A Mathematical Formalization Proposal for Business Growth
Directory of Open Access Journals (Sweden)
Gheorghe BAILESTEANU
2013-01-01
Full Text Available Economic sciences have known a spectacular evolution in the last century; beginning to use axiomatic methods, applying mathematical instruments as a decision-making tool. The quest to formalization needs to be addressed from various different angles, reducing entry and operating formal costs, increasing the incentives for firms to operate formally, reducing obstacles to their growth, and searching for inexpensive approaches through which to enforce compliancy with government regulations. This paper proposes a formalized approach to business growth, based on mathematics and logics, taking into consideration the particularities of the economic sector.
Measurements and mathematical formalism of quantum mechanics
Slavnov, D. A.
2007-03-01
A scheme for constructing quantum mechanics is given that does not have Hilbert space and linear operators as its basic elements. Instead, a version of algebraic approach is considered. Elements of a noncommutative algebra (observables) and functionals on this algebra (elementary states) associated with results of single measurements are used as primary components of the scheme. On the one hand, it is possible to use within the scheme the formalism of the standard (Kolmogorov) probability theory, and, on the other hand, it is possible to reproduce the mathematical formalism of standard quantum mechanics, and to study the limits of its applicability. A short outline is given of the necessary material from the theory of algebras and probability theory. It is described how the mathematical scheme of the paper agrees with the theory of quantum measurements, and avoids quantum paradoxes.
A Mathematical Account of the NEGF Formalism
Cornean, Horia D.; Moldoveanu, Valeriu; Pillet, Claude-Alain
2018-02-01
The main goal of this paper is to put on solid mathematical grounds the so-called Non-Equilibrium Green's Function (NEGF) transport formalism for open systems. In particular, we derive the Jauho-Meir-Wingreen formula for the time-dependent current through an interacting sample coupled to non-interacting leads. Our proof is non-perturbative and uses neither complex-time Keldysh contours, nor Langreth rules of 'analytic continuation'. We also discuss other technical identities (Langreth, Keldysh) involving various many body Green's functions. Finally, we study the Dyson equation for the advanced/retarded interacting Green's function and we rigorously construct its (irreducible) self-energy, using the theory of Volterra operators.
Formal logic rewrite system bachelor in teaching mathematical informatics
Habiballa, Hashim; Jendryscik, Radek
2017-07-01
The article presents capabilities of the formal rewrite logic system - Bachelor - for teaching theoretical computer science (mathematical informatics). The system Bachelor enables constructivist approach to teaching and therefore it may enhance the learning process in hard informatics essential disciplines. It brings not only detailed description of formal rewrite process but also it can demonstrate algorithmical principles for logic formulae manipulations.
QED Reloaded: Towards a Pluralistic Formal Library of Mathematical Knowledge
Directory of Open Access Journals (Sweden)
Michael Kohlhase
2016-01-01
Full Text Available Proposed in 1994, the ``QED project'' was one of the seminally influential initiatives in automated reasoning: It envisioned the formalization of ``all of mathematics'' and the assembly of these formalizations in a single coherent database. Even though it never led to the concrete system, communal resource, or even joint research envisioned in the QED manifesto, the idea lives on and shapes the research agendas of a significant part of the communityThis paper surveys a decade of work on representation languages and knowledge management tools for mathematical knowledge conducted in the KWARC research group at Jacobs University Bremen.It assembles the various research strands into a coherent agenda for realizing the QED dream with modern insights and technologies.
HILBERT BETWEEN THE FORMAL AND THE INFORMAL SIDE OF MATHEMATICS
Directory of Open Access Journals (Sweden)
GIORGIO VENTURI
Full Text Available Abstract: In this article we analyze the key concept of Hilbert's axiomatic method, namely that of axiom. We will find two different concepts: the first one from the period of Hilbert's foundation of geometry and the second one at the time of the development of his proof theory. Both conceptions are linked to two different notions of intuition and show how Hilbert's ideas are far from a purely formalist conception of mathematics. The principal thesis of this article is that one of the main problems that Hilbert encountered in his foundational studies consisted in securing a link between formalization and intuition. We will also analyze a related problem, that we will call "Frege's Problem", form the time of the foundation of geometry and investigate the role of the Axiom of Completeness in its solution.
Moving from Informal to Formal Mathematical Language in Maltese Classrooms
Farrugia, Marie Therese
2013-01-01
In Malta, mathematics is often taught through code-switching between Maltese and English, mainly due to the use of textbooks published in the UK. The mixing of the languages has been a source of discussion for several years, with some educators accepting the mixed pattern, and others arguing in favour of using English alone. Furthermore, the…
Accommodation in the Formal World of Mathematical Thinking
Stewart, Sepideh; Schmidt, Ralf
2017-01-01
In this study, we examined a mathematician and one of his students' teaching journals and thought processes concurrently as the class was moving towards the proof of the Fundamental Theorem of Galois Theory. We employed Tall's framework of three worlds of mathematical thinking as well as Piaget's notion of accommodation to theoretically study the…
Formalism and beyond on the nature of mathematical discourse
Link, Godehard
2014-01-01
The essays collected in this volume focus on the role of formalist aspects in mathematical theorizing and practice, examining issues such as infinity, finiteness, and proof procedures, as well as central historical figures in the field, including Frege, Russell, Hilbert and Wittgenstein. Using modern logico-philosophical tools and systematic conceptual and logical analyses, the volume provides a thorough, up-to-date account of the subject.
Libertus, Melissa E; Feigenson, Lisa; Halberda, Justin
2013-12-01
Previous research has found a relationship between individual differences in children's precision when nonverbally approximating quantities and their school mathematics performance. School mathematics performance emerges from both informal (e.g., counting) and formal (e.g., knowledge of mathematics facts) abilities. It remains unknown whether approximation precision relates to both of these types of mathematics abilities. In the current study, we assessed the precision of numerical approximation in 85 3- to 7-year-old children four times over a span of 2years. In addition, at the final time point, we tested children's informal and formal mathematics abilities using the Test of Early Mathematics Ability (TEMA-3). We found that children's numerical approximation precision correlated with and predicted their informal, but not formal, mathematics abilities when controlling for age and IQ. These results add to our growing understanding of the relationship between an unlearned nonsymbolic system of quantity representation and the system of mathematics reasoning that children come to master through instruction. Copyright © 2013 Elsevier Inc. All rights reserved.
Mathematical formalization of theories of motivation proposed by Maslow and Herzberg
Kotliarov,Ivan
2008-01-01
Maslow's theory is by far the most known theory of motivation, and the most common in the business and management practice. Herzberg's theory fits the observations and explains some aspects of human motivation left unexplained by Maslow. However, these theories have never been formalized on a strictly mathematical basis. The present article gives an outline of a mathematical model of theories of motivation proposed by Abraham Maslow and Frederick Herzberg. This model is built on a basis of sp...
Discrete mathematics, formal methods, the Z schema and the software life cycle
Bown, Rodney L.
1991-01-01
The proper role and scope for the use of discrete mathematics and formal methods in support of engineering the security and integrity of components within deployed computer systems are discussed. It is proposed that the Z schema can be used as the specification language to capture the precise definition of system and component interfaces. This can be accomplished with an object oriented development paradigm.
Mathematical formalization of theories of motivation proposed by Maslow and Herzberg
Directory of Open Access Journals (Sweden)
Ivan Kotliarov
2008-12-01
Full Text Available Maslow's theory is by far the most known theory of motivation, and the most common in the business and management practice. Herzberg's theory fits the observations and explains some aspects of human motivation left unexplained by Maslow. However, these theories have never been formalized on a strictly mathematical basis. The present article gives an outline of a mathematical model of theories of motivation proposed by Abraham Maslow and Frederick Herzberg. This model is built on a basis of special non-continuous functions. This description may be a good basis for HR software and may be useful for business and management.
Formal and Informal Mathematical Discourses: Bakhtin and Vygotsky, Dialogue and Dialectic
Barwell, Richard
2016-01-01
The importance of the role of language/discourse in the learning and teaching of mathematics is noted in many mathematics curricula and standards documents. In the research literature, this role has been widely theorised from a Vygotskian perspective. This perspective is limited by some of its underlying assumptions, including an instrumental and…
Nazarova, G.; Ivashkina, E.; Ivanchina, E.; Kiseleva, S.; Stebeneva, V.
2015-11-01
The issue of improving the energy and resource efficiency of advanced petroleum processing can be solved by the development of adequate mathematical model based on physical and chemical regularities of process reactions with a high predictive potential in the advanced petroleum refining. In this work, the development of formalized hydrocarbon conversion scheme of catalytic cracking was performed using thermodynamic parameters of reaction defined by the Density Functional Theory. The list of reaction was compiled according to the results of feedstock structural-group composition definition, which was done by the n-d-m-method, the Hazelvuda method, qualitative composition of feedstock defined by gas chromatography-mass spectrometry and individual composition of catalytic cracking gasoline fraction. Formalized hydrocarbon conversion scheme of catalytic cracking will become the basis for the development of the catalytic cracking kinetic model.
Ismail; Suwarsono, St.; Lukito, A.
2018-01-01
Critical thinking is one of the most important skills of the 21st century in addition to other learning skills such as creative thinking, communication skills and collaborative skills. This is what makes researchers feel the need to conduct research on critical thinking skills in junior high school students. The purpose of this study is to describe the critical thinking skills of junior high school female students with high mathematical skills in solving contextual and formal mathematical problems. To achieve this is used qualitative research. The subject of the study was a female student of eight grade junior high school. The students’ critical thinking skills are derived from in-depth problem-based interviews using interview guidelines. Interviews conducted in this study are problem-based interviews, which are done by the subject given a written assignment and given time to complete. The results show that critical thinking skills of female high school students with high math skills are as follows: In solving the problem at the stage of understanding the problem used interpretation skills with sub-indicators: categorization, decode, and clarify meaning. At the planning stage of the problem-solving strategy is used analytical skills with sub-indicators: idea checking, argument identification and argument analysis and evaluation skills with sub indicators: assessing the argument. In the implementation phase of problem solving, inference skills are used with subindicators: drawing conclusions, and problem solving and explanatory skills with sub-indicators: problem presentation, justification procedures, and argument articulation. At the re-checking stage all steps have been employed self-regulatory skills with sub-indicators: self-correction and selfstudy.
Making Explicit the Formalism Underlying Evaluation in Music Information Retrieval Research
DEFF Research Database (Denmark)
Sturm, Bob L.
2014-01-01
We make explicit the formalism underlying evaluation in music information retrieval research. We define a ``system,'' what it means to ``analyze'' one, and make clear the aims, parts, design, execution, interpretation, assumptions and limitations of its ``evaluation.'' We apply this formalism...
Elsner, R. F.; O'Dell, S. L.; Ramsey, B. D.; Weisskopf, M. C.
2011-01-01
We provide a mathematical formalism for optimizing the mirror nodal positions along the optical axis and the tilt of a commonly employed detector configuration at the focus of a x-ray telescope consisting of nested mirror shells with known mirror surface prescriptions. We adopt the spatial resolution averaged over the field-of-view as the figure of merit M. A more complete description appears in our paper in these proceedings.
MATHEMATICS TEACHER: MOVING KNOWLEDGE UNDER FORMATION
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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.
International Nuclear Information System (INIS)
Demazure, M.
1988-01-01
The 1988 progress report of the Mathematics center (Polytechnic School, France), is presented. The Center is composed of different research teams: analysis, Riemann geometry, group theory, formal calculus and algorithm geometry, dynamical systems, topology and singularity. For each team, the members, the research topics, the national and international cooperations, are given. The papers concerning the investigations carried out in 1988, are listed [fr
Ivan Kotliarov
2008-01-01
the present article gives an outline of a mathematical model of theories of motivation proposed by Abraham Maslow and Frederick Herzberg. This model is built on a basis of special non-continuous functions.
MATHEMATICAL FORMALISM AND SOFTWARE FOR PROCESSING OF IMAGES OF IRON-CARBON ALLOYS MICROSTRUCTURE
Directory of Open Access Journals (Sweden)
A. N. Chichko
2010-01-01
Full Text Available The description of mathematical apparatus, algorithms and software АОМ-1 and АОМ-2, used for computer processing and quantitative analysis of microstructures of pearlitic steels and grey irons, is given.
Category Theory as a Formal Mathematical Foundation for Model-Based Systems Engineering
Mabrok, Mohamed
2017-01-09
In this paper, we introduce Category Theory as a formal foundation for model-based systems engineering. A generalised view of the system based on category theory is presented, where any system can be considered as a category. The objects of the category represent all the elements and components of the system and the arrows represent the relations between these components (objects). The relationship between these objects are the arrows or the morphisms in the category. The Olog is introduced as a formal language to describe a given real-world situation description and requirement writing. A simple example is provided.
Mathematical modelling of water radiolysis kinetics under reactor conditions
International Nuclear Information System (INIS)
Khodulev, L.B.; Shapova, E.A.
1989-01-01
Experimental data on coolant radiolysis (RBMK-1000 reactor) were used to construct mathematical model of water radiolysis kinetics under reactor conditions. Good agreement of calculation results with the experiment is noted
Dillon, Moira R; Kannan, Harini; Dean, Joshua T; Spelke, Elizabeth S; Duflo, Esther
2017-07-07
Many poor children are underprepared for demanding primary school curricula. Research in cognitive science suggests that school achievement could be improved by preschool pedagogy in which numerate adults engage children's spontaneous, nonsymbolic mathematical concepts. To test this suggestion, we designed and evaluated a game-based preschool curriculum intended to exercise children's emerging skills in number and geometry. In a randomized field experiment with 1540 children (average age 4.9 years) in 214 Indian preschools, 4 months of math game play yielded marked and enduring improvement on the exercised intuitive abilities, relative to no-treatment and active control conditions. Math-trained children also showed immediate gains on symbolic mathematical skills but displayed no advantage in subsequent learning of the language and concepts of school mathematics. Copyright © 2017, American Association for the Advancement of Science.
Developing formal mathematical assessment for 4- to 8-year-olds
Doig, Brian
2005-10-01
The assessment of children in their years before school and their first years of school has been, traditionally, informal. Further, assessment of children's mathematical skills at this level has been infrequent compared to social, emotional and physical assessments. However, there are contexts where reliable, valid, standardised data from assessment in mathematics are required. This paper outlines the development of two assessment tools for mathematics that were originally developed for such contexts. Item Response Theory (IRT) analyses enabled the construction of assessment forms that address the range of abilities of 4- to 8-year-old children, and provided the scales used for constructing formative and summative reports of achievement. A description of the development of the assessment tools and the IRT analysis that provides the reporting formats are presented together with some research uses of the tools.
Hopkins, Megan; Spillane, James P.; Jakopovic, Paula; Heaton, Ruth M.
2013-01-01
Designing infrastructures to support instruction remains a challenge in educational reform. This article reports on a study of one school system's efforts to redesign its infrastructure for mathematics instruction by promoting teacher leadership. Using social network and interview data from 12 elementary schools, we explore how the district's…
Searching and retrieving in content-based repositories of formal mathematical knowledge
Guidi, Ferruccio
2003-01-01
In this thesis, the author presents a query language for an RDF (Resource Description Framework) database and discusses its applications in the context of the HELM project (the Hypertextual Electronic Library of Mathematics). This language aims at meeting the main requirements coming from the RDF community. in particular it includes: a human readable textual syntax and a machine-processable XML (Extensible Markup Language) syntax both for queries and for query results, a rigorously exposed fo...
Hilditch, David; Harms, Enno; Bugner, Marcus; Rüter, Hannes; Brügmann, Bernd
2018-03-01
A long-standing problem in numerical relativity is the satisfactory treatment of future null-infinity. We propose an approach for the evolution of hyperboloidal initial data in which the outer boundary of the computational domain is placed at infinity. The main idea is to apply the ‘dual foliation’ formalism in combination with hyperboloidal coordinates and the generalized harmonic gauge formulation. The strength of the present approach is that, following the ideas of Zenginoğlu, a hyperboloidal layer can be naturally attached to a central region using standard coordinates of numerical relativity applications. Employing a generalization of the standard hyperboloidal slices, developed by Calabrese et al, we find that all formally singular terms take a trivial limit as we head to null-infinity. A byproduct is a numerical approach for hyperboloidal evolution of nonlinear wave equations violating the null-condition. The height-function method, used often for fixed background spacetimes, is generalized in such a way that the slices can be dynamically ‘waggled’ to maintain the desired outgoing coordinate lightspeed precisely. This is achieved by dynamically solving the eikonal equation. As a first numerical test of the new approach we solve the 3D flat space scalar wave equation. The simulations, performed with the pseudospectral bamps code, show that outgoing waves are cleanly absorbed at null-infinity and that errors converge away rapidly as resolution is increased.
On the mathematical integration of the nervous tissue based on the S-propagator formalism.
Chauvet, Gilbert A
2002-06-01
The integration of physiological functions in living organisms corresponds to the reconstruction of a biological system from its components. This calls for a sound theoretical framework based on the rigorous definition of the elementary physiological function within the context of multiple levels of biological organization. One of the main problems encountered in the neurosciences is that of extending the current theory of automata, as used in the study of artificial neural networks, to real neural networks. The difficulty arises because the theory of automata fails to take into account the various levels of biological organization involved in nervous activity. This article recalls the main elements of G. A. Chauvet's novel n-level field theory, i.e., the properties of non-symmetry and non-locality of functional interactions, and the S-propagator formalism that governs the propagation of a functional interaction across the different levels of the structural organization of a biological system. The neural field equations derived from this theory allow the inclusion of multiple organizational levels of a biological system into the analysis by incorporating specific local models into a global non-local model. The main advantage of the method presented here is the simplification obtained by breaking down the physiological function into its components according to the time scales and space scales of operation. Moreover, the method takes into account the non-locality of the functional interaction, assuming it to be propagated at finite velocity in a continuous and hierarchical space. Finally, this approach allows the systematic study of physiological functions within a single theoretical framework, the complexity of which could be progressively increased by integrating specific local models as new findings become available.
Popovic, Gorjana; Lederman, Judith S.
2015-01-01
The Common Core Standard for Mathematical Practice 4: Model with Mathematics specifies that mathematically proficient students are able to make connections between school mathematics and its applications to solving real-world problems. Hence, mathematics teachers are expected to incorporate connections between mathematical concepts they teach and…
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…
A formally verified algorithm for interactive consistency under a hybrid fault model
Lincoln, Patrick; Rushby, John
1993-01-01
Consistent distribution of single-source data to replicated computing channels is a fundamental problem in fault-tolerant system design. The 'Oral Messages' (OM) algorithm solves this problem of Interactive Consistency (Byzantine Agreement) assuming that all faults are worst-cass. Thambidurai and Park introduced a 'hybrid' fault model that distinguished three fault modes: asymmetric (Byzantine), symmetric, and benign; they also exhibited, along with an informal 'proof of correctness', a modified version of OM. Unfortunately, their algorithm is flawed. The discipline of mechanically checked formal verification eventually enabled us to develop a correct algorithm for Interactive Consistency under the hybrid fault model. This algorithm withstands $a$ asymmetric, $s$ symmetric, and $b$ benign faults simultaneously, using $m+1$ rounds, provided $n is greater than 2a + 2s + b + m$, and $m\\geg a$. We present this algorithm, discuss its subtle points, and describe its formal specification and verification in PVS. We argue that formal verification systems such as PVS are now sufficiently effective that their application to fault-tolerance algorithms should be considered routine.
The topology of the possible: formal spaces underlying patterns of evolutionary change.
Stadler, B M; Stadler, P F; Wagner, G P; Fontana, W
2001-11-21
The current implementation of the Neo-Darwinian model of evolution typically assumes that the set of possible phenotypes is organized into a highly symmetric and regular space equipped with a notion of distance, for example, a Euclidean vector space. Recent computational work on a biophysical genotype-phenotype model based on the folding of RNA sequences into secondary structures suggests a rather different picture. If phenotypes are organized according to genetic accessibility, the resulting space lacks a metric and is formalized by an unfamiliar structure, known as a pre-topology. Patterns of phenotypic evolution-such as punctuation, irreversibility, modularity--result naturally from the properties of this space. The classical framework, however, addresses these patterns by exclusively invoking natural selection on suitably imposed fitness landscapes. We propose to extend the explanatory level for phenotypic evolution from fitness considerations alone to include the topological structure of phenotype space as induced by the genotype-phenotype map. We introduce the mathematical concepts and tools necessary to formalize the notion of accessibility pre-topology relative to which we can speak of continuity in the genotype-phenotype map and in evolutionary trajectories. We connect the factorization of a pre-topology into a product space with the notion of phenotypic character and derive a condition for factorization. Based on anecdotal evidence from the RNA model, we conjecture that this condition is not globally fulfilled, but rather confined to regions where the genotype-phenotype map is continuous. Equivalently, local regions of genotype space on which the map is discontinuous are associated with the loss of character autonomy. This is consistent with the importance of these regions for phenotypic innovation. The intention of the present paper is to offer a perspective, a framework to implement this perspective, and a few results illustrating how this framework can
International Nuclear Information System (INIS)
Corynen, G.C.
