’s works, it is said that set of forms of symmetry determines structure of scientific knowledge. On the one hand, these forms have got a deep empirical basis and a close connection with figurative perception of the validity; on the other – they have strict mathematical definitions and generate particular principles of symmetry of Mathematics and Physics based on axiomatic constructions of exact disciplines. Stages of formation and development of a number of scientific disciplines such as Mathematics, Physics, Chemistry and Biology are compared; the peculiarities and common features of its evolution are designated. Invariants and corresponding symmetries in formation of individual consciousness of the person are allocated. Scientific novelty. Developing V. I. Vernadsky’s idea, as he used only the short characteristic of a general scientific principle of symmetry, the authors of the present study consider symmetry forms in various branches of knowledge as particular displays of the given principle. Based on the principle of symmetry as a set of symmetry forms, this principle allows the authors to take a fresh look at the decision of methodological

Reasoning and mathematical skills contribute to normatively superior decision making under risk: evidence from the game of dice task.

Science.gov (United States)

Pertl, Marie-Theres; Zamarian, Laura; Delazer, Margarete

2017-08-01

In this study, we assessed to what extent reasoning improves performance in decision making under risk in a laboratory gambling task (Game of Dice Task-Double, GDT-D). We also investigated to what degree individuals with above average mathematical competence decide better than those with average mathematical competence. Eighty-five participants performed the GDT-D and several numerical tasks. Forty-two individuals were asked to calculate the probabilities and the outcomes associated with the different options of the GDT-D before performing it. The other 43 individuals performed the GDT-D at the beginning of the test session. Both reasoning and mathematical competence had a positive effect on decision making. Different measures of mathematical competence correlated with advantageous performance in decision making. Results suggest that decision making under explicit risk conditions improves when individuals are encouraged to reflect about the contingencies of a decision situation. Interventions based on numerical reasoning may also be useful for patients with difficulties in decision making.

Intuitionism vs. classicism a mathematical attack on classical logic

CERN Document Server

Haverkamp, Nick

2015-01-01

In the early twentieth century, the Dutch mathematician L.E.J. Brouwer launched a powerful attack on the prevailing mathematical methods and theories. He developed a new kind of constructive mathematics, called intuitionism, which seems to allow for a rigorous refutation of widely accepted mathematical assumptions including fundamental principles of classical logic. Following an intense mathematical debate esp. in the 1920s, Brouwer's revolutionary criticism became a central philosophical concern in the 1970s, when Michael Dummett tried to substantiate it with meaning-theoretic considerations.

Mathematical methods of electromagnetic theory

CERN Document Server

Friedrichs, Kurt O

2014-01-01

This text provides a mathematically precise but intuitive introduction to classical electromagnetic theory and wave propagation, with a brief introduction to special relativity. While written in a distinctive, modern style, Friedrichs manages to convey the physical intuition and 19th century basis of the equations, with an emphasis on conservation laws. Particularly striking features of the book include: (a) a mathematically rigorous derivation of the interaction of electromagnetic waves with matter, (b) a straightforward explanation of how to use variational principles to solve problems in el

Science Modelling in Pre-Calculus: How to Make Mathematics Problems Contextually Meaningful

Science.gov (United States)

Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen

2011-01-01

"Use of mathematical representations to model and interpret physical phenomena and solve problems is one of the major teaching objectives in high school math curriculum" [National Council of Teachers of Mathematics (NCTM), "Principles and Standards for School Mathematics", NCTM, Reston, VA, 2000]. Commonly used pre-calculus textbooks provide a…

What is the uncertainty principle of non-relativistic quantum mechanics?

Science.gov (United States)

Riggs, Peter J.

2018-05-01

After more than ninety years of discussions over the uncertainty principle, there is still no universal agreement on what the principle states. The Robertson uncertainty relation (incorporating standard deviations) is given as the mathematical expression of the principle in most quantum mechanics textbooks. However, the uncertainty principle is not merely a statement of what any of the several uncertainty relations affirm. It is suggested that a better approach would be to present the uncertainty principle as a statement about the probability distributions of incompatible variables and the resulting restrictions on quantum states.

short communication mathematical modelling for magnetite

African Journals Online (AJOL)

Preferred Customer

The present research focuses to develop mathematical model for the ..... Staler, M.J. The Principle of Ion Exchange Technology, Butterworth-Heinemann: Boston; ... Don, W.G. Perry's Chemical Engineering Hand Book, 7th ed., McGraw-Hill:.

Exploring boot camps for ‘gatekeeper’ service courses in mathematics

Directory of Open Access Journals (Sweden)

Anita Campbell

2015-11-01

Full Text Available Pressure to increase the throughput of university students in ethical ways has been a catalyst for innovations to improve learning and student success. Student dropout occurs mostly in the first year of study and poor performance is a major contributor to dropout even if the underlying reason for the poor performance is not academic under-preparedness. This article discusses the design and implementation of a mathematics tutored reassessment programme (TRP or ‘boot camp’ to improve the pass rate of students writing supplementary examinations for first year engineering mathematics. Interviews with students and tutors suggest that the TRP cultivated positive affective changes in students. A notable result from this case study was that students who qualified for a reassessment with marks in the range 40%–44% (and who would not normally have been granted a supplementary examination outperformed students qualifying with marks of 45%–49%, for whom attendance at the TRP was optional. Theoretical motivations for five principles guiding the design of the TRP are discussed.

Market valuation in the framework of modern life insurance mathematics

Directory of Open Access Journals (Sweden)

Maja Petrač

2013-12-01

Full Text Available In the traditional actuarial life insurance mathematics, liabilities to beneficiaries (technical reserves are calculated based on conservative assumptions of mortality and interest rates. However, this approach was found to be incomplete since it does not contain the market component which has become essential due to the development of the financial market. Since about 80% of total liabilities of life insurance companies are made up of technical reserves, this issue has a major impact on the overall performance of insuran - ce companies. The introduction of financial components into the actuarial valuation resulted in actuarial mathematics using more and more the elements of financial mathematics thus creating new, modern life insurance mathematics. Using a simple example, this paper compares the traditional and market approaches to valuation. For this purpose, one of the principles of modern life insurance mathematics, the principle of equivalence, was observed. The above market approach to valuation, together with operational risk management, forms the basis of Solvency II Directive, the new legislative and regulatory framework for insurance and reinsurance companies in the European Union.

Financial mathematics

CERN Document Server

Jothi, A Lenin

2009-01-01

Financial services, particularly banking and insurance services is the prominent sector for the development of a nation. After the liberalisation of financial sector in India, the scope of getting career opportunities has been widened. It is heartening to note that various universities in India have introduced professional courses on banking and insurance. A new field of applied mathematics has come into prominence under the name of Financial Mathematics. Financial mathematics has attained much importance in the recent years because of the role played by mathematical concepts in decision - m

Foundational Concepts and Underlying Theories for Majors in "Biochemistry and Molecular Biology"

Science.gov (United States)

Tansey, John T.; Baird, Teaster, Jr.; Cox, Michael M.; Fox, Kristin M.; Knight, Jennifer; Sears, Duane; Bell, Ellis

2013-01-01

Over the past two years, through an NSF RCN UBE grant, the ASBMB has held regional workshops for faculty members and science educators from around the country that focused on identifying: 1) core principles of biochemistry and molecular biology, 2) essential concepts and underlying theories from physics, chemistry, and mathematics, and 3)…

The mathematics of elections and voting

CERN Document Server

Wallis, W D

2014-01-01

The Mathematics of Elections and Voting  takes an in-depth look at the mathematics in the context of voting and electoral systems, with focus on simple ballots, complex elections, fairness, approval voting, ties, fair and unfair voting, and manipulation techniques. The exposition opens with a sketch of the mathematics behind the various methods used in conducting elections. The reader is lead to a comprehensive picture of the theoretical background of mathematics and elections through an analysis of Condorcet’s Principle and Arrow’s Theorem of conditions in electoral fairness. Further detailed discussion of various related topics include: methods of manipulating the outcome of an election, amendments, and voting on small committees. In recent years, electoral theory has been introduced into lower-level mathematics courses, as a way to illustrate the role of mathematics in our everyday life.  Few books have studied voting and elections from a more formal mathematical viewpoint.  This text wi...

A refresher course in mathematics

CERN Document Server

Camm, F J

2003-01-01

Readers wishing to renew and extend their acquaintance with a variety of branches of mathematics will find this volume a practical companion. Geared toward those who already possess some familiarity with its subjects, the easy-to-follow explanations and straightforward tone make this book highly accessible. The contents are arranged logically and in order of difficulty: fractions, decimals, square and cube root, the metric system, algebra, quadratic and cubic equations, graphs, and the calculus are among the topics. Explanations of mathematical principles are followed by worked examples, and t

A history of Japanese mathematics

CERN Document Server

Smith, David E

2004-01-01

One of the first books to show Westerners the nature of Japanese mathematics, this survey highlights the leading features in the development of the wasan, the Japanese system of mathematics. Topics include the use of the soroban, or abacus; the application of sangi, or counting rods, to algebra; the discoveries of the 17th-century sage Seki Kowa; the yenri, or circle principle; the work of 18th-century geometer Ajima Chokuyen; and Wada Nei's contributions to the understanding of hypotrochoids. Unabridged republication of the classic 1914 edition. 74 figures. Index.

The quantum beat principles and applications of atomic clocks

CERN Document Server

Major, F

2007-01-01

This work attempts to convey a broad understanding of the physical principles underlying the workings of these quantum-based atomic clocks, with introductory chapters placing them in context with the early development of mechanical clocks and the introduction of electronic time-keeping as embodied in the quartz-controlled clocks. While the book makes no pretense at being a history of atomic clocks, it nevertheless takes a historical perspective in its treatment of the subject. Intended for nonspecialists with some knowledge of physics or engineering, The Quantum Beat covers a wide range of salient topics relevant to atomic clocks, treated in a broad intuitive manner with a minimum of mathematical formalism. Detailed descriptions are given of the design principles of the rubidium, cesium, hydrogen maser, and mercury ion standards; the revolutionary changes that the advent of the laser has made possible, such as laser cooling, optical pumping, the formation of "optical molasses," and the cesium "fountain" stand...

Mathematical modeling of pigment dispersion taking into account the full agglomerate particle size distribution

DEFF Research Database (Denmark)

Kiil, Søren

2017-01-01

The purpose of this work is to develop a mathematical model that can quantify the dispersion of pigments, with a focus on the mechanical breakage of pigment agglomerates. The underlying physical mechanism was assumed to be surface erosion of spherical pigment agglomerates. The full agglomerate pa.......g., in the development of novel dispersion principles and for analysis of dispersion failures. The general applicability of the model, beyond the three pigments considered, needs to be confirmed....

An Examination of the Instructional Practices of Mathematics Teachers in Urban Schools

Science.gov (United States)

McKinney, Sueanne E.; Chappell, Shannan; Berry, Robert Q.; Hickman, Bythella T.

2009-01-01

Researchers have given increased attention to the teaching and learning of mathematics since the release of the National Council of Teachers of Mathematics (NCTM)'s Principles and Standards for School Mathematics (PSSM). Despite the clear and focused goals, recommendations, and standards set by the NCTM (2000), a majority of classrooms continue to…

General Principles and Convention on Contracts for the International Sale of Goods (CISG – Uniformity under an Interpretation Umbrella?

Directory of Open Access Journals (Sweden)

Laura Lassila

2017-01-01

Full Text Available Globalization and digitalization of international sales creates needs to harmonize rules of international commercial contracts. The question is whether the harmonization should be done by binding rules or using soft law tools or through digitalization. In this article I argue on favor of harmonization through international contracts law rules’ international interpretation.The international interpretation principles used in this article are found from on Art. 7(1 of the Convention on Contracts for the International Sale of Goods (CISG which sets three interpretation rules: international character; promoting uniformity; and observance of good faith in international trade. These principles are not only principles of the CISG, but also principles commonly recognized in international commercial practice and also in domestic contract rules. I argue that by adopting an international interpretation umbrella – the meta-principle of international interpretation, cross-border contracts could be interpreted under the same principle no matter applicable substantial law. The meta-principle functions as an interpretation umbrella covering general principles and Articles of the CISG, general principles of international commercial contracts, Lex Mercatoria, and cross-border contract provision under national law.The outcomes points out that arbitral tribunals have interpreted general principles of the CISG and Lex Mercatoria in various ways. General principles and their application in case law is analyzed in connection with the Civil Code of the Russian Federation. Tribunals found that general principles of the CISG are applicable even if the CISG is not. It follows Art.’s 7(2 logic to promote international standard to cross-border contracts where the closes connection is international commercial practice rather than any national jurisdiction.

Special relativity from observer's mathematics point of view

Science.gov (United States)

Khots, Boris; Khots, Dmitriy

2015-09-01

When we create mathematical models for quantum theory of light we assume that the mathematical apparatus used in modeling, at least the simplest mathematical apparatus, is infallible. In particular, this relates to the use of "infinitely small" and "infinitely large" quantities in arithmetic and the use of Newton - Cauchy definitions of a limit and derivative in analysis. We believe that is where the main problem lies in contemporary study of nature. We have introduced a new concept of Observer's Mathematics (see www.mathrelativity.com). Observer's Mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. We use Einstein special relativity principles and get the analogue of classical Lorentz transformation. This work considers this transformation from Observer's Mathematics point of view.

Impact of Thermodynamic Principles in Systems Biology

NARCIS (Netherlands)

Heijnen, J.J.

2010-01-01

It is shown that properties of biological systems which are relevant for systems biology motivated mathematical modelling are strongly shaped by general thermodynamic principles such as osmotic limit, Gibbs energy dissipation, near equilibria and thermodynamic driving force. Each of these aspects

Mathematical foundation of computer science

CERN Document Server

Singh, YN

2005-01-01

The interesting feature of this book is its organization and structure. That consists of systematizing of the definitions, methods, and results that something resembling a theory. Simplicity, clarity, and precision of mathematical language makes theoretical topics more appealing to the readers who are of mathematical or non-mathematical background. For quick references and immediate attentions¾concepts and definitions, methods and theorems, and key notes are presented through highlighted points from beginning to end. Whenever, necessary and probable a visual approach of presentation is used. The amalgamation of text and figures make mathematical rigors easier to understand. Each chapter begins with the detailed contents, which are discussed inside the chapter and conclude with a summary of the material covered in the chapter. Summary provides a brief overview of all the topics covered in the chapter. To demonstrate the principles better, the applicability of the concepts discussed in each topic are illustrat...

Mathematical grammar of biology

CERN Document Server

Yamagishi, Michel Eduardo Beleza

2017-01-01

This seminal, multidisciplinary book shows how mathematics can be used to study the first principles of DNA. Most importantly, it enriches the so-called “Chargaff’s grammar of biology” by providing the conceptual theoretical framework necessary to generalize Chargaff’s rules. Starting with a simple example of DNA mathematical modeling where human nucleotide frequencies are associated to the Fibonacci sequence and the Golden Ratio through an optimization problem, its breakthrough is showing that the reverse, complement and reverse-complement operators defined over oligonucleotides induce a natural set partition of DNA words of fixed-size. These equivalence classes, when organized into a matrix form, reveal hidden patterns within the DNA sequence of every living organism. Intended for undergraduate and graduate students both in mathematics and in life sciences, it is also a valuable resource for researchers interested in studying invariant genomic properties.

Online mathematics education: E-math for first year engineering students

DEFF Research Database (Denmark)

Markvorsen, Steen; Schmidt, Karsten

2012-01-01

We consider the technology enhanced learning of first year engineering mathematics and in particular the application of E-learning objects and principles in the course Mathematics 1 which has a yearly intake of 750 students at the technical University of Denmark. We show that with non-linear mult...

A Study of Visualization for Mathematics Education

Science.gov (United States)

Daugherty, Sarah C.

2008-01-01

Graphical representations such as figures, illustrations, and diagrams play a critical role in mathematics and they are equally important in mathematics education. However, graphical representations in mathematics textbooks are static, Le. they are used to illustrate only a specific example or a limited set. of examples. By using computer software to visualize mathematical principles, virtually there is no limit to the number of specific cases and examples that can be demonstrated. However, we have not seen widespread adoption of visualization software in mathematics education. There are currently a number of software packages that provide visualization of mathematics for research and also software packages specifically developed for mathematics education. We conducted a survey of mathematics visualization software packages, summarized their features and user bases, and analyzed their limitations. In this survey, we focused on evaluating the software packages for their use with mathematical subjects adopted by institutions of secondary education in the United States (middle schools and high schools), including algebra, geometry, trigonometry, and calculus. We found that cost, complexity, and lack of flexibility are the major factors that hinder the widespread use of mathematics visualization software in education.

Avoiding reification. Heuristic effectiveness of mathematics and the prediction of the Ω- particle

Science.gov (United States)

Ginammi, Michele

2016-02-01

According to Steiner (1998), in contemporary physics new important discoveries are often obtained by means of strategies which rely on purely formal mathematical considerations. In such discoveries, mathematics seems to have a peculiar and controversial role, which apparently cannot be accounted for by means of standard methodological criteria. M. Gell-Mann and Y. Ne'eman's prediction of the Ω- particle is usually considered a typical example of application of this kind of strategy. According to Bangu (2008), this prediction is apparently based on the employment of a highly controversial principle-what he calls the "reification principle". Bangu himself takes this principle to be methodologically unjustifiable, but still indispensable to make the prediction logically sound. In the present paper I will offer a new reconstruction of the reasoning that led to this prediction. By means of this reconstruction, I will show that we do not need to postulate any "reificatory" role of mathematics in contemporary physics and I will contextually clarify the representative and heuristic role of mathematics in science.

Academic Mathematicians' Dispositions toward Software Use in Mathematics Instruction: What Are the Underlying Reasons?

Science.gov (United States)

Khoshaim, Heba Bakr

2012-01-01

Academic mathematicians' opinions are divided regarding software use in undergraduate mathematics instruction. This study explored these opinions through interviews and a subsequent survey of mathematicians at PhD-granting institutions in the United States regarding their dispositions and the underlying attitudes. Most prior related work had…

Quaternions and the heuristic role of mathematical structures in physics

International Nuclear Information System (INIS)

Anderson, R.S.J.; Joshi, G.C.

1992-07-01

One of the important ways development takes place in mathematics is via a process of generalization. On the basis of a recent characterization of the process the authors propose that generalizations of mathematical structures that are already part of successful physical theories serve as good guides for the development of new physical theories. The principle is a more formal presentation and extension of a position stated earlier this century by Dirac. Quaternions form an excellent example of such a generalization, and a number of the ways in which their use in physical theories illustrates this principle, are discussed. 114 refs

To Issue of Mathematical Management Methods Applied for Investment-Building Complex under Conditions of Economic Crisis

Science.gov (United States)

Novikova, V.; Nikolaeva, O.

2017-11-01

In the article the authors consider a cognitive management method of the investment-building complex in the crisis conditions. The factors influencing the choice of an investment strategy are studied, the basic lines of the activity in the field of crisis-management from a position of mathematical modelling are defined. The general approach to decision-making on investment in real assets on the basis of the discrete systems based on the optimum control theory is offered. With the use of a discrete maximum principle the task in view of the decision is found. The numerical algorithm to define the optimum control is formulated by investments. Analytical decisions for the case of constant profitability of the basic means are obtained.

Principles of computational fluid dynamics

CERN Document Server

Wesseling, Pieter

2001-01-01

The book is aimed at graduate students, researchers, engineers and physicists involved in flow computations. An up-to-date account is given of the present state-of-the-art of numerical methods employed in computational fluid dynamics. The underlying numerical principles are treated with a fair amount of detail, using elementary mathematical analysis. Attention is given to difficulties arising from geometric complexity of the flow domain and of nonuniform structured boundary-fitted grids. Uniform accuracy and efficiency for singular perturbation problems is studied, pointing the way to accurate computation of flows at high Reynolds number. Much attention is given to stability analysis, and useful stability conditions are provided, some of them new, for many numerical schemes used in practice. Unified methods for compressible and incompressible flows are discussed. Numerical analysis of the shallow-water equations is included. The theory of hyperbolic conservation laws is treated. Godunov's order barrier and ho...

Variational principles are a powerful tool also for formulating field theories

OpenAIRE

Dell'Isola , Francesco; Placidi , Luca

2012-01-01

Variational principles and calculus of variations have always been an important tool for formulating mathematical models for physical phenomena. Variational methods give an efficient and elegant way to formulate and solve mathematical problems that are of interest for scientists and engineers and are the main tool for the axiomatization of physical theories

Problem solving as a challenge for mathematics education in The Netherlands

NARCIS (Netherlands)

Doorman, M.; Drijvers, P.; Dekker, T.; Heuvel-Panhuizen, T. van; Lange, J. de; Wijers, M.

2007-01-01

This paper deals with the challenge to establish problem solving as a living domain in mathematics education in The Netherlands. While serious attempts are made to implement a problem-oriented curriculum based on principles of realistic mathematics education with room for modelling and with

Philosophy and foundations of mathematics L. E. J. Brouwer

CERN Document Server

Heyting, A

1974-01-01

L.E.J. Brouwer: Collected Works, Volume 1: Philosophy and Foundations of Mathematics focuses on the principles, operations, and approaches promoted by Brouwer in studying the philosophy and foundations of mathematics. The publication first ponders on the construction of mathematics. Topics include arithmetic of integers, negative numbers, measurable continuum, irrational numbers, Cartesian geometry, similarity group, characterization of the linear system of the Cartesian or Euclidean and hyperbolic space, and non-Archimedean uniform groups on the one-dimensional continuum. The book then examin

Handicap principle implies emergence of dimorphic ornaments.

Science.gov (United States)

Clifton, Sara M; Braun, Rosemary I; Abrams, Daniel M

2016-11-30

Species spanning the animal kingdom have evolved extravagant and costly ornaments to attract mating partners. Zahavi's handicap principle offers an elegant explanation for this: ornaments signal individual quality, and must be costly to ensure honest signalling, making mate selection more efficient. Here, we incorporate the assumptions of the handicap principle into a mathematical model and show that they are sufficient to explain the heretofore puzzling observation of bimodally distributed ornament sizes in a variety of species. © 2016 The Author(s).

Russell's Unknown Logicism A Study in the History and Philosophy of Mathematics

CERN Document Server

Gandon, Professor Sebastien

2012-01-01

In this excellent book Sebastien Gandon focuses mainly on Russell's two major texts, Principa Mathematica and Principle of Mathematics, meticulously unpicking the details of these texts and bringing a new interpretation of both the mathematical and the philosophical content.

Introduction to mathematical fluid dynamics

CERN Document Server

Meyer, Richard E

2010-01-01

An introduction to the behavior of liquids and gases, this volume provides excellent coverage of kinematics, momentum principle, Newtonian fluid, rotating fluids, compressibility, and more. It is geared toward advanced undergraduate and graduate students of mathematics and general science, and it requires a background in calculus and vector analysis. 1971 edition.

Cultured Cortical Neurons Can Perform Blind Source Separation According to the Free-Energy Principle

Science.gov (United States)

Isomura, Takuya; Kotani, Kiyoshi; Jimbo, Yasuhiko

2015-01-01

Blind source separation is the computation underlying the cocktail party effect––a partygoer can distinguish a particular talker’s voice from the ambient noise. Early studies indicated that the brain might use blind source separation as a signal processing strategy for sensory perception and numerous mathematical models have been proposed; however, it remains unclear how the neural networks extract particular sources from a complex mixture of inputs. We discovered that neurons in cultures of dissociated rat cortical cells could learn to represent particular sources while filtering out other signals. Specifically, the distinct classes of neurons in the culture learned to respond to the distinct sources after repeating training stimulation. Moreover, the neural network structures changed to reduce free energy, as predicted by the free-energy principle, a candidate unified theory of learning and memory, and by Jaynes’ principle of maximum entropy. This implicit learning can only be explained by some form of Hebbian plasticity. These results are the first in vitro (as opposed to in silico) demonstration of neural networks performing blind source separation, and the first formal demonstration of neuronal self-organization under the free energy principle. PMID:26690814

Cultured Cortical Neurons Can Perform Blind Source Separation According to the Free-Energy Principle.

Directory of Open Access Journals (Sweden)

Takuya Isomura

2015-12-01

Full Text Available Blind source separation is the computation underlying the cocktail party effect--a partygoer can distinguish a particular talker's voice from the ambient noise. Early studies indicated that the brain might use blind source separation as a signal processing strategy for sensory perception and numerous mathematical models have been proposed; however, it remains unclear how the neural networks extract particular sources from a complex mixture of inputs. We discovered that neurons in cultures of dissociated rat cortical cells could learn to represent particular sources while filtering out other signals. Specifically, the distinct classes of neurons in the culture learned to respond to the distinct sources after repeating training stimulation. Moreover, the neural network structures changed to reduce free energy, as predicted by the free-energy principle, a candidate unified theory of learning and memory, and by Jaynes' principle of maximum entropy. This implicit learning can only be explained by some form of Hebbian plasticity. These results are the first in vitro (as opposed to in silico demonstration of neural networks performing blind source separation, and the first formal demonstration of neuronal self-organization under the free energy principle.

THE UNDERLYING PRINCIPLES OF SUSILO BAMBANG YUDHOYONO‘S THOUGHT PATTERNS IN HIS ENGLISH SPEECH TEXTS

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Sulistya ningsih

2014-10-01

Full Text Available The underlying principles of thought patterns as shown in SBY's English Speeches Texts are made because there are different responses from the public, a part of public praise that SBY is a good president, and others claim and criticize him that  he is slow (Djalal, 2007: forward page. This title so far has not been investigated. This research was aimed at finding out:  the underlying principles of SBY’s thought patterns in his English Speech Texts related to Javanese philosophy. This research is qualitative. The data selected from SBY’s speech Texts were analyzed using semantic and pragmastylistic theory then were related to Javanese philosophy. The findings are the underlying principles of SBY’s thought patterns based on Javanese philosophy manifested in his English Speech Texts are: first is Memayu Hayuning Bawana, Ambrasta dur Hangkara means to reach safety, peace, happiness and well-being of the world and its contents, to keep the world maintained and harmony. Second, Rukun agawe santosa crah agawe bubrah  means to build the condition of harmony, and avoid conflict, because conflict can be harmful to both parties. Third, tepa selira means keep thinking not to offend others or lighten the burdens of others, tolerance. Fourth is ana rembug becik dirembug means thru negotiations can avoid conflict and achieve cooperation, safety, peace and prosperity. In sum, the world peace can be reached thru discussions without war, soft powers.

Mathematics and engineering in real life through mathematical competitions

Science.gov (United States)

More, M.

2018-02-01

We bring out an experience of organizing mathematical competitions that can be used as a medium to motivate the student and teacher minds in new directions of thinking. This can contribute to fostering research, innovation and provide a hands-on experience of mathematical concepts with the real world. Mathematical competitions can be used to build curiosity and give an understanding of mathematical applications in real life. Participation in the competition has been classified under four broad categories. Student can showcase their findings in various forms of expression like model, poster, soft presentation, animation, live performance, art and poetry. The basic focus of the competition is on using open source computation tools and modern technology, to emphasize the relationship of mathematical concepts with engineering applications in real life.

Mathematics education for social justice

Science.gov (United States)

Suhendra

2016-02-01

Mathematics often perceived as a difficult subject with many students failing to understand why they learn mathematics. This situation has been further aggravated by the teaching and learning processes used, which is mechanistic without considering students' needs. The learning of mathematics tends to be just a compulsory subject, in which all students have to attend its classes. Social justice framework facilitates individuals or groups as a whole and provides equitable approaches to achieving equitable outcomes by recognising disadvantage. Applying social justice principles in educational context is related to how the teachers treat their students, dictates that all students the right to equal treatment regardless of their background and completed with applying social justice issues integrated with the content of the subject in order to internalise the principles of social justice simultaneously the concepts of the subject. The study examined the usefulness of implementing the social justice framework as a means of improving the quality of mathematics teaching in Indonesia involved four teacher-participants and their mathematics classes. The study used action research as the research methodology in which the teachers implemented and evaluated their use of social justice framework in their teaching. The data were collected using multiple research methods while analysis and interpretation of the data were carried out throughout the study. The findings of the study indicated that there were a number of challengesrelated to the implementation of the social justice framework. The findings also indicated that, the teachers were provided with a comprehensive guide that they could draw on to make decisions about how they could improve their lessons. The interactions among students and between the teachers and the students improved, they became more involved in teaching and learning process. Using social justice framework helped the teachers to make mathematics more

A Development of the Principle of Virtual Laws and its Conceptual Framework in Mechanics as Fundamental Relationship between Physics and Mathematics

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Raffaele Pisano

2017-06-01

Full Text Available Generally speaking, virtual displacement or work concerns to a timely idea according to which a motion of a certain body is not the unique possible motion. The process of reducing this motion to a particular magnitude and concept, eventually minimizing as a hypothesis, can be traced back to the Aristotelian school. In the history and philosophy of science one finds various enunciations of the Principle of Virtual Laws and its virtual displacement or work applications, i.e., from Aristotle to Leibniz’s vis viva, from Maupertuis’ least action to Euler and Lagrange with calculus of variations (statics and dynamics to Lazare Carnot’s mechanics. In this case study, I will demonstrate that a particular approach used by Lazare Carnot is original by explaining within the historical context of rival approaches such as the development of the Principle of virtual Laws (also known as the Principle of virtual velocity or of virtual work. I will also discuss Carnot’s geometric motion as one of the possible but invertible movements applied to virtual displacement as employed in his theories of machines and collisions. I will then go on to explore how the originality of an invertible motion within his mechanical and, in general, mathematical research program permitted Carnot to introduce a new way of structuring a scientific theory and making mechanics, with respect to the Newtonian paradigm, to scholars and his students of the École polytechnique de Paris.