1979-01-01
An important step in the analysis of large-scale systems is the development of economical and meaningful measures of system performance. In the literature on analysis of nuclear safeguard systems, many performance measures have been advanced, but their interrelationships and their relevance to overall system objectives have not received attention commensurate with the effort spent in developing detailed safeguard models. The work reported here is an attempt to improve the development and evaluation of performance measures for nuclear safeguard systems. This work falls into three main areas. First, we develop a new framework which provides an initial basis for defining and structuring performance measures. To demonstrate that this framework allows a clear understanding of the purposes of nuclear safeguard systems, we employ it to state various safeguard questions clearly and concisely. The framework reflects the rough subsystem structure of safeguard systems - the detection and response subsystems - and formally accommodates various safeguard models. We especially emphasize two of these models which are under development at Lawrence Livermore Laboratory, the structured assessment approach (SAA) and the systems vulnerability assessment method (SVAM). Second, we examine some performance measures presently used in the nuclear safeguards area and in reliability theory in general. Some of these we accept and modify to obtain system performance measures that are an additive combination of subsystem performance measures, a very convenient form indeed. Others we reject as impractical and meaningless. Finally, we determine some common features between the SAA and SVAM models by formally comparing these models in our framework
Energy Technology Data Exchange (ETDEWEB)
Corynen, G.C.
1979-05-15
An important step in the analysis of large-scale systems is the development of economical and meaningful measures of system performance. In the literature on analysis of nuclear safeguard systems, many performance measures have been advanced, but their interrelationships and their relevance to overall system objectives have not received attention commensurate with the effort spent in developing detailed safeguard models. The work reported here is an attempt to improve the development and evaluation of performance measures for nuclear safeguard systems. This work falls into three main areas. First, we develop a new framework which provides an initial basis for defining and structuring performance measures. To demonstrate that this framework allows a clear understanding of the purposes of nuclear safeguard systems, we employ it to state various safeguard questions clearly and concisely. The framework reflects the rough subsystem structure of safeguard systems - the detection and response subsystems - and formally accommodates various safeguard models. We especially emphasize two of these models which are under development at Lawrence Livermore Laboratory, the structured assessment approach (SAA) and the systems vulnerability assessment method (SVAM). Second, we examine some performance measures presently used in the nuclear safeguards area and in reliability theory in general. Some of these we accept and modify to obtain system performance measures that are an additive combination of subsystem performance measures, a very convenient form indeed. Others we reject as impractical and meaningless. Finally, we determine some common features between the SAA and SVAM models by formally comparing these models in our framework.
Formality theory from Poisson structures to deformation quantization
Esposito, Chiara
2015-01-01
This book is a survey of the theory of formal deformation quantization of Poisson manifolds, in the formalism developed by Kontsevich. It is intended as an educational introduction for mathematical physicists who are dealing with the subject for the first time. The main topics covered are the theory of Poisson manifolds, star products and their classification, deformations of associative algebras and the formality theorem. Readers will also be familiarized with the relevant physical motivations underlying the purely mathematical construction.
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...
Formal Models of the Network Co-occurrence Underlying Mental Operations.
Directory of Open Access Journals (Sweden)
Danilo Bzdok
2016-06-01
Full Text Available Systems neuroscience has identified a set of canonical large-scale networks in humans. These have predominantly been characterized by resting-state analyses of the task-unconstrained, mind-wandering brain. Their explicit relationship to defined task performance is largely unknown and remains challenging. The present work contributes a multivariate statistical learning approach that can extract the major brain networks and quantify their configuration during various psychological tasks. The method is validated in two extensive datasets (n = 500 and n = 81 by model-based generation of synthetic activity maps from recombination of shared network topographies. To study a use case, we formally revisited the poorly understood difference between neural activity underlying idling versus goal-directed behavior. We demonstrate that task-specific neural activity patterns can be explained by plausible combinations of resting-state networks. The possibility of decomposing a mental task into the relative contributions of major brain networks, the "network co-occurrence architecture" of a given task, opens an alternative access to the neural substrates of human cognition.
Under-Threes' Mathematical Learning--Teachers' Perspectives
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…
Economic-mathematical methods and models under uncertainty
Aliyev, A G
2013-01-01
Brief Information on Finite-Dimensional Vector Space and its Application in EconomicsBases of Piecewise-Linear Economic-Mathematical Models with Regard to Influence of Unaccounted Factors in Finite-Dimensional Vector SpacePiecewise Linear Economic-Mathematical Models with Regard to Unaccounted Factors Influence in Three-Dimensional Vector SpacePiecewise-Linear Economic-Mathematical Models with Regard to Unaccounted Factors Influence on a PlaneBases of Software for Computer Simulation and Multivariant Prediction of Economic Even at Uncertainty Conditions on the Base of N-Comp
Validity of the formal Edgeworth expansion when the underlying distribution is partly discrete
DEFF Research Database (Denmark)
Jensen, J.L.
1989-01-01
Validity of the formal Edgeworth expansion for the distribution of the statistic √ng(Xn/n, Yn/n) is considered. Here Xn is a continuous variate and Yn is a discrete variate. In general if (Xn, Yn) resemble the sum of i.i.d. variables and the partial derivative of g with respect to the first...... variable has full rank it is possible to establish an Edgeworth expansion. © 1989 Springer-Verlag....
Formalizing the concept of sound.
Energy Technology Data Exchange (ETDEWEB)
Kaper, H. G.; Tipei, S.
1999-08-03
The notion of formalized music implies that a musical composition can be described in mathematical terms. In this article we explore some formal aspects of music and propose a framework for an abstract approach.
Indian Academy of Sciences (India)
Keywords. formalization of mathematics; Mizar; social choice theory; Arrow's theorem; Gibbard–Satterthwaite theorem; proof errors. ... Author Affiliations. Freek Wiedijk1. Institute for Computing and Information Sciences, Radboud University Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands ...
Energy Technology Data Exchange (ETDEWEB)
Koran, J.J. Jr. [Florida Museum of Natural History, Gainesville, FL (United States)
1993-10-15
Twenty-four undergraduate science and mathematics majors who were juniors and seniors in the colleges of Liberal Arts and Sciences and Engineering were recruited, and paid, to participate in an orientation seminar and act as teacher aides in regional schools and the Florida Museum of Natural History. Aides worked with teachers in the schools one semester and as docents in the natural history museum a second semester. Mentoring took place by the principal investigator and participating teachers and docents throughout the program. Success of the program was measured by a specially prepared attitude instrument which was administered to participants before the mentoring started and when it ended each semester. Written logs (field notes) were also prepared and submitted by participants at the end of each semester. Further, a tally was kept of the number of participants who decided to go into science or mathematics teaching as a result of the experience.
Directory of Open Access Journals (Sweden)
Chayanopparat Piyanan
2016-01-01
Full Text Available Non-formal vocational education provides practical experiences in a particular occupational field to non-formal semi-skilled learners. Non-formal vocational teachers are the key persons to deliver particular occupational knowledge. The essential competencies enhancement for non-sformal vocational teachers will improve teaching performance. The question of the research is what the essential competencies for the nonformal vocational teachers are. The research method was 1 to review related literature, 2 to collect a needs assessment, and 3 to analyse the essential competencies for non-formal vocational teachers. The population includes non-formal vocational teachers at the executive level and nonformal vocational teachers. The results from the essential competencies analysis found that the essential competencies for non-formal vocational teachers consist of 5 capabilities including 1 Adult learning design capability, 2 Adult learning principle application capability, 3 ICT searching capability for teaching preparation, 4 Instructional plan development capability and 5 Instructional media development capability.
Energy Technology Data Exchange (ETDEWEB)
Guerrero, A. F., E-mail: afguerreror@uqvirtual.edu.co [Departamento de Física, Universidad Del Quindío Cra 15 # 12N Armenia, Quindío (Colombia); Mesa, J., E-mail: jmesa@ibb.unesp.br [Instituto de Biociências de Botucatu da UNESP Distrito de Rubião Jr. s/n°, 18618-000, Botucatu, SP (Brazil)
2016-07-07
Because of the behavior that charged particles have when they interact with biological material, proton therapy is shaping the future of radiation therapy in cancer treatment. The planning of radiation therapy is made up of several stages. The first one is the diagnostic image, in which you have an idea of the density, size and type of tumor being treated; to understand this it is important to know how the particles beam interacts with the tissue. In this work, by using de Lindhard formalism and the Y.R. Waghmare model for the charge distribution of the proton, the electronic stopping power (SP) for a proton beam interacting with a liquid water target in the range of proton energies 10{sup 1} eV - 10{sup 10} eV taking into account all the charge states is calculated.
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 exchange...
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.
Wodtke, Geoffrey T; Parbst, Matthew
2017-10-01
Although evidence indicates that neighborhoods affect educational outcomes, relatively little research has explored the mechanisms thought to mediate these effects. This study investigates whether school poverty mediates the effect of neighborhood context on academic achievement. Specifically, it uses longitudinal data from the Panel Study of Income Dynamics, counterfactual methods, and a value-added modeling strategy to estimate the total, natural direct, and natural indirect effects of exposure to an advantaged rather than disadvantaged neighborhood on reading and mathematics abilities during childhood and adolescence. Contrary to expectations, results indicate that school poverty is not a significant mediator of neighborhood effects during either developmental period. Although moving from a disadvantaged neighborhood to an advantaged neighborhood is estimated to substantially reduce subsequent exposure to school poverty and improve academic achievement, school poverty does not play an important mediating role because even the large differences in school composition linked to differences in neighborhood context appear to have no appreciable effect on achievement. An extensive battery of sensitivity analyses indicates that these results are highly robust to unobserved confounding, alternative model specifications, alternative measures of school context, and measurement error, which suggests that neighborhood effects on academic achievement are largely due to mediating factors unrelated to school poverty.
Mathematical Modeling of Intravascular Blood Coagulation under Wall Shear Stress
Rukhlenko, Oleksii S.; Dudchenko, Olga A.; Zlobina, Ksenia E.; Guria, Georgy Th.
2015-01-01
Increased shear stress such as observed at local stenosis may cause drastic changes in the permeability of the vessel wall to procoagulants and thus initiate intravascular blood coagulation. In this paper we suggest a mathematical model to investigate how shear stress-induced permeability influences the thrombogenic potential of atherosclerotic plaques. Numerical analysis of the model reveals the existence of two hydrodynamic thresholds for activation of blood coagulation in the system and unveils typical scenarios of thrombus formation. The dependence of blood coagulation development on the intensity of blood flow, as well as on geometrical parameters of atherosclerotic plaque is described. Relevant parametric diagrams are drawn. The results suggest a previously unrecognized role of relatively small plaques (resulting in less than 50% of the lumen area reduction) in atherothrombosis and have important implications for the existing stenting guidelines. PMID:26222505
Frías, María; Carrasco, Ana Cristina; Fraile, Alberto; Alemán, José
2018-03-02
A new organocatalytic strategy for the synthesis of enantioenriched aza-Baylis-Hillman type products via a frustrated vinylogous reaction is presented. This process proceeds under mild conditions with good yields, completed Z/E selectivity and excellent enantioselectivities. Moreover, easy derivatizations of the final products led to important building blocks of organic synthesis such as 1,3-aminoalcohols and Lewis base catalysts. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
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
Stein, Sherman K
2010-01-01
Anyone can appreciate the beauty, depth, and vitality of mathematics with the help of this highly readable text, specially developed from a college course designed to appeal to students in a variety of fields. Readers with little mathematical background are exposed to a broad range of subjects chosen from number theory, topology, set theory, geometry, algebra, and analysis. Starting with a survey of questions on weight, the text discusses the primes, the fundamental theorem of arithmetic, rationals and irrationals, tiling, tiling and electricity, probability, infinite sets, and many other topi
Mathematic modelling of circular cylinder deformation under inner grouwth
Directory of Open Access Journals (Sweden)
A. V. Siasiev
2009-09-01
Full Text Available A task on the intensive deformed state (IDS of a viscoelastic declivous cylinder, which is grown under the action of inner pressure, is considered. The process of continuous increase takes a place on an internal radius so, that a radius and pressure change on set to the given law. The special case of linear law of creeping is considered, and also numeral results are presented as the graphs of temporal dependence of tensions and moving for different points of cylinder.
Directory of Open Access Journals (Sweden)
Ibrahem Hussein
2018-01-01
Full Text Available Line start permanent magnet synchronous motors experience different types of failures, including static eccentricity. The first step in detecting such failures is the mathematical modeling of the motor under healthy and failed conditions. In this paper, an attempt to develop an accurate mathematical model for this motor under static eccentricity is presented. The model is based on the modified winding function method and coupled magnetic circuits approach. The model parameters are calculated directly from the motor winding layout and its geometry. Static eccentricity effects are considered in the motor inductances calculation. The performance of the line start permanent magnet synchronous motor using the developed mathematical model is investigated using MATLAB/SIMULINK® software (2013b, MathWorks, Natick, MA, USA under healthy and static eccentricity condition for different loading values. A finite element method analysis is conducted to verify the mathematical model results, using the commercial JMAG® software (16.0.02n, JSOL Corporation, Tokyo, Japan. The results show a fine agreement between JMAG® and the developed mathematical model simulation results.
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.
Formal verification - Robust and efficient code: Introduction to Formal Verification
CERN. Geneva
2016-01-01
In general, FV means "proving that certain properties hold for a given system using formal mathematics". This definition can certainly feel daunting, however, as we will learn, we can reap benefits from the paradigm without digging too deep into ...
Formalizing Probabilistic Safety Claims
Herencia-Zapana, Heber; Hagen, George E.; Narkawicz, Anthony J.
2011-01-01
A safety claim for a system is a statement that the system, which is subject to hazardous conditions, satisfies a given set of properties. Following work by John Rushby and Bev Littlewood, this paper presents a mathematical framework that can be used to state and formally prove probabilistic safety claims. It also enables hazardous conditions, their uncertainties, and their interactions to be integrated into the safety claim. This framework provides a formal description of the probabilistic composition of an arbitrary number of hazardous conditions and their effects on system behavior. An example is given of a probabilistic safety claim for a conflict detection algorithm for aircraft in a 2D airspace. The motivation for developing this mathematical framework is that it can be used in an automated theorem prover to formally verify safety claims.
Formalization of Database Systems -- and a Formal Definition of {IMS}
DEFF Research Database (Denmark)
Bjørner, Dines; Løvengreen, Hans Henrik
1982-01-01
Drawing upon an analogy between Programming Language Systems and Database Systems we outline the requirements that architectural specifications of database systems must futfitl, and argue that only formal, mathematical definitions may 6atisfy these. Then we illustrate home aspects and touch upon...... come ueee of formal definitions of data models and databaee management systems. A formal model of INS will carry this discussion. Finally we survey some of the exkting literature on formal definitions of database systems. The emphasis will be on constructive definitions in the denotationul semantics...... style of the VCM: Vienna Development Nethd. The role of formal definitions in international standardiaation efforts is briefly mentioned....
Formalization of Database Systems -- and a Formal Definition of {IMS}
DEFF Research Database (Denmark)
Bjørner, Dines; Løvengreen, Hans Henrik
1982-01-01
come ueee of formal definitions of data models and databaee management systems. A formal model of INS will carry this discussion. Finally we survey some of the exkting literature on formal definitions of database systems. The emphasis will be on constructive definitions in the denotationul semantics......Drawing upon an analogy between Programming Language Systems and Database Systems we outline the requirements that architectural specifications of database systems must futfitl, and argue that only formal, mathematical definitions may 6atisfy these. Then we illustrate home aspects and touch upon...... style of the VCM: Vienna Development Nethd. The role of formal definitions in international standardiaation efforts is briefly mentioned....
Formal Methods: Practice and Experience
DEFF Research Database (Denmark)
Woodcock, Jim; Larsen, Peter Gorm; Bicarregui, Juan
2009-01-01
Formal methods use mathematical models for analysis and verification at any part of the program life-cycle. We describe the state of the art in the industrial use of formal methods, concentrating on their increasing use at the earlier stages of specification and design. We do this by reporting on...
DEFF Research Database (Denmark)
Sørensen, John Aasted
2011-01-01
The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... 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......; 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...
Formalizing typical crosscutting concerns
Marin, A.M.
2006-01-01
We present a consistent system for referring crosscutting functionality, relating crosscutting concerns to specific implementation idioms, and formalizing their underlying relations through queries. The system is based on generic crosscutting concerns that we organize and describe in a catalog. We
Formal groups and applications
Hazewinkel, Michiel
2012-01-01
This book is a comprehensive treatment of the theory of formal groups and its numerous applications in several areas of mathematics. The seven chapters of the book present basics and main results of the theory, as well as very important applications in algebraic topology, number theory, and algebraic geometry. Each chapter ends with several pages of historical and bibliographic summary. One prerequisite for reading the book is an introductory graduate algebra course, including certain familiarity with category theory.
Experimental Validation of a Mathematical Model for Seabed Liquefaction Under Waves
DEFF Research Database (Denmark)
Sumer, B. Mutlu; Kirca, Özgür; Fredsøe, Jørgen
2012-01-01
This paper summarizes the results of an experimental study directed towards the validation of a mathematical model for the buildup of pore water pressure and resulting liquefaction of marine soils under progressive waves. Experiments were conducted under controlled conditions with silt (d(50) = 0.......070 mm) in a wave flume with a soil pit. Waves with wave heights in the range of 7.7-18 cm, 55-cm water depth and 1.6-s wave period enabled us to study both the liquefaction and no-liquefaction regime pore water pressure buildup. The experimental data were used to validate the model. A numerical example...
International Nuclear Information System (INIS)
Bohn, M.P.
1992-12-01
As part of the NRC-sponsored program to study the implications of Generic Issue 57, ''Effects of Fire Protection System Actuation on Safety-Related Equipment,'' a subtask was performed to evaluate the applicability of formal decision analysis methods to generic issues cost/benefit-type decisions and to apply these methods to the GI-57 results. In this report, the numerical results obtained from the analysis of three plants (two PWRs and one BWR) as developed in the technical resolution program for GI-57 were studied. For each plant, these results included a calculation of the person-REM averted due to various accident scenarios and various proposed modifications to mitigate the accident scenarios identified. These results were recomputed to break out the benefit in terms of contributions due to random event scenarios, fire event scenarios, and seismic event scenarios. Furthermore, the benefits associated with risk (in terms of person-REM) averted from earthquakes at three different seismic ground motion levels were separately considered. Given this data, formal decision methodologies involving decision trees, value functions, and utility functions were applied to this basic data. It is shown that the formal decision methodology can be applied at several different levels. Examples are given in which the decision between several retrofits is changed from that resulting from a simple cost/benefit-ratio criterion by virtue of the decision-makinger's expressed (and assumed) preferences
Relationships between mathematics and literacy: Exploring some underlying factors
Directory of Open Access Journals (Sweden)
Carol Bohlmann
2008-10-01
Full Text Available This paper focuses on Grade 7 learners in two township schools where the relationships between performance on language and reading tests in the home language and English were investigated in relation to examination performance in mathematics. In both schools reading ability rather than language proficiency in English emerged as a strong predictor of mathematics achievement. The schools serve as a case study for exploring some of the socio‐economic, teacher and classroom factors underlying differential school performance in mathematics. Because the new curriculum presupposes a highly literate environment, it is suggested that mathematics learning will be negatively affected if learners lack adequate reading skills. The findings suggest that quality schooling is a strong determinant of both reading and mathematical achievement. The new mathematics curriculum has the potential to make a difference only if schools improve learners’ literacy development.
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.
More on the fragility of performance: choking under pressure in mathematical problem solving.
Beilock, Sian L; Kulp, Catherine A; Holt, Lauren E; Carr, Thomas H
2004-12-01
In 3 experiments, the authors examined mathematical problem solving performance under pressure. In Experiment 1, pressure harmed performance on only unpracticed problems with heavy working memory demands. In Experiment 2, such high-demand problems were practiced until their answers were directly retrieved from memory. This eliminated choking under pressure. Experiment 3 dissociated practice on particular problems from practice on the solution algorithm by imposing a high-pressure test on problems practiced 1, 2, or 50 times each. Infrequently practiced high-demand problems were still performed poorly under pressure, whereas problems practiced 50 times each were not. These findings support distraction theories of choking in math, which contrasts with considerable evidence for explicit monitoring theories of choking in sensorimotor skills. This contrast suggests a skill taxonomy based on real-time control structures. (c) 2004 APA
Indian Academy of Sciences (India)
dimensional superfields, is a clear signature of the presence of the (anti-)BRST invariance in the original. 4D theory. Keywords. Non-Abelian 1-form gauge theory; Dirac fields; (anti-)Becchi–Roucet–Stora–. Tyutin invariance; superfield formalism; ...
Batchelder, William H
2010-09-01
Mathematical psychology is a sub-field of psychology that started in the 1950s and has continued to grow as an important contributor to formal psychological theory, especially in the cognitive areas of psychology such as learning, memory, classification, choice response time, decision making, attention, and problem solving. In addition, there are several scientific sub-areas that were originated by mathematical psychologists such as the foundations of measurement, stochastic memory models, and psychologically motivated reformulations of expected utility theory. Mathematical psychology does not include all uses of mathematics and statistics in psychology, and indeed there is a long history of such uses especially in the areas of perception and psychometrics. What is most unique about mathematical psychology is its approach to theory construction. While accepting the behaviorist dictum that the data in psychology must be observable and replicable, mathematical models are specified in terms of unobservable formal constructs that can predict detailed aspects of data across multiple experimental and natural settings. By now almost all the substantive areas of cognitive and experimental psychology have formal mathematical models and theories, and many of these are due to researchers that identify with mathematical psychology. Copyright © 2010 John Wiley & Sons, Ltd. For further resources related to this article, please visit the WIREs website. Copyright © 2010 John Wiley & Sons, Ltd.
Aberdein, Andrew
2014-01-01
This book presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. It offers large array of examples ranging from the history of mathematics to formal proof verification.
Mathematical logic in the human brain: syntax.
Friedrich, Roland; Friederici, Angela D
2009-05-28
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.
Indian Academy of Sciences (India)
framework of the usual superfield approach to BRST formalism [1–9]. This ap- proach, however, has not been able ... within the framework of the superfield formulation. The central theme of a couple of very ... define [23a] the curvature tensor Fµν = ∂µAν −∂νAµ +iAµ ×Aν. Here B and ¯B are the auxiliary fields that satisfy the ...
Denning, Peter J.
1991-01-01
The ongoing debate over the role of formalism and formal specifications in software features many speakers with diverse positions. Yet, in the end, they share the conviction that the requirements of a software system can be unambiguously specified, that acceptable software is a product demonstrably meeting the specifications, and that the design process can be carried out with little interaction between designers and users once the specification has been agreed to. This conviction is part of a larger paradigm prevalent in American management thinking, which holds that organizations are systems that can be precisely specified and optimized. This paradigm, which traces historically to the works of Frederick Taylor in the early 1900s, is no longer sufficient for organizations and software systems today. In the domain of software, a new paradigm, called user-centered design, overcomes the limitations of pure formalism. Pioneered in Scandinavia, user-centered design is spreading through Europe and is beginning to make its way into the U.S.
Stroh formalism and Rayleigh waves
Tanuma, Kazumi
2008-01-01
Introduces a powerful and elegant mathematical method for the analysis of anisotropic elasticity equationsThe reader can grasp the essentials as quickly as possibleCan be used as a textbook, which presents compactly introduction and applications of the Stroh formalismAppeals to the people not only in mathematics but also in mechanics and engineering sciencePrerequisites are only basic linear algebra, calculus and fundamentals of differential equations
Bertsimas, Dimitris; Silberholz, John; Trikalinos, Thomas
2018-03-01
Important decisions related to human health, such as screening strategies for cancer, need to be made without a satisfactory understanding of the underlying biological and other processes. Rather, they are often informed by mathematical models that approximate reality. Often multiple models have been made to study the same phenomenon, which may lead to conflicting decisions. It is natural to seek a decision making process that identifies decisions that all models find to be effective, and we propose such a framework in this work. We apply the framework in prostate cancer screening to identify prostate-specific antigen (PSA)-based strategies that perform well under all considered models. We use heuristic search to identify strategies that trade off between optimizing the average across all models' assessments and being "conservative" by optimizing the most pessimistic model assessment. We identified three recently published mathematical models that can estimate quality-adjusted life expectancy (QALE) of PSA-based screening strategies and identified 64 strategies that trade off between maximizing the average and the most pessimistic model assessments. All prescribe PSA thresholds that increase with age, and 57 involve biennial screening. Strategies with higher assessments with the pessimistic model start screening later, stop screening earlier, and use higher PSA thresholds at earlier ages. The 64 strategies outperform 22 previously published expert-generated strategies. The 41 most "conservative" ones remained better than no screening with all models in extensive sensitivity analyses. We augment current comparative modeling approaches by identifying strategies that perform well under all models, for various degrees of decision makers' conservativeness.
Mathematical modelling of phenotypic plasticity and conversion to a stem-cell state under hypoxia
Dhawan, Andrew; Madani Tonekaboni, Seyed Ali; Taube, Joseph H.; Hu, Stephen; Sphyris, Nathalie; Mani, Sendurai A.; Kohandel, Mohammad
2016-02-01
Hypoxia, or oxygen deficiency, is known to be associated with breast tumour progression, resistance to conventional therapies and poor clinical prognosis. The epithelial-mesenchymal transition (EMT) is a process that confers invasive and migratory capabilities as well as stem cell properties to carcinoma cells thus promoting metastatic progression. In this work, we examined the impact of hypoxia on EMT-associated cancer stem cell (CSC) properties, by culturing transformed human mammary epithelial cells under normoxic and hypoxic conditions, and applying in silico mathematical modelling to simulate the impact of hypoxia on the acquisition of CSC attributes and the transitions between differentiated and stem-like states. Our results indicate that both the heterogeneity and the plasticity of the transformed cell population are enhanced by exposure to hypoxia, resulting in a shift towards a more stem-like population with increased EMT features. Our findings are further reinforced by gene expression analyses demonstrating the upregulation of EMT-related genes, as well as genes associated with therapy resistance, in hypoxic cells compared to normoxic counterparts. In conclusion, we demonstrate that mathematical modelling can be used to simulate the role of hypoxia as a key contributor to the plasticity and heterogeneity of transformed human mammary epithelial cells.
A Mathematical Model and Its Application for Hydro Power Units under Different Operating Conditions
Directory of Open Access Journals (Sweden)
Weijia Yang
2015-09-01
Full Text Available This paper presents a mathematical model of hydro power units, especially the governor system model for different operating conditions, based on the basic version of the software TOPSYS. The mathematical model consists of eight turbine equations, one generator equation, and one governor equation, which are solved for ten unknown variables. The generator and governor equations, which are different under various operating conditions, are presented and discussed in detail. All the essential non-linear factors in the governor system (dead-zone, saturation, rate limiting, and backlash are also considered. Case studies are conducted based on one Swedish hydro power plant (HPP and three Chinese plants. The simulation and on-site measurements are compared for start-up, no-load operation, normal operation, and load rejection in different control modes (frequency, opening, and power feedback. The main error in each simulation is also discussed in detail. As a result, the model application is proved trustworthy for simulating different physical quantities of the unit (e.g., guide vane opening, active power, rotation speed, and pressures at volute and draft tube. The model has already been applied effectively in consultant analyses and scientific studies.
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.
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
Mathematical modelling of the destruction degree of cancer under the influence of a RF hyperthermia
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.
Introducing philosophy of mathematics
Friend, Michele
2014-01-01
What is mathematics about? Does the subject-matter of mathematics exist independently of the mind or are they mental constructions? How do we know mathematics? Is mathematical knowledge logical knowledge? And how is mathematics applied to the material world? In this introduction to the philosophy of mathematics, Michele Friend examines these and other ontological and epistemological problems raised by the content and practice of mathematics. Aimed at a readership with limited proficiency in mathematics but with some experience of formal logic it seeks to strike a balance between conceptual acc
Mathematical logic foundations for information science
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.
Proof and knowledge in mathematics
Detlefsen, Michael
2005-01-01
These questions arise from any attempt to discover an epistemology for mathematics. This collection of essays considers various questions concerning the nature of justification in mathematics and possible sources of that justification. Among these are the question of whether mathematical justification is a priori or a posteriori in character, whether logical and mathematical differ, and if formalization plays a significant role in mathematical justification,
Energy Technology Data Exchange (ETDEWEB)
Sharma, Shashi, E-mail: shashisharma1984@gmail.com; Katiyar, V.K.; Singh, Uaday
2015-04-01
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.
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
A Mathematical Model of Prostate Tumor Growth Under Hormone Therapy with Mutation Inhibitor
Tao, Youshan; Guo, Qian; Aihara, Kazuyuki
2010-04-01
This paper extends Jackson’s model describing the growth of a prostate tumor with hormone therapy to a new one with hypothetical mutation inhibitors. The new model not only considers the mutation by which androgen-dependent (AD) tumor cells mutate into androgen-independent (AI) ones but also introduces inhibition which is assumed to change the mutation rate. The tumor consists of two types of cells (AD and AI) whose proliferation and apoptosis rates are functions of androgen concentration. The mathematical model represents a free-boundary problem for a nonlinear system of parabolic equations, which describe the evolution of the populations of the above two types of tumor cells. The tumor surface is a free boundary, whose velocity is equal to the cell’s velocity there. Global existence and uniqueness of solutions of this model is proved. Furthermore, explicit formulae of tumor volume at any time t are found in androgen-deprived environment under the assumption of radial symmetry, and therefore the dynamics of tumor growth under androgen-deprived therapy could be predicted by these formulae. Qualitative analysis and numerical simulation show that controlling the mutation may improve the effect of hormone therapy or delay a tumor relapse.
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…
Concepts of formal concept analysis
Žáček, Martin; Homola, Dan; Miarka, Rostislav
2017-07-01
The aim of this article is apply of Formal Concept Analysis on concept of world. Formal concept analysis (FCA) as a methodology of data analysis, information management and knowledge representation has potential to be applied to a verity of linguistic problems. FCA is mathematical theory for concepts and concept hierarchies that reflects an understanding of concept. Formal concept analysis explicitly formalizes extension and intension of a concept, their mutual relationships. A distinguishing feature of FCA is an inherent integration of three components of conceptual processing of data and knowledge, namely, the discovery and reasoning with concepts in data, discovery and reasoning with dependencies in data, and visualization of data, concepts, and dependencies with folding/unfolding capabilities.
Coefficient rings of formal group laws
International Nuclear Information System (INIS)
Buchstaber, V M; Ustinov, A V
2015-01-01
We describe the coefficient rings of universal formal group laws which arise in algebraic geometry, algebraic topology and their application to mathematical physics. We also describe the homomorphisms of these coefficient rings coming from reductions of one formal group law to another. The proofs are based on the number-theoretic properties of binomial coefficients. Bibliography: 37 titles
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…
Directory of Open Access Journals (Sweden)
Xolani Khalo
2014-12-01
Full Text Available The main aim of the study was (1 to identify the underlying factors related to errors due to incorrect association, and (2 to understand why learners continue to make such errors so that mechanisms to avoid such errors could be devised. The study was conducted by means of a case study guided by the positivists’paradigm where the research sample comprised of 105 Grade 10 Mathematics Literacy learners as respondents. Having used Polya’s problem-solving techniques, Threshold Concept and Newman’s Error Analysis as the theoretical frameworks for the study, a four-point Likert scale and a content-based structure-interview questionnaire were developed to address the research question. Four sets of structured-interview questionnaires were used for collecting data, aimed at addressing the main objective of the study. In order to test the reliability and consistency of the questionnaires for this study, Cronbach’s Alpha was tested for standardised items (α = 0.705. Once the data was collected, it was analysed through content and correlation analysis. Based on the frequency table which summarises learner responses, it could be ascertained that the majority (n =63, 60% of learners admitted to sometimes confusing addition with multiplication. The relationship between learners forgetting to write units and learners writing down an incorrect number/figure revealed a significance where p = .04 (r = +.17 illustrated a weak correlation between the afore-stated variables.
Park, Joonkoo; Li, Rosa; Brannon, Elizabeth M
2014-03-01
In early childhood, humans learn culturally specific symbols for number that allow them entry into the world of complex numerical thinking. Yet little is known about how the brain supports the development of the uniquely human symbolic number system. Here, we use functional magnetic resonance imaging along with an effective connectivity analysis to investigate the neural substrates for symbolic number processing in young children. We hypothesized that, as children solidify the mapping between symbols and underlying magnitudes, important developmental changes occur in the neural communication between the right parietal region, important for the representation of non-symbolic numerical magnitudes, and other brain regions known to be critical for processing numerical symbols. To test this hypothesis, we scanned children between 4 and 6 years of age while they performed a magnitude comparison task with Arabic numerals (numerical, symbolic), dot arrays (numerical, non-symbolic), and lines (non-numerical). We then identified the right parietal seed region that showed greater blood-oxygen-level-dependent signal in the numerical versus the non-numerical conditions. A psychophysiological interaction method was used to find patterns of effective connectivity arising from this parietal seed region specific to symbolic compared to non-symbolic number processing. Two brain regions, the left supramarginal gyrus and the right precentral gyrus, showed significant effective connectivity from the right parietal cortex. Moreover, the degree of this effective connectivity to the left supramarginal gyrus was correlated with age, and the degree of the connectivity to the right precentral gyrus predicted performance on a standardized symbolic math test. These findings suggest that effective connectivity underlying symbolic number processing may be critical as children master the associations between numerical symbols and magnitudes, and that these connectivity patterns may serve as an
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
Directory of Open Access Journals (Sweden)
Diana-Maria Drigă
2015-12-01
Full Text Available The concept of resilience has represented during the recent years a leading concern both in Romania, within the European Union and worldwide. Specialists in economics, management, finance, legal sciences, political sciences, sociology, psychology, grant a particular interest to this concept. Multidisciplinary research of resilience has materialized throughout the time in multiple conceptualizations and theorizing, but without being a consensus between specialists in terms of content, specificity and scope. Through this paper it is intended to clarify the concept of resilience, achieving an exploration of the evolution of this concept in ecological, social and economic environment. At the same time, the paper presents aspects of feedback mechanisms and proposes a formalization of resilience using the logic and mathematical analysis.
A Mathematical Account of the NEGF Formalism
DEFF Research Database (Denmark)
Cornean, Decebal Horia; Moldoveanu, Valeriu; Pillet, Claude-Alain
2018-01-01
-interacting leads. Our proof is non-perturbative and uses neither complex-time Keldysh contours nor Langreth rules of ‘analytic continuation.’ We also discuss other technical identities (Langreth, Keldysh) involving various many-body Green’s functions. Finally, we study the Dyson equation for the advanced...
Early-Years Swimming: Creating Opportunities for Adding Mathematical Capital to Under 5s
Jorgensen, Robyn
2013-01-01
Drawing on survey data from over 2000 parents, this paper explores the possibility of early-years swimming to add mathematical capital to young children. Using developmental milestones as the basis, it was found that parents reported significantly earlier achievement on many of these milestones. Such data suggest that the early years swim…
Mammarella, Irene C; Caviola, Sara; Giofrè, David; Szűcs, Dénes
2017-08-18
This study examined visual, spatial-sequential, and spatial-simultaneous working memory (WM) performance in children with mathematical learning disability (MLD) and low mathematics achievement (LMA) compared with typically developing (TD) children. Groups were matched on reading decoding performance and verbal intelligence. Besides statistical significance testing, we used bootstrap confidence interval estimation and computed effect sizes. Children were individually tested with six computerized tasks, two for each visuospatial WM subcomponent. We found that both MLD and LMA children had low visuospatial WM function in both spatial-simultaneous and spatial-sequential WM tasks. The WM deficit was most expressed in MLD children and less in LMA children. This suggests that WM scores are distributed along a continuum with TD children achieving top scores and MLD children achieving low scores. The theoretical and practical significance of findings is discussed. Statement of Contribution What is already known on this subject? Working memory plays an important role in mathematical achievement. Children with mathematical learning disability (MLD) usually have low working memory resources. Conflicting results have been reported concerning the role of VSWM in individuals with MLD. What the present study adds? Children with different degree of impairment in math achievement and typically developing children were tested. Visual, spatial-sequential, and spatial-simultaneous working memory tasks were examined. Only spatial-sequential and spatial-simultaneous working memory tasks discriminated the two impairments groups. © 2017 The British Psychological Society.
Slot, E.M.; van Viersen, S.; de Bree, E.H.; Kroesbergen, E.H.
2016-01-01
High comorbidity rates have been reported between mathematical learning disabilities (MD) and reading and spelling disabilities (RSD). Research has identified skills related to math, such as number sense (NS) and visuospatial working memory (visuospatial WM), as well as to literacy, such as
Formal analysis of electromagnetic optics
Khan-Afshar, Sanaz; Hasan, Osman; Tahar, Sofiène
2014-09-01
Optical systems are increasingly being used in safety-critical applications. Due to the complexity and sensitivity of optical systems, their verification raises many challenges for engineers. Traditionally, the analysis of such systems has been carried out by paper-and-pencil based proofs and numerical computations. However, these techniques cannot provide accurate results due to the risk of human error and inherent approximations of numerical algorithms. In order to overcome these limitations, we propose to use theorem proving (i.e., a computer-based technique that allows to express mathematical expressions and reason about their correctness by taking into account all the details of mathematical reasoning) as a complementary approach to improve optical system analysis. This paper provides a higher-order logic (a language used to express mathematical theories) formalization of electromagnetic optics in the HOL Light theorem prover. In order to demonstrate the practical effectiveness of our approach, we present the analysis of resonant cavity enhanced photonic devices.
Representations of spacetime: Formalism and ontological commitment
Bain, Jonathan Stanley
This dissertation consists of two parts. The first is on the relation between formalism and ontological commitment in the context of theories of spacetime, and the second is on scientific realism. The first part begins with a look at how the substantivalist/relationist debate over the ontological status of spacetime has been influenced by a particular mathematical formalism, that of tensor analysis on differential manifolds (TADM). This formalism has motivated the substantivalist position known as manifold substantivalism. Chapter 1 focuses on the hole argument which maintains that manifold substantivalism is incompatible with determinism. I claim that the realist motivations underlying manifold substantivalism can be upheld, and the hole argument avoided, by adopting structural realism with respect to spacetime. In this context, this is the claim that it is the structure that spacetime points enter into that warrants belief and not the points themselves. In Chapter 2, an elimination principle is defined by means of which a distinction can be made between surplus structure and essential structure with respect to formulations of a theory in two distinct mathematical formulations and some prior ontological commitments. This principle is then used to demonstrate that manifold points may be considered surplus structure in the formulation of field theories. This suggests that, if we are disposed to read field theories literally, then, at most, it should be the essential structure common to all alternative formulations of such theories that should be taken literally. I also investigate how the adoption of alternative formalisms informs other issues in the philosophy of spacetime. Chapter 3 offers a realist position which takes a semantic moral from the preceding investigation and an epistemic moral from work done on reliability. The semantic moral advises us to read only the essential structure of our theories literally. The epistemic moral shows us that such structure
Rent pricing decision support mathematical model for finance leases under effective risks
Directory of Open Access Journals (Sweden)
Rabbani Masoud
2015-01-01
Full Text Available Nowadays, leasing has become an increasingly important and popular method for equipment acquisition. But, because of the rent pricing difficulties and some risks that affect the lessor and lessee's decision making, there are many people that still tend to buy equipment instead of lease it. In this paper we explore how risk can affect the leasing issue support mathematical model. For this purpose, we consider three types of risk; Credit risk, Transaction risk and Risk based pricing. In particular, our focus was on how to make decision about rent pricing in a leasing problem with different customers, various quality levels and different pricing methods. Finally, the mathematical model has been solved by Genetic Algorithm that is a search heuristic to optimize the problem. This algorithm was coded in MATLAB® R2012a to provide the best set of results.
SOLUTION OF MATHEMATICAL MODEL FOR TRACKED VEHICLE MOVEMENT UNDER DIFFERENT CONTROL ACTIONS
Directory of Open Access Journals (Sweden)
S. Volosnikov
2017-06-01
Full Text Available The paper presents a solution to the mathematical model of the caterpillar platform motion in the process of going into corner at various speed of movement. The presented model made it possible to obtain characteristic trajectories of a caterpillar platform in a turn for different road conditions and control actions. The «steering wheel» and «levers», which are most widely used in turn control systems, are considered as controls for the caterpillar platform.