Principles of musical acoustics

CERN Document Server

Hartmann, William M

2013-01-01

Principles of Musical Acoustics focuses on the basic principles in the science and technology of music. Musical examples and specific musical instruments demonstrate the principles. The book begins with a study of vibrations and waves, in that order. These topics constitute the basic physical properties of sound, one of two pillars supporting the science of musical acoustics. The second pillar is the human element, the physiological and psychological aspects of acoustical science. The perceptual topics include loudness, pitch, tone color, and localization of sound. With these two pillars in place, it is possible to go in a variety of directions. The book treats in turn, the topics of room acoustics, audio both analog and digital, broadcasting, and speech. It ends with chapters on the traditional musical instruments, organized by family. The mathematical level of this book assumes that the reader is familiar with elementary algebra. Trigonometric functions, logarithms and powers also appear in the book, but co...

An excursion through elementary mathematics, volume iii discrete mathematics and polynomial algebra

CERN Document Server

Caminha Muniz Neto, Antonio

2018-01-01

This book provides a comprehensive, in-depth overview of elementary mathematics as explored in Mathematical Olympiads around the world. It expands on topics usually encountered in high school and could even be used as preparation for a first-semester undergraduate course. This third and last volume covers Counting, Generating Functions, Graph Theory, Number Theory, Complex Numbers, Polynomials, and much more. As part of a collection, the book differs from other publications in this field by not being a mere selection of questions or a set of tips and tricks that applies to specific problems. It starts from the most basic theoretical principles, without being either too general or too axiomatic. Examples and problems are discussed only if they are helpful as applications of the theory. Propositions are proved in detail and subsequently applied to Olympic problems or to other problems at the Olympic level. The book also explores some of the hardest problems presented at National and International Mathematics Ol...

Effective Computer-Aided Assessment of Mathematics; Principles, Practice and Results

Science.gov (United States)

Greenhow, Martin

2015-01-01

This article outlines some key issues for writing effective computer-aided assessment (CAA) questions in subjects with substantial mathematical or statistical content, especially the importance of control of random parameters and the encoding of wrong methods of solution (mal-rules) commonly used by students. The pros and cons of using CAA and…

A practical course in differential equations and mathematical modeling

CERN Document Server

Ibragimov , Nail H

2009-01-01

A Practical Course in Differential Equations and Mathematical Modelling is a unique blend of the traditional methods of ordinary and partial differential equations with Lie group analysis enriched by the author's own theoretical developments. The book which aims to present new mathematical curricula based on symmetry and invariance principles is tailored to develop analytic skills and working knowledge in both classical and Lie's methods for solving linear and nonlinear equations. This approach helps to make courses in differential equations, mathematical modelling, distributions and fundame

A Subjective Logic Formalisation of the Principle of Polyrepresentation for Information Needs

DEFF Research Database (Denmark)

Lioma, Christina; Larsen, Birger; Schütze, Hinrich

2010-01-01

of the principle of Polyrepresentation, a theoretical framework for reasoning about different representations arising from interactive information retrieval in a given context. Although the principle of Polyrepresentation has received attention from many researchers, not much empirical work has been done based...... on it. One reason may be that it has not yet been formalised mathematically. In this paper we propose an up-to-date and flexible mathematical formalisation of the principle of Polyrepresentation for information needs. Specifically, we apply Subjective Logic to model different representations...... of information needs as beliefs marked by degrees of uncertainty. We combine such beliefs using different logical operators, and we discuss these combinations with respect to different retrieval scenarios and situations. A formal model is introduced and discussed, with illustrative applications to the modelling...

Mathematical model in economic environmental problems

Energy Technology Data Exchange (ETDEWEB)

Nahorski, Z. [Polish Academy of Sciences, Systems Research Inst. (Poland); Ravn, H.F. [Risoe National Lab. (Denmark)

1996-12-31

The report contains a review of basic models and mathematical tools used in economic regulation problems. It starts with presentation of basic models of capital accumulation, resource depletion, pollution accumulation, and population growth, as well as construction of utility functions. Then the one-state variable model is discussed in details. The basic mathematical methods used consist of application of the maximum principle and phase plane analysis of the differential equations obtained as the necessary conditions of optimality. A summary of basic results connected with these methods is given in appendices. (au) 13 ills.; 17 refs.

Laser interaction with biological material mathematical modeling

CERN Document Server

Kulikov, Kirill

2014-01-01

This book covers the principles of laser interaction with biological cells and tissues of varying degrees of organization. The problems of biomedical diagnostics are considered. Scattering of laser irradiation of blood cells is modeled for biological structures (dermis, epidermis, vascular plexus). An analytic theory is provided which is based on solving the wave equation for the electromagnetic field. It allows the accurate analysis of interference effects arising from the partial superposition of scattered waves. Treated topics of mathematical modeling are: optical characterization of biological tissue with large-scale and small-scale inhomogeneities in the layers, heating blood vessel under laser irradiation incident on the outer surface of the skin and thermo-chemical denaturation of biological structures at the example of human skin.

Nonlinear Optics: Principles and Applications

DEFF Research Database (Denmark)

Rottwitt, Karsten; Tidemand-Lichtenberg, Peter

of applications, Nonlinear Optics: Principles and Applications effectively bridges physics and mathematics with relevant applied material for real-world use. The book progresses naturally from fundamental aspects to illustrative examples, and presents a strong theoretical foundation that equips the reader...... and matter, this text focuses on the physical understanding of nonlinear optics, and explores optical material response functions in the time and frequency domain....

Philosophy of mathematics set theory, measuring theories, and nominalism

CERN Document Server

Preyer, Gerhard

2008-01-01

One main interest of philosophy is to become clear about the assumptions, premisses and inconsistencies of our thoughts and theories. And even for a formal language like mathematics it is controversial if consistency is acheivable or necessary like the articles in the firt part of the publication show. Also the role of formal derivations, the role of the concept of apriority, and the intuitions of mathematical principles and properties need to be discussed. The second part is a contribution on nominalistic and platonistic views in mathematics, like the ""indispensability argument"" of W. v. O.

Rockets: An Educator's Guide with Activities in Science, Mathematics, and Technology.

Science.gov (United States)

National Aeronautics and Space Administration, Washington, DC.

This educational guide discusses rockets and includes activities in science, mathematics, and technology. It begins with background information on the history of rocketry, scientific principles, and practical rocketry. The sections on scientific principles and practical rocketry focus on Sir Isaac Newton's Three Laws of Motion. These laws explain…

Mathematical Analysis for Non-reciprocal-interaction-based Model of Collective Behavior

Science.gov (United States)

Kano, Takeshi; Osuka, Koichi; Kawakatsu, Toshihiro; Ishiguro, Akio

2017-12-01

In many natural and social systems, collective behaviors emerge as a consequence of non-reciprocal interaction between their constituents. As a first step towards understanding the core principle that underlies these phenomena, we previously proposed a minimal model of collective behavior based on non-reciprocal interactions by drawing inspiration from friendship formation in human society, and demonstrated via simulations that various non-trivial patterns emerge by changing parameters. In this study, a mathematical analysis of the proposed model wherein the system size is small is performed. Through the analysis, the mechanism of the transition between several patterns is elucidated.

From Square Dance to Mathematics

Science.gov (United States)

Bremer, Zoe

2010-01-01

In this article, the author suggests a cross-curricular idea that can link with PE, dance, music and history. Teacher David Schmitz, a maths teacher in Illinois who was also a square dance caller, had developed a maths course that used the standard square dance syllabus to teach mathematical principles. He presents an intensive, two-week course…

An introduction to mathematical modeling a course in mechanics

CERN Document Server

Oden, Tinsley J

2011-01-01

A modern approach to mathematical modeling, featuring unique applications from the field of mechanics An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical models that form the foundations of modern science and incorporates examples that illustrate how the most successful models arise from basic principles in modern and classical mathematical physics. Written by a world authority on mathematical theory and computational mechanics, the book presents an account of continuum mechanics, electromagnetic field theory, quantum mechanics, and statistical mechanics for readers with varied backgrounds in engineering, computer science, mathematics, and physics. The author streamlines a comprehensive understanding of the topic in three clearly organized sections: Nonlinear Continuum Mechanics introduces kinematics as well as force and stress in deformable bodies; mass and momentum; balance of linear and angular momentum; conservation of energy; and constitutive equation...

Mathematical intuitionism

CERN Document Server

Dragalin, A G

1988-01-01

This monograph is intended to present the most important methods of proof theory in intuitionistic logic, assuming the reader to have mastered an introductory course in mathematical logic. The book starts with purely syntactical methods based on Gentzen's cut-elimination theorem, followed by intuitionistic arithmetic where Kleene's realizability method plays a central role. The author then studies algebraic models and completeness theorems for them. After giving a survey on the principles of intuitionistic analysis, the last part of the book presents the cut-elimination theorem in intuitionistic simple theory of types with an extensionality rule.

Viscous Regularization of the Euler Equations and Entropy Principles

KAUST Repository

Guermond, Jean-Luc; Popov, Bojan

2014-01-01

), pp. 2117-2127], and satisfies the minimum entropy principle. A connection with a recently proposed phenomenological model by [H. Brenner, Phys. A, 370 (2006), pp. 190-224] is made. © 2014 Society for Industrial and Applied Mathematics.

Effects of Mathematics Anxiety and Mathematical Metacognition on Word Problem Solving in Children with and without Mathematical Learning Difficulties

Science.gov (United States)

Lai, Yinghui; Zhu, Xiaoshuang; Chen, Yinghe; Li, Yanjun

2015-01-01

Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil’s Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA), typical achieving (TA), low achieving (LA), and mathematical learning difficulty (MLD). Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA) than the TA and HA children, but not in mathematical evaluation anxiety (MEA). MLD children’s LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions. PMID:26090806

Effects of Mathematics Anxiety and Mathematical Metacognition on Word Problem Solving in Children with and without Mathematical Learning Difficulties.

Directory of Open Access Journals (Sweden)

Yinghui Lai

Full Text Available Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA and mathematical metacognition on word problem solving (WPS. We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56 with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil's Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA, typical achieving (TA, low achieving (LA, and mathematical learning difficulty (MLD. Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA than the TA and HA children, but not in mathematical evaluation anxiety (MEA. MLD children's LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions.

Effects of Mathematics Anxiety and Mathematical Metacognition on Word Problem Solving in Children with and without Mathematical Learning Difficulties.

Science.gov (United States)

Lai, Yinghui; Zhu, Xiaoshuang; Chen, Yinghe; Li, Yanjun

2015-01-01

Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil's Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA), typical achieving (TA), low achieving (LA), and mathematical learning difficulty (MLD). Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA) than the TA and HA children, but not in mathematical evaluation anxiety (MEA). MLD children's LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions.

Principles, Economic and Institutional Prerequisites for Fiscal Decentralization under Conditions of Post-Conflict Reconstruction

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Vishnevsky Valentine P.

2016-11-01

Full Text Available The aim of the article is to study principles, economic and institutional prerequisites for fiscal decentralization on post-conflict territories. It is determined that fiscal decentralization is one of the main ways to solve problems of post-conflict areas. There justified principles, economic and institutional prerequisites of fiscal decentralization on post-conflict territories with regard to the specificity of individual spheres of fiscal relations. Moreover, different spheres of fiscal relations require different approaches: the sphere of public revenues — providing economic efficiency with the formation of the tax structure contributing to the expansion of the tax base; the sphere of public spending — ensuring social justice and transparency in allocation of social cost at the local level; the sphere of subsidies — narrowing the scope of application of intergovernmental transfers with organizing the redistribution of financial resources under the principle of «center - post-conflict regions - post-conflict recipients»; the sphere of external assistance — ensuring proper coordination for cultivation of new co-operative institutions.

The Pythagorean world why mathematics is unreasonably effective in physics

CERN Document Server

McDonnell, Jane

2017-01-01

This book explores precisely how mathematics allows us to model and predict the behaviour of physical systems, to an amazing degree of accuracy. One of the oldest explanations for this is that, in some profound way, the structure of the world is mathematical. The ancient Pythagoreans stated that “everything is number”. However, while exploring the Pythagorean method, this book chooses to add a second principle of the universe: the mind. This work defends the proposition that mind and mathematical structure are the grounds of reality.

Literature Review of Applying Visual Method to Understand Mathematics

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Yu Xiaojuan

2015-01-01

Full Text Available As a new method to understand mathematics, visualization offers a new way of understanding mathematical principles and phenomena via image thinking and geometric explanation. It aims to deepen the understanding of the nature of concepts or phenomena and enhance the cognitive ability of learners. This paper collates and summarizes the application of this visual method in the understanding of mathematics. It also makes a literature review of the existing research, especially with a visual demonstration of Euler’s formula, introduces the application of this method in solving relevant mathematical problems, and points out the differences and similarities between the visualization method and the numerical-graphic combination method, as well as matters needing attention for its application.

Temporal ventriloquism along the path of apparent motion: speed perception under different spatial grouping principles.

Science.gov (United States)

Ogulmus, Cansu; Karacaoglu, Merve; Kafaligonul, Hulusi

2018-03-01

The coordination of intramodal perceptual grouping and crossmodal interactions plays a critical role in constructing coherent multisensory percepts. However, the basic principles underlying such coordinating mechanisms still remain unclear. By taking advantage of an illusion called temporal ventriloquism and its influences on perceived speed, we investigated how audiovisual interactions in time are modulated by the spatial grouping principles of vision. In our experiments, we manipulated the spatial grouping principles of proximity, uniform connectedness, and similarity/common fate in apparent motion displays. Observers compared the speed of apparent motions across different sound timing conditions. Our results revealed that the effects of sound timing (i.e., temporal ventriloquism effects) on perceived speed also existed in visual displays containing more than one object and were modulated by different spatial grouping principles. In particular, uniform connectedness was found to modulate these audiovisual interactions in time. The effect of sound timing on perceived speed was smaller when horizontal connecting bars were introduced along the path of apparent motion. When the objects in each apparent motion frame were not connected or connected with vertical bars, the sound timing was more influential compared to the horizontal bar conditions. Overall, our findings here suggest that the effects of sound timing on perceived speed exist in different spatial configurations and can be modulated by certain intramodal spatial grouping principles such as uniform connectedness.

The principle of locality: Effectiveness, fate, and challenges

International Nuclear Information System (INIS)

Doplicher, Sergio

2010-01-01

The special theory of relativity and quantum mechanics merge in the key principle of quantum field theory, the principle of locality. We review some examples of its 'unreasonable effectiveness' in giving rise to most of the conceptual and structural frame of quantum field theory, especially in the absence of massless particles. This effectiveness shows up best in the formulation of quantum field theory in terms of operator algebras of local observables; this formulation is successful in digging out the roots of global gauge invariance, through the analysis of superselection structure and statistics, in the structure of the local observable quantities alone, at least for purely massive theories; but so far it seems unfit to cope with the principle of local gauge invariance. This problem emerges also if one attempts to figure out the fate of the principle of locality in theories describing the gravitational forces between elementary particles as well. An approach based on the need to keep an operational meaning, in terms of localization of events, of the notion of space-time, shows that, in the small, the latter must loose any meaning as a classical pseudo-Riemannian manifold, locally based on Minkowski space, but should acquire a quantum structure at the Planck scale. We review the geometry of a basic model of quantum space-time and some attempts to formulate interaction of quantum fields on quantum space-time. The principle of locality is necessarily lost at the Planck scale, and it is a crucial open problem to unravel a replacement in such theories which is equally mathematically sharp, namely, a principle where the general theory of relativity and quantum mechanics merge, which reduces to the principle of locality at larger scales. Besides exploring its fate, many challenges for the principle of locality remain; among them, the analysis of superselection structure and statistics also in the presence of massless particles, and to give a precise mathematical

Mathematical models of information and stochastic systems

CERN Document Server

Kornreich, Philipp

2008-01-01

From ancient soothsayers and astrologists to today's pollsters and economists, probability theory has long been used to predict the future on the basis of past and present knowledge. Mathematical Models of Information and Stochastic Systems shows that the amount of knowledge about a system plays an important role in the mathematical models used to foretell the future of the system. It explains how this known quantity of information is used to derive a system's probabilistic properties. After an introduction, the book presents several basic principles that are employed in the remainder of the t

Choking under Pressure: When an Additional Positive Stereotype Affects Performance for Domain Identified Male Mathematics Students

Science.gov (United States)

Rosenthal, Harriet E. S.; Crisp, Richard J.

2007-01-01

This research aimed to establish if the presentation of two positive stereotypes would result in choking under pressure for identified male mathematics students. Seventy-five 16 year old men, who had just commenced their AS-level study, were either made aware of their gender group membership (single positive stereotype), their school group…

Devising Principles of Design for Numeracy Tasks

Science.gov (United States)

Geiger, Vince; Forgasz, Helen; Goos, Merrilyn; Bennison, Anne

2014-01-01

Numeracy is a fundamental component of the Australian National Curriculum as a General Capability identified in each F-10 subject. In this paper, we consider the principles of design necessary for the development of numeracy tasks specific to subjects other than mathematics--in this case, the subject of English. We explore the nature of potential…

Modularizing Remedial Mathematics

Science.gov (United States)

Wong, Aaron

2013-01-01

As remedial mathematics education has become an increasingly important topic of conversation in higher education. Mathematics departments have been put under increased pressure to change their programs to increase the student success rate. A number of models have been introduced over the last decade that represent a wide range of new ideas and…

Computational anatomy based on whole body imaging basic principles of computer-assisted diagnosis and therapy

CERN Document Server

Masutani, Yoshitaka

2017-01-01

This book deals with computational anatomy, an emerging discipline recognized in medical science as a derivative of conventional anatomy. It is also a completely new research area on the boundaries of several sciences and technologies, such as medical imaging, computer vision, and applied mathematics. Computational Anatomy Based on Whole Body Imaging highlights the underlying principles, basic theories, and fundamental techniques in computational anatomy, which are derived from conventional anatomy, medical imaging, computer vision, and applied mathematics, in addition to various examples of applications in clinical data. The book will cover topics on the basics and applications of the new discipline. Drawing from areas in multidisciplinary fields, it provides comprehensive, integrated coverage of innovative approaches to computational anatomy. As well,Computational Anatomy Based on Whole Body Imaging serves as a valuable resource for researchers including graduate students in the field and a connection with ...

Developing Mathematical Literacy through project work: A teacher/teaching perspective

Directory of Open Access Journals (Sweden)

Renuka Vithal

2006-10-01

Full Text Available The implementation of the new Mathematical Literacy curriculum in South Africa is assuming several different conceptions of mathematics and therefore also being realised through a range of different pedagogies. In this paper I begin from a particular privileging of a critical perspective in mathematics education, which I argue is one (among others of the forces shaping the new South African curriculum reforms, particularly the Mathematical Literacy curriculum. If so, then the case for a specific pedagogy, that of project work, can be shown to support the development of a mathematical literacy from a critical perspective. In this paper a particular set of conceptual tools, principles and practices associated with project work, as developed in the Scandanavian context but researched in South Africa, are elaborated from the perspective of teachers/teaching of mathematical literacy.

Physical Principle for Generation of Randomness

Science.gov (United States)

Zak, Michail

2009-01-01

A physical principle (more precisely, a principle that incorporates mathematical models used in physics) has been conceived as the basis of a method of generating randomness in Monte Carlo simulations. The principle eliminates the need for conventional random-number generators. The Monte Carlo simulation method is among the most powerful computational methods for solving high-dimensional problems in physics, chemistry, economics, and information processing. The Monte Carlo simulation method is especially effective for solving problems in which computational complexity increases exponentially with dimensionality. The main advantage of the Monte Carlo simulation method over other methods is that the demand on computational resources becomes independent of dimensionality. As augmented by the present principle, the Monte Carlo simulation method becomes an even more powerful computational method that is especially useful for solving problems associated with dynamics of fluids, planning, scheduling, and combinatorial optimization. The present principle is based on coupling of dynamical equations with the corresponding Liouville equation. The randomness is generated by non-Lipschitz instability of dynamics triggered and controlled by feedback from the Liouville equation. (In non-Lipschitz dynamics, the derivatives of solutions of the dynamical equations are not required to be bounded.)

The nature and principles of the radiation-induced cancerogenesis

International Nuclear Information System (INIS)

Lips'ka, A.YI.; Serkyiz, Ya.Yi.

2004-01-01

The paper represents the analysis of the authors and literary data concerning the nature and principles of the radiation-induced neoplasms. The mechanisms of the radiation-induced cancerogenesis development are not clear understood. The experimental data altogether do not allow developing the mathematical model of the radiation-induced cancerogenesis at the molecular level. This model has to take into account all necessary indices including radiation factor and the state of the organism. The general principles of the radiation-induced cancerogenesis have been formulated in the present review. It is possible to use these principles in order to predict and calculate the risks of the radiation-induced neoplasms

The role of mathematical models in understanding pattern formation in developmental biology.

Science.gov (United States)

Umulis, David M; Othmer, Hans G

2015-05-01

In a Wall Street Journal article published on April 5, 2013, E. O. Wilson attempted to make the case that biologists do not really need to learn any mathematics-whenever they run into difficulty with numerical issues, they can find a technician (aka mathematician) to help them out of their difficulty. He formalizes this in Wilsons Principle No. 1: "It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations." This reflects a complete misunderstanding of the role of mathematics in all sciences throughout history. To Wilson, mathematics is mere number crunching, but as Galileo said long ago, "The laws of Nature are written in the language of mathematics[Formula: see text] the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word." Mathematics has moved beyond the geometry-based model of Galileo's time, and in a rebuttal to Wilson, E. Frenkel has pointed out the role of mathematics in synthesizing the general principles in science (Both point and counter-point are available in Wilson and Frenkel in Notices Am Math Soc 60(7):837-838, 2013). We will take this a step further and show how mathematics has been used to make new and experimentally verified discoveries in developmental biology and how mathematics is essential for understanding a problem that has puzzled experimentalists for decades-that of how organisms can scale in size. Mathematical analysis alone cannot "solve" these problems since the validation lies at the molecular level, but conversely, a growing number of questions in biology cannot be solved without mathematical analysis and modeling. Herein, we discuss a few examples of the productive intercourse between mathematics and biology.

An excursion through elementary mathematics

CERN Document Server

Caminha Muniz Neto, Antonio

2017-01-01

This book provides a comprehensive, in-depth overview of elementary mathematics as explored in Mathematical Olympiads around the world. It expands on topics usually encountered in high school and could even be used as preparation for a first-semester undergraduate course. This first volume covers Real Numbers, Functions, Real Analysis, Systems of Equations, Limits and Derivatives, and much more. As part of a collection, the book differs from other publications in this field by not being a mere selection of questions or a set of tips and tricks that applies to specific problems. It starts from the most basic theoretical principles, without being either too general or too axiomatic. Examples and problems are discussed only if they are helpful as applications of the theory. Propositions are proved in detail and subsequently applied to Olympic problems or to other problems at the Olympic level. The book also explores some of the hardest problems presented at National and International Mathematics Olympiads, as we...

An excursion through elementary mathematics

CERN Document Server

Caminha Muniz Neto, Antonio

This book provides a comprehensive, in-depth overview of elementary mathematics as explored in Mathematical Olympiads around the world. It expands on topics usually encountered in high school and could even be used as preparation for a first-semester undergraduate course. This first volume covers Real Numbers, Functions, Real Analysis, Systems of Equations, Limits and Derivatives, and much more. As part of a collection, the book differs from other publications in this field by not being a mere selection of questions or a set of tips and tricks that applies to specific problems. It starts from the most basic theoretical principles, without being either too general or too axiomatic. Examples and problems are discussed only if they are helpful as applications of the theory. Propositions are proved in detail and subsequently applied to Olympic problems or to other problems at the Olympic level. The book also explores some of the hardest problems presented at National and International Mathematics Olympiads, as we...

Protective relaying of power systems using mathematical morphology

CERN Document Server

Wu, QH; Ji, TY

2009-01-01

Discusses the development of novel protective relaying algorithms, using Mathematical Morphology (MM). This book introduces the fundamental principles of MM, and brings together the applications of MM to develop different protective relaying algorithms for the protection of a variety of power system components.

Connection of optimum temporal exponents with a principle of least action

Science.gov (United States)

Sergeev, E. V.; Karzanov, A. V.; Tremaskin, A. V.

2008-06-01

The principle of the least action states, that the motion of objects on optimum trajectories conjugates to the underload expenditure of activity. In the canonical approach this statement is reduced to searching extreme activity. For the immediate proof of the underload expenditure of activity on optimum trajectories the relevant mathematical algorithm in the basis of which bottom the concept of optimum time exponents lays is offered. Using this algorithm, various modes of a motion of charged particles are explored: the harmonic motion, a motion in the homogeneous force field, a motion in a central force field and a motion on inertia. The terrain clearance minimum under the rate of flux of activity for the harmonic motions is detected.

On quasistability radius of a vector trajectorial problem with a principle of optimality generalizing Pareto and lexicographic principles

Directory of Open Access Journals (Sweden)

Sergey E. Bukhtoyarov

2005-05-01

Full Text Available A multicriterion linear combinatorial problem with a parametric principle of optimality is considered. This principle is defined by a partitioning of partial criteria onto Pareto preference relation groups within each group and the lexicographic preference relation between them. Quasistability of the problem is investigated. This type of stability is a discrete analog of Hausdorff lower semi-continuity of the multiple-valued mapping that defines the choice function. A formula of quasistability radius is derived for the case of the metric l∞. Some known results are stated as corollaries. Mathematics Subject Classification 2000: 90C05, 90C10, 90C29, 90C31.

Is Russell's vicious circle principle false or meaningless?

NARCIS (Netherlands)

Fleischhacker, L.E.

1979-01-01

P. Vardy asserts the thesis that the vicious circle principle has the same structure as Russell's paradox. But structure is not the thing itself. It is the thing objectivated from the wiewpoint of a mathematician. So this structure can be expressed in a mathematical formalism, e. g. the Λ-calculus.

Maximum principle and convergence of central schemes based on slope limiters

KAUST Repository

Mehmetoglu, Orhan; Popov, Bojan

2012-01-01

A maximum principle and convergence of second order central schemes is proven for scalar conservation laws in dimension one. It is well known that to establish a maximum principle a nonlinear piecewise linear reconstruction is needed and a typical choice is the minmod limiter. Unfortunately, this implies that the scheme uses a first order reconstruction at local extrema. The novelty here is that we allow local nonlinear reconstructions which do not reduce to first order at local extrema and still prove maximum principle and convergence. © 2011 American Mathematical Society.

Educational Borrowing and Mathematics Curriculum: Realistic Mathematics Education in the Dutch and Indonesian Primary Curriculum

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Shintia Revina

2018-02-01

Full Text Available Since the late 1990s, Indonesian mathematics educators have considered Realistic Mathematics Education (RME, the Dutch approach to mathematics instruction, to be the basis for educational reform. In the National curriculum development, RME has, therefore, been reviewed as among the theoretical references to the curriculum goals and content. In the present study, an analysis of the consistency between RME and the curriculum descriptors and contents in Indonesia is presented. This is supplemented with some comparisons to that in the Netherlands. Findings in this study revealed that while most of RME principles are reflected in the Indonesian curriculum, the descriptions were often very general and less explicit compared to the Dutch curriculum. They were also limited by the content-based approach as well as by the centralized decision making process of the contents to be taught which have been pre-determined at the national level. This study suggests future research to see how the curriculum may influence teachers’ enactment of RME at classroom level.

Exact thermodynamic principles for dynamic order existence and evolution in chaos

International Nuclear Information System (INIS)

Mahulikar, Shripad P.; Herwig, Heinz

2009-01-01

The negentropy proposed first by Schroedinger is re-examined, and its conceptual and mathematical definitions are introduced. This re-definition of negentropy integrates Schroedinger's intention of its introduction, and the subsequent diverse notions in literature. This negentropy is further corroborated by its ability to state the two exact thermodynamic principles: negentropy principle for dynamic order existence and principle of maximum negentropy production (PMNEP) for dynamic order evolution. These principles are the counterparts of the existing entropy principle and the law of maximum entropy production, respectively. The PMNEP encompasses the basic concepts in the evolution postulates by Darwin and de Vries. Perspectives of dynamic order evolution in literature point to the validity of PMNEP as the law of evolution. These two additional principles now enable unified explanation of order creation, existence, evolution, and destruction; using thermodynamics.

Uncertainty, joint uncertainty, and the quantum uncertainty principle

International Nuclear Information System (INIS)

Narasimhachar, Varun; Poostindouz, Alireza; Gour, Gilad

2016-01-01

Historically, the element of uncertainty in quantum mechanics has been expressed through mathematical identities called uncertainty relations, a great many of which continue to be discovered. These relations use diverse measures to quantify uncertainty (and joint uncertainty). In this paper we use operational information-theoretic principles to identify the common essence of all such measures, thereby defining measure-independent notions of uncertainty and joint uncertainty. We find that most existing entropic uncertainty relations use measures of joint uncertainty that yield themselves to a small class of operational interpretations. Our notion relaxes this restriction, revealing previously unexplored joint uncertainty measures. To illustrate the utility of our formalism, we derive an uncertainty relation based on one such new measure. We also use our formalism to gain insight into the conditions under which measure-independent uncertainty relations can be found. (paper)

Fundamental quadratic variational principle underlying general relativity

International Nuclear Information System (INIS)

Atkins, W.K.