Sasanguie, Delphine; Göbel, Silke M; Moll, Kristina; Smets, Karolien; Reynvoet, Bert
2013-03-01
In this study, the performance of typically developing 6- to 8-year-old children on an approximate number discrimination task, a symbolic comparison task, and a symbolic and nonsymbolic number line estimation task was examined. For the first time, children's performances on these basic cognitive number processing tasks were explicitly contrasted to investigate which of them is the best predictor of their future mathematical abilities. Math achievement was measured with a timed arithmetic test and with a general curriculum-based math test to address the additional question of whether the predictive association between the basic numerical abilities and mathematics achievement is dependent on which math test is used. Results revealed that performance on both mathematics achievement tests was best predicted by how well childrencompared digits. In addition, an association between performance on the symbolic number line estimation task and math achievement scores for the general curriculum-based math test measuring a broader spectrum of skills was found. Together, these results emphasize the importance of learning experiences with symbols for later math abilities. Copyright © 2012 Elsevier Inc. All rights reserved.
Partridge, Chris; de Cesare, Sergio; Mitchell, Andrew; Odell, James
2018-01-01
Formalization is becoming more common in all stages of the development of information systems, as a better understanding of its benefits emerges. Classification systems are ubiquitous, no more so than in domain modeling. The classification pattern that underlies these systems provides a good case study of the move toward formalization in part because it illustrates some of the barriers to formalization, including the formal complexity of the pattern and the ontological issues surrounding the "one and the many." Powersets are a way of characterizing the (complex) formal structure of the classification pattern, and their formalization has been extensively studied in mathematics since Cantor's work in the late nineteenth century. One can use this formalization to develop a useful benchmark. There are various communities within information systems engineering (ISE) that are gradually working toward a formalization of the classification pattern. However, for most of these communities, this work is incomplete, in that they have not yet arrived at a solution with the expressiveness of the powerset benchmark. This contrasts with the early smooth adoption of powerset by other information systems communities to, for example, formalize relations. One way of understanding the varying rates of adoption is recognizing that the different communities have different historical baggage. Many conceptual modeling communities emerged from work done on database design, and this creates hurdles to the adoption of the high level of expressiveness of powersets. Another relevant factor is that these communities also often feel, particularly in the case of domain modeling, a responsibility to explain the semantics of whatever formal structures they adopt. This paper aims to make sense of the formalization of the classification pattern in ISE and surveys its history through the literature, starting from the relevant theoretical works of the mathematical literature and gradually shifting focus
Directory of Open Access Journals (Sweden)
R Fathi
2011-09-01
Full Text Available A three-body model is devised to study differential and total cross sections for the excitation of helium atom under impact of energetic protons. The actual process is a four body one but in the present model the process is simplified into a three-body one. In this model, an electron of helium atom is assumed to be inactive and only one electron of the atom is active. Therefore, the active electron is assumed to be in an atomic state with a potential of the nucleus, T, being screened by the inactive electron, e, and, thus, an effective charge of Ze. As a result, the ground state, 11S, or the excited states, 21S and 21P, wave function of the active electron is deduced from similar hydrogenic wave functions assuming effective charge, Ze for the combined nucleus (T+e. In this three-body model, the Faddeev-Watson-Lovelace formalism for excitation channel is used to calculate the transition amplitude. In the first order approximation, electronic and nuclear interaction is assumed in the collision to be A(1e=
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
DEFF Research Database (Denmark)
Masses of Formal Philosophy is an outgrowth of Formal Philosophy. That book gathered the responses of some of the most prominent formal philosophers to five relatively open and broad questions initiating a discussion of metaphilosophical themes and problems surrounding the use of formal methods...... in philosophy. Including contributions from a wide range of philosophers, Masses of Formal Philosophy contains important new responses to the original five questions....
Domínguez-Hüttinger, Elisa; Christodoulides, Panayiotis; Miyauchi, Kosuke; Irvine, Alan D; Okada-Hatakeyama, Mariko; Kubo, Masato; Tanaka, Reiko J
2017-06-01
The skin barrier acts as the first line of defense against constant exposure to biological, microbial, physical, and chemical environmental stressors. Dynamic interplay between defects in the skin barrier, dysfunctional immune responses, and environmental stressors are major factors in the development of atopic dermatitis (AD). A systems biology modeling approach can yield significant insights into these complex and dynamic processes through integration of prior biological data. We sought to develop a multiscale mathematical model of AD pathogenesis that describes the dynamic interplay between the skin barrier, environmental stress, and immune dysregulation and use it to achieve a coherent mechanistic understanding of the onset, progression, and prevention of AD. We mathematically investigated synergistic effects of known genetic and environmental risk factors on the dynamic onset and progression of the AD phenotype, from a mostly asymptomatic mild phenotype to a severe treatment-resistant form. Our model analysis identified a "double switch," with 2 concatenated bistable switches, as a key network motif that dictates AD pathogenesis: the first switch is responsible for the reversible onset of inflammation, and the second switch is triggered by long-lasting or frequent activation of the first switch, causing irreversible onset of systemic T H 2 sensitization and worsening of AD symptoms. Our mathematical analysis of the bistable switch predicts that genetic risk factors decrease the threshold of environmental stressors to trigger systemic T H 2 sensitization. This analysis predicts and explains 4 common clinical AD phenotypes from a mild and reversible phenotype through to severe and recalcitrant disease and provides a mechanistic explanation for clinically demonstrated preventive effects of emollient treatments against development of AD. Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.
Qualitative Behaviour of a Mathematical Model of Interacting ...
African Journals Online (AJOL)
The phenomenon of the interaction between two (2) populations indexed by the unit of time is as old as the famous Lotka-Volterra formalism. However, the qualitative analysis of interacting populations under the simplifying assumption of environmental perturbation is formidable mathematical problem which requires the ...
Zaitseva, N V; Kiryanov, D A; Lanin, D V; Chigvintsev, V M
2014-01-01
The concept of the triad regulatory metasystem, which includes the neuroendocrine and immune regulation systems, is currently generally accepted. Changes occurring in each of the regulatory systems in response to the impact of technogenic chemical factors are also well known. This paper presents mathematical models of the immune and neuroendocrine system functioning, using the interaction between these systems in response to bacterial invasion as an example, and changes in their performance under exposure to chemical factors, taking into account the stage of functional disorders in a producing organ, using the performance of the bone marrow as an example.
Shelomentsev, A. G.; Medvedev, M. A.; Berg, D. B.; Lapshina, S. N.; Taubayev, A. A.; Davletbaev, R. H.; Savina, D. V.
2017-12-01
Present study is devoted to the development of competition life cycle mathematical model in the closed business community with limited resources. Growth of each agent is determined by the balance of input and output resource flows: input (cash) flow W is covering the variable V and constant C costs and growth dA/dt of the agent's assets A. Value of V is proportional to assets A that allows us to write down a first order non-stationary differential equation of the agent growth. Model includes the number of such equations due to the number of agents. The amount of resources that is available for agents vary in time. The balances of their input and output flows are changing correspondingly to the different stages of the competition life cycle. According to the theory of systems, the most complete description of any object or process is the model of its life cycle. Such a model describes all stages of its development: from the appearance ("birth") through development ("growth") to extinction ("death"). The model of the evolution of an individual firm, not contradicting the economic meaning of events actually observed in the market, is the desired result from modern AVMs for applied use. With a correct description of the market, rules for participants' actions, restrictions, forecasts can be obtained, which modern mathematics and the economy can not give.
Crossley, J N; Brickhill, CJ; Stillwell, JC
2010-01-01
Although mathematical logic can be a formidably abstruse topic, even for mathematicians, this concise book presents the subject in a lively and approachable fashion. It deals with the very important ideas in modern mathematical logic without the detailed mathematical work required of those with a professional interest in logic.The book begins with a historical survey of the development of mathematical logic from two parallel streams: formal deduction, which originated with Aristotle, Euclid, and others; and mathematical analysis, which dates back to Archimedes in the same era. The streams beg
Beilock, Sian L; Decaro, Marci S
2007-11-01
Two experiments demonstrate how individual differences in working memory (WM) impact the strategies used to solve complex math problems and how consequential testing situations alter strategy use. In Experiment 1, individuals performed multistep math problems under low- or high-pressure conditions and reported their problem-solving strategies. Under low-pressure conditions, the higher individuals' WM, the more likely they were to use computationally demanding algorithms (vs. simpler shortcuts) to solve the problems, and the more accurate their math performance. Under high-pressure conditions, higher WM individuals used simpler (and less efficacious) problem-solving strategies, and their performance accuracy suffered. Experiment 2 turned the tables by using a math task for which a simpler strategy was optimal (produced accurate performance in few problem steps). Now, under low-pressure conditions, the lower individuals' WM, the better their performance (the more likely they relied on a simple, but accurate, problem strategy). And, under pressure, higher WM individuals performed optimally by using the simpler strategies lower WM individuals employed. WM availability influences how individuals approach math problems, with the nature of the task performed and the performance environment dictating skill success or failure. PsycINFO Database Record (c) 2007 APA, all rights reserved.
Directory of Open Access Journals (Sweden)
Nilceia Maciel Pinheiro
2009-04-01
Full Text Available With this work, it is intended to contribute for the reflection concerning the insertion of subjects that allow approaching the mathematics through its relations with the scientific-technological and social context. Developed under the foundations of the Critical Mathematical Education, the research had as its target-public students from the first grade of the secondary education of a public education institution of Ponta Grossa - Parana, in the mathematics subject. The problem question that led the study was the possibility to introduce into the teach-learning of the mathematics the research, reading and simulated cases which could approach the mathematical knowledge to the scientific and social context, allowing the student to ask, to reflect and to evaluate the influence and dependence of the mathematics, as science, face the other knowledge. The data analysis pointed to the aptness to introduce, besides the formal mathematical knowledge, the research, discussion and simulated cases in classroom, as form to break the traditionalism and to promote a new form to construct the knowledge, highlighting the possibilities of advances and limitations that the different knowledge possess. Keywords: Teaching-learning. Mathematical Knowledge. Scientific-technological and social context. Critical Mathematical Education.Com este trabalho, pretende-se contribuir para a reflexão acerca da inserção de temas que permitam abordar a matemática por meio de suas relações com o contexto científico-tecnológico e social. Desenvolvida sob os pressupostos da Educação Matemática Crítica, a pesquisa teve como público-alvo alunos da primeira série do Ensino Médio de uma instituição pública da cidade de Ponta Grossa-PR, na disciplina de matemática. A questão problema que norteou o estudo foi a possibilidade de introduzir no ensino-aprendizagem da matemática a pesquisa, leitura e casos simulados que pudessem aproximar o conhecimento matemático do
Directory of Open Access Journals (Sweden)
Javier Baez
2016-11-01
Full Text Available Predicting the timing of a castrate resistant prostate cancer is critical to lowering medical costs and improving the quality of life of advanced prostate cancer patients. We formulate, compare and analyze two mathematical models that aim to forecast future levels of prostate-specific antigen (PSA. We accomplish these tasks by employing clinical data of locally advanced prostate cancer patients undergoing androgen deprivation therapy (ADT. While these models are simplifications of a previously published model, they fit data with similar accuracy and improve forecasting results. Both models describe the progression of androgen resistance. Although Model 1 is simpler than the more realistic Model 2, it can fit clinical data to a greater precision. However, we found that Model 2 can forecast future PSA levels more accurately. These findings suggest that including more realistic mechanisms of androgen dynamics in a two population model may help androgen resistance timing prediction.
Zharinov, V. V.
2013-02-01
We propose a formal construction generalizing the classic de Rham complex to a wide class of models in mathematical physics and analysis. The presentation is divided into a sequence of definitions and elementary, easily verified statements; proofs are therefore given only in the key case. Linear operations are everywhere performed over a fixed number field {F} = {R},{C}. All linear spaces, algebras, and modules, although not stipulated explicitly, are by definition or by construction endowed with natural locally convex topologies, and their morphisms are continuous.
Formal methods for industrial critical systems a survey of applications
Margaria-Steffen, Tiziana
2012-01-01
"Today, formal methods are widely recognized as an essential step in the design process of industrial safety-critical systems. In its more general definition, the term formal methods encompasses all notations having a precise mathematical semantics, together with their associated analysis methods, that allow description and reasoning about the behavior of a system in a formal manner.Growing out of more than a decade of award-winning collaborative work within the European Research Consortium for Informatics and Mathematics, Formal Methods for Industrial Critical Systems: A Survey of Applications presents a number of mainstream formal methods currently used for designing industrial critical systems, with a focus on model checking. The purpose of the book is threefold: to reduce the effort required to learn formal methods, which has been a major drawback for their industrial dissemination; to help designers to adopt the formal methods which are most appropriate for their systems; and to offer a panel of state-of...
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
Closing the gap between formalism and application
DEFF Research Database (Denmark)
Christensen, Ole Ravn
2008-01-01
A common problem in learning mathematics concerns the gap between, on the one hand, doing the formalisms and calculations of abstract mathematics and, on the other hand, applying these in a specific contextualized setting for example the engineering world. The skills acquired through problem......-based learning (PBL), in the special model used at Aalborg University, Denmark, may give us some idea of how to bridge this gap. Through an investigation of a series of examples of student projects concerning the application of mathematical subjects-such as matrices, differential equations, cluster analysis...
Pragmatics for formal semantics
DEFF Research Database (Denmark)
Danvy, Olivier
2011-01-01
This tech talk describes how to write and how to inter-derive formal semantics for sequential programming languages. The progress reported here is (1) concrete guidelines to write each formal semantics to alleviate their proof obligations, and (2) simple calculational tools to obtain a formal sem...
Matrix formalism to describe functional states of transcriptional regulatory systems.
Directory of Open Access Journals (Sweden)
Erwin P Gianchandani
2006-08-01
Full Text Available Complex regulatory networks control the transcription state of a genome. These transcriptional regulatory networks (TRNs have been mathematically described using a Boolean formalism, in which the state of a gene is represented as either transcribed or not transcribed in response to regulatory signals. The Boolean formalism results in a series of regulatory rules for the individual genes of a TRN that in turn can be used to link environmental cues to the transcription state of a genome, thereby forming a complete transcriptional regulatory system (TRS. Herein, we develop a formalism that represents such a set of regulatory rules in a matrix form. Matrix formalism allows for the systemic characterization of the properties of a TRS and facilitates the computation of the transcriptional state of the genome under any given set of environmental conditions. Additionally, it provides a means to incorporate mechanistic detail of a TRS as it becomes available. In this study, the regulatory network matrix, R, for a prototypic TRS is characterized and the fundamental subspaces of this matrix are described. We illustrate how the matrix representation of a TRS coupled with its environment (R* allows for a sampling of all possible expression states of a given network, and furthermore, how the fundamental subspaces of the matrix provide a way to study key TRS features and may assist in experimental design.
Smith, Rebekah E.; Bayen, Ute Johanna; Martin, Claudia
2010-01-01
Fifty 7-year-olds (29 female), 53 10-year-olds (29 female), and 36 young adults (19 female), performed a computerized event-based prospective memory task. All three groups differed significantly in prospective memory performance with adults showing the best performance and 7-year-olds the poorest performance. We used a formal multinomial process tree model of event-based prospective memory to decompose age differences in cognitive processes that jointly contribute to prospective memory performance. The formal modeling results demonstrated that adults differed significantly from the 7-year-olds and 10-year-olds on both the prospective component and the retrospective component of the task. The 7-year-olds and 10-year-olds differed only in the ability to recognize prospective memory target events. The prospective memory task imposed a cost to ongoing activities in all three age groups. PMID:20053020
Smith, Rebekah E.; Bayen, Ute Johanna; Martin, Claudia
2010-01-01
Fifty 7-year-olds (29 female), 53 10-year-olds (29 female), and 36 young adults (19 female), performed a computerized event-based prospective memory task. All three groups differed significantly in prospective memory performance with adults showing the best performance and 7-year-olds the poorest performance. We used a formal multinomial process tree model of event-based prospective memory to decompose age differences in cognitive processes that jointly contribute to prospective memory perfor...
Towards a Formal Framework for Computational Trust
DEFF Research Database (Denmark)
Nielsen, Mogens; Krukow, Karl Kristian; Sassone, Vladimiro
2006-01-01
We define a mathematical measure for the quantitative comparison of probabilistic computational trust systems, and use it to compare a well-known class of algorithms based on the so-called beta model. The main novelty is that our approach is formal, rather than based on experimental simulation....
A mathematical model for the transfer of soil solutes to runoff under water scouring.
Yang, Ting; Wang, Quanjiu; Wu, Laosheng; Zhang, Pengyu; Zhao, Guangxu; Liu, Yanli
2016-11-01
The transfer of nutrients from soil to runoff often causes unexpected pollution in water bodies. In this study, a mathematical model that relates to the detachment of soil particles by water flow and the degree of mixing between overland flow and soil nutrients was proposed. The model assumes that the mixing depth is an integral of average water flow depth, and it was evaluated by experiments with three water inflow rates to bare soil surfaces and to surfaces with eight treatments of different stone coverages. The model predicted outflow rates were compared with the experimentally observed data to test the accuracy of the infiltration parameters obtained by curve fitting the models to the data. Further analysis showed that the comprehensive mixing coefficient (ke) was linearly correlated with Reynolds' number Re (R(2)>0.9), and this relationship was verified by comparing the simulated potassium concentration and cumulative mass with observed data, respectively. The best performance with the bias error analysis (Nash Sutcliffe coefficient of efficiency (NS), relative error (RE) and the coefficient of determination (R(2))) showed that the predicted data by the proposed model was in good agreement with the measured data. Thus the model can be used to guide soil-water and fertilization management to minimize nutrient runoff from cropland. Copyright © 2016 Elsevier B.V. All rights reserved.
Classical Mathematical Logic The Semantic Foundations of Logic
Epstein, Richard L
2011-01-01
In Classical Mathematical Logic, Richard L. Epstein relates the systems of mathematical logic to their original motivations to formalize reasoning in mathematics. The book also shows how mathematical logic can be used to formalize particular systems of mathematics. It sets out the formalization not only of arithmetic, but also of group theory, field theory, and linear orderings. These lead to the formalization of the real numbers and Euclidean plane geometry. The scope and limitations of modern logic are made clear in these formalizations. The book provides detailed explanations of all proo
Yin, X.; Struik, P.C.
2012-01-01
A generalized model for electron (e-) transport limited C4 photosynthesis of NAD–malic enzyme and NADP–malic enzyme subtypes is presented. The model is used to review the thylakoid stoichiometries in vivo under strictly limiting light conditions, using published data on photosynthetic quantum yield
International Nuclear Information System (INIS)
Akpinar, E. Kavak; Bicer, Y.
2008-01-01
An experimental study was performed to determine the thin layer drying characteristics in a solar dryer with forced convection and under open sun with natural convection of long green pepper. An indirect forced convection solar dryer consisting of a solar air collector and drying cabinet was used in the experiments. Natural sun drying experiments were conducted for comparison at the same time. The constant rate period is absent from the drying curves. The drying process took place in the falling rate period. The drying data were fitted to 13 different mathematical models. Among the models, the logarithmic model for forced solar drying and the Midilli and Kucuk model for natural sun drying were found best to explain the thin layer drying behaviour of long green peppers. The performance of these models was investigated by comparing the coefficient of determination (R), reduced chi-square (χ 2 ) and root mean square error (RMSE) between the observed and predicted moisture ratios
The Quantum Formalism and the GRW Formalism
Goldstein, Sheldon; Tumulka, Roderich; Zanghì, Nino
2012-10-01
The Ghirardi-Rimini-Weber (GRW) theory of spontaneous wave function collapse is known to provide a quantum theory without observers, in fact two different ones by using either the matter density ontology (GRWm) or the flash ontology (GRWf). Both theories are known to make predictions different from those of quantum mechanics, but the difference is so small that no decisive experiment can as yet be performed. While some testable deviations from quantum mechanics have long been known, we provide here something that has until now been missing: a formalism that succinctly summarizes the empirical predictions of GRWm and GRWf. We call it the GRW formalism. Its structure is similar to that of the quantum formalism but involves different operators. In other words, we establish the validity of a general algorithm for directly computing the testable predictions of GRWm and GRWf. We further show that some well-defined quantities cannot be measured in a GRWm or GRWf world.
Industrial use of formal methods formal verification
Boulanger, Jean-Louis
2012-01-01
At present the literature gives students and researchers of the very general books on the formal technics. The purpose of this book is to present in a single book, a return of experience on the used of the "formal technics" (such proof and model-checking) on industrial examples for the transportation domain. This book is based on the experience of people which are completely involved in the realization and the evaluation of safety critical system software based. The implication of the industrialists allows to raise the problems of confidentiality which could appear and so allow
Formal methods in software development: A road less travelled
Directory of Open Access Journals (Sweden)
John A van der Poll
2010-08-01
Full Text Available An integration of traditional verification techniques and formal specifications in software engineering is presented. Advocates of such techniques claim that mathematical formalisms allow them to produce quality, verifiably correct, or at least highly dependable software and that the testing and maintenance phases are shortened. Critics on the other hand maintain that software formalisms are hard to master, tedious to use and not well suited for the fast turnaround times demanded by industry. In this paper some popular formalisms and the advantages of using these during the early phases of the software development life cycle are presented. Employing the Floyd-Hoare verification principles during the formal specification phase facilitates reasoning about the properties of a specification. Some observations that may help to alleviate the formal-methods controversy are established and a number of formal methods successes is presented. Possible conditions for an increased acceptance of formalisms in oftware development are discussed.
Mathematical simulation and calculation of the soil compaction under dynamic loads
Zolotarevskaya, D. I.
2011-04-01
The deformation and compaction of loamy sandy soddy-podzolic soils under linear dynamic changes in the compressive stresses and in the course of the soil creeping were studied in field experiments. The rheological properties of these soils occurring in the viscoelastic state were described by a first-order differential equation relating the compressive stresses, the rates of their changes, and the velocities of the relative vertical compressive deformation. Regression equations were derived for the viscoelastic properties of the studied soil as functions of its density, moisture, and linear compaction velocity. Methods were proposed for the calculation of indices of the stress-strain state and the compaction of soils under specified conditions of changes in their compressive stresses with time and in the course of the soil creeping after the initial linear increase in load. Corresponding computer programs were developed. The effect of the main factors due to the linear increase in the compressive loads and in the course of the soil creeping on the rheological properties, the stress-strain state, and the density of soils was quantitatively estimated. The calculation showed that the values of the soil deformation and the density under compressive stresses lower than the ultimate strength were stabilized with time, and the properties of the viscoelastic soil approached elastic ones.
Formal Information Model for Representing Production Resources
Siltala, Niko; Järvenpää, Eeva; Lanz, Minna
2017-01-01
Part 2: Intelligent Manufacturing Systems; International audience; This paper introduces a concept and associated descriptions to formally describe physical production resources for modular and reconfigurable production systems. These descriptions are source of formal information for (automatic) production system design and (re-)configuration. They can be further utilized during the system deployment and execution. The proposed concept and the underlying formal resource description model is c...
Logicism, intuitionism, and formalism
Symons, John
2008-01-01
Aims to review the programmes in the foundations of mathematics from the classical period and to assess their possible relevance for contemporary philosophy of mathematics. This work is suitable for researchers and graduate students of philosophy, logic, mathematics and theoretical computer science.
Mathematical Modeling in the Undergraduate Curriculum
Toews, Carl
2012-01-01
Mathematical modeling occupies an unusual space in the undergraduate mathematics curriculum: typically an "advanced" course, it nonetheless has little to do with formal proof, the usual hallmark of advanced mathematics. Mathematics departments are thus forced to decide what role they want the modeling course to play, both as a component of the…
Integrating semi-formal and formal requirements
Wieringa, Roelf J.; Olivé, Antoni; Dubois, Eric; Pastor, Joan Antoni; Huyts, Sander
1997-01-01
In this paper, we report on the integration of informal, semiformal and formal requirements specification techniques. We present a framework for requirements specification called TRADE, within which several well-known semiformal specification techniques are placed. TRADE is based on an analysis of
International Nuclear Information System (INIS)
Santilli, R.M.
1981-01-01
A primary objective of the research is the achievement of clear experimental knowledge on the intrinsic characteristics of particles (such as magnetic moment, spin, space parity, etc.) under strong interactions. These characteristics, when known, have been measured a number of times, but all times for particles under long range electromagnetic interactions (e.g., for bubble chamber techniques). The same characteristics are then generally assumed to persist under the different physical conditions of the strong interactions, while no direct or otherwise final measurement under strong interactions exists at this time. The advocated physical knowledge is clearly important for controlled fusion, as well as for a serious study of the foundations of strong interactions. The paper initiates the study by considering the following alternatives. A: the electromagnetic characteristics of particles persist in the transition to the strong; or B: variations in these characteristics are physically conceivable, mathematically treatable, and experimentally detectable. The need to conduct additional experiments, and achieve a final resolution of the issue, is stressed throughout the paper. In the hope of contributing toward this future goal, the paper then reviews the quantitative treatment of possible deviations via the Lie-admissible generalization of Lie's theory, with particular reference to the Lie-admissible generalizations of Lie group, Lie algebras, and enveloping associative algebras. A generalized notion of extended particle under nonlocal nonpotential strong interactions emerge from these studies. The theory is applied to the re-elaboration of the data on the spinor symmetry via neutron interferometers. It is shown that the data are indeed consistent with a breaking of the SU(2)-spin symmetry due to nonlocal nonpotential forces. A number of experiments for the future resolution of the issue are indicated
Directory of Open Access Journals (Sweden)
Benjamin Werner
Full Text Available In the last decade, cancer research has been a highly active and rapidly evolving scientific area. The ultimate goal of all efforts is a better understanding of the mechanisms that discriminate malignant from normal cell biology in order to allow the design of molecular targeted treatment strategies. In individual cases of malignant model diseases addicted to a specific, ideally single oncogene, e.g. Chronic myeloid leukemia (CML, specific tyrosine kinase inhibitors (TKI have indeed been able to convert the disease from a ultimately life-threatening into a chronic disease with individual patients staying in remission even without treatment suggestive of operational cure. These developments have been raising hopes to transfer this concept to other cancer types. Unfortunately, cancer cells tend to develop both primary and secondary resistance to targeted drugs in a substantially higher frequency often leading to a failure of treatment clinically. Therefore, a detailed understanding of how cells can bypass targeted inhibition of signaling cascades crucial for malignant growths is necessary. Here, we have performed an in vitro experiment that investigates kinetics and mechanisms underlying resistance development in former drug sensitive cancer cells over time in vitro. We show that the dynamics observed in these experiments can be described by a simple mathematical model. By comparing these experimental data with the mathematical model, important parameters such as mutation rates, cellular fitness and the impact of individual drugs on these processes can be assessed. Excitingly, the experiment and the model suggest two fundamentally different ways of resistance evolution, i.e. acquisition of mutations and phenotype switching, each subject to different parameters. Most importantly, this complementary approach allows to assess the risk of resistance development in the different phases of treatment and thus helps to identify the critical periods where
DEFF Research Database (Denmark)
du Gay, Paul; Lopdrup-Hjorth, Thomas
Over recent decades, institutions exhibiting high degrees of formality have come in for severe criticism. From the private to the public sector, and across a whole spectrum of actors spanning from practitioners to academics, formal organization is viewed with increasing doubt and skepticism. In a...
Geometry and Formal Linguistics.
Huff, George A.
This paper presents a method of encoding geometric line-drawings in a way which allows sets of such drawings to be interpreted as formal languages. A characterization of certain geometric predicates in terms of their properties as languages is obtained, and techniques usually associated with generative grammars and formal automata are then applied…
Towards formalization of inspection using petrinets
International Nuclear Information System (INIS)
Javed, M.; Naeem, M.; Bahadur, F.; Wahab, A.
2014-01-01
Achieving better quality software has always been a challenge for software developers. Inspection is one of the most efficient techniques, which ensure the quality of software during its development. To the best of our knowledge, current inspection techniques are not realized by any formal approach. In this paper, we propose an inspection technique, which is not only backed by the formal mathematical semantics of Petri nets, but also supports inspecting concurrent processes. We also use a case study of an agent based distributed processing system to demonstrate the inspection of concurrent processes. (author)
Approaches to Foster Transfer of Formal Principles: Which Route to Take?
Schalk, Lennart; Saalbach, Henrik; Stern, Elsbeth
2016-01-01
Enabling learners to transfer knowledge about formal principles to new problems is a major aim of science and mathematics education, which, however, is notoriously difficult to reach. Previous research advocates different approaches of how to introduce principles to foster the transfer of knowledge about formal principles. One approach suggests teaching a generic formalism of the principles. Another approach suggests presenting (at least) two concrete cases instantiating the principle. A third approach suggests presenting a generic formalism accompanied by a case. As yet, though, empirical results regarding the transfer potential of these approaches are mixed and difficult to integrate as the three approaches have rarely been tested competitively. Furthermore, the approaches have been evaluated in relation to different control conditions, and they have been assessed using varying transfer measures. In the present experiment, we introduced undergraduates to the formal principles of propositional logic with the aim to systematically compare the transfer potential of the different approaches in relation to each other and to a common control condition by using various learning and transfer tasks. Results indicate that all approaches supported successful learning and transfer of the principles, but also caused systematic differences in the magnitude of transfer. Results indicate that the combination of a generic formalism with a case was surprisingly unsuccessful while learners who compared two cases outperformed the control condition. We discuss how the simultaneous assessment of the different approaches allows to more precisely capture the underlying learning mechanisms and to advance theory on how these mechanisms contribute to transfer performance.
Developing Non-Formal Education Competences as a Complement of Formal Education for STEM Lecturers
Terrazas-Marín, Roy Alonso
2018-01-01
This paper focuses on a current practice piece on professional development for university lecturers, transformative learning, dialogism and STEM (Science, Technology, Engineering and Mathematics) education. Its main goals are to identify the key characteristics that allow STEM educators to experiment with the usage of non-formal education…
Formal modeling of virtual machines
Cremers, A. B.; Hibbard, T. N.
1978-01-01
Systematic software design can be based on the development of a 'hierarchy of virtual machines', each representing a 'level of abstraction' of the design process. The reported investigation presents the concept of 'data space' as a formal model for virtual machines. The presented model of a data space combines the notions of data type and mathematical machine to express the close interaction between data and control structures which takes place in a virtual machine. One of the main objectives of the investigation is to show that control-independent data type implementation is only of limited usefulness as an isolated tool of program development, and that the representation of data is generally dictated by the control context of a virtual machine. As a second objective, a better understanding is to be developed of virtual machine state structures than was heretofore provided by the view of the state space as a Cartesian product.
Formal Requirements-Based Programming for Complex Systems
Rash, James L.; Hinchey, Michael G.; Rouff, Christopher A.; Gracanin, Denis
2005-01-01
Computer science as a field has not yet produced a general method to mechanically transform complex computer system requirements into a provably equivalent implementation. Such a method would be one major step towards dealing with complexity in computing, yet it remains the elusive holy grail of system development. Currently available tools and methods that start with a formal model of a system and mechanically produce a provably equivalent implementation are valuable but not sufficient. The gap that such tools and methods leave unfilled is that the formal models cannot be proven to be equivalent to the system requirements as originated by the customer For the classes of complex systems whose behavior can be described as a finite (but significant) set of scenarios, we offer a method for mechanically transforming requirements (expressed in restricted natural language, or appropriate graphical notations) into a provably equivalent formal model that can be used as the basis for code generation and other transformations. While other techniques are available, this method is unique in offering full mathematical tractability while using notations and techniques that are well known and well trusted. We illustrate the application of the method to an example procedure from the Hubble Robotic Servicing Mission currently under study and preliminary formulation at NASA Goddard Space Flight Center.
Necessity of Integral Formalism
International Nuclear Information System (INIS)
Tao Yong
2011-01-01
To describe the physical reality, there are two ways of constructing the dynamical equation of field, differential formalism and integral formalism. The importance of this fact is firstly emphasized by Yang in case of gauge field [Phys. Rev. Lett. 33 (1974) 445], where the fact has given rise to a deeper understanding for Aharonov-Bohm phase and magnetic monopole [Phys. Rev. D 12 (1975) 3845]. In this paper we shall point out that such a fact also holds in general wave function of matter, it may give rise to a deeper understanding for Berry phase. Most importantly, we shall prove a point that, for general wave function of matter, in the adiabatic limit, there is an intrinsic difference between its integral formalism and differential formalism. It is neglect of this difference that leads to an inconsistency of quantum adiabatic theorem pointed out by Marzlin and Sanders [Phys. Rev. Lett. 93 (2004) 160408]. It has been widely accepted that there is no physical difference of using differential operator or integral operator to construct the dynamical equation of field. Nevertheless, our study shows that the Schrödinger differential equation (i.e., differential formalism for wave function) shall lead to vanishing Berry phase and that the Schrödinger integral equation (i.e., integral formalism for wave function), in the adiabatic limit, can satisfactorily give the Berry phase. Therefore, we reach a conclusion: There are two ways of describing physical reality, differential formalism and integral formalism; but the integral formalism is a unique way of complete description. (general)
DEFF Research Database (Denmark)
du Gay, Paul; Lopdrup-Hjorth, Thomas
2016-01-01
Over recent decades, ‘formal’ organisations have come in for severe criticism. Not only is formal organisation represented as ill suited to the realities of the contemporary organisational world, but as a key source from which organisational dysfunctions themselves emerge. For that reason informal...... and spontaneous modes of organising have emerged, or better re-emerged, as preferable substitutes, because they, in contrast to the formal, allegedly allow for creativity, inventiveness, flexibility, speed, and freedom. Thus, the province of the formal is significantly devalued. In this paper, we explore what we...
Review of the helicity formalism
International Nuclear Information System (INIS)
Barreiro, F.; Cerrada, M.; Fernandez, E.
1972-01-01
Our purpose in these notes has been to present a brief and general review of the helicity formalism. We begin by discussing Lorentz invariance, spin and helicity ideas, in section 1 . In section 2 we deal with the construction of relativistic states and scattering amplitudes in the helicity basis and we study their transformation properties under discrete symmetries. Finally we present some more sophisticated topics like kinematical singularities of helicity amplitudes, kinematical constraints and crossing relations 3, 4, 5 respectively. (Author) 8 refs
Ujunwa, F A; Onwujekwe, O; Chinawa, J M
2014-01-01
Health insurance is a social security system that aims to facilitate fair financing of health costs through pooling and judicious utilization of financial resources, in order to provide financial risk protections and cost burden sharing for people against high cost of healthcare through various prepayment methods prior to falling ill. It is still unclear how the Federal Social Health insurance program for federal civil servants has affected the insured and uninsured civil servants in terms of health services cost and utilization in Enugu metropolis. The aim of the study was to compare the health services utilization and cost of insured with that of the non-insured federal civil servants with a view to generate information for policymaking on improving services of the National Health Insurance Scheme. A comparative, descriptive, cross-sectional survey of both the insured and uninsured federal civil servants was conducted in Enugu metropolis. Respondents were purposively enrolled and were grouped according to their insurance status after signing the informed consent form. Comparative analysis of health services utilization, satisfaction, and health services cost which include total cost, average cost, and catastrophic expenditures were done using SPSS version 17.0. There were 809 respondents; this comprised 451 insured and 358 uninsured respondents. There were 420 males (51.9%) and 389 females (48.1%). It was found that 657 respondents had at least easy access to health; this comprised 369 (56.7%) insured and 288 (43.3%) non-insured respondents while 70 (46%) of the non-insured and 82 (54%) of the insured civil servant had difficult access to health care ( P = 0.620). There are still federal civil servants yet to enroll into the formal sector social insurance program. The NHIS-insured civil servants have no appreciable advantage in terms of access to and cost of health services in Enugu metropolis.
Formalization of Hostel Management System. | Obi | Journal of the ...
African Journals Online (AJOL)
HMS) can invariably contribute greatly to the success, profitability and customerbased approach of such an organization. The use of formal specification creates a formal approach for specifying the underlying functions and properties of the ...
Directory of Open Access Journals (Sweden)
Michela Riz
2015-12-01
Full Text Available Intestinal L-cells sense glucose and other nutrients, and in response release glucagon-like peptide 1 (GLP-1, peptide YY and other hormones with anti-diabetic and weight-reducing effects. The stimulus-secretion pathway in L-cells is still poorly understood, although it is known that GLP-1 secreting cells use sodium-glucose co-transporters (SGLT and ATP-sensitive K+-channels (K(ATP-channels to sense intestinal glucose levels. Electrical activity then transduces glucose sensing to Ca2+-stimulated exocytosis. This particular glucose-sensing arrangement with glucose triggering both a depolarizing SGLT current as well as leading to closure of the hyperpolarizing K(ATP current is of more general interest for our understanding of glucose-sensing cells. To dissect the interactions of these two glucose-sensing mechanisms, we build a mathematical model of electrical activity underlying GLP-1 secretion. Two sets of model parameters are presented: one set represents primary mouse colonic L-cells; the other set is based on data from the GLP-1 secreting GLUTag cell line. The model is then used to obtain insight into the differences in glucose-sensing between primary L-cells and GLUTag cells. Our results illuminate how the two glucose-sensing mechanisms interact, and suggest that the depolarizing effect of SGLT currents is modulated by K(ATP-channel activity. Based on our simulations, we propose that primary L-cells encode the glucose signal as changes in action potential amplitude, whereas GLUTag cells rely mainly on frequency modulation. The model should be useful for further basic, pharmacological and theoretical investigations of the cellular signals underlying endogenous GLP-1 and peptide YY release.
Towards an Ashtekar formalism in eight dimensions
International Nuclear Information System (INIS)
Nieto, J A
2005-01-01
We investigate the possibility of extending the Ashtekar theory to eight dimensions. Our approach relies on two notions: the octonionic structure and the MacDowell-Mansouri formalism generalized to a spacetime of signature 1 + 7. The key mathematical tool for our construction is the self-dual (antiself-dual) four-rank fully antisymmetric octonionic tensor. Our results may be of particular interest in connection with a possible formulation of M -theory via matroid theory
Formal analogies in physics teacher education
DEFF Research Database (Denmark)
Avelar Sotomaior Karam, Ricardo; Ricardo, Elio
2012-01-01
the relevance of the subject, formal analogies are rarely systematically approached in physics education. In order to discuss this issue with pre-service physics teachers, we planned a lecture and designed a questionnaire with the goal of encouraging them to think about some “coincidences” in well known......Reasoning by similarities, especially the ones associated with formal aspects, is one of the most valuable sources for the development of physical theories. The essential role of formal analogies in science can be highlighted by the fact that several equations for different physical situations have...... the exact same appearance. Coulomb’s law’s similarity with Newton’s, Maxwell’s application of fluid theory to electromagnetism and Hamilton’s optical mechanical analogy are some among many other examples. These cases illustrate the power of mathematics in providing unifying structures for physics. Despite...
Eigenvalues and eigenvectors: embodied, symbolic and formal thinking
Thomas, Michael O. J.; Stewart, Sepideh
2011-09-01
Many beginning university students struggle with the new approaches to mathematics that they find in their courses due to a shift in presentation of mathematical ideas, from a procedural approach to concept definitions and deductive derivations, and ideas building upon each other in quick succession. This paper highlights this struggle by considering some conceptual processes and difficulties students find in learning about eigenvalues and eigenvectors. We use the theoretical framework of Tall's three worlds of mathematical thinking, along with perspectives from Dubinsky's APOS (action, process, object, schema) theory and Thomas's representational versatility. The results of the study describe thinking about these concepts by several groups of first- and second-year university students. In particular the obstacles they faced, and the emerging links some were constructing between parts of their concept images formed from the embodied, symbolic, and formal worlds are presented. We also identify some fundamental problems with student understanding of the definition of eigenvectors that lead to implementation problems, and some of the concepts underlying such difficulties.
Logic in elementary mathematics
Exner, Robert M
2011-01-01
This applications-related introductory treatment explores facets of modern symbolic logic useful in the exposition of elementary mathematics. The authors convey the material in a manner accessible to those trained in standard elementary mathematics but lacking any formal background in logic. Topics include the statement calculus, proof and demonstration, abstract mathematical systems, and the restricted predicate calculus. The final chapter draws upon the methods of logical reasoning covered in previous chapters to develop solutions of linear and quadratic equations, definitions of order and
Putting Foundations Into Mathematics
Hubbard, G. L.