1983-01-01

The fundamental result of Lanczos is used in a new type of quadratic variational principle whose field equations are the Einstein field equations together with the Yang-Mills type equations for the Riemann curvature. Additionally, a spin-2 theory of gravity for the special case of the Einstein vacuum is discussed

Mathematical Modeling of Column-Base Connections under Monotonic Loading

Directory of Open Access Journals (Sweden)

Gholamreza Abdollahzadeh

2014-12-01

Full Text Available Some considerable damage to steel structures during the Hyogo-ken Nanbu Earthquake occurred. Among them, many exposed-type column bases failed in several consistent patterns, such as brittle base plate fracture, excessive bolt elongation, unexpected early bolt failure, and inferior construction work, etc. The lessons from these phenomena led to the need for improved understanding of column base behavior. Joint behavior must be modeled when analyzing semi-rigid frames, which is associated with a mathematical model of the moment–rotation curve. The most accurate model uses continuous nonlinear functions. This article presents three areas of steel joint research: (1 analysis methods of semi-rigid joints; (2 prediction methods for the mechanical behavior of joints; (3 mathematical representations of the moment–rotation curve. In the current study, a new exponential model to depict the moment–rotation relationship of column base connection is proposed. The proposed nonlinear model represents an approach to the prediction of M–θ curves, taking into account the possible failure modes and the deformation characteristics of the connection elements. The new model has three physical parameters, along with two curve-fitted factors. These physical parameters are generated from dimensional details of the connection, as well as the material properties. The M–θ curves obtained by the model are compared with published connection tests and 3D FEM research. The proposed mathematical model adequately comes close to characterizing M–θ behavior through the full range of loading/rotations. As a result, modeling of column base connections using the proposed mathematical model can give crucial beforehand information, and overcome the disadvantages of time consuming workmanship and cost of experimental studies.

Mean field theories and dual variation mathematical structures of the mesoscopic model

CERN Document Server

Suzuki, Takashi

2015-01-01

Mean field approximation has been adopted to describe macroscopic phenomena from microscopic overviews. It is still in progress; fluid mechanics, gauge theory, plasma physics, quantum chemistry, mathematical oncology, non-equilibirum thermodynamics.  spite of such a wide range of scientific areas that are concerned with the mean field theory, a unified study of its mathematical structure has not been discussed explicitly in the open literature.  The benefit of this point of view on nonlinear problems should have significant impact on future research, as will be seen from the underlying features of self-assembly or bottom-up self-organization which is to be illustrated in a unified way. The aim of this book is to formulate the variational and hierarchical aspects of the equations that arise in the mean field theory from macroscopic profiles to microscopic principles, from dynamics to equilibrium, and from biological models to models that arise from chemistry and physics.

Examining the Design Features of a Communication-Rich, Problem-Centred Mathematics Professional Development

Science.gov (United States)

de Araujo, Zandra; Orrill, Chandra Hawley; Jacobson, Erik

2018-01-01

While there is considerable scholarship describing principles for effective professional development, there have been few attempts to examine these principles in practice. In this paper, we identify and examine the particular design features of a mathematics professional development experience provided for middle grades teachers over 14 weeks. The…

Variational principles of continuum mechanics. Vol. 1. Fundamentals

Energy Technology Data Exchange (ETDEWEB)

Berdichevsky, Victor L. [Wayne State Univ., Detroit, MI (United States). Dept. of Mechanical Engineering

2009-07-01

The book reviews the two features of the variational approach: its use as a universal tool to describe physical phenomena and as a source for qualitative and quantitative methods of studying particular problems. Berdichevsky's work differs from other books on the subject in focusing mostly on the physical origin of variational principles as well as establishing their interrelations. For example, the Gibbs principles appear as a consequence of the Einstein formula for thermodynamic fluctuations rather than as the first principles of the theory of thermodynamic equilibrium. Mathematical issues are considered as long as they shed light on the physical outcomes and/or provide a useful technique for the direct study of variational problems. In addition, a thorough account of variational principles discovered in various branches of continuum mechanics is given. In this book, the first volume, the author covers the variational principles for systems with a finite number of degrees of freedom; the variational principles of thermodynamics; the basics of continuum mechanics; the variational principles for classical models of continuum mechanics, such as elastic and plastic bodies, and ideal and viscous fluids; and direct methods of calculus of variations. (orig.)

Equilibrium I: Principles. Independent Learning Project for Advanced Chemistry (ILPAC). Unit P2.

Science.gov (United States)

Inner London Education Authority (England).

This unit on the principles of equilibrium is one of 10 first year units produced by the Independent Learning Project for Advanced Chemistry (ILPAC). The unit consists of two levels. After a treatment of non-mathematical aspects in level one (the idea of a reversible reaction, characteristics of an equilibrium state, the Le Chatelier's principle),…

Mathematical manipulative models: in defense of "beanbag biology".

Science.gov (United States)

Jungck, John R; Gaff, Holly; Weisstein, Anton E

2010-01-01

Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process-1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets-we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational research that has convincingly demonstrated the utility of multiple models that involve physical, kinesthetic learning to actual data and interactive simulations. Two projects that use this approach are introduced: The Biological Excel Simulations and Tools in Exploratory, Experiential Mathematics (ESTEEM) Project (http://bioquest.org/esteem) and Numerical Undergraduate Mathematical Biology Education (NUMB3R5 COUNT; http://bioquest.org/numberscount). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epidemiology. Mathematical manipulative models help learners break through prior fears to develop an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education.

Transformer design principles with applications to core-form power transformers

CERN Document Server

Del Vecchio, Robert M; Feeney, Mary-Ellen F

2001-01-01

Transformer Design Principles presents the theory of transformer operation and the methods and techniques of designing them. It emphasizes the physical principles and mathematical tools for simulating transformer behavior, including modern computer techniques. The scope of the book includes types of construction, circuit analysis, mechanical aspects of design, high voltage insulation requirements, and cooling design. The authors also address test procedures and reliability methods to assure successful design and discuss the economic analysis of designs. Summarizing material currently scattered

Teaching mathematics in colleges and universities faculty edition

CERN Document Server

Friedberg, Solomon

2001-01-01

Progress in mathematics frequently occurs first by studying particular examples and then by generalizing the patterns that have been observed into far-reaching theorems. Similarly, in teaching mathematics one often employs examples to motivate a general principle or to illustrate its use. This volume uses the same idea in the context of learning how to teach: By analyzing particular teaching situations, one can develop broadly applicable teaching skills useful for the professional mathematician. These teaching situations are the Case Studies of the title. Just as a good mathematician seeks bot

Mathematically equivalent hydraulic analogue for teaching the pharmcokinetics and pharmacodynamics of atracurium

NARCIS (Netherlands)

Nikkelen, A.L.J.M.; Meurs, van W.L.; Ohrn, M.A.K.

1997-01-01

We evaluated the mathematical equivalence between the two-compartment pharmacokinetic model of the neuromuscular blocking agent atracurium and a hydraulic analogue that includes harmacodynamic principles.

An ant colony optimization algorithm for phylogenetic estimation under the minimum evolution principle

Directory of Open Access Journals (Sweden)

Milinkovitch Michel C

2007-11-01

Full Text Available Abstract Background Distance matrix methods constitute a major family of phylogenetic estimation methods, and the minimum evolution (ME principle (aiming at recovering the phylogeny with shortest length is one of the most commonly used optimality criteria for estimating phylogenetic trees. The major difficulty for its application is that the number of possible phylogenies grows exponentially with the number of taxa analyzed and the minimum evolution principle is known to belong to the NP MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGacaGaaiaabeqaaeqabiWaaaGcbaWenfgDOvwBHrxAJfwnHbqeg0uy0HwzTfgDPnwy1aaceaGae8xdX7Kaeeiuaafaaa@3888@-hard class of problems. Results In this paper, we introduce an Ant Colony Optimization (ACO algorithm to estimate phylogenies under the minimum evolution principle. ACO is an optimization technique inspired from the foraging behavior of real ant colonies. This behavior is exploited in artificial ant colonies for the search of approximate solutions to discrete optimization problems. Conclusion We show that the ACO algorithm is potentially competitive in comparison with state-of-the-art algorithms for the minimum evolution principle. This is the first application of an ACO algorithm to the phylogenetic estimation problem.

Principles of protection: a formal approach for evaluating dose distributions

International Nuclear Information System (INIS)

Wikman-Svahn, Per; Peterson, Martin; Hansson, Sven Ove

2006-01-01

One of the central issues in radiation protection consists in determining what weight should be given to individual doses in relation to collective or aggregated doses. A mathematical framework is introduced in which such assessments can be made precisely in terms of comparisons between alternative distributions of individual doses. In addition to evaluation principles that are well known from radiation protection, a series of principles that are derived from parallel discussions in moral philosophy and welfare economics is investigated. A battery of formal properties is then used to investigate the evaluative principles. The results indicate that one of the new principles, bilinear prioritarianism, may be preferable to current practices, since it satisfies efficiency-related properties better without sacrificing other desirable properties

The underlying principles of relativistic theory of gravitation

International Nuclear Information System (INIS)

Logunov, A.A.

1989-01-01

The paper deals with the main statements of relativistic theory of gravitation, constructed in result of critical analysis of the general theory of relativity. The principle of geometrization is formulated

Variational principles for the projected breakup amplitude

International Nuclear Information System (INIS)

Hahn, Y.

1976-01-01

Two alternate forms of variational principles for the breakup amplitude describing the two- to three-cluster transition are derived such that all the integrals involved in the intermediate stages are well defined. The first form contains a trial Green's function with which both the initial and final state trial wave functions are constructed. The earlier form of the Kohn-type variational principle derived by Lieber, Rosenberg, and Spruch is recovered, however, when this connection between the trial functions is removed. The second form of the variational principle is derived by projecting out from the trial functions all the open channel components which correspond to the two-cluster structures including the rearrangement channels. The remaining part of the wave functions describes the channels with three-cluster structures, and the integrals involving this part are then mathematically well defined

Five Easy Principles to Make Math Moments Count

Science.gov (United States)

Cutler, Carrie S.

2011-01-01

Preschool children are learning so many skills--how to cut with scissors, zip zippers, recognize the alphabet and their names, and share toys with others. A strong academic curriculum also requires that children learn more about math (National Council of Teachers of Mathematics [NCTM], 2000). By following the five easy principles outlined here,…

The principle of finiteness – a guideline for physical laws

International Nuclear Information System (INIS)

Sternlieb, Abraham

2013-01-01

I propose a new principle in physics-the principle of finiteness (FP). It stems from the definition of physics as a science that deals with measurable dimensional physical quantities. Since measurement results including their errors, are always finite, FP postulates that the mathematical formulation of legitimate laws in physics should prevent exactly zero or infinite solutions. I propose finiteness as a postulate, as opposed to a statement whose validity has to be corroborated by, or derived theoretically or experimentally from other facts, theories or principles. Some consequences of FP are discussed, first in general, and then more specifically in the fields of special relativity, quantum mechanics, and quantum gravity. The corrected Lorentz transformations include an additional translation term depending on the minimum length epsilon. The relativistic gamma is replaced by a corrected gamma, that is finite for v=c. To comply with FP, physical laws should include the relevant extremum finite values in their mathematical formulation. An important prediction of FP is that there is a maximum attainable relativistic mass/energy which is the same for all subatomic particles, meaning that there is a maximum theoretical value for cosmic rays energy. The Generalized Uncertainty Principle required by Quantum Gravity is actually a necessary consequence of FP at Planck's scale. Therefore, FP may possibly contribute to the axiomatic foundation of Quantum Gravity.

Investigation of the dual-gauge principle for eliminating measurement interference in nuclear density and moisture gauges

International Nuclear Information System (INIS)

Dunn, W.L.

1974-07-01

The development of mathematical models for an application of the dual-gauge principle to surface neutron moisture content gauges were made under an Agency co-ordinated research programme. The response of a detector (such as a BF 3 proportional counter) to low-energy neutrons is dependent on the hydrogen present in the sample in the form of water. Other factors which affect the gauge response are sample density, composition (particularly with regard to the presence of strong thermal neutron absorbers), and bound hydrogen content. In this work mathematical models for epicadmium and bare BF 3 detector response have been developed for surface neutron moisture content gauges. These models are based on epithermal and thermal line and area flux models obtained from Diffusion Theory and Transport Theory, where flux as a function of radial distance, r, from the source is phi(r), line flux ∫ phi (r) dr, and area flux is ∫ phi (r)rdr. All models have been checked by calculation and comparison to experimental results except for the Transport Theory thermal flux models. The computer calculations were made on an IBM 370/165 system. In addition, the dual-gauge principle was applied and demonstrated as a means of minimizing the composition measurement interference

MATHEMATICAL MODELLING OF AIRCRAFT PILOTING PROSSESS UNDER SPECIFIED FLIGHT PATH

Directory of Open Access Journals (Sweden)

И. Кузнецов

2012-04-01

Full Text Available The author suggests mathematical model of pilot’s activity as follow up system and mathematical methods of pilot’s activity description. The main idea of the model is flight path forming and aircraft stabilization on it during instrument flight. Input of given follow up system is offered to be aircraft deflection from given path observed by pilot by means of sight and output is offered to be pilot’s regulating actions for aircraft stabilization on flight path.

Graphic Organizer in Action: Solving Secondary Mathematics Word Problems

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Khoo Jia Sian

2016-09-01

Full Text Available Mathematics word problems are one of the most challenging topics to learn and teach in secondary schools. This is especially the case in countries where English is not the first language for the majority of the people, such as in Brunei Darussalam. Researchers proclaimed that limited language proficiency and limited Mathematics strategies are the possible causes to this problem. However, whatever the reason is behind difficulties students face in solving Mathematical word problems, it is perhaps the teaching and learning of the Mathematics that need to be modified. For example, the use of four-square-and-a-diamond graphic organizer that infuses model drawing skill; and Polya’s problem solving principles, to solve Mathematical word problems may be some of the strategies that can help in improving students’ word problem solving skills. This study, through quantitative analysis found that the use of graphic organizer improved students’ performance in terms of Mathematical knowledge, Mathematical strategy and Mathematical explanation in solving word problems. Further qualitative analysis revealed that the use of graphic organizer boosted students’ confidence level and positive attitudes towards solving word problems.Keywords: Word Problems, Graphic Organizer, Algebra, Action Research, Secondary School Mathematics DOI: http://dx.doi.org/10.22342/jme.7.2.3546.83-90

"Real Teaching" in the Mathematics Classroom: A Comparison of the Instructional Practices of Elementary Teachers in Urban High-Poverty Schools

Science.gov (United States)

McKinney, Sueanne E.; Robinson, Jack; Berube, Clair T.

2013-01-01

The National Council of Teachers of Mathematics' "Principles and Standards for School Mathematics" outlines fundamental elements that are crucial for creating a problem-solving and inquiry-driven classroom learning environment that highlights conceptual understandings of mathematics ideas. Even though this document outlines…

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

... consistent model for incompressible two-phase flows with phase transitions is considered mathematically. The model is based on first principles, i.e., balance of mass, momentum and energy. In the isothermal case, this problem is analysed to obtain local well-posedness, stability of non-degenerate equilibria, and global ...

Structured pigeonhole principle, search problems and hard tautologies

Czech Academy of Sciences Publication Activity Database

Krajíček, Jan

2005-01-01

Roč. 70, č. 2 (2005), s. 619-630 ISSN 0022-4812 R&D Projects: GA AV ČR(CZ) IAA1019401; GA MŠk(CZ) LN00A056 Institutional research plan: CEZ:AV0Z10190503 Keywords : proof complexity * pigeonhole principle * serch problems Subject RIV: BA - General Mathematics Impact factor: 0.470, year: 2005

Classical and Weak Solutions for Two Models in Mathematical Finance

Science.gov (United States)

Gyulov, Tihomir B.; Valkov, Radoslav L.

2011-12-01

We study two mathematical models, arising in financial mathematics. These models are one-dimensional analogues of the famous Black-Scholes equation on finite interval. The main difficulty is the degeneration at the both ends of the space interval. First, classical solutions are studied. Positivity and convexity properties of the solutions are discussed. Variational formulation in weighted Sobolev spaces is introduced and existence and uniqueness of the weak solution is proved. Maximum principle for weak solution is discussed.

Principles of broadband switching and networking

CERN Document Server

Liew, Soung C

2010-01-01

An authoritative introduction to the roles of switching and transmission in broadband integrated services networks Principles of Broadband Switching and Networking explains the design and analysis of switch architectures suitable for broadband integrated services networks, emphasizing packet-switched interconnection networks with distributed routing algorithms. The text examines the mathematical properties of these networks, rather than specific implementation technologies. Although the pedagogical explanations in this book are in the context of switches, many of the fundamenta

On the invariance principle

Energy Technology Data Exchange (ETDEWEB)

Moller-Nielsen, Thomas [University of Oxford (United Kingdom)

2014-07-01

Physicists and philosophers have long claimed that the symmetries of our physical theories - roughly speaking, those transformations which map solutions of the theory into solutions - can provide us with genuine insight into what the world is really like. According to this 'Invariance Principle', only those quantities which are invariant under a theory's symmetries should be taken to be physically real, while those quantities which vary under its symmetries should not. Physicists and philosophers, however, are generally divided (or, indeed, silent) when it comes to explaining how such a principle is to be justified. In this paper, I spell out some of the problems inherent in other theorists' attempts to justify this principle, and sketch my own proposed general schema for explaining how - and when - the Invariance Principle can indeed be used as a legitimate tool of metaphysical inference.

SIGNIFICANCE OF EARLY-AGE LEARNING OF MATHEMATICAL SKILLS

Directory of Open Access Journals (Sweden)

Sead Rešić

2011-12-01

Full Text Available It is a fact that only hereditary, i.e. genetic factors are not sufficient for development of a child’s brain; on the contrary, a child needs external stimuli expressed through touch, speech, images, which lead to the conclusion that immediate and extended surroundings shape the brain, meaning that the external stimuli, stronger or weaker, mutually connect the brain cells and neurons. Questions regarding the development of mathematical manner of thinking are mostly based on the natural process of learning, however, this paper deals with deeper set of problems, which are not only difficult to resolve but possibly there is no resolution. Namely, a question is posed what is the appropriate age when a child is ready and able to solve certain mathematical problems or notice mathematical principles, that is, whether they are actually exist clearly defined age boundaries based on which a conclusion could be made about the time and individual is ready to solve mathematical problems of a concrete difficulty level or to notice mathematical laws.

The precautionary principle in fisheries management under climate change: How the international legal framework formulate it?

Science.gov (United States)

Latifah, E.; Imanullah, M. N.

2018-03-01

One of the objectives of fisheries management is to reach long-term sustainable benefits of the fish stocks while reducing the risk of severe or irreversible damage to the marine ecosystem. Achieving this objective needs, the good scientific knowledge and understanding on fisheries management including scientific data and information on the fish stock, fishing catch, distribution, migration, the proportion of mature fish, the mortality rate, reproduction as well as the knowledge on the impact of fishing on dependent and associated species and other species belonging to the same ecosystem, and further the impact of climate change and climate variability on the fish stocks and marine ecosystem. Lack of this scientific knowledge may lead to high levels of uncertainty. The precautionary principle is one of the basic environmental principles needed in overcoming this problem. An essence of this principle is that, in facing the serious risk as a result of the limited scientific knowledge or the absence of complete evidence of harm, it should not prevent the precautionary measures in minimizing risks and protecting the fish stocks and ecosystem. This study aims to examine how the precautionary principle in fisheries management be formulated into the international legal framework, especially under the climate change framework.

INFORMATIONAL-METHODICAL SUPPORT OF THE COURSE «MATHEMATICAL LOGIC AND THEORY OF ALGORITHMS»

Directory of Open Access Journals (Sweden)

Y. I. Sinko

2010-06-01

Full Text Available In this article the basic principles of training technique of future teachers of mathematics to foundations of mathematical logic and theory of algorithms in the Kherson State University with the use of information technologies are examined. General description of functioning of the methodical system of learning of mathematical logic with the use of information technologies, in that variant, when information technologies are presented by the integrated specialized programmatic environment of the educational purpose «MatLog» is given.

Elements of the history of mathematics

CERN Document Server

Bourbaki, Nicolas

1994-01-01

This work gathers together, without substantial modification, the major­ ity of the historical Notes which have appeared to date in my Elements de M atMmatique. Only the flow has been made independent of the Elements to which these Notes were attached; they are therefore, in principle, accessible to every reader who possesses a sound classical mathematical background, of undergraduate standard. Of course, the separate studies which make up this volume could not in any way pretend to sketch, even in a summary manner, a complete and con­ nected history of the development of Mathematics up to our day. Entire parts of classical mathematics such as differential Geometry, algebraic Geometry, the Calculus of variations, are only mentioned in passing; others, such as the theory of analytic functions, that of differential equations or partial differ­ ential equations, are hardly touched on; all the more do these gaps become more numerous and more important as the modern era is reached. It goes without saying that t...

Principles of Mobile Communication

CERN Document Server

Stüber, Gordon L

2012-01-01

This mathematically rigorous overview of physical layer wireless communications is now in a third, fully revised and updated edition. Along with coverage of basic principles sufficient for novice students, the volume includes plenty of finer details that will satisfy the requirements of graduate students aiming to research the topic in depth. It also has a role as a handy reference for wireless engineers. The content stresses core principles that are applicable to a broad range of wireless standards. Beginning with a survey of the field that introduces an array of issues relevant to wireless communications and which traces the historical development of today’s accepted wireless standards, the book moves on to cover all the relevant discrete subjects, from radio propagation to error probability performance and cellular radio resource management. A valuable appendix provides a succinct and focused tutorial on probability and random processes, concepts widely used throughout the book. This new edition, revised...

Principles of mobile communication

CERN Document Server

Stüber, Gordon L

2017-01-01

This mathematically rigorous overview of physical layer wireless communications is now in a 4th, fully revised and updated edition. The new edition features new content on 4G cellular systems, 5G cellular outlook, bandpass signals and systems, and polarization, among many other topics, in addition to a new chapters on channel assignment techniques. Along with coverage of fundamentals and basic principles sufficient for novice students, the volume includes finer details that satisfy the requirements of graduate students aiming to conduct in-depth research. The book begins with a survey of the field, introducing issues relevant to wireless communications. The book moves on to cover relevant discrete subjects, from radio propagation, to error probability performance, and cellular radio resource management. An appendix provides a tutorial on probability and random processes. The content stresses core principles that are applicable to a broad range of wireless standards. New examples are provided throughout the bo...

THE INTEGRATION MODEL OF SYSTEMS OF DISTANCE AND OF TRADITIONAL MATHEMATICS LEARNING OF SENIOR PUPILS

OpenAIRE

Игорь Николаевич Макарьев

2013-01-01

In this article the author dwells on the content and structure of the model of integration of system of distance learning to mathematics of senior pupils and traditional paradigm of education. This kind of integration is based on such principles as independence, individualization, flexibility, nonlinearity, openness. Specifics of the methodological support of distance mathematics learning are also analyzed. Particularly the author asserts that the system of distance mathematics learning can t...

Development of an electromechanical principle for wet and dry milling

Science.gov (United States)

Halbedel, Bernd; Kazak, Oleg

2018-05-01

The paper presents a novel electromechanical principle for wet and dry milling of different materials, in which the milling beads are moved under a time- and local-variable magnetic field. A possibility to optimize the milling process in such a milling machine by simulation of the vector gradient distribution of the electromagnetic field in the process room is presented. The mathematical model and simulation methods based on standard software packages are worked out. The results of numerical simulations and experimental measurements of the electromagnetic field in the working chamber of a developed and manufactured laboratory plant correlate well with each other. Using the obtained operating parameters, dry milling experiments with crushed cement clinker and wet milling experiments of organic agents in the laboratory plant are performed and the results are discussed here.

An experimental and mathematical analysis of lymphopoiesis dynamics under continuous irradiation

International Nuclear Information System (INIS)

Zukhbaya, T.M.; Smirnova, O.A.

1991-01-01

A mathematical model describing the dynamics of lymphopoiesis in mammals continuously exposed to ionizing radiation has been developed. It is based on the theory of chalone regulation of hematopoiesis. The model comprises a system of nine differential equations. Results from the model were compared with our experimental data for bone marrow and blood lymphocytes of rats continuously exposed to gamma radiation in a wide range of dose rates. The model reproduces the lymphopoiesis dynamics that we observed in our experiment, in particular, the radiation hormesis at low dose rates, the reduction of lymphopoiesis at intermediate dose rates, and extinction of lymphopoiesis at high dose rates of continuous radiation. The possible explanation of the hormesis is suggested by the framework of the model. The model can be used for predicting the lymphopoiesis dynamics in mammals under continuous irradiation

Using a Card Trick to Teach Discrete Mathematics

Science.gov (United States)

Simonson, Shai; Holm, Tara S.

2003-01-01

We present a card trick that can be used to review or teach a variety of topics in discrete mathematics. We address many subjects, including permutations, combinations, functions, graphs, depth first search, the pigeonhole principle, greedy algorithms, and concepts from number theory. Moreover, the trick motivates the use of computers in…

Design of Learning Objects for Concept Learning: Effects of Multimedia Learning Principles and an Instructional Approach

Science.gov (United States)

Chiu, Thomas K. F.; Churchill, Daniel

2016-01-01

Literature suggests using multimedia learning principles in the design of instructional material. However, these principles may not be sufficient for the design of learning objects for concept learning in mathematics. This paper reports on an experimental study that investigated the effects of an instructional approach, which includes two teaching…

26 CFR 1.671-2 - Applicable principles.

Science.gov (United States)

2010-04-01

... 26 Internal Revenue 8 2010-04-01 2010-04-01 false Applicable principles. 1.671-2 Section 1.671-2...) INCOME TAXES Grantors and Others Treated As Substantial Owners § 1.671-2 Applicable principles. (a) Under... included in a portion of the trust are set forth in § 1.671-3. (b) Since the principle underlying subpart E...

Design Principles for Serious Video Games in Mathematics Education: From Theory to Practice

OpenAIRE

Konstantinos Chorianopoulos; Michail Giannakos

2014-01-01

There is growing interest in the employment of serious video games in science education, but there are no clear design principles. After surveying previous work in serious video game design, we highlighted the following design principles: 1) engage the students with narrative (hero, story), 2) employ familiar gameplay mechanics from popular video games, 3) engage students into constructive trial and error game-play and 4) situate collaborative learning. As illustrated examples we designed two...

Solutions manual to accompany finite mathematics models and applications

CERN Document Server

Morris, Carla C

2015-01-01

A solutions manual to accompany Finite Mathematics: Models and Applications In order to emphasize the main concepts of each chapter, Finite Mathematics: Models and Applications features plentiful pedagogical elements throughout such as special exercises, end notes, hints, select solutions, biographies of key mathematicians, boxed key principles, a glossary of important terms and topics, and an overview of use of technology. The book encourages the modeling of linear programs and their solutions and uses common computer software programs such as LINDO. In addition to extensive chapters on pr

La Meme Chose: How Mathematics Can Explain the Thinking of Children and the Thinking of Children Can Illuminate Mathematical Philosophy

Science.gov (United States)

Cable, John

2014-01-01

This article offers a new interpretation of Piaget's decanting experiments, employing the mathematical notion of equivalence instead of conservation. Some reference is made to Piaget's theories and to his educational legacy, but the focus in on certain of the experiments. The key to the new analysis is the abstraction principle, which…

Case Study of an Epistemic Mathematics Computer Game

Science.gov (United States)

Buteau, Chantal; Muller, Eric

2018-01-01

E-Brock Bugs is a serious educational game (SEG) about probability which was created based on Devlin's design principles for games whose players adopt identities of mathematically able persons. This kind of games in which "players think and act like real world professionals" has been called epistemic. This article presents an empirical…

The mathematical models of solution mining and case study

International Nuclear Information System (INIS)

Jacobson, R.H.; Waskovsky, J.; Wang Xiwen; Wang Haifeng

1991-01-01

The mathematical model of parameters which describe solution mining and the principle of ore leaching are presented theoretically and thoroughly with the emphasis on in-situ leaching with a biolixiviant, furthermore, the example of bioleach mining, or biomining, in an abandoned underground copper mine is discussed

Examining the design features of a communication-rich, problem-centred mathematics professional development

Science.gov (United States)

de Araujo, Zandra; Orrill, Chandra Hawley; Jacobson, Erik

2018-04-01

While there is considerable scholarship describing principles for effective professional development, there have been few attempts to examine these principles in practice. In this paper, we identify and examine the particular design features of a mathematics professional development experience provided for middle grades teachers over 14 weeks. The professional development was grounded in a set of mathematical tasks that each had one right answer, but multiple solution paths. The facilitator engaged participants in problem solving and encouraged participants to work collaboratively to explore different solution paths. Through analysis of this collaborative learning environment, we identified five design features for supporting teacher learning of important mathematics and pedagogy in a problem-solving setting. We discuss these design features in depth and illustrate them by presenting an elaborated example from the professional development. This study extends the existing guidance for the design of professional development by examining and operationalizing the relationships among research-based features of effective professional development and the enacted features of a particular design.

Structured Mathematical Modeling of Industrial Boiler

Directory of Open Access Journals (Sweden)

Abdullah Nur Aziz

2014-04-01

Full Text Available As a major utility system in industry, boilers consume a large portion of the total energy and costs. Significant reduction of boiler cost operation can be gained through improvements in efficiency. In accomplishing such a goal, an adequate dynamic model that comprehensively reflects boiler characteristics is required. This paper outlines the idea of developing a mathematical model of a water-tube industrial boiler based on first principles guided by the bond graph method in its derivation. The model describes the temperature dynamics of the boiler subsystems such as economizer, steam drum, desuperheater, and superheater. The mathematical model was examined using industrial boiler performance test data.It can be used to build a boiler simulator or help operators run a boiler effectively.

Mathematical model of two-phase flow in accelerator channel

Directory of Open Access Journals (Sweden)

О.Ф. Нікулін

2010-01-01

Full Text Available  The problem of  two-phase flow composed of energy-carrier phase (Newtonian liquid and solid fine-dispersed phase (particles in counter jet mill accelerator channel is considered. The mathematical model bases goes on the supposition that the phases interact with each other like independent substances by means of aerodynamics’ forces in conditions of adiabatic flow. The mathematical model in the form of system of differential equations of order 11 is represented. Derivations of equations by base physical principles for cross-section-averaged quantity are produced. The mathematical model can be used for estimation of any kinematic and thermodynamic flow characteristics for purposely parameters optimization problem solving and transfer functions determination, that take place in  counter jet mill accelerator channel design.