1972-01-01
For meaningful learning of mathematics, a learning set is required which demands that all things accepted as true should be demonstrable in terms of a paradigm appropriate to the child's cognitive development: preparatory, concrete-particular, concrete-general, formal-abstract. Future teachers should experience all paradigms to become aware that…
Foundations of mathematical logic
Curry, Haskell B
2010-01-01
Written by a pioneer of mathematical logic, this comprehensive graduate-level text explores the constructive theory of first-order predicate calculus. It covers formal methods, including algorithms and epitheory, and offers a brief treatment of Markov's approach to algorithms, explains elementary facts about lattices and similar algebraic systems, and more. 1963 edition.
Mathematics for quantum chemistry
Anderson, Jay Martin
2005-01-01
This concise volume offers undergraduates an introduction to mathematical formalism in problems of molecular structure and motion. The main topics cover the calculus of orthogonal functions, algebra of vector spaces, and Lagrangian and Hamiltonian formulation of classical mechanics and applications to molecular motion. Answers to problems. 1966 edition.
Directory of Open Access Journals (Sweden)
Yi Li
2017-02-01
Full Text Available A highly diastereoselective cyclopropanation of cyclic enones with sulfur ylides was developed under catalyst-free conditions, producing multifunctional spirocyclopropanes in generally excellent yields (up to 99% yield and >99:1 d.r.. The asymmetric version of this method was realized by using an easily available chiral sulfur ylide, affording products with moderate to good stereoselectivity.
Formalizing ICD coding rules using Formal Concept Analysis.
Jiang, Guoqian; Pathak, Jyotishman; Chute, Christopher G
2009-06-01
With the 11th revision of the International Classification of Disease (ICD) being officially launched by the World Health Organization (WHO), the significance of a formal representation for ICD coding rules has emerged as a pragmatic concern. To explore the role of Formal Concept Analysis (FCA) on examining ICD10 coding rules and to develop FCA-based auditing approaches for the formalization process. We propose a model for formalizing ICD coding rules underlying the ICD Index using FCA. The coding rules are generated from FCA models and represented in the Semantic Web Rule Language (SWRL). Two auditing approaches were developed focusing upon non-disjoint nodes and anonymous nodes manifest in the FCA model. The candidate domains (i.e. any three character code with their sub-codes) of all 22 chapters of the ICD10 2006 version were analyzed using the two auditing approaches. Case studies and a preliminary evaluation were performed for validation. A total of 2044 formal contexts from the candidate domains of 22 ICD chapters were generated and audited. We identified 692 ICD codes having non-disjoint nodes in all chapters; chapters 19 and 21 contained the highest proportion of candidate domains with non-disjoint nodes (61.9% and 45.6%). We also identified 6996 anonymous nodes from 1382 candidate domains. Chapters 7, 11, 13, and 17, have the highest proportion of candidate domains having anonymous nodes (97.5%, 95.4%, 93.6% and 93.0%) while chapters 15 and 17 have the highest proportion of anonymous nodes among all chapters (45.5% and 44.0%). Case studies and a limited evaluation demonstrate that non-disjoint nodes and anonymous nodes arising from FCA are effective mechanisms for auditing ICD10. FCA-based models demonstrate a practical solution for formalizing ICD coding rules. FCA techniques could not only audit ICD domain knowledge completeness for a specific domain, but also provide a high level auditing profile for all ICD chapters.
The simplest formal argument for fitness optimization.
Grafen, Alen
2008-12-01
The Formal Darwinism Project aims to provide a formal argument linking population genetics to fitness optimization, which of necessity includes defining fitness. This bridges the gulf between those biologists who assume that natural selection leads to something close to fitness optimization and those biologists who believe on theoretical grounds that there is no sense of fitness that can usefully be said to be optimized. The current paper's main objective is to provide a careful mathematical introduction to the project, and it also reflects on the project's scope and limitations. The central argument is the proof of close ties between the mathematics of motion, as embodied in the Price equation, and the mathematics of optimization, as represented by optimization programmes. To make these links, a general and abstract model linking genotype, phenotype and number of successful gametes is assumed. The project has begun with simple dynamic models and simple linking models, and its progress will involve more realistic versions of them. The versions given here are fully mathematically rigorous, but elementary enough to serve as an introduction.
Introduction to formal languages
Révész, György E
1991-01-01
Covers all areas, including operations on languages, context-sensitive languages, automata, decidability, syntax analysis, derivation languages, and more. Numerous worked examples, problem exercises, and elegant mathematical proofs. 1983 edition.
DEFF Research Database (Denmark)
Garsten, Christina; Nyqvist, Anette
suits’ (Nyqvist 2013), and of doing ‘ethnography by failure’ (Garsten 2013). In this paper, we explore the layers of informality and formality in our fieldwork experiences among financial investors and policy experts, and discuss how to ethnographically represent embodied fieldwork practices. How do we...... stage and informal for others. Walking the talk, donning the appropriate attire, wearing the proper suit, may be part of what is takes to figure out the code of formal organizational settings – an entrance ticket to the backstage, as it were. Oftentimes, it involves a degree of mimicry, of ‘following...... conceptualize and articulate the informal and the formal? How do we represent the multidimensional character of organizations while maintaining a degree of integrity of informants? And how do we decide on relevance as we transpose our fieldwork experiences into text? We suggest that ethnographic organization...
Mathematics, anxiety, and the brain.
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.
Žáček, Martin
2017-07-01
Ontology or formal ontology? Which word is correct? The aim of this article is to introduce correct terms and explain their basis. Ontology describes a particular area of interest (domain) in a formal way - defines the classes of objects that are in that area, and relationships that may exist between them. Meaning of ontology consists mainly in facilitating communication between people, improve collaboration of software systems and in the improvement of systems engineering. Ontology in all these areas offer the possibility of unification of view, maintaining consistency and unambiguity.
The Markov process admits a consistent steady-state thermodynamic formalism
Peng, Liangrong; Zhu, Yi; Hong, Liu
2018-01-01
The search for a unified formulation for describing various non-equilibrium processes is a central task of modern non-equilibrium thermodynamics. In this paper, a novel steady-state thermodynamic formalism was established for general Markov processes described by the Chapman-Kolmogorov equation. Furthermore, corresponding formalisms of steady-state thermodynamics for the master equation and Fokker-Planck equation could be rigorously derived in mathematics. To be concrete, we proved that (1) in the limit of continuous time, the steady-state thermodynamic formalism for the Chapman-Kolmogorov equation fully agrees with that for the master equation; (2) a similar one-to-one correspondence could be established rigorously between the master equation and Fokker-Planck equation in the limit of large system size; (3) when a Markov process is restrained to one-step jump, the steady-state thermodynamic formalism for the Fokker-Planck equation with discrete state variables also goes to that for master equations, as the discretization step gets smaller and smaller. Our analysis indicated that general Markov processes admit a unified and self-consistent non-equilibrium steady-state thermodynamic formalism, regardless of underlying detailed models.
Formal verification of medical monitoring software using Z language: a representative sample.
Babamir, Seyed Morteza; Borhani, Mehdi
2012-08-01
Medical monitoring systems are useful aids assisting physicians in keeping patients under constant surveillance; however, taking sound decision by the systems is a physician concern. As a result, verification of the systems behavior in monitoring patients is a matter of significant. The patient monitoring is undertaken by software in modern medical systems; so, software verification of modern medial systems have been noticed. Such verification can be achieved by the Formal Languages having mathematical foundations. Among others, the Z language is a suitable formal language has been used to formal verification of systems. This study aims to present a constructive method to verify a representative sample of a medical system by which the system is visually specified and formally verified against patient constraints stated in Z Language. Exploiting our past experience in formal modeling Continuous Infusion Insulin Pump (CIIP), we think of the CIIP system as a representative sample of medical systems in proposing our present study. The system is responsible for monitoring diabetic's blood sugar.
DEFF Research Database (Denmark)
Westphael, Henning; Mogensen, Arne
2013-01-01
In this article we present the notion of Mathematical competences as a tool to describe the mathematically gifted students.......In this article we present the notion of Mathematical competences as a tool to describe the mathematically gifted students....
Formal specification is an experimental science
Energy Technology Data Exchange (ETDEWEB)
Bjorner, D. [Technical Univ., Lyngby (Denmark)
1992-09-01
Traditionally, abstract models of large, complex systems have been given in free-form mathematics, combining - often in ad-hoc, not formally supported ways - notions from the disciplines of partial differential equations, functional analysis, mathematical statistics, etc. Such models have been very useful for assimilation of information, analysis (investigation), and prediction (simulation). These models have, however, usually not been helpful in deriving computer representations of the modelled systems - for the purposes of computerized monitoring and control, Computing science, concerned with how to construct objects that can exist within the computer, offers ways of complementing, and in some cases, replacing or combining traditional mathematical models. Formal, model-, as well as property-oriented, specifications in the styles of denotational (respectively, algebraic semantics) represent major approaches to such modelling. In this expository, discursive paper we illustrate what we mean by model-oriented specifications of large, complex technological computing systems. The three modelling examples covers the introvert programming methodological subject of SDEs: software development environments, the distributed computing system subject of wfs`s: (transaction) work flow systems, and the extrovert subject of robots: robotics! the thesis is, just as for mathematical modelling, that we can derive much understanding, etc., from experimentally creating such formally specified models - on paper - and that we gain little in additionally building ad-hoc prototypes. Our models are expressed in a model-oriented style using the VDM specification language Meta-IV In this paper the models only reflect the {open_quotes}data modelling{close_quotes} aspects. We observe that such data models are more easily captured in the model-oriented siyle than in the algebraic semantics property-oriented style which originally was built of the abstraction of operations. 101 refs., 4 figs.
Criteria for logical formalization
Czech Academy of Sciences Publication Activity Database
Peregrin, Jaroslav; Svoboda, Vladimír
2013-01-01
Roč. 190, č. 14 (2013), s. 2897-2924 ISSN 0039-7857 R&D Projects: GA ČR(CZ) GAP401/10/1279 Institutional support: RVO:67985955 Keywords : logic * logical form * formalization * reflective equilibrium Subject RIV: AA - Philosophy ; Religion Impact factor: 0.637, year: 2013
Indian Academy of Sciences (India)
This is a short tutorial on formal methods which are techniques for specifying and verifying com- plex software and hardware systems. A few ex- amples of successful industrial use of these are also presented. Computers are ubiquitous these days and are used to control various safety critical systems like aircrafts, satel-.
Formalization of Medical Guidelines
Czech Academy of Sciences Publication Activity Database
Peleška, Jan; Anger, Z.; Buchtela, David; Šebesta, K.; Tomečková, Marie; Veselý, Arnošt; Zvára, K.; Zvárová, Jana
2005-01-01
Roč. 1, - (2005), s. 133-141 ISSN 1801-5603 R&D Projects: GA AV ČR 1ET200300413 Institutional research plan: CEZ:AV0Z10300504 Keywords : GLIF model * formalization of guidelines * prevention of cardiovascular diseases Subject RIV: IN - Informatics, Computer Science
DEFF Research Database (Denmark)
Rand, John; Torm, Nina Elisabeth
2012-01-01
Based on unique panel data consisting of both formal and informal firms, this paper uses a matched double difference approach to examine the relationship between legal status and firm level outcomes in micro, small and medium manufacturing enterprises (SMEs) in Vietnam. Controlling for determining...
Indian Academy of Sciences (India)
a formalization is done using a computer program called a proof checker or proof assistant. Such a proof assistant .... means 'Prototype Verification System', but the system is far more than a prototype. It actually is one of the ... related to the Lisp programming language (ACL2 means 'A Computational Logic for. Applicative ...
Formalizing physical security procedures
Meadows, C.; Pavlovic, Dusko
Although the problems of physical security emerged more than 10,000 years before the problems of computer security, no formal methods have been developed for them, and the solutions have been evolving slowly, mostly through social procedures. But as the traffic on physical and social networks is now
Unifying Class-Based Representation Formalisms
Calvanese, D.; Lenzerini, M.; Nardi, D.
2011-01-01
The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases. In this paper we study the basic issues underlying such representation formalisms and single out both their common characteristics and their distinguishing features. Such investigation leads us to propose a unifying framework in which we are able to capture the fundamental aspects of several representatio...
Pluralism in mathematics a new position in philosophy of mathematics
Friend, Michèle
2014-01-01
This book is about philosophy, mathematics and logic, giving a philosophical account of Pluralism which is a family of positions in the philosophy of mathematics. There are four parts to this book, beginning with a look at motivations for Pluralism by way of Realism, Maddy's Naturalism, Shapiro's Structuralism and Formalism. In the second part of this book the author covers: the philosophical presentation of Pluralism; using a formal theory of logic metaphorically; rigour and proof for the Pluralist; and mathematical fixtures. In the third part the author goes on to focus on the transcendental presentation of Pluralism, and in part four looks at applications of Pluralism, such as a Pluralist approach to proof in mathematics and how Pluralism works in regard to together-inconsistent philosophies of mathematics. The book finishes with suggestions for further Pluralist enquiry. In this work the author takes a deeply radical approach in developing a new position that will either convert readers, or act as a stron...
Thermodynamic and multifractal formalism and the Bowen-series map
International Nuclear Information System (INIS)
Rudolph, O.
1994-07-01
In the theory of quantum chaos one studies the semiclassical behaviour of quantum mechanical systems whose corresponding classical counterparts exhibit chaos. These systems are sometimes considered as model systems in the theory of quantum chaos since they are well understood from a mathematical point of view. In this work we study the multifractal formalism for the geodesic flow on surfaces with constant negative curvature. The multifractal analysis of measures has been developed in order to characterize the scaling behaviour of measures on attractors of classical chaotic dynamical systems globally. In order to relate the multifractal formalism with quantities usually considered in the study of the geodesic flow on Riemann surfaces with constant negative curvature, it is necessary to establish the assertions of the multifractal formalism in a mathematically rigorous way. This is achieved with the help of the thermodynamic formalism for hyperbolic dynamical systems developed by Ruelle, Bowen and others. (orig.)
Mathematical logic foundations for information science
Li, Wei
2014-01-01
Mathematical logic is a branch of mathematics that takes axiom systems and mathematical proofs as its objects of study. This book shows how it can also provide a foundation for the development of information science and technology. The first five chapters systematically present the core topics of classical mathematical logic, including the syntax and models of first-order languages, formal inference systems, computability and representability, and Gödel’s theorems. The last five chapters present extensions and developments of classical mathematical logic, particularly the concepts of version sequences of formal theories and their limits, the system of revision calculus, proschemes (formal descriptions of proof methods and strategies) and their properties, and the theory of inductive inference. All of these themes contribute to a formal theory of axiomatization and its application to the process of developing information technology and scientific theories. The book also describes the paradigm of three kinds...
Михаил Владимирович Поспелов; Мария Семеновна Хозяинова
2013-01-01
This article describes the model of the organization of working with training mathematical text for technical university students. Need for development of training text works competencies of first-year students is proved. The impact of learning materials transition into hypertext format on training text works organizing theory is cleared. Training text works organizing stages are described.
An Ontology for a TripTych Formal Software Development
DEFF Research Database (Denmark)
Bjørner, Dines
2003-01-01
An ontology, ie., a formalised set of strongly interrelated definitions, is given for an approach to software development that spans domain engineering, requirements engineering and software design - and which is otherwise based on a judicious use of both informal and formal, mathematics-based te......An ontology, ie., a formalised set of strongly interrelated definitions, is given for an approach to software development that spans domain engineering, requirements engineering and software design - and which is otherwise based on a judicious use of both informal and formal, mathematics...
DEFF Research Database (Denmark)
Levinsen, Karin Tweddell; Sørensen, Birgitte Holm
2013-01-01
are examined and the relation between network society competences, learners’ informal learning strategies and ICT in formalized school settings over time is studied. The authors find that aspects of ICT like multimodality, intuitive interaction design and instant feedback invites an informal bricoleur approach......Longitudinal research projects into social practices are both subject to and capture changes in society, meaning that research is conducted in a fluid context and that new research questions appear during the project’s life cycle. In the present study emerging new performances and uses of ICT....... When integrated into certain designs for teaching and learning, this allows for Formalized Informal Learning and support is found for network society competences building....
Readings in Formal Epistemology
DEFF Research Database (Denmark)
‘Formal epistemology’ is a term coined in the late 1990s for a new constellation of interests in philosophy,the roots of which are found in earlier works of epistemologists, philosophers of science, and logicians. It addresses a growing agenda of problems concerning knowledge, belief, certainty......, rationality, deliberation, decision, strategy, action and agent interaction – and it does so using methods from logic, probability, computability, decision, and game theory. This volume presents 42 classic texts in formal epistemology, and strengthens the ties between research into this area of philosophy...... and its neighbouring intellectual disciplines. The editors provide introductions to five basic subsections: Bayesian Epistemology, Belief Change, Decision Theory, Interactive Epistemology and Logics of Knowledge and Belief. The volume also includes a thorough index and suggestions for further reading...
Formalism and the notion of truth
Spencer, Joseph M.
The most widely acknowledged conceptions of truth take some kind of relation to be at truth's core. This dissertation attempts to establish that an adequate conception of this relation begins with an investigation of the entanglement of the formal and the material as set forth in the model theoretical development of set theoretical mathematics. Truth concerns first and most crucially a certain commerce across the border between the formal and the material, between the ideal and the real. The entanglement of the formal and the material must be thought in itself, apart from or prior to any assimilation into philosophical schemas committed to larger metaphysical claims. This is accomplished in model theory. The twentieth century witnessed two attempts at bringing model theoretical mathematics to bear on accounting philosophically for the concept of truth: that of Alfred Tarski, and that of Alain Badiou. In order to investigate the relevance of model theory to the task of working out a philosophical conception of truth, this dissertation investigates, through comparative work, these two thinkers. It is necessary to see where their projects converge in important ways, as well as where their projects diverge in equally important ways. What brings their work into close proximity is their shared conviction that truth must be thought in light of model theory. Nonetheless, the two do not agree about exactly how model theory sheds light on truth. Comparative study thus reveals both a shared site for thinking and a struggle over the significance of that site. Agreement between Tarski and Badiou concerns the excess of the purely formal over itself, marked by the generation of an undecidable statement within formal systems of a certain level of complexity. Both thinkers determine that this formal excess touches on the material, and both further determine that the consequent entanglement of the formal and the material provides the basic frame for any philosophical consideration
A Survey of Formal Methods for Intelligent Swarms
Truszkowski, Walt; Rash, James; Hinchey, Mike; Rouff, Chrustopher A.
2004-01-01
cutting edge in system correctness, and requires higher levels of assurance than other (traditional) missions that use a single or small number of spacecraft that are deterministic in nature and have near continuous communication access. One of the highest possible levels of assurance comes from the application of formal methods. Formal methods are mathematics-based tools and techniques for specifying and verifying (software and hardware) systems. They are particularly useful for specifying complex parallel systems, such as exemplified by the ANTS mission, where the entire system is difficult for a single person to fully understand, a problem that is multiplied with multiple developers. Once written, a formal specification can be used to prove properties of a system (e.g., the underlying system will go from one state to another or not into a specific state) and check for particular types of errors (e.g., race or livelock conditions). A formal specification can also be used as input to a model checker for further validation. This report gives the results of a survey of formal methods techniques for verification and validation of space missions that use swarm technology. Multiple formal methods were evaluated to determine their effectiveness in modeling and assuring the behavior of swarms of spacecraft using the ANTS mission as an example system. This report is the first result of the project to determine formal approaches that are promising for formally specifying swarm-based systems. From this survey, the most promising approaches were selected and are discussed relative to their possible application to the ANTS mission. Future work will include the application of an integrated approach, based on the selected approaches identified in this report, to the formal specification of the ANTS mission.
Transforming PLC Programs into Formal Models for Verification Purposes
Darvas, D; Blanco, E
2013-01-01
Most of CERN’s industrial installations rely on PLC-based (Programmable Logic Controller) control systems developed using the UNICOS framework. This framework contains common, reusable program modules and their correctness is a high priority. Testing is already applied to find errors, but this method has limitations. In this work an approach is proposed to transform automatically PLC programs into formal models, with the goal of applying formal verification to ensure their correctness. We target model checking which is a precise, mathematical-based method to check formalized requirements automatically against the system.
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....
The Reasonable Effectiveness of Mathematics in the Physical Sciences
Harvey, Alex
2012-01-01
Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism - mathematics exists and is discovered; Logicism - all mathematics may be deduced through pure logic; Formalism - mathematics is just the manipulation of formulas and rules invented for the purpose; Intuitionism - mathematics comprises mental constructs governed by self evident rules. The debat...
Formalism and physical interpretation in Schroedinger
International Nuclear Information System (INIS)
Paty, M.