On Independence of Variants of the Weak Pigeonhole Principle

Czech Academy of Sciences Publication Activity Database

Jeřábek, Emil

2007-01-01

Roč. 17, č. 3 (2007), s. 587-604 ISSN 0955-792X R&D Projects: GA AV ČR IAA1019401; GA MŠk(CZ) 1M0545 Institutional research plan: CEZ:AV0Z10190503 Keywords : bounded arithmetic * pigeonhole principle * KPT witnessing Subject RIV: BA - General Mathematics Impact factor: 0.821, year: 2007

On the Huygens principle for bianisotropic mediums with symmetric permittivity and permeability dyadics

Energy Technology Data Exchange (ETDEWEB)

Faryad, Muhammad, E-mail: muhammad.faryad@lums.edu.pk [Department of Physics, Lahore University of Management Sciences, Lahore 54792 (Pakistan); Lakhtakia, Akhlesh [Department of Engineering Science and Mechanics, The Pennsylvania State University, University Park, PA 16802 (United States)

2017-02-19

Mathematical statements of the Huygens principle relate the electric and magnetic field phasors at an arbitrary location in a source-free region enclosed by a surface to the tangential components of the electric and magnetic field phasors over that surface, via the dyadic Green functions applicable to the linear homogeneous medium occupying that region. We have mathematically formulated the Huygens principle for the electric and magnetic field phasors when the permittivity and permeability dyadics of the medium are symmetric, the symmetric parts of the two magnetoelectric dyadics of the medium are negative of each other, and both magnetoelectric dyadics also contain anti-symmetric terms. We have also formulated the Huygens principle for the electric (resp. magnetic) field phasor in a medium whose permittivity (resp. permeability) is scalar, the permeability (resp. permittivity) is symmetric, the symmetric parts of the two magnetoelectric dyadics reduce to dissimilar scalars, and anti-symmetric parts of the two magnetoelectric dyadics are identical. - Highlights: • The Huygens principle was formulated for bianistropic mediums when the permittivity and permeability dyadics of the medium are symmetric. • The formulation covers isotropic, biisotropic, and gyrotropic-like uniaxial mediums for which the Huygens principle is already available. • The formulation also covers new mediums like biaxial, chiro-omega, pseudo chiral, gyrotropic-like biaxial, and Lorentz reciprocal mediums.

The constitutive laws of one-dimensional, two-fluid models for two-phase flows - Possible mathematical forms - Restrictions resulting from basic principles

International Nuclear Information System (INIS)

Boure, Jean.

1978-05-01

From both the theoretical and the practical points of view, the problem of constitutive laws is a part and parcel of the modeling problem. In particular, the necessity to restore in the model, through topological laws, some of the information lost during the usual averaging process is emphasized. It is shown that the customary 'void fraction' topological law Psub(V)=Psub(L) should be proscribed whenever propagation phenomena are involved. A new void fraction topological law is proposed. The limitations of the current assumption of constant pressure within any phase in any cross section are also illustrated. The importance of proximity effects (neighborhood and history effects, related to characteristic lengths and times) is brought out. It results in the importance of the mathematical form of the constitutive laws. Various approaches to the constitutive law problem and possible mathematical forms for the transfer laws are reviewed. The simplest form (transfert terms as functions of the dependent variables only) may have some usefulness if interpretation of the results in terms of propagation phenomena is banned. A good compromise between the necessity to take proximity effects into account and to obtain a tractable set of equations is carried out when so called 'differential terms' are introduced in the transfer laws. The last part of the paper is devoted to some restrictions, which are imposed to the transfer terms because of some basic principles: indifference to Galilean changes of frame and to some changes of origins, second law of thermodynamics and assumption of local thermodynamic equilibrium, closure constraints. Practical recommendations are formulated [fr

Control Engineering, System Theory and Mathematics: The Teacher's Challenge

Science.gov (United States)

Zenger, K.

2007-01-01

The principles, difficulties and challenges in control education are discussed and compared to the similar problems in the teaching of mathematics and systems science in general. The difficulties of today's students to appreciate the classical teaching of engineering disciplines, which are based on rigorous and scientifically sound grounds, are…

Principles of computational fluid dynamics

International Nuclear Information System (INIS)

Wesseling, P.

2001-01-01

The book is aimed at graduate students, researchers, engineers and physicists involved in flow computations. An up-to-date account is given of the present state- of-the-art of numerical methods employed in computational fluid dynamics. The underlying numerical principles are treated with a fair amount of detail, using elementary mathematical analysis. Attention is given to difficulties arising from geometric complexity of the flow domain and of nonuniform structured boundary-fitted grids. Uniform accuracy and efficiency for singular perturbation problems is studied, pointing the way to accurate computation of flows at high Reynolds number. Much attention is given to stability analysis, and useful stability conditions are provided, some of them new, for many numerical schemes used in practice. Unified methods for compressible and incompressible flows are discussed. Numerical analysis of the shallow-water equations is included. The theory of hyperbolic conservation laws is treated. Godunov's order barrier and how to overcome it by means of slope-limited schemes is discussed. An introduction is given to efficient iterative solution methods, using Krylov subspace and multigrid acceleration. Many pointers are given to recent literature, to help the reader to quickly reach the current research frontier. (orig.)

Psychological effects and epistemological education through mathematics "abstraction" and "construction"

Directory of Open Access Journals (Sweden)

Aurel Pera

2015-10-01

Full Text Available This study is part of a broader research which will be found in future work, Psychology and epistemology of mathematical creation, complementary work of experimental research psychology mathematics, whose investigative approach, promoting the combination type cross section paradigms and quantitative methods and qualitative and comparative method and the analytic-synthetic, based on the following idea: to make learning as efficient, contents and methods must be appropriate to the individual particularities of the pupils, a measure of the balance between converging and diverging dosing tasks as a promising opening to the transition from education proficiency in math performance. At this juncture, mathematical existence as ontological approach against the background of a history of "abstraction" mathematical and theoretical observations on the abstraction, realization and other mathematical thought processes, explanatory approach fulfills the context in which s mathematics constituted an important factor in psychological and methodological perspective, in a context of maximizing the educational effectiveness that depends on the quality of the methods used in teaching, focused on knowledge of the general principles of psycho-didactics not only mathematical and mental organization individual student or knowledge of the factors that make possible psycho-educational learning process.

Methods of modern mathematical physics

CERN Document Server

Reed, Michael

1980-01-01

This book is the first of a multivolume series devoted to an exposition of functional analysis methods in modern mathematical physics. It describes the fundamental principles of functional analysis and is essentially self-contained, although there are occasional references to later volumes. We have included a few applications when we thought that they would provide motivation for the reader. Later volumes describe various advanced topics in functional analysis and give numerous applications in classical physics, modern physics, and partial differential equations.

Tensor Arithmetic, Geometric and Mathematic Principles of Fluid Mechanics in Implementation of Direct Computational Experiments

Directory of Open Access Journals (Sweden)

Bogdanov Alexander

2016-01-01

Full Text Available The architecture of a digital computing system determines the technical foundation of a unified mathematical language for exact arithmetic-logical description of phenomena and laws of continuum mechanics for applications in fluid mechanics and theoretical physics. The deep parallelization of the computing processes results in functional programming at a new technological level, providing traceability of the computing processes with automatic application of multiscale hybrid circuits and adaptive mathematical models for the true reproduction of the fundamental laws of physics and continuum mechanics.

Didactic trajectory of research in mathematics education using research-based learning

Science.gov (United States)

Charitas Indra Prahmana, Rully; Kusumah, Yaya S.; Darhim

2017-10-01

This study aims to describe the role of research-based learning in design a learning trajectory of research in mathematics education to enhance research and academic writing skills for pre-service mathematics teachers. The method used is a design research with three stages, namely the preliminary design, teaching experiment, and retrospective analysis. The research subjects are pre-service mathematics teacher class of 2012 from one higher education institution in Tangerang - Indonesia. The use of research-based learning in designing learning trajectory of research in mathematics education plays a crucial role as a trigger to enhancing math department preservice teachers research and academic writing skills. Also, this study also describes the design principles and characteristics of the learning trajectory namely didactic trajectory generated by the role of research-based learning syntax.

First-principles studies of PETN molecular crystal vibrational frequencies under high pressure

Science.gov (United States)

Perger, Warren; Zhao, Jijun

2005-07-01

The vibrational frequencies of the PETN molecular crystal were calculated using the first-principles CRYSTAL03 program which employs an all-electron LCAO approach and calculates analytic first derivatives of the total energy with respect to atomic displacements. Numerical second derivatives were used to enable calculation of the vibrational frequencies at ambient pressure and under various states of compression. Three different density functionals, B3LYP, PW91, and X3LYP were used to examine the effect of the exchange-correlation functional on the vibrational frequencies. The pressure-induced shift of the vibrational frequencies will be presented and compared with experiment. The average deviation with experimental results is shown to be on the order of 2-3%, depending on the functional used.

Mathematical modeling of flow-injection techniques and their applications for environmental monitoring

International Nuclear Information System (INIS)

Begum, N.N.; Ahmed, J.

2006-01-01

A classification of the existing mathematical models of flow-injection (FI) manifolds based on the main principles on which they are built, have been proposed. Numerous mathematical models of FI systems employing ideas from different scientific areas (e.g. mathematical statistics, chemical engineering, chromatography) have been developed so far. The models have been compared with respect to their predictive power, the complexity of their mathematical treatment, and the requirements for computation time when applied to single-line, multi-channel and conjugated two-line FI systems. It is concluded that the axially dispersed plug flow model deserves special attention because it offers an acceptable compromise between the conflicting requirements for maximal possible mathematical simplicity and maximal possible precision. Applicability of these existing flow-injection models to single-line, multi-channel and conjugated two-line systems for environmental monitoring have been discussed. (author)

Licensure tests for special education teachers: how well they assess knowledge of reading instruction and mathematics.

Science.gov (United States)

Stotsky, Sandra

2009-01-01

To determine the extent to which knowledge of evidence-based reading instruction and mathematics is assessed on licensure tests for prospective special education teachers, this study drew on information provided by Educational Testing Service (ETS), the American Board for Certification of Teacher Excellence, and National Evaluation Systems (now Evaluation Systems group of Pearson). It estimated the percentage of test items on phonemic awareness, phonics, and vocabulary knowledge and on mathematics content. It also analyzed descriptions of ETS's tests of "principles of teaching and learning." Findings imply that prospective special education teachers should be required to take both a dedicated test of evidence-based reading instructional knowledge, as in California, Massachusetts, and Virginia, and a test of mathematical knowledge, as in Massachusetts. States must design their own tests of teaching principles to assess knowledge of evidence-based educational theories.

Damped oscillations of linear systems a mathematical introduction

CERN Document Server

Veselić, Krešimir

2011-01-01

The theory of linear damped oscillations was originally developed more than hundred years ago and is still of vital research interest to engineers, mathematicians and physicists alike. This theory plays a central role in explaining the stability of mechanical structures in civil engineering, but it also has applications in other fields such as electrical network systems and quantum mechanics. This volume gives an introduction to linear finite dimensional damped systems as they are viewed by an applied mathematician. After a short overview of the physical principles leading to the linear system model, a largely self-contained mathematical theory for this model is presented. This includes the geometry of the underlying indefinite metric space, spectral theory of J-symmetric matrices and the associated quadratic eigenvalue problem. Particular attention is paid to the sensitivity issues which influence numerical computations. Finally, several recent research developments are included, e.g. Lyapunov stability and ...

From bacteria to mollusks: the principles underlying the biomineralization of iron oxide materials.

Science.gov (United States)

Faivre, Damien; Godec, Tina Ukmar

2015-04-13

Various organisms possess a genetic program that enables the controlled formation of a mineral, a process termed biomineralization. The variety of biological material architectures is mind-boggling and arises from the ability of organisms to exert control over crystal nucleation and growth. The structure and composition of biominerals equip biomineralizing organisms with properties and functionalities that abiotically formed materials, made of the same mineral, usually lack. Therefore, elucidating the mechanisms underlying biomineralization and morphogenesis is of interdisciplinary interest to extract design principles that will enable the biomimetic formation of functional materials with similar capabilities. Herein, we summarize what is known about iron oxides formed by bacteria and mollusks for their magnetic and mechanical properties. We describe the chemical and biological machineries that are involved in controlling mineral precipitation and organization and show how these organisms are able to form highly complex structures under physiological conditions. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

5 CFR 551.202 - General principles.

Science.gov (United States)

2010-01-01

... 5 Administrative Personnel 1 2010-01-01 2010-01-01 false General principles. 551.202 Section 551... ADMINISTRATION UNDER THE FAIR LABOR STANDARDS ACT Exemptions and Exclusions § 551.202 General principles. In all exemption determinations, the agency must observe the following principles: (a) Each employee is presumed to...

24 CFR 3282.402 - General principles.

Science.gov (United States)

2010-04-01

... 24 Housing and Urban Development 5 2010-04-01 2010-04-01 false General principles. 3282.402... and Remedial Actions § 3282.402 General principles. (a) Nothing in this subpart or in these... manufactured home manufacturers to provide remedial actions under this subpart is limited by the principle that...

Application of a mathematical model for ergonomics in lean manufacturing.

Science.gov (United States)

Botti, Lucia; Mora, Cristina; Regattieri, Alberto

2017-10-01

The data presented in this article are related to the research article "Integrating ergonomics and lean manufacturing principles in a hybrid assembly line" (Botti et al., 2017) [1]. The results refer to the application of the mathematical model for the design of lean processes in hybrid assembly lines, meeting both the lean principles and the ergonomic requirements for safe assembly work. Data show that the success of a lean strategy is possible when ergonomics of workers is a parameter of the assembly process design.

Mathematical Biology Modules Based on Modern Molecular Biology and Modern Discrete Mathematics

Science.gov (United States)

Davies, Robin; Hodge, Terrell; Enyedi, Alexander

2010-01-01

We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network. PMID:20810955

Mathematical biology modules based on modern molecular biology and modern discrete mathematics.

Science.gov (United States)

Robeva, Raina; Davies, Robin; Hodge, Terrell; Enyedi, Alexander

2010-01-01

We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network.

Implicit Lagrangian equations and the mathematical modeling of physical systems

NARCIS (Netherlands)

Moreau, Luc; van der Schaft, Arjan

2002-01-01

We introduce a class of optimal control problems on manifolds which gives rise (via the Pontryagin maximum principle) to a class of implicit Lagrangian systems (a notion which is introduced in the paper). We apply this to the mathematical modeling of interconnected mechanical systems and mechanical

Teaching Undergraduate Mathematics Using CAS Technology: Issues and Prospects

Science.gov (United States)

Tobin, Patrick C.; Weiss, Vida

2016-01-01

The use of handheld CAS technology in undergraduate mathematics courses in Australia is paradoxically shrinking under sustained disapproval or disdain from the professional mathematics community. Mathematics education specialists argue with their mathematics colleagues over a range of issues in course development and this use of CAS or even…

General principles underlying the decommissioning of nuclear facilities

International Nuclear Information System (INIS)

1988-03-01

Previous statements on the use of the term 'decommissioning' by the International Atomic Energy Agency, the Atomic Energy Control Board, and the Advisory Committee on Nuclear Safety are reviewed, culminating in a particular definition for its use in this paper. Three decommissioning phases are identified and discussed, leading to eight general principles governing decommissioning including one related to financing

Principles underlying rational design of live attenuated influenza vaccines

Science.gov (United States)

Jang, Yo Han

2012-01-01

Despite recent innovative advances in molecular virology and the developments of vaccines, influenza virus remains a serious burden for human health. Vaccination has been considered a primary countermeasure for prevention of influenza infection. Live attenuated influenza vaccines (LAIVs) are particularly attracting attention as an effective strategy due to several advantages over inactivated vaccines. Cold-adaptation, as a classical means for attenuating viral virulence, has been successfully used for generating safe and effective donor strains of LAIVs against seasonal epidemics and occasional pandemics. Recently, the advent of reverse genetics technique expedited a variety of rational strategies to broaden the pool of LAIVs. Considering the breadth of antigenic diversity of influenza virus, the pool of LAIVs is likely to equip us with better options for controlling influenza pandemics. With a brief reflection on classical attenuating strategies used at the initial stage of development of LAIVs, especially on the principles underlying the development of cold-adapted LAIVs, we further discuss and outline other attenuation strategies especially with respect to the rationales for attenuation, and their practicality for mass production. Finally, we propose important considerations for a rational vaccine design, which will provide us with practical guidelines for improving the safety and effectiveness of LAIVs. PMID:23596576

Using Mathematics, Mathematical Applications, Mathematical Modelling, and Mathematical Literacy: A Theoretical Study

Science.gov (United States)

Mumcu, Hayal Yavuz

2016-01-01

The purpose of this theoretical study is to explore the relationships between the concepts of using mathematics in the daily life, mathematical applications, mathematical modelling, and mathematical literacy. As these concepts are generally taken as independent concepts in the related literature, they are confused with each other and it becomes…

Teaching mathematics to able children

CERN Document Server

Koshy, Valsa

2012-01-01

This book enables teachers to effectively meet the needs of their most able mathematicians. Using a tried and tested set of principles developed and used by The Able Children's Education Unit at Brunel University, the author demonstrates how to: identify high mathematical ability in a pupil, plan suitably challenging activities and teach them most effectively within the existing National Numeracy framework, make the most of the classroom resources available, including ICT and external agencies, implement strategies for differentiation, illustrated with real-life classroom examples. Ac

A mathematical model in cellular manufacturing system considering subcontracting approach under constraints

Directory of Open Access Journals (Sweden)

Kamran Forghani

2012-10-01

Full Text Available In this paper, a new mathematical model in cellular manufacturing systems (CMSs has been presented. In order to increase the performance of manufacturing system, the production quantity of parts has been considered as a decision variable, i.e. each part can be produced and outsourced, simultaneously. This extension would be minimized the unused capacity of machines. The exceptional elements (EEs are taken into account and would be totally outsourced to the external supplier in order to remove intercellular material handling cost. The problem has been formulated as a mixed-integer programming to minimize the sum of manufacturing variable costs under budget, machines capacity and demand constraints. Also, to evaluate advantages of the model, several illustrative numerical examples have been provided to compare the performance of the proposed model with the available classical approaches in the literature.

Architecture and mathematics from antiquity to the future

CERN Document Server

2015-01-01

The aim of this collection of essays is to present a broad portrait of the ways in which two seemingly different disciplines are interconnected. The diversity and varied texture of the essays richly illustrates the affinity between architecture and mathematics. As the almost 100 papers presented in this two-volume publication show, every age and every culture has relied on principles of mathematics incorporated in their works of architecture to imbue their built environment with meaning and order. Included are discussions of geometry, proportional systems, linear algebra, periodic and aperiodic tilings, fractals, perspective, computer science and mechanics. Western architecture of every period is examined: Egyptian, Roman, Medieval, Renaissance, Baroque, Enlightenment, twentieth-century and beyond, as is the architecture of Turkey, China, India, Japan, Australia and Islam. The mathematical nature of the architecture of Leon Battista Alberti, Andrea Palladio and Frank Lloyd Wright is examined, and the philosop...

ABOUT THE RELEVANCE AND METHODOLOGY ASPECTS OF TEACHING THE MATHEMATICAL MODELING TO PEDAGOGICAL STUDENTS

Directory of Open Access Journals (Sweden)

Y. A. Perminov

2014-01-01

Full Text Available The paper substantiates the need for profile training in mathematical modeling for pedagogical students, caused by the total penetration of mathematics into different sciences, including the humanities; fast development of the information communications technologies; and growing importance of mathematical modeling, combining the informal scientific and formal mathematical languages with the unique opportunities of computer programming. The author singles out the reasons for mastering and using the mathematical apparatus by teaches in every discipline. Indeed, among all the modern mathematical methods and ideas, mathematical modeling retains its priority in all professional spheres. Therefore, the discipline of “Mathematical Modeling” can play an important role in integrating different components of specialists training in various profiles. By mastering the basics of mathematical modeling, students acquire skills of methodological thinking; learn the principles of analysis, synthesis, generalization of ideas and methods in different disciplines and scientific spheres; and achieve general culture competences. In conclusion, the author recommends incorporating the “Methods of Profile Training in Mathematical Modeling” into the pedagogical magistracy curricula. 

The Comonotonic Sure-Thing Principle

NARCIS (Netherlands)

Wakker, P.P.; Chew, S.H.

1996-01-01

This article identifies the common characterizing condition, the comonotonic sure-thing principle, that underlies the rank-dependent direction in non-expected utility. This condition restricts Savage's sure-thing principle to comonotonic acts, and is characterized in full generality by means of a

Mathematical modeling of a process the rolling delivery

Science.gov (United States)

Stepanov, Mikhail A.; Korolev, Andrey A.

2018-03-01

An adduced analysis of the scientific researches in a domain of the rolling equipments, also research of properties the working material. A one of perspective direction of scientific research this is mathematical modeling. That is broadly used in many scientific disciplines and especially at the technical, applied sciences. With the aid of mathematical modeling it can be study of physical properties of the researching objects and systems. A research of the rolling delivery and transporting devices realized with the aid of a construction of mathematical model of appropriate process. To be described the basic principles and conditions of a construction of mathematical models of the real objects. For example to be consider a construction of mathematical model the rolling delivery device. For a construction that is model used system of the equations, which consist of: Lagrange’s equation of a motion, describing of the law conservation of energy of a mechanical system, and the Navier - Stokes equations, which characterize of the flow of a continuous non-compressed fluid. A construction of mathematical model the rolling deliver to let determined of a total energy of device, and therefore to got the dependence upon the power of drive to a gap between of rolls. A corroborate the hypothesis about laminar the flow of a material into the rolling gap of deliver.

Mathematical Footprints Discovering Mathematics Everywhere

CERN Document Server

Pappas, Theoni

1999-01-01

MATHEMATICAL FOOTPRINTS takes a creative look at the role mathematics has played since prehistoric times, and will play in the future, and uncovers mathematics where you least expect to find it from its many uses in medicine, the sciences, and its appearance in art to its patterns in nature and its central role in the development of computers. Pappas presents mathematical ideas in a readable non-threatening manner. MATHEMATICAL FOOTPRINTS is another gem by the creator of THE MATHEMATICS CALENDAR and author of THE JOY OF MATHEMATICS. "Pappas's books have been gold mines of mathematical ent

Multi-band effective mass approximations advanced mathematical models and numerical techniques

CERN Document Server

Koprucki, Thomas

2014-01-01

This book addresses several mathematical models from the most relevant class of kp-Schrödinger systems. Both mathematical models and state-of-the-art numerical methods for adequately solving the arising systems of differential equations are presented. The operational principle of modern semiconductor nano structures, such as quantum wells, quantum wires or quantum dots, relies on quantum mechanical effects. The goal of numerical simulations using quantum mechanical models in the development of semiconductor nano structures is threefold: First they are needed for a deeper understanding of experimental data and of the operational principle. Secondly, they allow us to predict and optimize in advance the qualitative and quantitative properties of new devices in order to minimize the number of prototypes needed. Semiconductor nano structures are embedded as an active region in semiconductor devices. Thirdly and finally, the results of quantum mechanical simulations of semiconductor nano structures can be used wit...

Nanofabrication principles, capabilities and limits

CERN Document Server

Cui, Zheng

2017-01-01

This second edition of Nanofabrication is one of the most comprehensive introductions on nanofabrication technologies and processes. A practical guide and reference, this book introduces readers to all of the developed technologies that are capable of making structures below 100nm. The principle of each technology is introduced and illustrated with minimum mathematics involved. Also analyzed are the capabilities of each technology in making sub-100nm structures, and the limits of preventing a technology from going further down the dimensional scale. This book provides readers with a toolkit that will help with any of their nanofabrication challenges.

A mathematical model of weight loss under total starvation: evidence against the thrifty-gene hypothesis

Directory of Open Access Journals (Sweden)

John R. Speakman

2013-01-01

The thrifty-gene hypothesis (TGH posits that the modern genetic predisposition to obesity stems from a historical past where famine selected for genes that promote efficient fat deposition. It has been previously argued that such a scenario is unfeasible because under such strong selection any gene favouring fat deposition would rapidly move to fixation. Hence, we should all be predisposed to obesity: which we are not. The genetic architecture of obesity that has been revealed by genome-wide association studies (GWAS, however, calls into question such an argument. Obesity is caused by mutations in many hundreds (maybe thousands of genes, each with a very minor, independent and additive impact. Selection on such genes would probably be very weak because the individual advantages they would confer would be very small. Hence, the genetic architecture of the epidemic may indeed be compatible with, and hence support, the TGH. To evaluate whether this is correct, it is necessary to know the likely effects of the identified GWAS alleles on survival during starvation. This would allow definition of their advantage in famine conditions, and hence the likely selection pressure for such alleles to have spread over the time course of human evolution. We constructed a mathematical model of weight loss under total starvation using the established principles of energy balance. Using the model, we found that fatter individuals would indeed survive longer and, at a given body weight, females would survive longer than males, when totally starved. An allele causing deposition of an extra 80 g of fat would result in an extension of life under total starvation by about 1.1–1.6% in an individual with 10 kg of fat and by 0.25–0.27% in an individual carrying 32 kg of fat. A mutation causing a per allele effect of 0.25% would become completely fixed in a population with an effective size of 5 million individuals in 6000 selection events. Because there have probably been about 24

The Role and relevance of mathematics in the maritime industry ...

African Journals Online (AJOL)

Maritime activities occupy more than three-quarters of the world space and provide a huge occupational industry for mankind. Of late, ship construction and usage including space management onboard the vessels and the ports have brought about a great dependency on mathematical principles or models such as time ...

Structured Mathematical Modeling of Industrial Boiler

OpenAIRE

Aziz, Abdullah Nur; Nazaruddin, Yul Yunazwin; Siregar, Parsaulian; Bindar, Yazid

2014-01-01

As a major utility system in industry, boilers consume a large portion of the total energy and costs. Significant reduction of boiler cost operation can be gained through improvements in efficiency. In accomplishing such a goal, an adequate dynamic model that comprehensively reflects boiler characteristics is required. This paper outlines the idea of developing a mathematical model of a water-tube industrial boiler based on first principles guided by the bond graph method in its derivation. T...

Using Technology (Instead of Calculus) To Derive the Law of Reflection for Parabolic Mirrors from Fermat's Principle of Least Time.

Science.gov (United States)

Helfgott, Michel; Simonsen, Linda M.

1998-01-01

Presents an activity to investigate physico-mathematical concepts and provide mathematics arguments that are very close to a proof with the advent and availability of powerful technology. Demonstrates without using calculus how the law of reflection for parabolas is derived from Fermat's principle of least time. (ASK)

Hooke's Law: Applications of a Recurring Principle

Science.gov (United States)

Giuliodori, Mauricio J.; Lujan, Heidi L.; Briggs, Whitney S.; Palani, Gurunanthan; DiCarlo, Stephen E.

2009-01-01

Students generally approach topics in physiology as a series of unrelated phenomena that share few underlying principles. However, if students recognized that the same underlying principles can be used to explain many physiological phenomena, they may gain a more unified understanding of physiological systems. To address this concern, we…

Perspectives on Equity and Access in Mathematics and Science for a 21st-Century Democracy: Re-Visioning Our Gaze

Science.gov (United States)

Williams, Brian A.; Lemons-Smith, Shonda

2009-01-01

In 1996, the National Research Council (NRC) published the "National Science Education Standards." Similarly in 2000, the National Council of Teachers of Mathematics (NCTM) published the "Principles and Standards for School Mathematics." These standards provided the nation with a framework for conceptualizing what and how…

Tracing organizing principles: Learning from the history of systems biology

DEFF Research Database (Denmark)

Green, Sara; Wolkenhauer, Olaf

2014-01-01

on this historical background in order to increase the understanding of the motivation behind the search for general principles and to clarify different epistemic aims within systems biology. We pinpoint key aspects of earlier approaches that also underlie the current practice. These are i) the focus on relational......With the emergence of systems biology, the identification of organizing principles is being highlighted as a key research aim. Researchers attempt to “reverse engineer” the functional organization of biological systems using methodologies from mathematics, engineering and computer science while...... taking advantage of data produced by new experimental techniques. While systems biology is a relatively new approach, the quest for general principles of biological organization dates back to systems theoretic approaches in early and mid-twentieth century. The aim of this paper is to draw...

On the foundation of a variational principle for decaying systems

International Nuclear Information System (INIS)

Szasz, G.I.

1976-01-01

Taking into account the circumstances that the decay of an unstable microscopic system into two fragments is established by the counting of one of the decay products in a detector, the observed exponential decay law then asserts only knowledge of the spatiotemporal behaviour of the probability density (and therewith knowledge of the decaying state) at a large finite distance from the site of decay. We therefore formulate a variational principle, of which stationary functions show this decay behaviour. In addition to the resonant wave functions there are also solutions of the variational principle, which decrease exponentially with increasing distance, i.e., functions which could be used to describe the bound states. As the time-dependent treatment shows, the decaying states cannot occur in isolation in a scattering process. The mathematical characterisation of the decaying states via a variational principle is incorporated in a theory of open physical systems. In contradiction to the variational principle of Schroedinger our principle does not provide complete knowledge of the quantum states, but this is not needed in order to describe the decay. (orig.) [de

The beauty of physics patterns, principles, and perspectives

CERN Document Server

Rau, A R P

2014-01-01

The beauty of physics lies in its coherence in terms of a few fundamental concepts and principles. Even physicists have occasion to marvel at the overarching reach of basic principles and their ability to account for features stretching from the microscopic sub-atomic world to the cosmological expanses of the Universe. While mathematics is its natural language, physics is mostly about patterns, connections, and relations between objects and phenomena, and it is this aspect that is emphasized in this book. Since science tries to connect phenomena that at first sight appear widely different, while boiling them down to a small set of essential principles and laws, metaphor and analogy pervade our subject. Consider the pendulum, its swing from one extreme to the other often invoked in social or economic contexts. In molecular vibrations, such as in the CO2 molecule, the quantum motions of electrons and nuclei are metaphorically the pendulums. In electromagnetic radiation, including the visible light we observe, t...