1992-01-01
The question of the relation between a formalism and its physical interpretation arises not only when theoretical and conceptual systems are reorganized, but in the theoretical elaboration as well. The Schroedinger's work and thought are examined in this paper with this double concern. His work on the mathematical formalism is constantly sustained by a proper physical thought which takes the form of a wave intuition that guarantees him intelligibility. Concerning his interpretation of quantum mechanics, his thought remains characterized, through its evolution, by a w ave image of the world . The way he deals with space-time structure in General Relativity and favours the possibility of a direct interpretation of space-time geometrical quantities, is also studied. (author). 75 refs
Generalizing Prototype Theory: A Formal Quantum Framework
Aerts, Diederik; Broekaert, Jan; Gabora, Liane; Sozzo, Sandro
2016-01-01
Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has instead been successful in capturing these phenomena such as graded membership, situational meaning, composition of categories, and also more complex decision making situations, which cannot be modeled in traditional probabilistic approaches. We show how a formal quantum approach to concepts and their combinations can provide a powerful extension of prototype theory. We explain how prototypes can interfere in conceptual combinations as a consequence of their contextual interactions, and provide an illustration of this using an intuitive wave-like diagram. This quantum-conceptual approach gives new life to original prototype theory, without however making it a privileged concept theory, as we explain at the end of our paper. PMID:27065436
Generalizing Prototype Theory: A Formal Quantum Framework
Directory of Open Access Journals (Sweden)
Diederik eAerts
2016-03-01
Full Text Available Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has instead been successful in capturing these phenomena such as graded membership, situational meaning, composition of categories, and also more complex decision making situations, which cannot be modeled in traditional probabilistic approaches. We show how a formal quantum approach to concepts and their combinations can provide a powerful extension of prototype theory. We explain how prototypes can interfere in conceptual combinations as a consequence of their contextual interactions, and provide an illustration of this using an intuitive wave-like diagram. This quantum-conceptual approach gives new life to original prototype theory, without however making it a privileged concept theory, as we explain at the end of our paper.
A comprehensive overview on the foundations of formal concept analysis
Directory of Open Access Journals (Sweden)
K. Sumangali
2017-12-01
Full Text Available The immersion of voluminous collection of data is inevitable almost everywhere. The invention of mathematical models to analyse the patterns and trends of the data is an emerging necessity to extract and predict useful information in any Knowledge Discovery from Data (KDD process. The Formal Concept Analysis (FCA is an efficient mathematical model used in the process of KDD which is specially designed to portray the structure of the data in a context and depict the underlying patterns and hierarchies in it. Due to the huge increase in the application of FCA in various fields, the number of research and review articles on FCA has raised to a large extent. This review differs from the existing ones in presenting the comprehensive survey on the fundamentals of FCA in a compact and crisp manner to benefit the beginners and its focuses on the scalability issues in FCA. Further, we present the generic anatomy of FCA apart from its origin and growth at a primary level.
van Kerkhove, Bart
2007-01-01
Philosophy of mathematics today has transformed into a very complex network of diverse ideas, viewpoints, and theories. Sometimes the emphasis is on the ""classical"" foundational work (often connected with the use of formal logical methods), sometimes on the sociological dimension of the mathematical research community and the ""products"" it produces, then again on the education of future mathematicians and the problem of how knowledge is or should be transmitted from one generation to the next. The editors of this book felt the urge, first of all, to bring together the widest variety of aut
Asymptotic freedom in the BV formalism
Elliott, Chris; Williams, Brian; Yoo, Philsang
2018-01-01
We define the β-function of a perturbative quantum field theory in the mathematical framework introduced by Costello - combining perturbative renormalization and the BV formalism - as the cohomology class of a certain functional measuring scale dependence of the effective interaction. We show that the one-loop β-function is a well-defined element of the obstruction-deformation complex for translation-invariant and classically scale-invariant theories, and furthermore that it is locally constant as a function on the space of classical interactions and computable as a rescaling anomaly, or as the logarithmic one-loop counterterm. We compute the one-loop β-function in first-order Yang-Mills theory, recovering the famous asymptotic freedom for Yang-Mills in a mathematical context.
Directory of Open Access Journals (Sweden)
Alexei Serna A.
2012-12-01
Full Text Available The application of formal methods in industry has progressed extensively over the past decade and the results are promising. But despite these achievements and it have been documented in numerous studies, it is still very common the skepticism about its usefulness and applicability. The goal of this paper is to show that its evolution over the past decade exceeds all previous processes and each time they do a better job to satisfy industrial needs. This is achieved by the description of some experiments and the result of various applications in industry and through an analyzing of the needs of companies that must be satisfy the research community in this field.
Directory of Open Access Journals (Sweden)
Olga Marín-Arias
2016-05-01
Full Text Available In the Vocational Schools of Art (EVA the issue of curricular organicidad is connoted by merely learning the music from the integration between subjects Mathematics and Musical Initiation and therefore the teaching conditions suitable for teaching process developer. From this perspective, an analysis of the essential relationships that underlie the methodology for the integration of the contents of these subjects, embodied in the theoretical foundations, the general procedure and specific procedures for this integration is necessary, from teacher preparation as premise for the subsequent implementation of such methodological.
Formal Methods in Knowledge Engineering
Harmelen, van F.A.H.; Fensel, D.
1995-01-01
This paper presents a general discussion of the role of formal methods in Knowledge Engineering. We give an historical account of the development of the field of Knowledge Engineering towards the use of formal methods. Subsequently, we discuss the pro's and cons of formal methods. We do this by
Foundations and fundamental concepts of mathematics
Eves, Howard
1997-01-01
Third edition of popular undergraduate-level text offers historic overview, readable treatment of mathematics before Euclid, Euclid's Elements, non-Euclidean geometry, algebraic structure, formal axiomatics, sets, more. Problems, some with solutions. Bibliography.
Fuzzy and rough formal concept analysis: a survey
Poelmans, J.; Ignatov, D.I.; Kuznetsov, S.O.; Dedene, G.
2014-01-01
Formal Concept Analysis (FCA) is a mathematical technique that has been extensively applied to Boolean data in knowledge discovery, information retrieval, web mining, etc. applications. During the past years, the research on extending FCA theory to cope with imprecise and incomplete information made
A Test of the Formal and Modern Theories of Matching
Dallery, Jesse; Soto, Paul L.; McDowell, J. J.
2005-01-01
The present study tested a formal, or purely mathematical, theory of matching, and a modern account derived by McDowell (1986) that incorporates deviations from strict matching--bias and sensitivity. Six humans pressed a lever for monetary reinforcers on five concurrent variable interval (VI) schedules of reinforcement. All schedules were…
Transitioning from Introductory Calculus to Formal Limit Conceptions
Nagle, Courtney
2013-01-01
The limit concept is a fundamental mathematical notion both for its practical applications and its importance as a prerequisite for later calculus topics. Past research suggests that limit conceptualizations promoted in introductory calculus are far removed from the formal epsilon-delta definition of limit. In this article, I provide an overview…
Formal Assurance Certifiable Tooling Formal Assurance Certifiable Tooling Strategy Final Report
Bush, Eric; Oglesby, David; Bhatt, Devesh; Murugesan, Anitha; Engstrom, Eric; Mueller, Joe; Pelican, Michael
2017-01-01
This is the Final Report of a research project to investigate issues and provide guidance for the qualification of formal methods tools under the DO-330 qualification process. It consisted of three major subtasks spread over two years: 1) an assessment of theoretical soundness issues that may affect qualification for three categories of formal methods tools, 2) a case study simulating the DO-330 qualification of two actual tool sets, and 3) an investigation of risk mitigation strategies that might be applied to chains of such formal methods tools in order to increase confidence in their certification of airborne software.
Algorithmic Principles of Mathematical Programming
Faigle, Ulrich; Kern, Walter; Still, Georg
2002-01-01
Algorithmic Principles of Mathematical Programming investigates the mathematical structures and principles underlying the design of efficient algorithms for optimization problems. Recent advances in algorithmic theory have shown that the traditionally separate areas of discrete optimization, linear
Alice and Bob: Reconciling Formal Models and Implementation
DEFF Research Database (Denmark)
Almousa, Omar; Mödersheim, Sebastian Alexander; Viganò, Luca
2015-01-01
This paper defines the “ultimate” formal semantics for Alice and Bob notation, i.e., what actions the honest agents have to perform, in the presence of an arbitrary set of cryptographic operators and their algebraic theory. Despite its generality, this semantics is mathematically simpler than any...... previous attempt. For practical applicability, we introduce the language SPS and an automatic translation to robust real-world implementations and corresponding formal models, and we prove this translation correct with respect to the semantics.......This paper defines the “ultimate” formal semantics for Alice and Bob notation, i.e., what actions the honest agents have to perform, in the presence of an arbitrary set of cryptographic operators and their algebraic theory. Despite its generality, this semantics is mathematically simpler than any...
A Formal Calculus for Categories
DEFF Research Database (Denmark)
Cáccamo, Mario José
This dissertation studies the logic underlying category theory. In particular we present a formal calculus for reasoning about universal properties. The aim is to systematise judgements about functoriality and naturality central to categorical reasoning. The calculus is based on a language which...... extends the typed lambda calculus with new binders to represent universal constructions. The types of the languages are interpreted as locally small categories and the expressions represent functors. The logic supports a syntactic treatment of universality and duality. Contravariance requires a definition...... of universality generous enough to deal with functors of mixed variance. Ends generalise limits to cover these kinds of functors and moreover provide the basis for a very convenient algebraic manipulation of expressions. The equational theory of the lambda calculus is extended with new rules for the definitions...
Directory of Open Access Journals (Sweden)
Alan Smart
2017-12-01
Full Text Available Addressing a variety of locations and subjects across several social contexts and countries, this forum intends to stimulate novel ways of conceptualizing the inevitable interpenetration and entanglement of formalization and informalization as two interlinked social processes. Rather than proposing a new coherent definition of “informality”, we propose to consider “in/formalization” as a space of practice and reflection which is crucial for engaging with contemporary economy, law and politics and their current local and global articulations and scenarios. The forum features contributions by Stamatis Amarianakis, Lenka Brunclíková, Dolores Koenig, B. Lynne Milgram, Sarah Muir, Antonio Maria Pusceddu, Alan Smart, Mechthild von Vacano, Filippo M. Zerilli & Julie Trappe.
DEFF Research Database (Denmark)
Levinsen, Karin; Sørensen, Birgitte Holm
2011-01-01
This paper presents findings from a large-scale longitudinal, qualitative study - Project ICT and Learning (PIL) - that engaged the participation of eight primary schools in Denmark, and was conducted between 2006 and 2008. The research design was based on action research, involving teachers...... and other relevant stakeholders, as well as participant observations in the classroom documented by thick descriptions, formal and informal interviews and focus group interviews. The aim of the study was to explore and identify relations between designs for teaching and learning and the students' learning...... of school subjects within defined learning goals and curricula, along with various implementations of ICT in the pedagogical everyday practice (Levinsen & Sørensen 2008). However, another research strand - the topic of this paper - emerged during the project's life cycle as a consequence of ongoing changes...
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.
Mathematical Footprints Discovering Mathematics Everywhere
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
From Fuzzy Logic to Fuzzy Mathematics: A Methodological Manifesto
Czech Academy of Sciences Publication Activity Database
Běhounek, Libor; Cintula, Petr
2006-01-01
Roč. 157, č. 5 (2006), s. 642-646 ISSN 0165-0114 R&D Projects: GA AV ČR KJB100300502 Institutional research plan: CEZ:AV0Z10300504 Keywords : non-classical logics * formal fuzzy logic * formal fuzzy mathematics * high-order fuzzy logic Subject RIV: BA - General Mathematics Impact factor: 1.181, year: 2006
Conceptual Complexity and Apparent Contradictions in Mathematics Language
Gough, John
2007-01-01
Mathematics is like a language, although technically it is not a natural or informal human language, but a formal, that is, artificially constructed language. Importantly, educators use their natural everyday language to teach the formal language of mathematics. At times, however, instructors encounter problems when the technical words they use,…
Directory of Open Access Journals (Sweden)
Mauricio Ayala-Rincón
2013-01-01
Full Text Available In this work, we present an algebraic approach for modeling the two-party cascade protocol of Dolev-Yao and for fully formalizing its security in the specification language of the Prototype Verification System PVS. Although cascade protocols could be argued to be a very limited model, it should be stressed here that they are the basis of more sophisticated protocols of great applicability, such as those which allow treatment of multiparty, tuples, nonces, name-stamps, signatures, etc. In the current algebraic approach, steps of the protocol are modeled in a monoid freely generated by the cryptographic operators. Words in this monoid are specified as finite sequences and the whole protocol as a finite sequence of protocol steps, that are functions from pairs of users to sequences of cryptographic operators. In a previous work, assuming that for balanced protocols admissible words produced by a potential intruder should be balanced, a formalization of the characterization of security of this kind of protocols was given in PVS. In this work, the previously assumed property is also formalized, obtaining in this way a complete formalization which mathematically guarantees the security of these protocols. Despite such property being relatively easy to specify, obtaining a complete formalization requires a great amount of effort, because several algebraic properties, that are related to the preservation of the balancing property of the admissible language of the intruder, should be formalized in the granularity of the underlying data structure (of finite sequences used in the specification. Among these properties, the most complex are related to the notion of linkage property, which allows for a systematic analysis of words of the admissible language of a potential saboteur, showing how he/she is unable to isolate private keys of other users under the assumption of balanced protocols. The difficulties that arose in conducting this formalization are
Lele, Tanmay P; Ingber, Donald E
2006-03-01
Fluorescence recovery after photobleaching (FRAP) analyses of binding and unbinding of molecules that interact with insoluble scaffolds, such as the cytoskeleton and nuclear matrix, in living cells commonly assume that this process is at equilibrium over the time scale of fluorescence recovery. This assumption breaks down for relatively fast intracellular processes like focal adhesion assembly at the leading edge of a migrating cell, or changes of transcriptional activation in the nucleus, that can occur in a matter of a few minutes. In this paper, we formulate a mathematical model that permits FRAP to be used to determine kinetic rate constants of molecules that interact with insoluble cellular structures under non-steady state conditions. We show that unlike steady state FRAP, fluorescence recovery time scales under these unsteady conditions are determined not only by unbinding rates, but also by the overall assembly and disassembly dynamics of the structural scaffold which supports these binding interactions. Experimental data from FRAP analysis and quantification of scaffold assembly dynamics may be combined and used with our mathematical model to estimate kinetic rate constants, as well as the apparent rate constant of scaffold assembly and disassembly.
29 CFR 101.20 - Formal hearing.
2010-07-01
... 29 Labor 2 2010-07-01 2010-07-01 false Formal hearing. 101.20 Section 101.20 Labor Regulations Relating to Labor NATIONAL LABOR RELATIONS BOARD STATEMENTS OF PROCEDURES Representation Cases Under... a copy of the petition, is served on the unions and employer filing or named in the petition and on...
A Formal Approach to User Interface Design using Hybrid System Theory Project
National Aeronautics and Space Administration — Optimal Synthesis Inc.(OSI) proposes to develop an aiding tool for user interface design that is based on mathematical formalism of hybrid system theory. The...
A Formal Approach to User Interface Design using Hybrid System Theory, Phase I
National Aeronautics and Space Administration — Optimal Synthesis Inc.(OSI) proposes to develop an aiding tool for user interface design that is based on mathematical formalism of hybrid system theory. The...
Directory of Open Access Journals (Sweden)
Reginaldo Santana Figueiredo
1994-12-01
Full Text Available O presente trabalho tem por objetivo a sistematização e a apresentação dos conceitos fundamentais da Teoria dos Jogos, a formalização matemática dos principais conceitos clássicos de solução de um jogo e ilustrar sua aplicação ao problema da distribuição de custo conjunto. Como produto de uma pesquisa de alguns anos, conseguimos reunir sistematicamente o conjunto de conceitos de solução de jogos donde se derivam todos conceitos encontrados nos textos atuais. Apresentamos os conceitos de solução para os chamados jogos cooperativos através do conceito de objeção e contra-objeção de forma a mostrar que os mesmos podem ser vistos como um processo de negociação.This paper presents the basic concepts of Game Theory and the mathematical formalizations of classic concepts of game solutions. We surveyed the fundamental concepts from where we derive the concepts of game solutions that can be found in the modern papers. We feature the concepts to the game named cooperative-games by concepts of objection and counterobjection to show that they can be understood as a negotiation process. In addition, we show how the Game Theory can be applied to the problem of the assignment of joint cost.
Mathematical models of morphogenesis
Directory of Open Access Journals (Sweden)
Dilão Rui
2015-01-01
Full Text Available Morphogenesis is the ensemble of phenomena that generates the form and shape of organisms. Organisms are classified according to some of its structural characteristics, to its metabolism and to its form. In particular, the empirical classification associated with the phylum concept is related with the form and shape of organisms. In the first part of this talk, we introduce the class of mathematical models associated the Turing approach to pattern formation. In the Turing approach, morphogenesis models are described by reaction-diffusion parabolic partial differential equations. Based on this formalism, we present a mathematical model describing the first two hours of development of the fruit fly Drosophila. In the second part of this talk, we present results on Pareto optimality to calibrate and validate mathematical models.
Spinor formalism and complex-vector formalism of general relativity
International Nuclear Information System (INIS)
Han-ying, G.; Yong-shi, W.; Gendao, L.
1974-01-01
In this paper, using E. Cartan's exterior calculus, we give the spinor form of the structure equations, which leads naturally to the Newman--Penrose equations. Furthermore, starting from the spinor spaces and the el (2C) algebra, we construct the general complex-vector formalism of general relativity. We find that both the Cahen--Debever--Defrise complex-vector formalism and that of Brans are its special cases. Thus, the spinor formalism and the complex-vector formalism of general relativity are unified on the basis of the uni-modular group SL(2C) and its Lie algebra
Gauge theory and gravitation: an approach to a fiber bundle formalism
International Nuclear Information System (INIS)
Mello, L.A. de.
1986-01-01
The thesis is composed of two different parts. A formal complete and rigorous mathematical part-of topics of differential manilfolds, exterior calculus, riemannian geometry, principal fiber bundle (p.f.) with connections and linear connections and a second part of application of this mathematical formalism concerning physical theories, particularly the Maxwell eletromagnetism (EM), gauge theory of Yang-Mills (Y-M), the GRT, and the gravitation theory of Einstein-Cartan. (E.C.) [pt
Directory of Open Access Journals (Sweden)
Juan J. Arbeláez-Toro
2013-11-01
Full Text Available A computational simulation is Implemented, in order to response to a problem of dynamics associated With The assessment of adherence in suspension systems. The process begins with the lifting of the most representative geometries of a MacPherson system of a Nissan Sentra B13, where each of the devices is created and assembled into a CAD software to give a dynamic solution on a CAE multibody package. Afterwards a mathematical model was created whose differential equations are generated substantiated on Newton's second law and this are resolved using Matlab-Simulink applications. Once the model developing process is over, the variables are fed with accurate information of the studied vehicle to obtain the graphs that give an answer to EuSAMA (European Shock Absorber Manufacturers Association test protocol for the adherence analysis. The results presented show the reliability of the developed models when compared with the experimental test; furthermore, it demonstrates that the decrease of the damping coefficient compromises the vehicle´s adherence on the track, affecting its stability and maneuverability.
Formal methods in design and verification of functional specifications
International Nuclear Information System (INIS)
Vaelisuo, H.
1995-01-01
It is claimed that formal methods should be applied already when specifying the functioning of the control/monitoring system, i.e. when planning how to implement the desired operation of the plant. Formal methods are seen as a way to mechanize and thus automate part of the planning. All mathematical methods which can be applied on related problem solving should be considered as formal methods. Because formal methods can only support the designer, not replace him/her, they must be integrated into a design support tool. Such a tool must also aid the designer in getting the correct conception of the plant and its behaviour. The use of a hypothetic design support tool is illustrated to clarify the requirements such a tool should fulfill. (author). 3 refs, 5 figs
Fourier Series Formalization in ACL2(r
Directory of Open Access Journals (Sweden)
Cuong K. Chau
2015-09-01
Full Text Available We formalize some basic properties of Fourier series in the logic of ACL2(r, which is a variant of ACL2 that supports reasoning about the real and complex numbers by way of non-standard analysis. More specifically, we extend a framework for formally evaluating definite integrals of real-valued, continuous functions using the Second Fundamental Theorem of Calculus. Our extended framework is also applied to functions containing free arguments. Using this framework, we are able to prove the orthogonality relationships between trigonometric functions, which are the essential properties in Fourier series analysis. The sum rule for definite integrals of indexed sums is also formalized by applying the extended framework along with the First Fundamental Theorem of Calculus and the sum rule for differentiation. The Fourier coefficient formulas of periodic functions are then formalized from the orthogonality relations and the sum rule for integration. Consequently, the uniqueness of Fourier sums is a straightforward corollary. We also present our formalization of the sum rule for definite integrals of infinite series in ACL2(r. Part of this task is to prove the Dini Uniform Convergence Theorem and the continuity of a limit function under certain conditions. A key technique in our proofs of these theorems is to apply the overspill principle from non-standard analysis.