Principles of parametric estimation in modeling language competition.

Science.gov (United States)

Zhang, Menghan; Gong, Tao

2013-06-11

It is generally difficult to define reasonable parameters and interpret their values in mathematical models of social phenomena. Rather than directly fitting abstract parameters against empirical data, we should define some concrete parameters to denote the sociocultural factors relevant for particular phenomena, and compute the values of these parameters based upon the corresponding empirical data. Taking the example of modeling studies of language competition, we propose a language diffusion principle and two language inheritance principles to compute two critical parameters, namely the impacts and inheritance rates of competing languages, in our language competition model derived from the Lotka-Volterra competition model in evolutionary biology. These principles assign explicit sociolinguistic meanings to those parameters and calculate their values from the relevant data of population censuses and language surveys. Using four examples of language competition, we illustrate that our language competition model with thus-estimated parameter values can reliably replicate and predict the dynamics of language competition, and it is especially useful in cases lacking direct competition data.

Mathematical foundations of event trees

International Nuclear Information System (INIS)

Papazoglou, Ioannis A.

1998-01-01

A mathematical foundation from first principles of event trees is presented. The main objective of this formulation is to offer a formal basis for developing automated computer assisted construction techniques for event trees. The mathematical theory of event trees is based on the correspondence between the paths of the tree and the elements of the outcome space of a joint event. The concept of a basic cylinder set is introduced to describe joint event outcomes conditional on specific outcomes of basic events or unconditional on the outcome of basic events. The concept of outcome space partition is used to describe the minimum amount of information intended to be preserved by the event tree representation. These concepts form the basis for an algorithm for systematic search for and generation of the most compact (reduced) form of an event tree consistent with the minimum amount of information the tree should preserve. This mathematical foundation allows for the development of techniques for automated generation of event trees corresponding to joint events which are formally described through other types of graphical models. Such a technique has been developed for complex systems described by functional blocks and it is reported elsewhere. On the quantification issue of event trees, a formal definition of a probability space corresponding to the event tree outcomes is provided. Finally, a short discussion is offered on the relationship of the presented mathematical theory with the more general use of event trees in reliability analysis of dynamic systems

A mathematical model for the motion analysis of embedded straight microcantilevers under a pressure-driven flow

International Nuclear Information System (INIS)

Ezkerra, A; Mayora, K; Ruano-López, J M; Wilson, P A

2008-01-01

A mathematical model that estimates the deflection of straight microcantilevers embedded in a microchannel under a pressure-driven flow at low Reynolds numbers is presented. The model makes use of the Schwarz–Christoffel mapping in order to couple the geometry of the structure and the flow passing around it. Therefore, it allows the determination of the most influential parameters and suitable modifications in order to achieve the desired performance. The model does not require specific knowledge of the flow conditions in the vicinity of the structure, which improves its practical use during the early stages of design. Estimations have been made for two straight cantilevers under a range of pressures. The results obtained show good agreement with measurements from experiments

Modelling non-equilibrium thermodynamic systems from the speed-gradient principle.

Science.gov (United States)

Khantuleva, Tatiana A; Shalymov, Dmitry S

2017-03-06

The application of the speed-gradient (SG) principle to the non-equilibrium distribution systems far away from thermodynamic equilibrium is investigated. The options for applying the SG principle to describe the non-equilibrium transport processes in real-world environments are discussed. Investigation of a non-equilibrium system's evolution at different scale levels via the SG principle allows for a fresh look at the thermodynamics problems associated with the behaviour of the system entropy. Generalized dynamic equations for finite and infinite number of constraints are proposed. It is shown that the stationary solution to the equations, resulting from the SG principle, entirely coincides with the locally equilibrium distribution function obtained by Zubarev. A new approach to describe time evolution of systems far from equilibrium is proposed based on application of the SG principle at the intermediate scale level of the system's internal structure. The problem of the high-rate shear flow of viscous fluid near the rigid plane plate is discussed. It is shown that the SG principle allows closed mathematical models of non-equilibrium processes to be constructed.This article is part of the themed issue 'Horizons of cybernetical physics'. © 2017 The Author(s).

Developing a pedagogical problem solving view for mathematics teachers with two reflection programs

Directory of Open Access Journals (Sweden)

Bracha KRAMARSKI

2009-10-01

Full Text Available The study investigated the effects of two reflection support programs on elementary school mathematics teachers’ pedagogical problem solving view. Sixty-two teachers participated in a professional development program. Thirty teachers were assigned to the self-questioning (S_Q training and thirty two teachers were assigned to the reflection discourse (R_D training. The S_Q program was based on the IMPROVE self-questioning approach which emphasizes systematic discussion along the phases of mathematical or pedagogical problem solving as student and teacher. The R_D program emphasized discussion of standard based teaching and learning principles. Findings indicated that systematic reflection support (S_Q is effective for developing mathematics PCK, and strengthening metacognitive knowledge of mathematics teachers, more than reflection discourse (R_D. No differences were found between the groups in developing beliefs about teaching mathematics in using problem solving view.

Reflective Awareness in Mathematics Teachers' Learning and Teaching

Science.gov (United States)

Chapman, Olive

2015-01-01

The nature of mathematics teachers' knowledge specific to teaching mathematics [MTK] is of ongoing concern in mathematics education research. This article contributes to our under-standing of this knowledge with particular focus on reflective awareness. It discusses MTK based on ways it has been used in research. It highlights reflective awareness…

Principles of the theory of solids

CERN Document Server

Ziman, J M

1972-01-01

Professor Ziman's classic textbook on the theory of solids was first pulished in 1964. This paperback edition is a reprint of the second edition, which was substantially revised and enlarged in 1972. The value and popularity of this textbook is well attested by reviewers' opinions and by the existence of several foreign language editions, including German, Italian, Spanish, Japanese, Polish and Russian. The book gives a clear exposition of the elements of the physics of perfect crystalline solids. In discussing the principles, the author aims to give students an appreciation of the conditions which are necessary for the appearance of the various phenomena. A self-contained mathematical account is given of the simplest model that will demonstrate each principle. A grounding in quantum mechanics and knowledge of elementary facts about solids is assumed. This is therefore a textbook for advanced undergraduates and is also appropriate for graduate courses.

Design principles and operating principles: the yin and yang of optimal functioning.

Science.gov (United States)

Voit, Eberhard O

2003-03-01

Metabolic engineering has as a goal the improvement of yield of desired products from microorganisms and cell lines. This goal has traditionally been approached with experimental biotechnological methods, but it is becoming increasingly popular to precede the experimental phase by a mathematical modeling step that allows objective pre-screening of possible improvement strategies. The models are either linear and represent the stoichiometry and flux distribution in pathways or they are non-linear and account for the full kinetic behavior of the pathway, which is often significantly effected by regulatory signals. Linear flux analysis is simpler and requires less input information than a full kinetic analysis, and the question arises whether the consideration of non-linearities is really necessary for devising optimal strategies for yield improvements. The article analyzes this question with a generic, representative pathway. It shows that flux split ratios, which are the key criterion for linear flux analysis, are essentially sufficient for unregulated, but not for regulated branch points. The interrelationships between regulatory design on one hand and optimal patterns of operation on the other suggest the investigation of operating principles that complement design principles, like a user's manual complements the hardwiring of electronic equipment.

Factors Considered by Elementary Teachers When Developing and Modifying Mathematical Tasks to Support Children's Mathematical Thinking

Science.gov (United States)

Fredenberg, Michael Duane

The idea that problems and tasks play a pivotal role in a mathematics lesson has a long standing in mathematics education research. Recent calls for teaching reform appeal for training teachers to better understand how students learn mathematics and to employ students' mathematical thinking as the basis for pedagogy (CCSSM, 2010; NCTM, 2000; NRC 1999). The teaching practices of (a) developing a task for a mathematics lesson and, (b) modifying the task for students while enacting the lesson fit within the scope of supporting students' mathematical thinking. Surprisingly, an extensive search of the literature did not yield any research aimed to identify and refine the constituent parts of the aforementioned teaching practices in the manner called for by Grossman and xiii colleagues (2009). Consequently, my research addresses the two questions: (a) what factors do exemplary elementary teachers consider when developing a task for a mathematics lesson? (b) what factors do they consider when they modify a task for a student when enacting a lesson? I conducted a multiple case study involving three elementary teachers, each with extensive training in the area of Cognitively Guided Instruction (CGI), as well as several years experience teaching mathematics following the principles of CGI (Carpenter et al., 1999). I recorded video of three mathematics lessons with each participant and after each lesson I conducted a semi-structured stimulated recall interview. A subsequent follow-up clinical interview was conducted soon thereafter to further explore the teacher's thoughts (Ginsberg, 1997). In addition, my methodology included interjecting myself at select times during a lesson to ask the teacher to explain her reasoning. Qualitative analysis led to a framework that identified four categories of influencing factors and seven categories of supporting objectives for the development of a task. Subsets of these factors and objectives emerged as particularly relevant when the

The basic science and mathematics of random mutation and natural selection.

Science.gov (United States)

Kleinman, Alan

2014-12-20

The mutation and natural selection phenomenon can and often does cause the failure of antimicrobial, herbicidal, pesticide and cancer treatments selection pressures. This phenomenon operates in a mathematically predictable behavior, which when understood leads to approaches to reduce and prevent the failure of the use of these selection pressures. The mathematical behavior of mutation and selection is derived using the principles given by probability theory. The derivation of the equations describing the mutation and selection phenomenon is carried out in the context of an empirical example. Copyright © 2014 John Wiley & Sons, Ltd.

Biochemical principles underlying the stable maintenance of LTP by the CaMKII/NMDAR complex.

Science.gov (United States)

Lisman, John; Raghavachari, Sridhar

2015-09-24

Memory involves the storage of information at synapses by an LTP-like process. This information storage is synapse specific and can endure for years despite the turnover of all synaptic proteins. There must, therefore, be special principles that underlie the stability of LTP. Recent experimental results suggest that LTP is maintained by the complex of CaMKII with the NMDAR. Here we consider the specifics of the CaMKII/NMDAR molecular switch, with the goal of understanding the biochemical principles that underlie stable information storage by synapses. Consideration of a variety of experimental results suggests that multiple principles are involved. One switch requirement is to prevent spontaneous transitions from the off to the on state. The highly cooperative nature of CaMKII autophosphorylation by Ca(2+) (Hill coefficient of 8) and the fact that formation of the CaMKII/NMDAR complex requires release of CaMKII from actin are mechanisms that stabilize the off state. The stability of the on state depends critically on intersubunit autophosphorylation, a process that restores any loss of pT286 due to phosphatase activity. Intersubunit autophosphorylation is also important in explaining why on state stability is not compromised by protein turnover. Recent evidence suggests that turnover occurs by subunit exchange. Thus, stability could be achieved if a newly inserted unphosphorylated subunit was autophosphorylated by a neighboring subunit. Based on other recent work, we posit a novel mechanism that enhances the stability of the on state by protection of pT286 from phosphatases. We posit that the binding of the NMNDAR to CaMKII forces pT286 into the catalytic site of a neighboring subunit, thereby protecting pT286 from phosphatases. A final principle concerns the role of structural changes. The binding of CaMKII to the NMDAR may act as a tag to organize the binding of further proteins that produce the synapse enlargement that underlies late LTP. We argue that these

Two-dimensional models as testing ground for principles and concepts of local quantum physics

Energy Technology Data Exchange (ETDEWEB)

Schroer, Bert [FU Berlin (Germany). Institut fuer Theoretische Physik

2005-04-15

In the past two-dimensional models of QFT have served as theoretical laboratories for testing new concepts under mathematically controllable condition. In more recent times low-dimensional models (e.g. chiral models, factoring models) often have been treated by special recipes in a way which sometimes led to a loss of unity of QFT. In the present work I try to counteract this apartheid tendency by reviewing past results within the setting of the general principles of QFT. To this I add two new ideas: (1) a modular interpretation of the chiral model Diff(S)-covariance with a close connection to the recently formulated local covariance principle for QFT in curved spacetime and (2) a derivation of the chiral model temperature duality from a suitable operator formulation of the angular Wick rotation (in analogy to the Nelson-Symanzik duality in the Ostertwalder-Schrader setting) for rational chiral theories. The SL(2,Z) modular Verlinde relation is a special case of this thermal duality and (within the family of rational models) the matrix S appearing in the thermal duality relation becomes identified with the statistics character matrix S. The relevant angular 'Euclideanization' is done in the setting of the Tomita-Takesaki modular formalism of operator algebras. I find it appropriate to dedicate this work to the memory of J. A. Swieca with whom I shared the interest in two-dimensional models as a testing ground for QFT for more than one decade. This is a significantly extended version of an 'Encyclopedia of Mathematical Physics' contribution hep-th/0502125. (author)

Two-dimensional models as testing ground for principles and concepts of local quantum physics

International Nuclear Information System (INIS)

Schroer, Bert

2005-04-01

In the past two-dimensional models of QFT have served as theoretical laboratories for testing new concepts under mathematically controllable condition. In more recent times low-dimensional models (e.g. chiral models, factoring models) often have been treated by special recipes in a way which sometimes led to a loss of unity of QFT. In the present work I try to counteract this apartheid tendency by reviewing past results within the setting of the general principles of QFT. To this I add two new ideas: (1) a modular interpretation of the chiral model Diff(S)-covariance with a close connection to the recently formulated local covariance principle for QFT in curved spacetime and (2) a derivation of the chiral model temperature duality from a suitable operator formulation of the angular Wick rotation (in analogy to the Nelson-Symanzik duality in the Ostertwalder-Schrader setting) for rational chiral theories. The SL(2,Z) modular Verlinde relation is a special case of this thermal duality and (within the family of rational models) the matrix S appearing in the thermal duality relation becomes identified with the statistics character matrix S. The relevant angular 'Euclideanization' is done in the setting of the Tomita-Takesaki modular formalism of operator algebras. I find it appropriate to dedicate this work to the memory of J. A. Swieca with whom I shared the interest in two-dimensional models as a testing ground for QFT for more than one decade. This is a significantly extended version of an 'Encyclopedia of Mathematical Physics' contribution hep-th/0502125. (author)

Professional Learning for Cultural Mathematics in Papua New Guinea's Elementary Schools

Science.gov (United States)

Owens, Kay; Edmonds-Wathen, Cris; Kravia, Geori; Sakopa, Priscilla

2014-01-01

A design of principles for teacher professional learning was developed to improve the teaching of "Cultural Mathematics" in elementary schools in Papua New Guinea. The design's appropriateness for PNG elementary schools is the focus of the research implemented through week-long workshops using technology enhancement. Implementation has…

The enhancement of students' mathematical self-efficacy through teaching with metacognitive scaffolding approach

Science.gov (United States)

Prabawanto, S.

2018-05-01

This research aims to investigate the enhancement of students’ mathematical self- efficacy through teaching with metacognitive scaffolding approach. This research used a quasi- experimental design with pre-post respon control. The subjects were pre-service elementary school teachers in a state university in Bandung. In this study, there were two groups: experimental and control groups. The experimental group consists of 60 students who acquire teaching mathematics under metacognitive approach, while the control group consists of 58 students who acquire teaching mathematics under direct approach. Students were classified into three categories based on the mathematical prior ability, namely high, middle, and low. Data collection instruments consist of mathematical self-efficacy instruments. By using mean difference test, two conclusions of the research: (1) there is a significant difference in the enhancement of mathematical self-efficacy between the students who attended the course under metacognitive scaffolding approach and students who attended the course under direct approach, and (2) there is no significant interaction effect of teaching approaches and ability level based on the mathematical prior ability toward enhancement of students’ mathematical self-efficacy.

Intuitive Mathematical Knowledge as an Essential Aspect of Contemporary Adult Learning: A case of women street vendors in the city of Gaborone

OpenAIRE

Nthogo Lekoko, Rebecca; Getrude Garegae, Kgomotso

2006-01-01

The findings of a phenomenological interview study with women street vendors showed a strong link between participants’ perceptions of everyday use of mathematical literacy and the speculations that mathematical use arose spontaneously in response to a practical need. The concept of intuitive mathematics as used indicates that mathematical thinking is an indispensable element of everyday conversation. Although the study finds that intuition and spontaneity are essential principles of lifelong...

On integral formulation of the Mach principle in a conformally flat space

International Nuclear Information System (INIS)

Mal'tsev, V.K.

1976-01-01

The integral formulation of the Mach principle represents a rather complicated mathematical formalism in which many aspects of the physical content of theory are not clear. Below an attempt is made to consider the integral representation for the most simple case of conformally flat spaces. The fact that this formalism there is only one scalar function makes it possible to analyse in more detail many physical peculiarities of this representation of the Mach principle: the absence of asymptotically flat spaces, problems of inertia and gravity, constraints on state equations, etc

SUBJECT «NUMBER SYSTEMS» IN TWO-LEVELED FORMAT PREPARATION TEACHERS OF MATHEMATICS

Directory of Open Access Journals (Sweden)

V. I. Igoshin

2017-01-01

Full Text Available The aim of this article is to analyze the format of a two-leveled training – bachelor and master – future teachers of mathematics from the point of view of the content of mathematical material, which is to develop prospective teachers of mathematics at those two levels, shaping their professional competence.Methods. The study involves the theoretical methods: the analysis of pedagogical and methodical literature, normative documents; historical, comparative and logical analysis of the content of pedagogical mathematical education; forecasting, planning and designing of two-leveled methodical system of training of future teachers of mathematics.Results and scientific novelty. The level differentiation of the higher education system requires developing the appropriate curricula for undergraduate and graduate programs. The fundamental principle must be the principle of continuity – the magister must continue to deepen and broaden knowledge and skills, along with competences acquired, developed and formed on the undergraduate level. From these positions, this paper examines the course «Number Systems» – the most important in terms of methodology course for future mathematics teachers, and shows what content should be filled with this course at the undergraduate level and the graduate level. At the undergraduate level it is proposed to study classical number systems – natural, integer, rational, real and complex. Further extensions of the number systems are studied at the graduate level. The theory of numeric systems is presented as a theory of algebraic systems, arising at the intersection of algebra and mathematical logic. Here we study algebras over a field, division algebra over a field, an alternative algebra with division over the field, Jordan algebra, Lie algebra. Comprehension of bases of the theory of algebras by the master of the «mathematical education» profile will promote more conscious

The discrete maximum principle for Galerkin solutions of elliptic problems

Czech Academy of Sciences Publication Activity Database

Vejchodský, Tomáš

2012-01-01

Roč. 10, č. 1 (2012), s. 25-43 ISSN 1895-1074 R&D Projects: GA AV ČR IAA100760702 Institutional research plan: CEZ:AV0Z10190503 Keywords : discrete maximum principle * monotone methods * Galerkin solution Subject RIV: BA - General Mathematics Impact factor: 0.405, year: 2012 http://www.springerlink.com/content/x73624wm23x4wj26

MATHEMATICAL ASPECTS OF AIRCRAFT ENGINES RUNNING OPTIMIZATION FOR MINIMUM FUEL CONSUMPTION WHILE LANDING

Directory of Open Access Journals (Sweden)

Yuriy Michaylovich Chinyuchin

2017-01-01

Full Text Available The consistency of the potential increase of fuel efficiency, based on aircraft maintenance optimization, is mathe- matically proved. The mathematical apparatus and a set mathematical model of aircraft spatial motion allow to analyze aircraft behavior on the stage before landing and to draw optimal flight path for minimum fuel consumption with fixed time.For effective problem solving the choice and realization of optimal flight paths are made. The algorithm for the problem of optimal civil aircraft flight control aimed at the most accurate realization of chosen soft path under limited time conditions is proposed. The optimization of the given process is made by solving a point-to-point boundary canonical sys- tem based on the Pontryagin maximum principle.The necessary initial data and conditions for the statement of problem are given. The mathematical model for the simplification of calculations is created and its equivalent representation is given by uniting problems of controls by thrust channels and the angle of attack as the thrust control function. The boundary-value problem is mathematically composed and the analytical apparatus of its solution is presented. Optimal aircraft landing paths reflecting the behavior of the angle of attack and thrust are constructed. The potential of this method is proved by the economic justifiability and its effectiveness, in particular the compar- ison of total aircraft fuel consumption on obtained optimal path to the classic path on which there are rectilinear sections what allowed to confirm the conclusion about the economical expedience and effectiveness of the method of aircraft con- stant landing while making flights.

Variational principles in physics

CERN Document Server

Basdevant, Jean-Louis

2007-01-01

Optimization under constraints is an essential part of everyday life. Indeed, we routinely solve problems by striking a balance between contradictory interests, individual desires and material contingencies. This notion of equilibrium was dear to thinkers of the enlightenment, as illustrated by Montesquieu’s famous formulation: "In all magistracies, the greatness of the power must be compensated by the brevity of the duration." Astonishingly, natural laws are guided by a similar principle. Variational principles have proven to be surprisingly fertile. For example, Fermat used variational methods to demonstrate that light follows the fastest route from one point to another, an idea which came to be known as Fermat’s principle, a cornerstone of geometrical optics. Variational Principles in Physics explains variational principles and charts their use throughout modern physics. The heart of the book is devoted to the analytical mechanics of Lagrange and Hamilton, the basic tools of any physicist. Prof. Basdev...

Using Collective Argumentation to Engage Students in a Primary Mathematics Classroom

Science.gov (United States)

Brown, Raymond

2017-01-01

This article focuses on using sociocultural theory to support student engagement with mathematics. The sociocultural approach used, collective argumentation (CA), is based on interactive principles necessary for coordinating student engagement in the discourse of the classroom. A goal of the research was to explore the affordances and constraints…

Maximal frustration as an immunological principle.

Science.gov (United States)

de Abreu, F Vistulo; Mostardinha, P

2009-03-06

A fundamental problem in immunology is that of understanding how the immune system selects promptly which cells to kill without harming the body. This problem poses an apparent paradox. Strong reactivity against pathogens seems incompatible with perfect tolerance towards self. We propose a different view on cellular reactivity to overcome this paradox: effector functions should be seen as the outcome of cellular decisions which can be in conflict with other cells' decisions. We argue that if cellular systems are frustrated, then extensive cross-reactivity among the elements in the system can decrease the reactivity of the system as a whole and induce perfect tolerance. Using numerical and mathematical analyses, we discuss two simple models that perform optimal pathogenic detection with no autoimmunity if cells are maximally frustrated. This study strongly suggests that a principle of maximal frustration could be used to build artificial immune systems. It would be interesting to test this principle in the real adaptive immune system.

Three principles of competitive nonlinear pricing

OpenAIRE

Page Junior, Frank H.; Monteiro, P. K.

2002-01-01

We make three contributions to the theory of contracting under asymmetric information. First , we establish a competitive analog to the revelation principle which we call the implementation principle. This principle provides a complete characterization of all incentive compatible, indirect contracting mechanisms in terms of contract catalogs (or menus), and allows us to conclude that in competitive contracting situations, firms in choosing their contracting strategies can restrict attention, ...

Discrete Maximum Principle for Higher-Order Finite Elements in 1D

Czech Academy of Sciences Publication Activity Database

Vejchodský, Tomáš; Šolín, Pavel

2007-01-01

Roč. 76, č. 260 (2007), s. 1833-1846 ISSN 0025-5718 R&D Projects: GA ČR GP201/04/P021 Institutional research plan: CEZ:AV0Z10190503; CEZ:AV0Z20760514 Keywords : discrete maximum principle * discrete Grren´s function * higher-order elements Subject RIV: BA - General Mathematics Impact factor: 1.230, year: 2007

The conceptual basis of mathematics in cardiology: (I) algebra, functions and graphs.

Science.gov (United States)

Bates, Jason H T; Sobel, Burton E

2003-02-01

This is the first in a series of four articles developed for the readers of. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas. This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease, abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to cardiovascular medicine and

Greatest Happiness Principle in a Complex System: Maximisation versus Driving Force

Directory of Open Access Journals (Sweden)

Katalin Martinás

2012-06-01

Full Text Available From philosophical point of view, micro-founded economic theories depart from the principle of the pursuit of the greatest happiness. From mathematical point of view, micro-founded economic theories depart from the utility maximisation program. Though economists are aware of the serious limitations of the equilibrium analysis, they remain in that framework. We show that the maximisation principle, which implies the equilibrium hypothesis, is responsible for this impasse. We formalise the pursuit of the greatest happiness principle by the help of the driving force postulate: the volumes of activities depend on the expected wealth increase. In that case we can get rid of the equilibrium hypothesis and have new insights into economic theory. For example, in what extent standard economic results depend on the equilibrium hypothesis?

Mathematical Methods of System Analysis in Construction Materials

Science.gov (United States)

Garkina, Irina; Danilov, Alexander

2017-10-01

System attributes of construction materials are defined: complexity of an object, integrity of set of elements, existence of essential, stable relations between elements defining integrative properties of system, existence of structure, etc. On the basis of cognitive modelling (intensive and extensive properties; the operating parameters) materials (as difficult systems) and creation of the cognitive map the hierarchical modular structure of criteria of quality is under construction. It actually is a basis for preparation of the specification on development of material (the required organization and properties). Proceeding from a modern paradigm (model of statement of problems and their decisions) of development of materials, levels and modules are specified in structure of material. It when using the principles of the system analysis allows to considered technological process as the difficult system consisting of elements of the distinguished specification level: from atomic before separate process. Each element of system depending on an effective objective is considered as separate system with more detailed levels of decomposition. Among them, semantic and qualitative analyses of an object (are considered a research objective, decomposition levels, separate elements and communications between them come to light). Further formalization of the available knowledge in the form of mathematical models (structural identification) is carried out; communications between input and output parameters (parametrical identification) are defined. Hierarchical structures of criteria of quality are under construction for each allocated level. On her the relevant hierarchical structures of system (material) are under construction. Regularities of structurization and formation of properties, generally are considered at the levels from micro to a macrostructure. The mathematical model of material is represented as set of the models corresponding to private criteria by which separate

Longitudinal bunch diagnostics using coherent transition radiation spectroscopy. Physical principles, multichannel spectrometer, experimental results, mathematical methods

International Nuclear Information System (INIS)

Schmidt, Bernhard; Wesch, Stephan; Behrens, Christopher; Koevener, Toke; Hass, Eugen; Casalbuoni, Sara

2018-03-01

The generation and properties of transition radiation (TR) are thoroughly treated. The spectral energy density, as described by the Ginzburg-Frank formula, is computed analytically, and the modifications caused by the finite size of the TR screen and by near-field diffraction effects are carefully analyzed. The principles of electron bunch shape reconstruction using coherent transition radiation are outlined. Spectroscopic measurements yield only the magnitude of the longitudinal form factor but not its phase. Two phase retrieval methods are investigated and illustrated with model calculations: analytic phase computation by means of the Kramers-Kronig dispersion relation, and iterative phase retrieval. Particular attention is paid to the ambiguities which are unavoidable in the reconstruction of longitudinal charge density profiles from spectroscopic data. The origin of these ambiguities has been identified and a thorough mathematical analysis is presented. The experimental part of the paper comprises a description of our multichannel infrared and THz spectrometer and a selection of measurements at FLASH, comparing the bunch profiles derived from spectroscopic data with those determined with a transversely deflecting microwave structure. A rigorous derivation of the Kramers-Kronig phase formula is presented in Appendix A. Numerous analytic model calculations can be found in Appendix B. The differences between normal and truncated Gaussians are discussed in Appendix C. Finally, Appendix D contains a short description of the propagation of an electromagnetic wave front by two-dimensional fast Fourier transformation. This is the basis of a powerful numerical Mathematica trademark code THzTransport, which permits the propagation of electromagnetic wave fronts through a beam line consisting of drift spaces, lenses, mirrors and apertures.

Longitudinal bunch diagnostics using coherent transition radiation spectroscopy. Physical principles, multichannel spectrometer, experimental results, mathematical methods

Energy Technology Data Exchange (ETDEWEB)

Schmidt, Bernhard; Wesch, Stephan; Behrens, Christopher [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Koevener, Toke [Hamburg Univ. (Germany); European Organization for Nuclear Research (CERN), Geneva (Switzerland); Hass, Eugen [Hamburg Univ. (Germany); Casalbuoni, Sara [Karlsruhe Institute of Technology (Germany). Inst. for Beam Physics and Technology; Schmueser, Peter [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Hamburg Univ. (Germany)

2018-03-15

The generation and properties of transition radiation (TR) are thoroughly treated. The spectral energy density, as described by the Ginzburg-Frank formula, is computed analytically, and the modifications caused by the finite size of the TR screen and by near-field diffraction effects are carefully analyzed. The principles of electron bunch shape reconstruction using coherent transition radiation are outlined. Spectroscopic measurements yield only the magnitude of the longitudinal form factor but not its phase. Two phase retrieval methods are investigated and illustrated with model calculations: analytic phase computation by means of the Kramers-Kronig dispersion relation, and iterative phase retrieval. Particular attention is paid to the ambiguities which are unavoidable in the reconstruction of longitudinal charge density profiles from spectroscopic data. The origin of these ambiguities has been identified and a thorough mathematical analysis is presented. The experimental part of the paper comprises a description of our multichannel infrared and THz spectrometer and a selection of measurements at FLASH, comparing the bunch profiles derived from spectroscopic data with those determined with a transversely deflecting microwave structure. A rigorous derivation of the Kramers-Kronig phase formula is presented in Appendix A. Numerous analytic model calculations can be found in Appendix B. The differences between normal and truncated Gaussians are discussed in Appendix C. Finally, Appendix D contains a short description of the propagation of an electromagnetic wave front by two-dimensional fast Fourier transformation. This is the basis of a powerful numerical Mathematica trademark code THzTransport, which permits the propagation of electromagnetic wave fronts through a beam line consisting of drift spaces, lenses, mirrors and apertures.

The Effects of Constructivist Learning Environment on Prospective Mathematics Teachers' Opinions

Science.gov (United States)

Narli, Serkan; Baser, Nes'e

2010-01-01

To explore the effects of constructivist learning environment on prospective teachers' opinions about "mathematics, department of mathematics, discrete mathematics, countable and uncountable infinity" taught under the subject of Cantorian Set Theory in discrete mathematics class, 60 first-year students in the Division of Mathematics…

Using collective argumentation to engage students in a primary mathematics classroom

Science.gov (United States)

Brown, Raymond

2017-02-01

This article focuses on using sociocultural theory to support student engagement with mathematics. The sociocultural approach used, collective argumentation (CA), is based on interactive principles necessary for coordinating student engagement in the discourse of the classroom. A goal of the research was to explore the affordances and constraints of using CA to enrich student engagement with mathematics. The design of the research was based on a teaching experiment that sought to capture the influence of social and cultural processes on learning and development. Participants included primary and secondary school teachers and their mathematics classes. This article focuses on the practice of one female primary school teacher. Data sources included interview transcripts, report writings, journal entries and observational records. Data were analysed using a participation framework. Findings suggest that aspects of CA such as students explaining and justifying ideas and presenting ideas to the whole class can be used by teachers to promote student engagement with mathematics.

A cyclic symmetry principle in physics

International Nuclear Information System (INIS)

Green, H.S.; Adelaide Univ., SA

1994-01-01

Many areas of modern physics are illuminated by the application of a symmetry principle, requiring the invariance of the relevant laws of physics under a group of transformations. This paper examines the implications and some of the applications of the principle of cyclic symmetry, especially in the areas of statistical mechanics and quantum mechanics, including quantized field theory. This principle requires invariance under the transformations of a finite group, which may be a Sylow π-group, a group of Lie type, or a symmetric group. The utility of the principle of cyclic invariance is demonstrated in finding solutions of the Yang-Baxter equation that include and generalize known solutions. It is shown that the Sylow π-groups have other uses, in providing a basis for a type of generalized quantum statistics, and in parametrising a new generalization of Lie groups, with associated algebras that include quantized algebras. 31 refs

Applied mathematics made simple

CERN Document Server

Murphy, Patrick

1982-01-01

Applied Mathematics: Made Simple provides an elementary study of the three main branches of classical applied mathematics: statics, hydrostatics, and dynamics. The book begins with discussion of the concepts of mechanics, parallel forces and rigid bodies, kinematics, motion with uniform acceleration in a straight line, and Newton's law of motion. Separate chapters cover vector algebra and coplanar motion, relative motion, projectiles, friction, and rigid bodies in equilibrium under the action of coplanar forces. The final chapters deal with machines and hydrostatics. The standard and conte

Predicting Relationships between Mathematics Anxiety, Mathematics Teaching Anxiety, Self-efficacy Beliefs towards Mathematics and Mathematics Teaching

OpenAIRE

Unlu, Melihan; Ertekin, Erhan; Dilmac, Bulent

2017-01-01

The purpose of the research is to investigate the relationships betweenself-efficacy beliefs toward mathematics, mathematics anxiety and self-efficacybeliefs toward mathematics teaching, mathematics teaching anxiety variables andtesting the relationships between these variables with structural equationmodel. The sample of the research, which was conducted in accordance withrelational survey model, consists of 380 university students, who studied atthe department of Elementary Mathematics Educ...

Design based Investigation on Construction of Mathematical Modelling Problems: Example of Financial Content

Directory of Open Access Journals (Sweden)

Melike TURAL SÖNMEZ

2017-12-01

Full Text Available The purpose of this study is to examine the construction of mathematical modelling problems process in the content of financial literacy. It is also aimed to create design proposals for construction of mathematical modelling problems. A design based research method was used in this study. The participants were three seventh grade students, six finance experts and nine mathematics education experts. Data collection tools were transcription of video and tapes group discussions, presentations and worksheets during mathematical modelling activities, and participant experts’ feedback form about mathematical modelling problems. There were three stages in this study. First stage was application of preliminary study. This stage gave information about convenience of problems to grade level, students’ timing for solution of problems, clarity of problems and students’ background about content. In second stage, finance experts commented on convenience of mathematical modelling problems to financial literacy standards. In third stage, mathematics education experts commented on convenience of problems to students’ grade level, mathematical modelling principles and seventh grade mathematics lesson objectives. They also gave suggestion on progress. The frequency value of theme in feedback forms was calculated and experts’ expressions were given as citation. It was given suggestion about stages and application of the design guide

Obtaining learning independence and academic success through self-assessment and referral to a Mathematics Learning Centre

Directory of Open Access Journals (Sweden)

Nadine Adams

2012-08-01

Full Text Available Globally, universities are striving to increase enrolment rates, especially for low socioeconomic status and mature-aged students. In order to meet these targets, universities are accepting a broader range of students, often resulting in a widening mathematical knowledge gap between secondary school and university (Hoyles, Newman & Noss, 2001. Therefore, even amid the growing trend of scaling back services, there exists a need for extra learning support in mathematics. Mathematics support services are recognised as vital in assisting students to both bridge the knowledge gap and become independent learners. Through a survey of students using the Mathematics Learning Centre at Central Queensland University Australia, it was found that the implementation of scaffolding, adult learning principles and the embedding of mathematics support provides students with not only fundamental mathematical knowledge but also the skills required to become self-directed learners. 

Viscous Regularization of the Euler Equations and Entropy Principles

KAUST Repository

Guermond, Jean-Luc

2014-03-11

This paper investigates a general class of viscous regularizations of the compressible Euler equations. A unique regularization is identified that is compatible with all the generalized entropies, à la [Harten et al., SIAM J. Numer. Anal., 35 (1998), pp. 2117-2127], and satisfies the minimum entropy principle. A connection with a recently proposed phenomenological model by [H. Brenner, Phys. A, 370 (2006), pp. 190-224] is made. © 2014 Society for Industrial and Applied Mathematics.

Structural, Mechanical and Thermodynamic Properties under Pressure Effect of Rubidium Telluride: First Principle Calculations

Directory of Open Access Journals (Sweden)

Bidai K.

2017-06-01

Full Text Available First-principles density functional theory calculations have been performed to investigate the structural, elastic and thermodynamic properties of rubidium telluride in cubic anti-fluorite (anti-CaF2-type structure. The calculated ground-state properties of Rb2Te compound such as equilibrium lattice parameter and bulk moduli are investigated by generalized gradient approximation (GGA-PBE that are based on the optimization of total energy. The elastic constants, Young’s and shear modulus, Poisson ratio, have also been calculated. Our results are in reasonable agreement with the available theoretical and experimental data. The pressure dependence of elastic constant and thermodynamic quantities under high pressure are also calculated and discussed.

Exhibition - Mathematics, A Beautiful Elsewhere

CERN Multimedia

2011-01-01

From 21 October 2011 to 18 March 2012, the Fondation Cartier pour l’art contemporain will present the exhibition Mathematics: A Beautiful Elsewhere, an exhibition developed in association with the Institut des Hautes Études Scientifiques (IHÉS) and under the patronage of UNESCO. For this unprecedented event, the foundation invited mathematicians to work with artists with whom it has previously worked to create an exhibition that allows visitors to see, hear, do, interpret and think about mathematics. By bringing mathematics into its premises, the Fondation Cartier is itself undergoing the “sudden change of scenery” described by mathematician Alexandre Grothendieck. More information is available here. Fondation Cartier pour l’art contemporain 261, boulevard Raspail 75014 Paris http://fondation.cartier.com Private Visit For professors, researchers and all the staff of Mathematics departments...

An excursion through elementary mathematics, volume ii euclidean geometry

CERN Document Server

Caminha Muniz Neto, Antonio

2018-01-01

This book provides a comprehensive, in-depth overview of elementary mathematics as explored in Mathematical Olympiads around the world. It expands on topics usually encountered in high school and could even be used as preparation for a first-semester undergraduate course. This second volume covers Plane Geometry, Trigonometry, Space Geometry, Vectors in the Plane, Solids and much more. As part of a collection, the book differs from other publications in this field by not being a mere selection of questions or a set of tips and tricks that applies to specific problems. It starts from the most basic theoretical principles, without being either too general or too axiomatic. Examples and problems are discussed only if they are helpful as applications of the theory. Propositions are proved in detail and subsequently applied to Olympic problems or to other problems at the Olympic level. The book also explores some of the hardest problems presented at National and International Mathematics Olympiads, as well as many...

48 CFR 252.231-7000 - Supplemental cost principles.

Science.gov (United States)

2010-10-01

... principles. 252.231-7000 Section 252.231-7000 Federal Acquisition Regulations System DEFENSE ACQUISITION... of Provisions And Clauses 252.231-7000 Supplemental cost principles. As prescribed in 231.100-70, use the following clause: Supplemental Cost Principles (DEC 1991) When the allowability of costs under...

Insights into teaching mathematics

CERN Document Server

Orton, Anthony

2004-01-01

Providing essential guidance and background information about teaching mathematics, this book is intended particularly for teachers who do not regard themselves as specialists in mathematics. It deals with issues of learning and teaching, including the delivery of content and the place of problems and investigations. Difficulties which pupils encounter in connection with language and symbols form important sections of the overall discussion of how to enhance learning. The curriculum is considered in brief under the headings of number, algebra, shape and space, and data handling, and special at

Concepts of modern mathematics

CERN Document Server

Stewart, Ian

1995-01-01

Some years ago, ""new math"" took the country's classrooms by storm. Based on the abstract, general style of mathematical exposition favored by research mathematicians, its goal was to teach students not just to manipulate numbers and formulas, but to grasp the underlying mathematical concepts. The result, at least at first, was a great deal of confusion among teachers, students, and parents. Since then, the negative aspects of ""new math"" have been eliminated and its positive elements assimilated into classroom instruction.In this charming volume, a noted English mathematician uses humor an

Predicting Relationships between Mathematics Anxiety, Mathematics Teaching Anxiety, Self-Efficacy Beliefs towards Mathematics and Mathematics Teaching

Science.gov (United States)

Unlu, Melihan; Ertekin, Erhan; Dilmac, Bulent

2017-01-01

The purpose of the research is to investigate the relationships between self-efficacy beliefs toward mathematics, mathematics anxiety and self-efficacy beliefs toward mathematics teaching, mathematics teaching anxiety variables and testing the relationships between these variables with structural equation model. The sample of the research, which…

Electronic Topological Transitions in CuNiMnAl and CuNiMnSn under pressure from first principles study

Science.gov (United States)

Rambabu, P.; Kanchana, V.

2018-06-01

A detailed study on quaternary ordered full Heusler alloys CuNiMnAl and CuNiMnSn at ambient and under different compressions is presented using first principles electronic structure calculations. Both the compounds are found to possess ferromagnetic nature at ambient with magnetic moment of Mn being 3.14 μB and 3.35 μB respectively in CuNiMnAl and CuNiMnSn. The total magnetic moment for both the compounds is found to decrease under compression. Fermi surface (FS) topology change is observed in both compounds under pressure at V/V0 = 0.90, further leading to Electronic Topological Transitions (ETTs) and is evidenced by the anomalies visualized in density of states and elastic constants under compression.

Digital image processing mathematical and computational methods

CERN Document Server

Blackledge, J M

2005-01-01

This authoritative text (the second part of a complete MSc course) provides mathematical methods required to describe images, image formation and different imaging systems, coupled with the principle techniques used for processing digital images. It is based on a course for postgraduates reading physics, electronic engineering, telecommunications engineering, information technology and computer science. This book relates the methods of processing and interpreting digital images to the 'physics' of imaging systems. Case studies reinforce the methods discussed, with examples of current research

Mathematical Modelling of Unmanned Aerial Vehicles with Four Rotors

Directory of Open Access Journals (Sweden)

Zoran Benić

2016-01-01

Full Text Available Mathematical model of an unmanned aerial vehicle with four propulsors (quadcopter is indispensable in quadcopter movement simulation and later modelling of the control algorithm. Mathematical model is, at the same time, the first step in comprehending the mathematical principles and physical laws which are applied to the quadcopter system. The objective is to define the mathematical model which will describe the quadcopter behavior with satisfactory accuracy and which can be, with certain modifications, applicable for the similar configurations of multirotor aerial vehicles. At the beginning of mathematical model derivation, coordinate systems are defined and explained. By using those coordinate systems, relations between parameters defined in the earth coordinate system and in the body coordinate system are defined. Further, the quadcopter kinematic is described which enables setting those relations. Also, quadcopter dynamics is used to introduce forces and torques to the model through usage of Newton-Euler method. Final derived equation is Newton’s second law in the matrix notation. For the sake of model simplification, hybrid coordinate system is defined, and quadcopter dynamic equations derived with the respect to it. Those equations are implemented in the simulation. Results of behavior of quadcopter mathematical model are graphically shown for four cases. For each of the cases the propellers revolutions per minute (RPM are set in a way that results in the occurrence of the controllable variables which causes one of four basic quadcopter movements in space.

The comprehension of mathematic problems in primary school

Directory of Open Access Journals (Sweden)

Karel Pérez Ariza

2015-05-01

Full Text Available The paper describes the result of the research project “A study of causes of difficulties in learning comprehension from an interdisciplinary perspective in Camagüey. The main objective of that study is to propose a methodology for the comprehension of mathematic problems in primary school. In designing the methodology, the characteristics of this text variety, basic principle of the theory of reading comprehension and problem solving were taking into account. In this research work several theoretical methods were used —analysis-synthesis, historical-logical, inductive-deductive— to elaborate the theoretical framework, while modeling and system approach in the methodology construction. Additionally, empirical methods were used in order to assess the knowledge about comprehension of mathematic problems; among them observation and analysis of the activity results.

Mathematical model for a novel cryogenic flow sensor using fibre Bragg gratings

OpenAIRE

Thekkethil, S.R.; Reby Roy, K.E.; Thomas, R.J.; Neumann, H.; Ramalingam, R.

2016-01-01

In this work, a mathematical model is presented for a newly developed cryogenic flow meter which is based on fibre Bragg grating (FBG) principle. The principle of operation is to use the viscous drag force induced by a flowing fluid on an optical fibre placed transverse to the flow. An optical fibre will have a 5 mm long grating element inscribed in it and will be placed so that the sensor is at the centre of the pipe. The fibre will act as the bluff body, while the FBG sensor will pick up th...

5 CFR 551.401 - Basic principles.

Science.gov (United States)

2010-01-01

... 5 Administrative Personnel 1 2010-01-01 2010-01-01 false Basic principles. 551.401 Section 551.401 Administrative Personnel OFFICE OF PERSONNEL MANAGEMENT CIVIL SERVICE REGULATIONS PAY ADMINISTRATION UNDER THE FAIR LABOR STANDARDS ACT Hours of Work General Provisions § 551.401 Basic principles. (a) All time...

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

Home; Journals; Proceedings – Mathematical Sciences. Shobha Madan. Articles written in Proceedings – Mathematical Sciences. Volume 113 Issue 2 May 2003 pp 171-178. Wavelet Subspaces Invariant Under Groups of Translation Operators · Biswaranjan Behera Shobha Madan · More Details Abstract Fulltext PDF.

The conceptual basis of mathematics in cardiology: (II). Calculus and differential equations.

Science.gov (United States)

Bates, Jason H T; Sobel, Burton E

2003-04-01

This is the second in a series of four articles developed for the readers of Coronary Artery Disease. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas. This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to

The conceptual basis of mathematics in cardiology IV: statistics and model fitting.

Science.gov (United States)

Bates, Jason H T; Sobel, Burton E

2003-06-01

This is the fourth in a series of four articles developed for the readers of Coronary Artery Disease. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas. This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to

Cognitive mechanisms underlying third graders' arithmetic skills: Expanding the pathways to mathematics model.

Science.gov (United States)

Träff, Ulf; Olsson, Linda; Skagerlund, Kenny; Östergren, Rickard

2018-03-01

A modified pathways to mathematics model was used to examine the cognitive mechanisms underlying arithmetic skills in third graders. A total of 269 children were assessed on tasks tapping the four pathways and arithmetic skills. A path analysis showed that symbolic number processing was directly supported by the linguistic and approximate quantitative pathways. The direct contribution from the four pathways to arithmetic proficiency varied; the linguistic pathway supported single-digit arithmetic and word problem solving, whereas the approximate quantitative pathway supported only multi-digit calculation. The spatial processing and verbal working memory pathways supported only arithmetic word problem solving. The notion of hierarchical levels of arithmetic was supported by the results, and the different levels were supported by different constellations of pathways. However, the strongest support to the hierarchical levels of arithmetic were provided by the proximal arithmetic skills. Copyright © 2017 Elsevier Inc. All rights reserved.

System for corrosion monitoring in pipeline applying fuzzy logic mathematics

Science.gov (United States)

Kuzyakov, O. N.; Kolosova, A. L.; Andreeva, M. A.

2018-05-01

A list of factors influencing corrosion rate on the external side of underground pipeline is determined. Principles of constructing a corrosion monitoring system are described; the system performance algorithm and program are elaborated. A comparative analysis of methods for calculating corrosion rate is undertaken. Fuzzy logic mathematics is applied to reduce calculations while considering a wider range of corrosion factors.

Do medical students with A-level mathematics have a better understanding of the principles behind evidence-based medicine?

Science.gov (United States)

Ben-Shlomo, Y; Fallon, U; Sterne, J; Brookes, S

2004-12-01

With the advent of evidence-based medicine, medical students, doctors and other healthcare professionals are required to be more skilled in the interpretation and manipulation of numerical data. The authors observed that undergraduate students without A-level mathematics expressed concern as to their ability to cope with an epidemiology and biostatistics course. It was hypothesized that these anxieties reflected differences in attitudes to numerical manipulation rather than any real lack of competence. Mean exam performance scores were compared for 498 first-year medical students between 2000 and 2002 depending on whether the students did or did not have A-level mathematics. The data revealed no difference in performance. Students without mathematics A-level scored marginally worse (-1.1%, 95% CI -3.1% to 0.8%, p=0.20) but were no more likely to fail the exam (odds ratio=0.98, 95% CI 0.40 to 2.6, p=0.9). It is concluded that some students experience 'numerophobia'-- a perceived and, it is thought, disproportionate fear of numbers and simple mathematical manipulation. This may act as a psychological barrier for future evidence-based practitioners.

Cosmological principles. II. Physical principles

International Nuclear Information System (INIS)

Harrison, E.R.

1974-01-01

The discussion of cosmological principle covers the uniformity principle of the laws of physics, the gravitation and cognizability principles, and the Dirac creation, chaos, and bootstrap principles. (U.S.)

What is behind small deviations of quantum mechanics theory from experiments? Observer's mathematics point of view

Science.gov (United States)

Khots, Boris; Khots, Dmitriy

2014-12-01

Certain results that have been predicted by Quantum Mechanics (QM) theory are not always supported by experiments. This defines a deep crisis in contemporary physics and, in particular, quantum mechanics. We believe that, in fact, the mathematical apparatus employed within today's physics is a possible reason. In particular, we consider the concept of infinity that exists in today's mathematics as the root cause of this problem. We have created Observer's Mathematics that offers an alternative to contemporary mathematics. This paper is an attempt to relay how Observer's Mathematics may explain some of the contradictions in QM theory results. We consider the Hamiltonian Mechanics, Newton equation, Schrodinger equation, two slit interference, wave-particle duality for single photons, uncertainty principle, Dirac equations for free electron in a setting of arithmetic, algebra, and topology provided by Observer's Mathematics (see www.mathrelativity.com). Certain results and communications pertaining to solution of these problems are provided.

The structural, mechanical, and electronic properties of LiAlB{sub 4} under pressure from first principles

Energy Technology Data Exchange (ETDEWEB)

Tayran, Ceren; Aydin, Sezgin [Department of Physics, Sciences Faculty, Gazi University, 06500, Ankara (Turkey)

2017-05-15

The structural, elastic, mechanical, and electronic properties of lithium aluminum tetraboride (LiAlB{sub 4}) under hydrostatic pressure have been investigated by using first-principles density functional theory calculations. The effects of pressure on the lattice parameters, volume, and bond lengths are studied. It is indicated from the calculated elastic constants that LiAlB{sub 4} compound is mechanically stable on 0-40 GPa pressure range. And, by means of these elastic constants set, some mechanical properties such as bulk, shear and Young's moduli, and then Poisson's ratio are determined as a function of pressure. Also, the ductile or brittle nature of LiAlB{sub 4} is examined. Additionally, using the first-principles data obtained from the geometry optimizations, the hardness of LiAlB{sub 4} is calculated, and its nature is investigated under pressure. Furthermore, in order to reveal the effects of pressure on the electronic and binding behavior of the compound, band structures, total and partial density of states, charge densities, Mulliken atomic charges, and bond overlap populations are searched as a function of pressure. To check the stability of the compound, phonon dispersion curves are calculated. And, the results are compared with the other convenient borides. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

A Primer on Mathematical Modeling in the Study of Organisms and Their Parts.

Science.gov (United States)

Montévil, Maël

2018-01-01

Mathematical modeling is a very powerful tool for understanding natural phenomena. Such a tool carries its own assumptions and should always be used critically. In this chapter, we highlight the key ingredients and steps of modeling and focus on their biological interpretation. In particular, we discuss the role of theoretical principles in writing models. We also highlight the meaning and interpretation of equations. The main aim of this chapter is to facilitate the interaction between biologists and mathematical modelers. We focus on the case of cell proliferation and motility in the context of multicellular organisms.

Mathematics related anxiety: Mathematics bogeyman or not?

Directory of Open Access Journals (Sweden)

Videnović Marina

2011-01-01

Full Text Available Data of the PISA 2003 survey indicate high levels of mathematics anxiety of students in Serbia. More than half of our students worry whether they will have difficulties in mathematics class or whether they will earn poor marks. Aims of this study therefore are: examining relationship between math anxiety and achievement at mathematics literacy scale; establishing possible predictors of math anxiety and identification of students' groups in relations to their relationship towards mathematics as a subject. Mathematics anxiety is statistically negatively correlated with school achievement and achievement at mathematics literacy scale. Socio-demographic factors, motivational and cognitive aspects related to learning mathematics, perception of school and classroom climate explain 40% variance of mathematics anxiety. Based on students' relationship towards mathematics they cam be divided into three groups; while dimensions that apart them are uninterested-interested in mathematics and presence-absence of anxiety. The group displaying anxiety scores lowest among the three. Applying qualitative analysis students' and teachers' attitudes on specific issues related to teaching and learning mathematics was examined.

The LeChatelier-Samuelson principle revisited

NARCIS (Netherlands)

Dietzenbacher, E

1992-01-01

Within the context of a linear Leontief model, the LeChatelier-Samuelson principle examines the effects of an increase in some final demand on the output levels under the constraint that the production of certain goods is held at its original value. The principle states that the increase in any

31 CFR 29.321 - General principle.

Science.gov (United States)

2010-07-01

... 31 Money and Finance: Treasury 1 2010-07-01 2010-07-01 false General principle. 29.321 Section 29.321 Money and Finance: Treasury Office of the Secretary of the Treasury FEDERAL BENEFIT PAYMENTS UNDER....321 General principle. Any service performed after June 30, 1997, may never be credited toward Federal...

31 CFR 29.341 - General principle.

Science.gov (United States)

2010-07-01

... 31 Money and Finance: Treasury 1 2010-07-01 2010-07-01 false General principle. 29.341 Section 29.341 Money and Finance: Treasury Office of the Secretary of the Treasury FEDERAL BENEFIT PAYMENTS UNDER... Benefit Payments § 29.341 General principle. Except for disability retirements after June 30, 1997, and...

Teaching Proofs and Algorithms in Discrete Mathematics with Online Visual Logic Puzzles

Science.gov (United States)

Cigas, John; Hsin, Wen-Jung

2005-01-01

Visual logic puzzles provide a fertile environment for teaching multiple topics in discrete mathematics. Many puzzles can be solved by the repeated application of a small, finite set of strategies. Explicitly reasoning from a strategy to a new puzzle state illustrates theorems, proofs, and logic principles. These provide valuable, concrete…

Improvement of Statistical Decisions under Parametric Uncertainty

Science.gov (United States)

Nechval, Nicholas A.; Nechval, Konstantin N.; Purgailis, Maris; Berzins, Gundars; Rozevskis, Uldis

2011-10-01

A large number of problems in production planning and scheduling, location, transportation, finance, and engineering design require that decisions be made in the presence of uncertainty. Decision-making under uncertainty is a central problem in statistical inference, and has been formally studied in virtually all approaches to inference. The aim of the present paper is to show how the invariant embedding technique, the idea of which belongs to the authors, may be employed in the particular case of finding the improved statistical decisions under parametric uncertainty. This technique represents a simple and computationally attractive statistical method based on the constructive use of the invariance principle in mathematical statistics. Unlike the Bayesian approach, an invariant embedding technique is independent of the choice of priors. It allows one to eliminate unknown parameters from the problem and to find the best invariant decision rule, which has smaller risk than any of the well-known decision rules. To illustrate the proposed technique, application examples are given.

Organizing principles as tools for bridging the gap between system theory and biological experimentation.

Science.gov (United States)

Mekios, Constantinos

2016-04-01

Twentieth-century theoretical efforts towards the articulation of general system properties came short of having the significant impact on biological practice that their proponents envisioned. Although the latter did arrive at preliminary mathematical formulations of such properties, they had little success in showing how these could be productively incorporated into the research agenda of biologists. Consequently, the gap that kept system-theoretic principles cut-off from biological experimentation persisted. More recently, however, simple theoretical tools have proved readily applicable within the context of systems biology. In particular, examples reviewed in this paper suggest that rigorous mathematical expressions of design principles, imported primarily from engineering, could produce experimentally confirmable predictions of the regulatory properties of small biological networks. But this is not enough for contemporary systems biologists who adopt the holistic aspirations of early systemologists, seeking high-level organizing principles that could provide insights into problems of biological complexity at the whole-system level. While the presented evidence is not conclusive about whether this strategy could lead to the realization of the lofty goal of a comprehensive explanatory integration, it suggests that the ongoing quest for organizing principles is pragmatically advantageous for systems biologists. The formalisms postulated in the course of this process can serve as bridges between system-theoretic concepts and the results of molecular experimentation: they constitute theoretical tools for generalizing molecular data, thus producing increasingly accurate explanations of system-wide phenomena.

Physical principles of filamentous protein self-assembly kinetics

Science.gov (United States)

Michaels, Thomas C. T.; Liu, Lucie X.; Meisl, Georg; Knowles, Tuomas P. J.

2017-04-01

The polymerization of proteins and peptides into filamentous supramolecular structures is an elementary form of self-organization of key importance to the functioning biological systems, as in the case of actin biofilaments that compose the cellular cytoskeleton. Aberrant filamentous protein self-assembly, however, is associated with undesired effects and severe clinical disorders, such as Alzheimer’s and Parkinson’s diseases, which, at the molecular level, are associated with the formation of certain forms of filamentous protein aggregates known as amyloids. Moreover, due to their unique physicochemical properties, protein filaments are finding extensive applications as biomaterials for nanotechnology. With all these different factors at play, the field of filamentous protein self-assembly has experienced tremendous activity in recent years. A key question in this area has been to elucidate the microscopic mechanisms through which filamentous aggregates emerge from dispersed proteins with the goal of uncovering the underlying physical principles. With the latest developments in the mathematical modeling of protein aggregation kinetics as well as the improvement of the available experimental techniques it is now possible to tackle many of these complex systems and carry out detailed analyses of the underlying microscopic steps involved in protein filament formation. In this paper, we review some classical and modern kinetic theories of protein filament formation, highlighting their use as a general strategy for quantifying the molecular-level mechanisms and transition states involved in these processes.

Teachers' Mathematics as Mathematics-at-Work

Science.gov (United States)

Bednarz, Nadine; Proulx, Jérôme

2017-01-01

Through recognising mathematics teachers as professionals who use mathematics in their workplace, this article traces a parallel between the mathematics enacted by teachers in their practice and the mathematics used in workplaces found in studies of professionals (e.g. nurses, engineers, bankers). This parallel is developed through the five…

Discrete maximum principle for FE solutions of the diffusion-reaction problem on prismatic meshes

Czech Academy of Sciences Publication Activity Database

Hannukainen, A.; Korotov, S.; Vejchodský, Tomáš

2009-01-01

Roč. 226, č. 2 (2009), s. 275-287 ISSN 0377-0427 R&D Projects: GA AV ČR IAA100760702 Institutional research plan: CEZ:AV0Z10190503 Keywords : diffusion-reaction problem * maximum principle * prismatic finite elements Subject RIV: BA - General Mathematics Impact factor: 1.292, year: 2009

Students’ Mathematical Literacy in Solving PISA Problems Based on Keirsey Personality Theory

Science.gov (United States)

Masriyah; Firmansyah, M. H.

2018-01-01

This research is descriptive-qualitative research. The purpose is to describe students’ mathematical literacy in solving PISA on space and shape content based on Keirsey personality theory. The subjects are four junior high school students grade eight with guardian, artisan, rational or idealist personality. Data collecting methods used test and interview. Data of Keirsey Personality test, PISA test, and interview were analysed. Profile of mathematical literacy of each subject are described as follows. In formulating, guardian subject identified mathematical aspects are formula of rectangle area and sides length; significant variables are terms/conditions in problem and formula of ever encountered question; translated into mathematical language those are measurement and arithmetic operations. In employing, he devised and implemented strategies using ease of calculation on area-subtraction principle; declared truth of result but the reason was less correct; didn’t use and switch between different representations. In interpreting, he declared result as area of house floor; declared reasonableness according measurement estimation. In formulating, artisan subject identified mathematical aspects are plane and sides length; significant variables are solution procedure on both of daily problem and ever encountered question; translated into mathematical language those are measurement, variables, and arithmetic operations as well as symbol representation. In employing, he devised and implemented strategies using two design comparison; declared truth of result without reason; used symbol representation only. In interpreting, he expressed result as floor area of house; declared reasonableness according measurement estimation. In formulating, rational subject identified mathematical aspects are scale and sides length; significant variables are solution strategy on ever encountered question; translated into mathematical language those are measurement, variable, arithmetic

LAWS AND PRINCIPLES OF UNIVERSAL VALUE IN SUSTAINABLE DEVELOPMENT INDICATORS ANALYSIS

Directory of Open Access Journals (Sweden)

Andreea CONSTANTINESCU

2014-11-01

Full Text Available Each extension of the scope of laws and principles that allow both mathematical and statistical remodeling as well as reaffirming the appropriateness of proven methods, stirs up a special study interest. The ever-expanding computational power of laws of power offers to the scientific universe possibility of new approach to the crucial relationship between quantity and quality, between micro and macro dimensions. Boosting broadening the use of quasi-universal value theories in research in order to deepen the analysis of sustainable development indicators can lead to a greater understanding of all aspects of this area and to facilitate understanding of the arguments which underlie any responsible decision making. This assumption underlies the logical conclusion that sustainability becomes even stronger as it benefits from scientific arguments support resulting from research. Although we have confined ourselves in drafting some coordinates for application of each method presented to particular issues of sustainable development, this research theme will be strengthened and pursued through appropriate extensive analysis.

Schaum's outline of theory and problems of Lagrangian dynamics with a treatment of Euler's equations of motion, Hamilton's equations and Hamilton's principle

CERN Document Server

Wells, Dare A

1967-01-01

The book clearly and concisely explains the basic principles of Lagrangian dynamicsand provides training in the actual physical and mathematical techniques of applying Lagrange's equations, laying the foundation for a later study of topics that bridge the gap between classical and quantum physics, engineering, chemistry and applied mathematics, and for practicing scientists and engineers.

Quantum Mechanics and the Principle of Least Radix Economy

Science.gov (United States)

Garcia-Morales, Vladimir

2015-03-01

A new variational method, the principle of least radix economy, is formulated. The mathematical and physical relevance of the radix economy, also called digit capacity, is established, showing how physical laws can be derived from this concept in a unified way. The principle reinterprets and generalizes the principle of least action yielding two classes of physical solutions: least action paths and quantum wavefunctions. A new physical foundation of the Hilbert space of quantum mechanics is then accomplished and it is used to derive the Schrödinger and Dirac equations and the breaking of the commutativity of spacetime geometry. The formulation provides an explanation of how determinism and random statistical behavior coexist in spacetime and a framework is developed that allows dynamical processes to be formulated in terms of chains of digits. These methods lead to a new (pre-geometrical) foundation for Lorentz transformations and special relativity. The Parker-Rhodes combinatorial hierarchy is encompassed within our approach and this leads to an estimate of the interaction strength of the electromagnetic and gravitational forces that agrees with the experimental values to an error of less than one thousandth. Finally, it is shown how the principle of least-radix economy naturally gives rise to Boltzmann's principle of classical statistical thermodynamics. A new expression for a general (path-dependent) nonequilibrium entropy is proposed satisfying the Second Law of Thermodynamics.

31 CFR 29.331 - General principle.

Science.gov (United States)

2010-07-01

... 31 Money and Finance: Treasury 1 2010-07-01 2010-07-01 false General principle. 29.331 Section 29.331 Money and Finance: Treasury Office of the Secretary of the Treasury FEDERAL BENEFIT PAYMENTS UNDER... Satisfied by June 30, 1997 § 29.331 General principle. To determine whether service is creditable for the...

38 CFR 70.30 - Payment principles.

Science.gov (United States)

2010-07-01

... 38 Pensions, Bonuses, and Veterans' Relief 2 2010-07-01 2010-07-01 false Payment principles. 70.30 Section 70.30 Pensions, Bonuses, and Veterans' Relief DEPARTMENT OF VETERANS AFFAIRS (CONTINUED) VHA BENEFICIARY TRAVEL UNDER 38 U.S.C. 111 § 70.30 Payment principles. (a) Subject to the other provisions of this...

Principles of European Contract Law

DEFF Research Database (Denmark)

Lando, Ole; Beale, Hugh

This text provides a comprehensive guide to the principles of European contract law. They have been drawn up by an independent body of experts from each Member State of the EU, under a project supported by the European Commission and many other organizations. The principles are stated in the form...... of articles, with a detailed commentary explaining the purpose and operation of each article and its relation to the remainder. Each article also has extensive comparative notes surveying the national laws and other international provisions on the topic. "The Principles of European Contract Law Parts I &...... in developing a common European legal culture. The European Parliament has twice called for the creation of a European Civil Code. The principles of European contract law are essential steps in these projects. This text provides a comprehensive guide to the Principles of European contract law. They have been...

The four variational principles of mechanics

International Nuclear Information System (INIS)

Gray, C.G.; Karl, G.; Novikov, V.A.

1996-01-01

We argue that there are four basic forms of the variational principles of mechanics: Hamilton close-quote s least action principle (HP), the generalized Maupertuis principle (MP), and their two reciprocal principles, RHP and RMP. This set is invariant under reciprocity and Legendre transformations. One of these forms (HP) is in the literature: only special cases of the other three are known. The generalized MP has a weaker constraint compared to the traditional formulation, only the mean energy bar E is kept fixed between virtual paths. This reformulation of MP alleviates several weaknesses of the old version. The reciprocal Maupertuis principle (RMP) is the classical limit of Schroedinger close-quote s variational principle of quantum mechanics, and this connection emphasizes the importance of the reciprocity transformation for variational principles. Two unconstrained formulations (UHP and UMP) of these four principles are also proposed, with completely specified Lagrange multipliers Percival close-quote s variational principle for invariant tori and variational principles for scattering orbits are derived from the RMP. The RMP is very convenient for approximate variational solutions to problems in mechanics using Ritz type methods Examples are provided. Copyright copyright 1996 Academic Press, Inc

Arche papers on the mathematics of abstraction

CERN Document Server

Cook, Roy T

2007-01-01

This volume collects together a number of important papers concerning both the method of abstraction generally and the use of particular abstraction principles to reconstruct central areas of mathematics along logicist lines. Gottlob Frege's original logicist project was, in effect, refuted by Russell's paradox. Crispin Wright has recently revived Frege's enterprise, however, providing a philosophical and technical framework within which a reconstruction of arithmetic is possible. While the Neo-Fregean project has recieved extensive attention and discussion, the present volume is unique in pre

The unique and shared contributions of arithmetic operation understanding and numerical magnitude representation to children's mathematics achievement.

Science.gov (United States)

Wong, Terry Tin-Yau

2017-12-01

The current study examined the unique and shared contributions of arithmetic operation understanding and numerical magnitude representation to children's mathematics achievement. A sample of 124 fourth graders was tested on their arithmetic operation understanding (as reflected by their understanding of arithmetic principles and the knowledge about the application of arithmetic operations) and their precision of rational number magnitude representation. They were also tested on their mathematics achievement and arithmetic computation performance as well as the potential confounding factors. The findings suggested that both arithmetic operation understanding and numerical magnitude representation uniquely predicted children's mathematics achievement. The findings highlight the significance of arithmetic operation understanding in mathematics learning. Copyright © 2017 Elsevier Inc. All rights reserved.

Examining Fourth-Grade Mathematics Writing: Features of Organization, Mathematics Vocabulary, and Mathematical Representations

Science.gov (United States)

Hebert, Michael A.; Powell, Sarah R.

2016-01-01

Increasingly, students are expected to write about mathematics. Mathematics writing may be informal (e.g., journals, exit slips) or formal (e.g., writing prompts on high-stakes mathematics assessments). In order to develop an effective mathematics-writing intervention, research needs to be conducted on how students organize mathematics writing and…

Implementing Computer Algebra Enabled Questions for the Assessment and Learning of Mathematics

Science.gov (United States)

Sangwin, Christopher J.; Naismith, Laura

2008-01-01

We present principles for the design of an online system to support computer algebra enabled questions for use within the teaching and learning of mathematics in higher education. The introduction of a computer algebra system (CAS) into a computer aided assessment (CAA) system affords sophisticated response processing of student provided answers.…

Effects of SKF-83566 and haloperidol on performance on progressive ratio schedules maintained by sucrose and corn oil reinforcement: quantitative analysis using a new model derived from the Mathematical Principles of Reinforcement (MPR).

Science.gov (United States)

Olarte-Sánchez, C M; Valencia-Torres, L; Cassaday, H J; Bradshaw, C M; Szabadi, E

2013-12-01

Mathematical models can assist the interpretation of the effects of interventions on schedule-controlled behaviour and help to differentiate between processes that may be confounded in traditional performance measures such as response rate and the breakpoint in progressive ratio (PR) schedules. The effects of a D1-like dopamine receptor antagonist, 8-bromo-2,3,4,5-tetrahydro-3-methyl-5-phenyl-1H-3-benzazepin-7-ol hydrobromide (SKF-83566), and a D2-like receptor antagonist, haloperidol, on rats' performance on PR schedules maintained by sucrose and corn oil reinforcers were assessed using a new model derived from Killeen's (Behav Brain Sci 17:105-172, 1994) Mathematical Principles of Reinforcement. Separate groups of rats were trained under a PR schedule using sucrose or corn oil reinforcers. SKF-83566 (0.015 and 0.03 mg kg(-1)) and haloperidol (0.05 and 0.1 mg kg(-1)) were administered intraperitoneally (five administrations of each treatment). Running and overall response rates in successive ratios were analysed using the new model, and estimates of the model's parameters were compared between treatments. Haloperidol reduced a (the parameter expressing incentive value) in the case of both reinforcers, but did not affect the parameters related to response time and post-reinforcement pausing. SKF-83566 reduced a and k (the parameter expressing sensitivity of post-reinforcement pausing to the prior inter-reinforcement interval) in the case of sucrose, but did not affect any of the parameters in the case of corn oil. The results are consistent with the hypothesis that blockade of both D1-like and D2-like receptors reduces the incentive value of sucrose, whereas the incentive value of corn oil is more sensitive to blockade of D2-like than D1-like receptors.

Modeling physiological processes in plankton on enzyme kinetic principles

Directory of Open Access Journals (Sweden)

Ted Packard

2004-04-01

Full Text Available Many ecologically important chemical transformations in the ocean are controlled by biochemical enzyme reactions in plankton. Nitrogenase regulates the transformation of N2 to ammonium in some cyanobacteria and serves as the entryway for N2 into the ocean biosphere. Nitrate reductase controls the reduction of NO3 to NO2 and hence new production in phytoplankton. The respiratory electron transfer system in all organisms links the carbon oxidation reactions of intermediary metabolism with the reduction of oxygen in respiration. Rubisco controls the fixation of CO2 into organic matter in phytoplankton and thus is the major entry point of carbon into the oceanic biosphere. In addition to these, there are the enzymes that control CO2 production, NH4 excretion and the fluxes of phosphate. Some of these enzymes have been recognized and researched by marine scientists in the last thirty years. However, until recently the kinetic principles of enzyme control have not been exploited to formulate accurate mathematical equations of the controlling physiological expressions. Were such expressions available they would increase our power to predict the rates of chemical transformations in the extracellular environment of microbial populations whether this extracellular environment is culture media or the ocean. Here we formulate from the principles of bisubstrate enzyme kinetics, mathematical expressions for the processes of NO3 reduction, O2 consumption, N2 fixation, total nitrogen uptake.

Opting in and Creating Demand: Why Young People Choose to Teach Mathematics to Each Other

Science.gov (United States)

Tucker-Raymond, Eli; Lewis, Naama; Moses, Maisha; Milner, Chad

2016-12-01

Access to science, technology, engineering, and mathematics fields serves as a key entry point to economic mobility and civic enfranchisement. Such access must take seriously the intellectual power of the knowledge and practices of non-dominant youth. In our case, this has meant to shift epistemic authority in mathematics from academic institutions to young people themselves. This article is about why high school-aged students, from underrepresented groups, choose to participate in an out-of-school time program in which they teach younger children in the domains of mathematics and computer science. It argues for programmatic principles based on access, identity engagement, relationship building, and connections to community to support underrepresented youth as learners, teachers, leaders, and organizers in mathematics-related activities using game design as the focus of activity.

Teaching Mathematical Modeling in Mathematics Education

Science.gov (United States)

Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant

2016-01-01

Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…

How was Mathematics taught in the Arab-Islamic Civilization? – Part 1: The Pedagogical Principles of Teaching & Learning

OpenAIRE

Mr. Moktadir ZERROUKI; Prof. Abdelkader KHELLADI

2015-01-01

No matter how societies have differed throughout history in their values, cultures, politics and systems of life, there has always been a common consensus regarding the importance of mathematics and its role in the social life. Arab-Islamic civilisation -like many others- had a reasonable command of many aspects of mathematics. This was apparent in various applications including not just in everyday life, civil and business transactions, and financial dealings, but also in certain...

Developmental principles: fact or fiction.

Science.gov (United States)

Durston, A J

2012-01-01

While still at school, most of us are deeply impressed by the underlying principles that so beautifully explain why the chemical elements are ordered as they are in the periodic table, and may wonder, with the theoretician Brian Goodwin, "whether there might be equally powerful principles that account for the awe-inspiring diversity of body forms in the living realm". We have considered the arguments for developmental principles, conclude that they do exist and have specifically identified features that may generate principles associated with Hox patterning of the main body axis in bilaterian metazoa in general and in the vertebrates in particular. We wonder whether this exercise serves any purpose. The features we discuss were already known to us as parts of developmental mechanisms and defining developmental principles (how, and at which level?) adds no insight. We also see little profit in the proposal by Goodwin that there are principles outside the emerging genetic mechanisms that need to be taken into account. The emerging developmental genetic hierarchies already reveal a wealth of interesting phenomena, whatever we choose to call them.

Mathematical Modeling and Pure Mathematics

Science.gov (United States)

Usiskin, Zalman

2015-01-01

Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…

Mathematical modelling for trajectories of magnetic nanoparticles in a blood vessel under magnetic field

International Nuclear Information System (INIS)

Sharma, Shashi; Katiyar, V.K.; Singh, Uaday

2015-01-01

A mathematical model is developed to describe the trajectories of a cluster of magnetic nanoparticles in a blood vessel for the application of magnetic drug targeting (MDT). The magnetic nanoparticles are injected into a blood vessel upstream from a malignant tissue and are captured at the tumour site with help of an applied magnetic field. The applied field is produced by a rare earth cylindrical magnet positioned outside the body. All forces expected to significantly affect the transport of nanoparticles were incorporated, including magnetization force, drag force and buoyancy force. The results show that particles are slow down and captured under the influence of magnetic force, which is responsible to attract the magnetic particles towards the magnet. It is optimized that all particles are captured either before or at the centre of the magnet (z≤0) when blood vessel is very close proximity to the magnet (d=2.5 cm). However, as the distance between blood vessel and magnet (d) increases (above 4.5 cm), the magnetic nanoparticles particles become free and they flow away down the blood vessel. Further, the present model results are validated by the simulations performed using the finite element based COMSOL software. - Highlights: • A mathematical model is developed to describe the trajectories of magnetic nanoparticles. • The dominant magnetic, drag and buoyancy forces are considered. • All particles are captured when distance between blood vessel and magnet (d) is up to 4.5 cm. • Further increase in d value (above 4.5 cm) results the free movement of magnetic particles

Power electronics basics operating principles, design, formulas, and applications

CERN Document Server

Rozanov, Yuriy; Chaplygin, Evgeny; Voronin, Pavel

2015-01-01

Power Electronics Basics: Operating Principles, Design, Formulas, and Applications provides fundamental knowledge for the analysis and design of modern power electronic devices. This concise and user-friendly resource:Explains the basic concepts and most important terms of power electronicsDescribes the power assemblies, control, and passive components of semiconductor power switchesCovers the control of power electronic devices, from mathematical modeling to the analysis of the electrical processesAddresses pulse-width modulation, power quality control, and multilevel, modular, and multicell

Linking Preservice Teachers' Mathematics Self-Efficacy and Mathematics Teaching Efficacy to Their Mathematical Performance

Science.gov (United States)

Bates, Alan B.; Latham, Nancy; Kim, Jin-ah

2011-01-01

This study examined preservice teachers' mathematics self-efficacy and mathematics teaching efficacy and compared them to their mathematical performance. Participants included 89 early childhood preservice teachers at a Midwestern university. Instruments included the Mathematics Self-Efficacy Scale (MSES), Mathematics Teaching Efficacy Beliefs…

Universal uncertainty principle in the measurement operator formalism

International Nuclear Information System (INIS)

Ozawa, Masanao

2005-01-01

Heisenberg's uncertainty principle has been understood to set a limitation on measurements; however, the long-standing mathematical formulation established by Heisenberg, Kennard, and Robertson does not allow such an interpretation. Recently, a new relation was found to give a universally valid relation between noise and disturbance in general quantum measurements, and it has become clear that the new relation plays a role of the first principle to derive various quantum limits on measurement and information processing in a unified treatment. This paper examines the above development on the noise-disturbance uncertainty principle in the model-independent approach based on the measurement operator formalism, which is widely accepted to describe a class of generalized measurements in the field of quantum information. We obtain explicit formulae for the noise and disturbance of measurements given by measurement operators, and show that projective measurements do not satisfy the Heisenberg-type noise-disturbance relation that is typical in the gamma-ray microscope thought experiments. We also show that the disturbance on a Pauli operator of a projective measurement of another Pauli operator constantly equals √2, and examine how this measurement violates the Heisenberg-type relation but satisfies the new noise-disturbance relation

Geometrodynamic steering principle reveals the determiners of inertia

International Nuclear Information System (INIS)

Wheeler, J.A.

1988-01-01

What shall the authors need to grasp the essence of quantum gravity? One requirement, at least, is essential: to understand the steering principle of classical geometrodynamics. The authors outline here the physical content of that steering principle - heat of the so-called initial value problem - in its J.W. York, Jr. formulation. The central idea epitomizes itself in a single simple sentence: Mass-energy there determines inertia here. They spell out this steering principle both in its precise form and in its poor man's version. At both levels of analysis considerations of physics and mathematics alike require that the effective mass-energy of gravity waves must make itself felt on the spacetime geometry - and therefore on the gyro-defined local inertial frame of reference - on the same level as matter itself. Additional to the (mass)/(distance) Newtonian potential so familiar as measure of the effect of a nearby mass on the local frame is the Thirring and Lense gravitomagnetic potential, proportional to (angular momentum) x (distance vector)/(distance). The recent proposal of Ciufolini for a dual laser-ranged LAGEOS satellite to detect the thus-predicted gravitomagnetism of the earth is briefly described

Contrasts in Mathematical Challenges in A-Level Mathematics and Further Mathematics, and Undergraduate Mathematics Examinations

Science.gov (United States)

Darlington, Ellie

2014-01-01

This article describes part of a study which investigated the role of questions in students' approaches to learning mathematics at the secondary-tertiary interface, focussing on the enculturation of students at the University of Oxford. Use of the Mathematical Assessment Task Hierarchy taxonomy revealed A-level Mathematics and Further Mathematics…

General principles of radiotherapy

International Nuclear Information System (INIS)

Easson, E.C.

1985-01-01

The daily practice of any established branch of medicine should be based on some acceptable principles. This chapter is concerned with the general principles on which the radiotherapy of the Manchester school is based. Though many radiotherapists in other centres would doubtless accept these principles, there are sufficiently wide differences in practice throughout the world to suggest that some therapists adhere to a fundamentally different philosophy. The authors believe it is important, especially for those beginning their formal training in radiotherapy, to subscribe to an internally consistent school of thought, employing methods of treatment for each type of lesion in each anatomical site that are based on accepted principles and subjected to continuous rigorous scrutiny to test their effectiveness. Not only must each therapeutic technique be evaluated, but the underlying principles too must be questioned if and when this seems indicated. It is a feature of this hospital that similar lesions are all treated by the same technique, so long as statistical evidence justifies such a policy. All members of the staff adhere to the accepted policy until or unless reliable reasons are adduced to change this policy

Physical principles underlying the experimental methods for studying the orientational order of liquid crystals

International Nuclear Information System (INIS)

Limmer, S.

1989-01-01

The basic physical principles underlying different experimental methods frequently used for the determination of orientational order parameters of liquid crystals are reviewed. The methods that are dealt with here include the anisotropy of the diamagnetic susceptibility, birefringence, linear dichroism, Raman scattering, fluorescence depolarization, electron paramagnetic resonance (EPR), and nuclear magnetic resonance (NMR). The fundamental assertions that can be obtained by the different methods as well as their advantages, drawbacks and limitations are inspected. Typical sources of uncertainties and inaccuracies are discussed. To quantitatively evaluate the experimental data with reference to the orientational order the general tensor formalism developed by Schmiedel was employed throughout according to which the order matrix comprises 25 real elements yet. Within this context the interplay of orientational ordering and molecular conformation is scrutinized. (author)

Drying of materials in fluidized bed: mathematical modeling

International Nuclear Information System (INIS)

Wildhagen, Gloria Regina S.; Silva, Eder F.; Calcada, Luis A.; Massarani, Giulio

2000-01-01

A three phase mathematical model for drying process in a fluidized bed was established. This model representing a bubble, interstitial gas and solid phase was based on principles of mass and energy conservation and on empirical relations for heat and mass transfer between phases. A fluidized bed dryer was built to test the results of proposed model with those obtained by experiments using alumina particles as a bed charge. A good agreement between the numerical and the experimental results were observed(author)

A Mathematical Model of the Thermo-Anemometric Flowmeter.

Science.gov (United States)

Korobiichuk, Igor; Bezvesilna, Olena; Ilchenko, Andriі; Shadura, Valentina; Nowicki, Michał; Szewczyk, Roman

2015-09-11

A thermo-anemometric flowmeter design and the principles of its work are presented in the article. A mathematical model of the temperature field in a stream of biofuel is proposed. This model allows one to determine the fuel consumption with high accuracy. Numerical modeling of the heater heat balance in the fuel flow of a thermo-anemometric flowmeter is conducted and the results are analyzed. Methods for increasing the measurement speed and accuracy of a thermo-anemometric flowmeter are proposed.

Theoretical mechanics an introduction to mathematical physics

CERN Document Server

Sweetman Ames, Joseph

1958-01-01

In this book Professors Ames and Murnaghan undertake a mathematically rigorous development of theoretical mechanics from the point of view of modern physics. It gives an intensive survey of this basis field with extensive and extremely thorough discussions of vector and tensor methods, the displacement and motion of a rigid body, dynamics of inertial and non-inertial reference frames, dynamics of a particle, harmonic vibrations, nonrectilinear motion of a particle, central forces and universal gravitation, dynamics of a systems of material particle,impulsive forces, motion of a rigid body about a fixed point, gyroscopic and barygyroscopic theory, general dynamical theorems, vibrations about a point of equilibrium, the principle of least action, holonomic and nonholonomic systems, the principle of least constraint, general methods of integration and the three body problem, the potential function (including simple-layer and double-layer potentials), wave motion, the Lorentz-Einstein transformation and an illumi...

Existence and characterization of optimal control in mathematics model of diabetics population

Science.gov (United States)

Permatasari, A. H.; Tjahjana, R. H.; Udjiani, T.

2018-03-01

Diabetes is a chronic disease with a huge burden affecting individuals and the whole society. In this paper, we constructed the optimal control mathematical model by applying a strategy to control the development of diabetic population. The constructed mathematical model considers the dynamics of disabled people due to diabetes. Moreover, an optimal control approach is proposed in order to reduce the burden of pre-diabetes. Implementation of control is done by preventing the pre-diabetes develop into diabetics with and without complications. The existence of optimal control and characterization of optimal control is discussed in this paper. Optimal control is characterized by applying the Pontryagin minimum principle. The results indicate that there is an optimal control in optimization problem in mathematics model of diabetic population. The effect of the optimal control variable (prevention) is strongly affected by the number of healthy people.

Mathematical literacy of school leaving pupils in South Africa

NARCIS (Netherlands)

Howie, S.; Plomp, T.

2002-01-01

This paper discusses some results of South African (SA) grade 12 pupils on an international test of mathematical literacy, administered in the framework of the Third International Mathematics and Science Study (TIMSS) under the auspices of the International Association for the Evaluation of

Principles of Lasers

CERN Document Server

Svelto, Orazio

2010-01-01

This new Fifth Edition of Principles of Lasers incorporates corrections to the previous edition. The text’s essential mission remains the same: to provide a wide-ranging yet unified description of laser behavior, physics, technology, and current applications. Dr. Svelto emphasizes the physical rather than the mathematical aspects of lasers, and presents the subject in the simplest terms compatible with a correct physical understanding. Praise for earlier editions: "Professor Svelto is himself a longtime laser pioneer and his text shows the breadth of his broad acquaintance with all aspects of the field … Anyone mastering the contents of this book will be well prepared to understand advanced treatises and research papers in laser science and technology." (Arthur L. Schawlow, 1981 Nobel Laureate in Physics) "Already well established as a self-contained introduction to the physics and technology of lasers … Professor Svelto’s book, in this lucid translation by David Hanna, can be strongly recommended for...

How Many Is Enough?—Statistical Principles for Lexicostatistics

Science.gov (United States)

Zhang, Menghan; Gong, Tao

2016-01-01

Lexicostatistics has been applied in linguistics to inform phylogenetic relations among languages. There are two important yet not well-studied parameters in this approach: the conventional size of vocabulary list to collect potentially true cognates and the minimum matching instances required to confirm a recurrent sound correspondence. Here, we derive two statistical principles from stochastic theorems to quantify these parameters. These principles validate the practice of using the Swadesh 100- and 200-word lists to indicate degree of relatedness between languages, and enable a frequency-based, dynamic threshold to detect recurrent sound correspondences. Using statistical tests, we further evaluate the generality of the Swadesh 100-word list compared to the Swadesh 200-word list and other 100-word lists sampled randomly from the Swadesh 200-word list. All these provide mathematical support for applying lexicostatistics in historical and comparative linguistics. PMID:28018261

Contributions from sociology of science to mathematics education in Brazil: logic as a system of beliefs

Science.gov (United States)

de Andrade, Thales Haddad Novaes; Vilela, Denise Silva

2013-09-01

In Brazil, mathematics education was associated with Jean Piaget's theory. Scholars in the field of education appropriated Piaget's work in different ways, but usually emphasized logical aspects of thought, which probably lead to an expansion of mathematics education influenced by psychology. This study attempts to extend the range of interlocutions and pose a dialogue between the field of mathematics education in Brazil and the sociology of science proposed by David Bloor. The main point of Bloor's theory is that logical-mathematical knowledge is far from being true and universal and is socially conditioned. In particular we will be discussing the first principle of the strong program, which deals with conditions that generate beliefs promoted by education policies in Brazil, such as the MEC/USAID treaties. In this case the "naturalization of logic" was stimulated by a widespread diffusion of both Piaget studies and the Modern Mathematics Movement.

Using Mathematics Literature with Prospective Secondary Mathematics Teachers

Science.gov (United States)

Jett, Christopher C.

2014-01-01

Literature in mathematics has been found to foster positive improvements in mathematics learning. This manuscript reports on a mathematics teacher educator's use of literature via literature circles with 11 prospective secondary mathematics teachers in a mathematics content course. Using survey and reflection data, the author found that…

Mathematical Biology Modules Based on Modern Molecular Biology and Modern Discrete Mathematics

Science.gov (United States)

Robeva, Raina; Davies, Robin; Hodge, Terrell; Enyedi, Alexander

2010-01-01

We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to…

Progress in classical and quantum variational principles

International Nuclear Information System (INIS)

Gray, C G; Karl, G; Novikov, V A

2004-01-01

We review the development and practical uses of a generalized Maupertuis least action principle in classical mechanics in which the action is varied under the constraint of fixed mean energy for the trial trajectory. The original Maupertuis (Euler-Lagrange) principle constrains the energy at every point along the trajectory. The generalized Maupertuis principle is equivalent to Hamilton's principle. Reciprocal principles are also derived for both the generalized Maupertuis and the Hamilton principles. The reciprocal Maupertuis principle is the classical limit of Schroedinger's variational principle of wave mechanics and is also very useful to solve practical problems in both classical and semiclassical mechanics, in complete analogy with the quantum Rayleigh-Ritz method. Classical, semiclassical and quantum variational calculations are carried out for a number of systems, and the results are compared. Pedagogical as well as research problems are used as examples, which include nonconservative as well as relativistic systems. '... the most beautiful and important discovery of Mechanics.' Lagrange to Maupertuis (November 1756)

Intuitive Mathematical Knowledge as an Essential Aspect of Contemporary Adult Learning: A case of women street vendors in the city of Gaborone

Directory of Open Access Journals (Sweden)

Rebecca Nthogo Lekoko

2006-04-01

Full Text Available The findings of a phenomenological interview study with women street vendors showed a strong link between participants’ perceptions of everyday use of mathematical literacy and the speculations that mathematical use arose spontaneously in response to a practical need. The concept of intuitive mathematics as used indicates that mathematical thinking is an indispensable element of everyday conversation. Although the study finds that intuition and spontaneity are essential principles of lifelong learning, it concludes with recommendations for an empowerment curriculum that interweaves participants’ experiences and intuition with formal/academic mathematical literacy and psychosocial skills necessary for success in a highly competitive business world.

Socio-functional dynamics of the mathematical contents

Directory of Open Access Journals (Sweden)

Isabel Alonso-Berenguer

2018-01-01

Full Text Available The article presents a model of the socio-functional dynamics of the mathematical contents that offers a novel theoretical-methodological basement for the development of the process of teaching-learning of the mathematical one. The investigation, of theoretical character, used the methods of analysis-synthesis, inductive-deductive and historical-logical to elaborate the one mentioned model that leaves of considering that the future professors have appropriated previously of the mathematical contents, foreseen in the curriculum, and they are, therefore, under conditions of understanding the potentialities of the same ones to facilitate the formation of socio-functional values.   

Hydrodynamic equations for electrons in graphene obtained from the maximum entropy principle

Energy Technology Data Exchange (ETDEWEB)

Barletti, Luigi, E-mail: luigi.barletti@unifi.it [Dipartimento di Matematica e Informatica “Ulisse Dini”, Università degli Studi di Firenze, Viale Morgagni 67/A, 50134 Firenze (Italy)

2014-08-15

The maximum entropy principle is applied to the formal derivation of isothermal, Euler-like equations for semiclassical fermions (electrons and holes) in graphene. After proving general mathematical properties of the equations so obtained, their asymptotic form corresponding to significant physical regimes is investigated. In particular, the diffusive regime, the Maxwell-Boltzmann regime (high temperature), the collimation regime and the degenerate gas limit (vanishing temperature) are considered.

Doing Mathematics with Purpose: Mathematical Text Types

Science.gov (United States)

Dostal, Hannah M.; Robinson, Richard

2018-01-01

Mathematical literacy includes learning to read and write different types of mathematical texts as part of purposeful mathematical meaning making. Thus in this article, we describe how learning to read and write mathematical texts (proof text, algorithmic text, algebraic/symbolic text, and visual text) supports the development of students'…

Development of a Mathematics, Science, and Technology Education Integrated Program for a Maglev

Science.gov (United States)

Park, Hyoung Seo

2006-01-01

The purpose of the study was to develop an MST Integrated Program for making a Maglev hands-on activity for higher elementary school students in Korea. In this MST Integrated Program, students will apply Mathematics, Science, and Technology principles and concepts to the design, construction, and evaluation of a magnetically levitated vehicle. The…

The Patterns of Music: Young Children Learning Mathematics through Beat, Rhythm, and Melody

Science.gov (United States)

Geist, Kamile; Geist, Eugene A.; Kuznik, Kathleen

2012-01-01

Research on music and music therapy suggests that math and music are related in the brain from very early in life. Musical elements such as steady beat, rhythm, melody, and tempo possess inherent mathematical principles such as spatial properties, sequencing, counting, patterning, and one-to-one correspondence. With new understanding about the…

Annual Perspectives in Mathematics Education 2016: Mathematical Modeling and Modeling Mathematics

Science.gov (United States)

Hirsch, Christian R., Ed.; McDuffie, Amy Roth, Ed.

2016-01-01

Mathematical modeling plays an increasingly important role both in real-life applications--in engineering, business, the social sciences, climate study, advanced design, and more--and within mathematics education itself. This 2016 volume of "Annual Perspectives in Mathematics Education" ("APME") focuses on this key topic from a…

The mathematics of random mutation and natural selection for multiple simultaneous selection pressures and the evolution of antimicrobial drug resistance.

Science.gov (United States)

Kleinman, Alan

2016-12-20

The random mutation and natural selection phenomenon act in a mathematically predictable behavior, which when understood leads to approaches to reduce and prevent the failure of the use of these selection pressures when treating infections and cancers. The underlying principle to impair the random mutation and natural selection phenomenon is to use combination therapy, which forces the population to evolve to multiple selection pressures simultaneously that invoke the multiplication rule of probabilities simultaneously as well. Recently, it has been seen that combination therapy for the treatment of malaria has failed to prevent the emergence of drug-resistant variants. Using this empirical example and the principles of probability theory, the derivation of the equations describing this treatment failure is carried out. These equations give guidance as to how to use combination therapy for the treatment of cancers and infectious diseases and prevent the emergence of drug resistance. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Mathematical modelling of the destruction degree of cancer under the influence of a RF hyperthermia

Science.gov (United States)

Paruch, Marek; Turchan, Łukasz

2018-01-01

The article presents the mathematical modeling of the phenomenon of artificial hyperthermia which is caused by the interaction of an electric field. The electric field is induced by the applicator positioned within the biological tissue with cancer. In addition, in order to estimate the degree of tumor destruction under the influence of high temperature an Arrhenius integral has been used. The distribution of electric potential in the domain considered is described by the Laplace system of equations, while the temperature field is described by the Pennes system of equations. These problems are coupled by source function being the additional component in the Pennes equation and resulting from the electric field action. The boundary element method is applied to solve the coupled problem connected with the heating of biological tissues.

Developmental Principles: Fact or Fiction

Directory of Open Access Journals (Sweden)

A. J. Durston

2012-01-01

Full Text Available While still at school, most of us are deeply impressed by the underlying principles that so beautifully explain why the chemical elements are ordered as they are in the periodic table, and may wonder, with the theoretician Brian Goodwin, “whether there might be equally powerful principles that account for the awe-inspiring diversity of body forms in the living realm”. We have considered the arguments for developmental principles, conclude that they do exist and have specifically identified features that may generate principles associated with Hox patterning of the main body axis in bilaterian metazoa in general and in the vertebrates in particular. We wonder whether this exercise serves any purpose. The features we discuss were already known to us as parts of developmental mechanisms and defining developmental principles (how, and at which level? adds no insight. We also see little profit in the proposal by Goodwin that there are principles outside the emerging genetic mechanisms that need to be taken into account. The emerging developmental genetic hierarchies already reveal a wealth of interesting phenomena, whatever we choose to call them.

Optimal Shakedown of the Thin-Wall Metal Structures Under Strength and Stiffness Constraints

Directory of Open Access Journals (Sweden)

Alawdin Piotr

2017-06-01

Full Text Available Classical optimization problems of metal structures confined mainly with 1st class cross-sections. But in practice it is common to use the cross-sections of higher classes. In this paper, a new mathematical model for described shakedown optimization problem for metal structures, which elements are designed from 1st to 4th class cross-sections, under variable quasi-static loads is presented. The features of limited plastic redistribution of forces in the structure with thin-walled elements there are taken into account. Authors assume the elastic-plastic flexural buckling in one plane without lateral torsional buckling behavior of members. Design formulae for Methods 1 and 2 for members are analyzed. Structures stiffness constrains are also incorporated in order to satisfy the limit serviceability state requirements. With the help of mathematical programming theory and extreme principles the structure optimization algorithm is developed and justified with the numerical experiment for the metal plane frames.

The Principle-Based Method of Practical Ethics.

Science.gov (United States)

Spielthenner, Georg

2017-09-01

This paper is about the methodology of doing practical ethics. There is a variety of methods employed in ethics. One of them is the principle-based approach, which has an established place in ethical reasoning. In everyday life, we often judge the rightness and wrongness of actions by their conformity to principles, and the appeal to principles plays a significant role in practical ethics, too. In this paper, I try to provide a better understanding of the nature of principle-based reasoning. To accomplish this, I show in the first section that these principles can be applied to cases in a meaningful and sufficiently precise way. The second section discusses the question how relevant applying principles is to the resolution of ethical issues. This depends on their nature. I argue that the principles under consideration in this paper should be interpreted as presumptive principles and I conclude that although they cannot be expected to bear the weight of definitely resolving ethical problems, these principles can nevertheless play a considerable role in ethical research.

Evolutionary principles and their practical application.

Science.gov (United States)

Hendry, Andrew P; Kinnison, Michael T; Heino, Mikko; Day, Troy; Smith, Thomas B; Fitt, Gary; Bergstrom, Carl T; Oakeshott, John; Jørgensen, Peter S; Zalucki, Myron P; Gilchrist, George; Southerton, Simon; Sih, Andrew; Strauss, Sharon; Denison, Robert F; Carroll, Scott P

2011-03-01

Evolutionary principles are now routinely incorporated into medicine and agriculture. Examples include the design of treatments that slow the evolution of resistance by weeds, pests, and pathogens, and the design of breeding programs that maximize crop yield or quality. Evolutionary principles are also increasingly incorporated into conservation biology, natural resource management, and environmental science. Examples include the protection of small and isolated populations from inbreeding depression, the identification of key traits involved in adaptation to climate change, the design of harvesting regimes that minimize unwanted life-history evolution, and the setting of conservation priorities based on populations, species, or communities that harbor the greatest evolutionary diversity and potential. The adoption of evolutionary principles has proceeded somewhat independently in these different fields, even though the underlying fundamental concepts are the same. We explore these fundamental concepts under four main themes: variation, selection, connectivity, and eco-evolutionary dynamics. Within each theme, we present several key evolutionary principles and illustrate their use in addressing applied problems. We hope that the resulting primer of evolutionary concepts and their practical utility helps to advance a unified multidisciplinary field of applied evolutionary biology.

Mathematical logic in the human brain: syntax.

Directory of Open Access Journals (Sweden)

Roland Friedrich

Full Text Available Theory predicts a close structural relation of formal languages with natural languages. Both share the aspect of an underlying grammar which either generates (hierarchically structured expressions or allows us to decide whether a sentence is syntactically correct or not. The advantage of rule-based communication is commonly believed to be its efficiency and effectiveness. A particularly important class of formal languages are those underlying the mathematical syntax. Here we provide brain-imaging evidence that the syntactic processing of abstract mathematical formulae, written in a first order language, is, indeed efficient and effective as a rule-based generation and decision process. However, it is remarkable, that the neural network involved, consisting of intraparietal and prefrontal regions, only involves Broca's area in a surprisingly selective way. This seems to imply that despite structural analogies of common and current formal languages, at the neural level, mathematics and natural language are processed differently, in principal.

The conceptual basis of mathematics in cardiology III: linear systems theory and integral transforms.

Science.gov (United States)

Bates, Jason H T; Sobel, Burton E

2003-05-01

This is the third in a series of four articles developed for the readers of Coronary Artery Disease. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas.This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to

A mathematical foundation for controlling radiation health risks

International Nuclear Information System (INIS)

Kumazawa, S.

2000-01-01

Radiation protection is to attain an adequate control of radiation health risk compared with other risks. Our society in the 21 st century is predicted by some experts to seek the high priority of safety for expanding activity of human beings. The law of controlling risks will be a key subject to serve the safety of human beings and their environment. The main principles of the ICRP system of radiological system are strongly relating to the general law of various risk controls. The individual-based protection concept clearly gives us a mathematical model of controlling risks in general. This paper discusses the simplest formulation of controlling risks in the ICRP system, including other relating systems. First, the basic characteristics of occupational exposure as a risk control is presented by analyzing the data compiled over half a century. It shows the relation ship between dose control levels and individually controlled doses. The individual-based control also exerts some influence on the resultant collective dose. The study of occupational exposure concludes the simple mathematical expression of controlling doses under the ICRP system as shown by Kumazawa and Numakunai. Second, the typical characteristics of biological effects with repair or recovery of bio-systems are given by analyzing the data published. Those show the relationship between dose and biologically controlled or regulated response. The bio-system is undoubtedly relating to cybernetics that contains many functions of controlling risks. Consequently radiation effects might somewhat express the feature of biological risk controls. The shouldered survival of irradiated cells shows cybernetic characteristics that are assumed to be the mathematical foundation of controlling risks. The dose-response relationship shows another type of cybernetic characteristics, which could be reduced to the same basic form of controlling risks. The limited study of radiation effects definitely confirms the two

Physical principles of filamentous protein self-assembly kinetics

International Nuclear Information System (INIS)

Michaels, Thomas C T; Liu, Lucie X; Meisl, Georg; Knowles, Tuomas P J

2017-01-01

The polymerization of proteins and peptides into filamentous supramolecular structures is an elementary form of self-organization of key importance to the functioning biological systems, as in the case of actin biofilaments that compose the cellular cytoskeleton. Aberrant filamentous protein self-assembly, however, is associated with undesired effects and severe clinical disorders, such as Alzheimer’s and Parkinson’s diseases, which, at the molecular level, are associated with the formation of certain forms of filamentous protein aggregates known as amyloids. Moreover, due to their unique physicochemical properties, protein filaments are finding extensive applications as biomaterials for nanotechnology. With all these different factors at play, the field of filamentous protein self-assembly has experienced tremendous activity in recent years. A key question in this area has been to elucidate the microscopic mechanisms through which filamentous aggregates emerge from dispersed proteins with the goal of uncovering the underlying physical principles. With the latest developments in the mathematical modeling of protein aggregation kinetics as well as the improvement of the available experimental techniques it is now possible to tackle many of these complex systems and carry out detailed analyses of the underlying microscopic steps involved in protein filament formation. In this paper, we review some classical and modern kinetic theories of protein filament formation, highlighting their use as a general strategy for quantifying the molecular-level mechanisms and transition states involved in these processes. (topical review)

A mathematical medley fifty easy pieces on mathematics

CERN Document Server

Szpiro, George G

2010-01-01

Szpiro's book provides a delightful, well-written, eclectic selection of mathematical tidbits that makes excellent airplane reading for anyone with an interest in mathematics, regardless of their mathematical background. Excellent gift material. -Keith Devlin, Stanford University, author of The Unfinished Game and The Language of Mathematics It is great to have collected in one volume the many varied, insightful and often surprising mathematical stories that George Szpiro has written in his mathematical columns for the newspapers through the years. -Marcus du Sautoy, Oxford University, author

History of mathematics and history of science reunited?

Science.gov (United States)

Gray, Jeremy

2011-09-01

For some years now, the history of modern mathematics and the history of modern science have developed independently. A step toward a reunification that would benefit both disciplines could come about through a revived appreciation of mathematical practice. Detailed studies of what mathematicians actually do, whether local or broadly based, have often led in recent work to examinations of the social, cultural, and national contexts, and more can be done. Another recent approach toward a historical understanding of the abstractness of modern mathematics has been to see it as a species of modernism, and this thesis will be tested by the raft of works on the history of modern applied mathematics currently under way.

The Relationship among Elementary Teachers’ Mathematics Anxiety, Mathematics Instructional Practices, and Student Mathematics Achievement

OpenAIRE

Hadley, Kristin M.; Dorward, Jim

2011-01-01

Many elementary teachers have been found to have high levels of mathematics anxiety but the impact on student achievement was unknown. Elementary teachers (N = 692) completed the modified Mathematics Anxiety Rating Scale-Revised (Hopko, 2003) along with a questionnaire probing anxiety about teaching mathematics and current mathematics instructional practices. Student mathematics achievement data were collected for the classrooms taught by the teachers. A positive relationship was found betwee...

Learning Mathematics with Creative Drama

Directory of Open Access Journals (Sweden)

Baki Şahin

2018-04-01

Full Text Available In this study, a mathematics activity that used creative drama method to teach the fifth grade standard “Expresses a position with respect to another point using direction and unit” under geometry and measurement was implemented. Twenty students attending the fifth grade of a public school participated in the study. The lesson plan involved four activities in warm-up, role-play, and evaluation stages. Activities include processes that will ensure active participation of students. The activity lasted two lesson hours. Two prospective mathematics teachers and a mathematics teacher were available in the class during the activity to observe student participation and reactions. Additionally, 10 students were interviewed to learn their views about the lesson. Comments of the observers and the responses of the students to the interview questions indicate that the lesson was successful.

Competence with fractions predicts gains in mathematics achievement.

Science.gov (United States)

Bailey, Drew H; Hoard, Mary K; Nugent, Lara; Geary, David C

2012-11-01

Competence with fractions predicts later mathematics achievement, but the codevelopmental pattern between fractions knowledge and mathematics achievement is not well understood. We assessed this codevelopment through examination of the cross-lagged relation between a measure of conceptual knowledge of fractions and mathematics achievement in sixth and seventh grades (N=212). The cross-lagged effects indicated that performance on the sixth grade fractions concepts measure predicted 1-year gains in mathematics achievement (ß=.14, pmathematics achievement did not predict gains on the fractions concepts measure (ß=.03, p>.50). In a follow-up assessment, we demonstrated that measures of fluency with computational fractions significantly predicted seventh grade mathematics achievement above and beyond the influence of fluency in computational whole number arithmetic, performance on number fluency and number line tasks, central executive span, and intelligence. Results provide empirical support for the hypothesis that competence with fractions underlies, in part, subsequent gains in mathematics achievement. Copyright © 2012 Elsevier Inc. All rights reserved.

Hybrid modelling framework by using mathematics-based and information-based methods

International Nuclear Information System (INIS)

Ghaboussi, J; Kim, J; Elnashai, A

2010-01-01

Mathematics-based computational mechanics involves idealization in going from the observed behaviour of a system into mathematical equations representing the underlying mechanics of that behaviour. Idealization may lead mathematical models that exclude certain aspects of the complex behaviour that may be significant. An alternative approach is data-centric modelling that constitutes a fundamental shift from mathematical equations to data that contain the required information about the underlying mechanics. However, purely data-centric methods often fail for infrequent events and large state changes. In this article, a new hybrid modelling framework is proposed to improve accuracy in simulation of real-world systems. In the hybrid framework, a mathematical model is complemented by information-based components. The role of informational components is to model aspects which the mathematical model leaves out. The missing aspects are extracted and identified through Autoprogressive Algorithms. The proposed hybrid modelling framework has a wide range of potential applications for natural and engineered systems. The potential of the hybrid methodology is illustrated through modelling highly pinched hysteretic behaviour of beam-to-column connections in steel frames.

Computer programming in the UK undergraduate mathematics curriculum

Science.gov (United States)

Sangwin, Christopher J.; O'Toole, Claire

2017-11-01

This paper reports a study which investigated the extent to which undergraduate mathematics students in the United Kingdom are currently taught to programme a computer as a core part of their mathematics degree programme. We undertook an online survey, with significant follow-up correspondence, to gather data on current curricula and received replies from 46 (63%) of the departments who teach a BSc mathematics degree. We found that 78% of BSc degree courses in mathematics included computer programming in a compulsory module but 11% of mathematics degree programmes do not teach programming to all their undergraduate mathematics students. In 2016, programming is most commonly taught to undergraduate mathematics students through imperative languages, notably MATLAB, using numerical analysis as the underlying (or parallel) mathematical subject matter. Statistics is a very popular choice in optional courses, using the package R. Computer algebra systems appear to be significantly less popular for compulsory first-year courses than a decade ago, and there was no mention of logic programming, functional programming or automatic theorem proving software. The modal form of assessment of computing modules is entirely by coursework (i.e. no examination).

The language of mathematics telling mathematical tales

CERN Document Server

Barton, Bill

2008-01-01

Everyday mathematical ideas are expressed differently in different languages. This book probes those differences and explores their implications for mathematics education, arguing for alternatives to how we teach and learn mathematics.

Principle of natural and artificial radioactive series equivalency

International Nuclear Information System (INIS)

Vasilyeva, A.N.; Starkov, O.V.

2001-01-01

In the present paper one approach used under development of radioactive waste management conception is under consideration. This approach is based on the principle of natural and artificial radioactive series radiotoxic equivalency. The radioactivity of natural and artificial radioactive series has been calculated for 10 9 - years period. The toxicity evaluation for natural and artificial series has also been made. The correlation between natural radioactive series and their predecessors - actinides produced in thermal and fast reactors - has been considered. It has been shown that systematized reactor series data had great scientific significance and the principle of differential calculation of radiotoxicity was necessary to realize long-lived radioactive waste and uranium and thorium ore radiotoxicity equivalency conception. The calculations show that the execution of equivalency principle is possible for uranium series (4n+2, 4n+1). It is a problem for thorium. series. This principle is impracticable for neptunium series. (author)

Basic principles of Hasse diagram technique in chemistry.

Science.gov (United States)

Brüggemann, Rainer; Voigt, Kristina

2008-11-01

Principles of partial order applied to ranking are explained. The Hasse diagram technique (HDT) is the application of partial order theory based on a data matrix. In this paper, HDT is introduced in a stepwise procedure, and some elementary theorems are exemplified. The focus is to show how the multivariate character of a data matrix is realized by HDT and in which cases one should apply other mathematical or statistical methods. Many simple examples illustrate the basic theoretical ideas. Finally, it is shown that HDT is a useful alternative for the evaluation of antifouling agents, which was originally performed by amoeba diagrams.

The mathematics of geometrical and physical optics. The k-funktion and its ramifications

Energy Technology Data Exchange (ETDEWEB)

Stavroudis, O.N. [Centro de Investigaciones en Optica, Leon, Guanajuato (Mexico)

2006-07-01

In this sequel to his book, 'The Optics of Rays, Wavefronts, and Caustics', Stavroudis not only covers his own research results, but also includes more recent developments. The book is divided into three parts, starting with basic mathematical concepts that are further applied in the book. Surface geometry is treated with classical mathematics, while the second part covers the k-function, discussing and solving the eikonal equation as well as Maxwell equations in this context. A final part on applications consists of conclusions drawn or developed in the first two parts of the book, discussing such topics as the Cartesian oval, the modern Schiefspiegler, Huygen's principle, and Maxwell's model of Gauss' perfect lens. From the contents: Part I: Preliminaries - Calculus of variations - Calculus of variations: differential geometry of space curves (helix and ellipse) - Fermat's principle and the ray equation for inhomogeneous isotropic media - Hilbert integral, the derivation of the Hamilton-Jacobi theory, and the eikonal equation - First-order partial differential equations. Part II: The k-Function - Calculation of surface differential geometry parameters - Ray tracing - Refraction of wavefronts at surfaces - Solution of the Maxwell equation in the context of the k-function. Part III: Applications - Pseudo Maxwell equations - Derivation and discussion of the Cartesian oval - The modern Schiefspiegler - Huygen's principle - Maxwell's model of Gauss' perfect lens. (orig.)

Researches on Mathematical Relationship of Five Elements of Containing Notes and Fibonacci Sequence Modulo 5

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Zhaoxue Chen

2015-01-01

Full Text Available Considering the five periods and six qi’s theory in TCM almost shares a common basis of stem-branch system with the five elements of containing notes, studying the principle or mathematical structure behind the five elements of containing notes can surely bring a novel view for the five periods and six qi’s researches. By analyzing typical mathematical rules included in He tu, Luo shu, and stem-branch theory in TCM as well as the Fibonacci sequence especially widely existent in the biological world, novel researches are performed on mathematical relationship between the five elements of containing notes and the Fibonacci sequence modulo 5. Enlightened by elementary Yin or Yang number grouping principle of He tu, Luo shu, the 12534 and 31542 key number series of Fibonacci sequence modulo 5 are obtained. And three new arrangements about the five elements of containing notes are then introduced, which have shown close relationship with the two obtained key subsequences of the Fibonacci sequence modulo 5. The novel discovery is quite helpful to recover the scientific secret of the five periods and six qi’s theory in TCM as well as that of whole traditional Chinese culture system, but more data is needed to elucidate the TCM theory further.

Applying the principles of thermoeconomics to the organic Rankine Cycle for low temperature waste heat recovery

International Nuclear Information System (INIS)

Xiao, F.; Lilun, Q.; Changsun, S.

1989-01-01

In this paper, thermoeconomic principle is used to study the selection of working fluids and the option of the cycle parameters in the organic Rankine cycle of low temperature waste heat recovery. The parameter ξ, the product of the ratio of waste heat recovery and real cycle thermal efficiency, is suggested as a unified thermodynamic criterion for the selection of the working fluids. The mathematical expressions are developed to determine the optimal boiling temperature and the optimal pin point temperature difference in the heat recovery exchanger by way of thermoeconomic principle

On Mathematical Anti-Evolutionism

Science.gov (United States)

Rosenhouse, Jason

2016-03-01

The teaching of evolution in American high schools has long been a source of controversy. The past decade has seen an important shift in the rhetoric of anti-evolutionists, toward arguments of a strongly mathematical character. These mathematical arguments, while different in their specifics, follow the same general program and rely on the same underlying model of evolution. We shall discuss the nature and history of this program and model and describe general reasons for skepticism with regard to any anti-evolutionary arguments based upon them. We shall then survey the major arguments used by anti-evolutionists, to show how our general considerations make it possible to quickly identify their weakest points.

Quantum theory and statistical thermodynamics principles and worked examples

CERN Document Server

Hertel, Peter

2017-01-01

This textbook presents a concise yet detailed introduction to quantum physics. Concise, because it condenses the essentials to a few principles. Detailed, because these few principles –  necessarily rather abstract – are illustrated by several telling examples. A fairly complete overview of the conventional quantum mechanics curriculum is the primary focus, but the huge field of statistical thermodynamics is covered as well. The text explains why a few key discoveries shattered the prevailing broadly accepted classical view of physics. First, matter appears to consist of particles which, when propagating, resemble waves. Consequently, some observable properties cannot be measured simultaneously with arbitrary precision. Second, events with single particles are not determined, but are more or less probable. The essence of this is that the observable properties of a physical system are to be represented by non-commuting mathematical objects instead of real numbers.  Chapters on exceptionally simple, but h...

Mathematical Modelling Approach in Mathematics Education

Science.gov (United States)

Arseven, Ayla

2015-01-01

The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…

Mathematics Underground

Science.gov (United States)

Luther, Kenneth H.

2012-01-01

Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…

Three essays in mathematical finance

Science.gov (United States)

Wang, Ruming

This dissertation uses mathematical techniques to solve three problems in mathematical finance. The first two problems are on model-independent pricing and hedging of financial derivatives. We use asymptotic expansions to express derivative prices and implied volatilities. Then just by using the first few terms in the expansions, we get simple and accurate formulas, which can also help us find connections between different products. The last problem is on optimal trading strategies in a limit order book. Under a very general setup, we solve explicitly for a dynamic decision problem involving choosing between limit order and market order.

Mathematical Rigor in Introductory Physics

Science.gov (United States)

Vandyke, Michael; Bassichis, William

2011-10-01

Calculus-based introductory physics courses intended for future engineers and physicists are often designed and taught in the same fashion as those intended for students of other disciplines. A more mathematically rigorous curriculum should be more appropriate and, ultimately, more beneficial for the student in his or her future coursework. This work investigates the effects of mathematical rigor on student understanding of introductory mechanics. Using a series of diagnostic tools in conjunction with individual student course performance, a statistical analysis will be performed to examine student learning of introductory mechanics and its relation to student understanding of the underlying calculus.

What is behind small deviations of quantum mechanics theory from experiments? Observer's mathematics point of view

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Khots, Boris, E-mail: bkhots@cccglobal.com [Compressor Controls Corp., Des Moines, Iowa (United States); Khots, Dmitriy, E-mail: dkhots@imathconsulting.com [iMath Consulting LLC Omaha, Nebraska (United States)

2014-12-10

Certain results that have been predicted by Quantum Mechanics (QM) theory are not always supported by experiments. This defines a deep crisis in contemporary physics and, in particular, quantum mechanics. We believe that, in fact, the mathematical apparatus employed within today's physics is a possible reason. In particular, we consider the concept of infinity that exists in today's mathematics as the root cause of this problem. We have created Observer's Mathematics that offers an alternative to contemporary mathematics. This paper is an attempt to relay how Observer's Mathematics may explain some of the contradictions in QM theory results. We consider the Hamiltonian Mechanics, Newton equation, Schrodinger equation, two slit interference, wave-particle duality for single photons, uncertainty principle, Dirac equations for free electron in a setting of arithmetic, algebra, and topology provided by Observer's Mathematics (see www.mathrelativity.com). Certain results and communications pertaining to solution of these problems are provided.

What is behind small deviations of quantum mechanics theory from experiments? Observer's mathematics point of view

International Nuclear Information System (INIS)

Khots, Boris; Khots, Dmitriy

2014-01-01

Certain results that have been predicted by Quantum Mechanics (QM) theory are not always supported by experiments. This defines a deep crisis in contemporary physics and, in particular, quantum mechanics. We believe that, in fact, the mathematical apparatus employed within today's physics is a possible reason. In particular, we consider the concept of infinity that exists in today's mathematics as the root cause of this problem. We have created Observer's Mathematics that offers an alternative to contemporary mathematics. This paper is an attempt to relay how Observer's Mathematics may explain some of the contradictions in QM theory results. We consider the Hamiltonian Mechanics, Newton equation, Schrodinger equation, two slit interference, wave-particle duality for single photons, uncertainty principle, Dirac equations for free electron in a setting of arithmetic, algebra, and topology provided by Observer's Mathematics (see www.mathrelativity.com). Certain results and communications pertaining to solution of these problems are provided

The Effect of Teacher Beliefs on Student Competence in Mathematical Modeling--An Intervention Study

Science.gov (United States)

Mischo, Christoph; Maaß, Katja

2013-01-01

This paper presents an intervention study whose aim was to promote teacher beliefs about mathematics and learning mathematics and student competences in mathematical modeling. In the intervention, teachers received written curriculum materials about mathematical modeling. The concept underlying the materials was based on constructivist ideas and…

Mathematical bridges

CERN Document Server

Andreescu, Titu; Tetiva, Marian

2017-01-01

Building bridges between classical results and contemporary nonstandard problems, Mathematical Bridges embraces important topics in analysis and algebra from a problem-solving perspective. Blending old and new techniques, tactics and strategies used in solving challenging mathematical problems, readers will discover numerous genuine mathematical gems throughout that will heighten their appreciation of the inherent beauty of mathematics. Most of the problems are original to the authors and are intertwined in a well-motivated exposition driven by representative examples. The book is structured to assist the reader in formulating and proving conjectures, as well as devising solutions to important mathematical problems by making connections between various concepts and ideas from different areas of mathematics. Instructors and educators teaching problem-solving courses or organizing mathematics clubs, as well as motivated mathematics students from high school juniors to college seniors, will find Mathematical Bri...