Formal modeling of robot behavior with learning.
Kirwan, Ryan; Miller, Alice; Porr, Bernd; Di Prodi, P
2013-11-01
We present formal specification and verification of a robot moving in a complex network, using temporal sequence learning to avoid obstacles. Our aim is to demonstrate the benefit of using a formal approach to analyze such a system as a complementary approach to simulation. We first describe a classical closed-loop simulation of the system and compare this approach to one in which the system is analyzed using formal verification. We show that the formal verification has some advantages over classical simulation and finds deficiencies our classical simulation did not identify. Specifically we present a formal specification of the system, defined in the Promela modeling language and show how the associated model is verified using the Spin model checker. We then introduce an abstract model that is suitable for verifying the same properties for any environment with obstacles under a given set of assumptions. We outline how we can prove that our abstraction is sound: any property that holds for the abstracted model will hold in the original (unabstracted) model.
Conditional Inference and Advanced Mathematical Study
Inglis, Matthew; Simpson, Adrian
2008-01-01
Many mathematicians and curriculum bodies have argued in favour of the theory of formal discipline: that studying advanced mathematics develops one's ability to reason logically. In this paper we explore this view by directly comparing the inferences drawn from abstract conditional statements by advanced mathematics students and well-educated arts…
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...
Multifractal formalisms of human behavior.
Ihlen, Espen A F; Vereijken, Beatrix
2013-08-01
With the mounting realization that variability is an inevitable part of human behavior comes the need to integrate this phenomenon in concomitant models and theories of motor control. Among other things, this has resulted in a debate throughout the last decades about the origin of variability in behavior, the outcome of which has important implications for motor control theories. To date, a monofractal formalism of variability has been used as the basis for arguing for component- versus interaction-oriented theories of motor control. However, monofractal formalism alone cannot decide between the opposing sides of the debate. The present theoretical overview introduces multifractal formalisms as a necessary extension of the conventional monofractal formalism. In multifractal formalisms, the scale invariance of behavior is numerically defined as a spectrum of scaling exponents, rather than a single average exponent as in the monofractal formalism. Several methods to estimate the multifractal spectrum of scaling exponents - all within two multifractal formalisms called large deviation and Legendre formalism - are introduced and briefly discussed. Furthermore, the multifractal analyses within these two formalisms are applied to several performance tasks to illustrate how explanations of motor control vary with the methods used. The main section of the theoretical overview discusses the implications of multifractal extensions of the component- and interaction-oriented models for existing theories of motor control. Copyright © 2013 Elsevier B.V. All rights reserved.
The challenge of computer mathematics.
Barendregt, Henk; Wiedijk, Freek
2005-10-15
Progress in the foundations of mathematics has made it possible to formulate all thinkable mathematical concepts, algorithms and proofs in one language and in an impeccable way. This is not in spite of, but partially based on the famous results of Gödel and Turing. In this way statements are about mathematical objects and algorithms, proofs show the correctness of statements and computations, and computations are dealing with objects and proofs. Interactive computer systems for a full integration of defining, computing and proving are based on this. The human defines concepts, constructs algorithms and provides proofs, while the machine checks that the definitions are well formed and the proofs and computations are correct. Results formalized so far demonstrate the feasibility of this 'computer mathematics'. Also there are very good applications. The challenge is to make the systems more mathematician-friendly, by building libraries and tools. The eventual goal is to help humans to learn, develop, communicate, referee and apply mathematics.
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…
The objective of this study was to develop primary and secondary models to describe the growth of Salmonella in raw ground beef. Primary and secondary models can be integrated into a dynamic model that can predict the microbial growth under varying environmental conditions. Growth data of Salmonel...
On the Equivalence of Formal Grammars and Machines.
Lund, Bruce
1991-01-01
Explores concepts of formal language and automata theory underlying computational linguistics. A computational formalism is described known as a "logic grammar," with which computational systems process linguistic data, with examples in declarative and procedural semantics and definite clause grammars. (13 references) (CB)
Leibniz' First Formalization of Syllogistics
DEFF Research Database (Denmark)
Robering, Klaus
2014-01-01
of letters just those which belong to the useful, i.e., valid, modes. The set of codes of valid modes turns out to be a so-called "regular" language (in the sense of formal-language-theory). Leibniz' formalization of syllogistics in his Dissertatio thus contains an estimation of the computational complexity...
Outline of Neutron Scattering Formalism
Berk, N. F.
1993-01-01
Neutron scattering formalism is briefly surveyed. Topics touched upon include coherent and incoherent scattering, bound and free cross-sections, the Van Hove formalism, magnetic scattering, elastic scattering, the static approximation, sum rules, small angle scattering, inelastic scattering, thermal diffuse scattering, quasielastic scattering, and neutron optics.
A Formalization of Linkage Analysis
DEFF Research Database (Denmark)
Ingolfsdottir, Anna; Christensen, A.I.; Hansen, Jens A.
In this report a formalization of genetic linkage analysis is introduced. Linkage analysis is a computationally hard biomathematical method, which purpose is to locate genes on the human genome. It is rooted in the new area of bioinformatics and no formalization of the method has previously been ...
... this page: //medlineplus.gov/ency/article/001534.htm Mathematics disorder To use the sharing features on this page, please enable JavaScript. Mathematics disorder is a condition in which a child's ...
Towards a simple mathematical theory of citation distributions.
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.
New procedure for departure formalities
HR & GS Departments
2011-01-01
As part of the process of simplifying procedures and rationalising administrative processes, the HR and GS Departments have introduced new personalised departure formalities on EDH. These new formalities have applied to students leaving CERN since last year and from 17 October 2011 this procedure will be extended to the following categories of CERN personnel: Staff members, Fellows and Associates. It is planned to extend this electronic procedure to the users in due course. What purpose do departure formalities serve? The departure formalities are designed to ensure that members of the personnel contact all the relevant services in order to return any necessary items (equipment, cards, keys, dosimeter, electronic equipment, books, etc.) and are aware of all the benefits to which they are entitled on termination of their contract. The new departure formalities on EDH have the advantage of tailoring the list of services that each member of the personnel must visit to suit his individual contractual and p...
Some Implications of a Behavioral Analysis of Verbal Behavior for Logic and Mathematics.
Palmer, David C
2013-01-01
The evident power and utility of the formal models of logic and mathematics pose a puzzle: Although such models are instances of verbal behavior, they are also essentialistic. But behavioral terms, and indeed all products of selection contingencies, are intrinsically variable and in this respect appear to be incommensurate with essentialism. A distinctive feature of verbal contingencies resolves this puzzle: The control of behavior by the nonverbal environment is often mediated by the verbal behavior of others, and behavior under control of verbal stimuli is blind to the intrinsic variability of the stimulating environment. Thus, words and sentences serve as filters of variability and thereby facilitate essentialistic model building and the formal structures of logic, mathematics, and science. Autoclitic frames, verbal chains interrupted by interchangeable variable terms, are ubiquitous in verbal behavior. Variable terms can be substituted in such frames almost without limit, a feature fundamental to formal models. Consequently, our fluency with autoclitic frames fosters generalization to formal models, which in turn permit deduction and other kinds of logical and mathematical inference.
Mathematics is always invisible, Professor Dowling
Cable, John
2015-09-01
This article provides a critical evaluation of a technique of analysis, the Social Activity Method, recently offered by Dowling (2013) as a `gift' to mathematics education. The method is found to be inadequate, firstly, because it employs a dichotomy (between `expression' and `content') instead of a finer analysis (into symbols, concepts and setting or phenomena), and, secondly, because the distinction between `public' and `esoteric' mathematics, although interesting, is allowed to obscure the structure of the mathematics itself. There is also criticism of what Dowling calls the `myth of participation', which denies the intimate links between mathematics and the rest of the universe that lie at the heart of mathematical pedagogy. Behind all this lies Dowling's `essentially linguistic' conception of mathematics, which is criticised on the dual ground that it ignores the chastening experience of formalism in mathematical philosophy and that linguistics itself has taken a wrong turn and ignores lessons that might be learnt from mathematics education.
Trinajstić, Nenad; Gutman, Ivan
2002-01-01
A brief description is given of the historical development of mathematics and chemistry. A path leading to the meeting of these two sciences is described. An attempt is made to define mathematical chemistry, and journals containing the term mathematical chemistry in their titles are noted. In conclusion, the statement is made that although chemistry is an experimental science aimed at preparing new compounds and materials, mathematics is very useful in chemistry, among other things, to produc...
Formal specification and animation of a water level monitoring system
International Nuclear Information System (INIS)
Jackson, P.S.; Stokes, P.A.
1993-03-01
This report describes the Vienna Development Method (VDM), which is a formal method for software specification and development. VDM evolved out of attempts to use mathematics in programming language specifications in order to avoid ambiguities in specifications written in natural language. This report also describes the use of VDM for a real-time application, where it is used to formally specify the requirements of a water level monitoring system. The procedures and techniques used to produce an executable form (animation) of the specification are covered. (Author)
Digital system verification a combined formal methods and simulation framework
Li, Lun
2010-01-01
Integrated circuit capacity follows Moore's law, and chips are commonly produced at the time of this writing with over 70 million gates per device. Ensuring correct functional behavior of such large designs before fabrication poses an extremely challenging problem. Formal verification validates the correctness of the implementation of a design with respect to its specification through mathematical proof techniques. Formal techniques have been emerging as commercialized EDA tools in the past decade. Simulation remains a predominantly used tool to validate a design in industry. After more than 5
Mathematical Sense-Making in Quantum Mechanics: An Initial Peek
Dreyfus, Benjamin W.; Elby, Andrew; Gupta, Ayush; Sohr, Erin Ronayne
2017-01-01
Mathematical sense-making--looking for coherence between the structure of the mathematical formalism and causal or functional relations in the world--is a core component of physics expertise. Some physics education research studies have explored what mathematical sense-making looks like at the introductory physics level, while some historians and…
African Journals Online (AJOL)
... and JHS teachers toward mathematics, both upper primary and JHS teachers were found to have significantly more positive attitudes toward mathematics than the lower primary teachers. The study recommended the need to encourage lower primary school teachers to develop more positive attitudes toward mathematics.
Directory of Open Access Journals (Sweden)
Suguru Arimoto
2011-01-01
Full Text Available A computable model of grasping and manipulation of a 3D rigid object with arbitrary smooth surfaces by multiple robot fingers with smooth fingertip surfaces is derived under rolling contact constraints between surfaces. Geometrical conditions of pure rolling contacts are described through the moving-frame coordinates at each rolling contact point under the postulates: (1 two surfaces share a common single contact point without any mutual penetration and a common tangent plane at the contact point and (2 each path length of running of the contact point on the robot fingertip surface and the object surface is equal. It is shown that a set of Euler-Lagrange equations of motion of the fingers-object system can be derived by introducing Lagrange multipliers corresponding to geometric conditions of contacts. A set of 1st-order differential equations governing rotational motions of each fingertip and the object and updating arc-length parameters should be accompanied with the Euler-Lagrange equations. Further more, nonholonomic constraints arising from twisting between the two normal axes to each tangent plane are rewritten into a set of Frenet-Serre equations with a geometrically given normal curvature and a motion-induced geodesic curvature.
Lectures on formal and rigid geometry
Bosch, Siegfried
2014-01-01
A first version of this work appeared in 2005 as a Preprint of the Collaborative Research Center "Geometrical Structures in Mathematics" at the University of Münster. Its aim was to offer a concise and self-contained 'lecture-style' introduction to the theory of classical rigid geometry established by John Tate, together with the formal algebraic geometry approach launched by Michel Raynaud. These Lectures are now viewed commonly as an ideal means of learning advanced rigid geometry, regardless of the reader's level of background. Despite its parsimonious style, the presentation illustrates a number of key facts even more extensively than any other previous work. This Lecture Notes Volume is a revised and slightly expanded version of the original preprint and has been published at the suggestion of several experts in the field.
The formalisms of quantum mechanics an introduction
David, Francois
2015-01-01
These lecture notes present a concise and introductory, yet as far as possible coherent, view of the main formalizations of quantum mechanics and of quantum field theories, their interrelations and their theoretical foundations. The “standard” formulation of quantum mechanics (involving the Hilbert space of pure states, self-adjoint operators as physical observables, and the probabilistic interpretation given by the Born rule) on one hand, and the path integral and functional integral representations of probabilities amplitudes on the other, are the standard tools used in most applications of quantum theory in physics and chemistry. Yet, other mathematical representations of quantum mechanics sometimes allow better comprehension and justification of quantum theory. This text focuses on two of such representations: the algebraic formulation of quantum mechanics and the “quantum logic” approach. Last but not least, some emphasis will also be put on understanding the relation between quantum physics and ...
Formal models in animal-metacognition research: the problem of interpreting animals' behavior.
Smith, J David; Zakrzewski, Alexandria C; Church, Barbara A
2016-10-01
Ongoing research explores whether animals have precursors to metacognition-that is, the capacity to monitor mental states or cognitive processes. Comparative psychologists have tested apes, monkeys, rats, pigeons, and a dolphin using perceptual, memory, foraging, and information-seeking paradigms. The consensus is that some species have a functional analog to human metacognition. Recently, though, associative modelers have used formal-mathematical models hoping to describe animals' "metacognitive" performances in associative-behaviorist ways. We evaluate these attempts to reify formal models as proof of particular explanations of animal cognition. These attempts misunderstand the content and proper application of models. They embody mistakes of scientific reasoning. They blur fundamental distinctions in understanding animal cognition. They impede theoretical development. In contrast, an energetic empirical enterprise is achieving strong success in describing the psychology underlying animals' metacognitive performances. We argue that this careful empirical work is the clear path to useful theoretical development. The issues raised here about formal modeling-in the domain of animal metacognition-potentially extend to biobehavioral research more broadly.
Formal models in animal-metacognition research: the problem of interpreting animals’ behavior
Smith, J. David; Zakrzewski, Alexandria C.; Church, Barbara A.
2015-01-01
Ongoing research explores whether animals have precursors to metacognition—that is, the capacity to monitor mental states or cognitive processes. Comparative psychologists have tested apes, monkeys, rats, pigeons, and a dolphin using perceptual, memory, foraging, and information-seeking paradigms. The consensus is that some species have a functional analog to human metacognition. Recently, though, associative modelers have used formal-mathematical models hoping to describe animals’ “metacognitive” performances in associative-behaviorist ways. We evaluate these attempts to reify formal models as proof of particular explanations of animal cognition. These attempts misunderstand the content and proper application of models. They embody mistakes of scientific reasoning. They blur fundamental distinctions in understanding animal cognition. They impede theoretical development. In contrast, an energetic empirical enterprise is achieving strong success in describing the psychology underlying animals’ metacognitive performances. We argue that this careful empirical work is the clear path to useful theoretical development. The issues raised here about formal modeling—in the domain of animal metacognition—potentially extend to biobehavioral research more broadly. PMID:26669600
Morozov, V. A.
2009-06-01
The time-dependences of the populations of molecular states are determined by the numerical solution of a set of equations for the matrix elements of a density operator for the five-level model of a molecule with different values of parameters of two nonoverlapping in time irradiation pulses and of the constants governing the rates of induced radiative transitions of the molecule, as well as the radiative and nonradiative decays of molecular states. It is proposed to use the results obtained as reference points in interpreting experimental data on the spectro-temporal characteristics of secondary emission upon photoisomerization of molecules with an intramolecular hydrogen bond under irradiation by two light pulses and in determining the mechanism of phototransfer of the hydrogen-bond proton occurring in this process.
DEFF Research Database (Denmark)
Blomhøj, Morten
2004-01-01
modelling, however, can be seen as a practice of teaching that place the relation between real life and mathematics into the centre of teaching and learning mathematics, and this is relevant at all levels. Modelling activities may motivate the learning process and help the learner to establish cognitive......Developing competences for setting up, analysing and criticising mathematical models are normally seen as relevant only from and above upper secondary level. The general belief among teachers is that modelling activities presuppose conceptual understanding of the mathematics involved. Mathematical...... roots for the construction of important mathematical concepts. In addition competences for setting up, analysing and criticising modelling processes and the possible use of models is a formative aim in this own right for mathematics teaching in general education. The paper presents a theoretical...
Mathematical Modeling and Pure Mathematics
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…
Scalable Techniques for Formal Verification
Ray, Sandip
2010-01-01
This book presents state-of-the-art approaches to formal verification techniques to seamlessly integrate different formal verification methods within a single logical foundation. It should benefit researchers and practitioners looking to get a broad overview of the spectrum of formal verification techniques, as well as approaches to combining such techniques within a single framework. Coverage includes a range of case studies showing how such combination is fruitful in developing a scalable verification methodology for industrial designs. This book outlines both theoretical and practical issue
Leibniz' First Formalization of Syllogistics
DEFF Research Database (Denmark)
Robering, Klaus
2014-01-01
of letters just those which belong to the useful, i.e., valid, modes. The set of codes of valid modes turns out to be a so-called "regular" language (in the sense of formal-language-theory). Leibniz' formalization of syllogistics in his Dissertatio thus contains an estimation of the computational complexity......In his Dissertatio de Arte Combinatoria from 1666 Leibniz provides a formal presentation of syllogistics within the framework of his general-combinatoric program. He does not set up an axiomatic system for the derivation of all valid syllogistic mode, rather he formulates a set of rules which...
On Mathematical Aspects of Dual Variables in Continuum Mechanics. Part 1 : Mathematical Principles
Giessen, E. van der; Kollmann, F.G.
1996-01-01
In this paper consisting of two parts we consider mathematical aspects of dual variables appearing in continuum mechanics. Tensor calculus on manifolds as introduced into continuum mechanics is used as a point of departure. This mathematical formalism leads to additional structure of continuum
Formalism and Interpretation in Quantum Theory
Wilce, Alexander
2010-04-01
Quantum Mechanics can be viewed as a linear dynamical theory having a familiar mathematical framework but a mysterious probabilistic interpretation, or as a probabilistic theory having a familiar interpretation but a mysterious formal framework. These points of view are usually taken to be somewhat in tension with one another. The first has generated a vast literature aiming at a “realistic” and “collapse-free” interpretation of quantum mechanics that will account for its statistical predictions. The second has generated an at least equally large literature aiming to derive, or at any rate motivate, the formal structure of quantum theory in probabilistically intelligible terms. In this paper I explore, in a preliminary way, the possibility that these two programmes have something to offer one another. In particular, I show that a version of the measurement problem occurs in essentially any non-classical probabilistic theory, and ask to what extent various interpretations of quantum mechanics continue to make sense in such a general setting. I make a start on answering this question in the case of a rudimentary version of the Everett interpretation.
Versatile Formal Methods Applied to Quantum Information.
Energy Technology Data Exchange (ETDEWEB)
Witzel, Wayne [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Rudinger, Kenneth Michael [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Sarovar, Mohan [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
2015-11-01
Using a novel formal methods approach, we have generated computer-veri ed proofs of major theorems pertinent to the quantum phase estimation algorithm. This was accomplished using our Prove-It software package in Python. While many formal methods tools are available, their practical utility is limited. Translating a problem of interest into these systems and working through the steps of a proof is an art form that requires much expertise. One must surrender to the preferences and restrictions of the tool regarding how mathematical notions are expressed and what deductions are allowed. Automation is a major driver that forces restrictions. Our focus, on the other hand, is to produce a tool that allows users the ability to con rm proofs that are essentially known already. This goal is valuable in itself. We demonstrate the viability of our approach that allows the user great exibility in expressing state- ments and composing derivations. There were no major obstacles in following a textbook proof of the quantum phase estimation algorithm. There were tedious details of algebraic manipulations that we needed to implement (and a few that we did not have time to enter into our system) and some basic components that we needed to rethink, but there were no serious roadblocks. In the process, we made a number of convenient additions to our Prove-It package that will make certain algebraic manipulations easier to perform in the future. In fact, our intent is for our system to build upon itself in this manner.
Valla, Jeffrey M; Williams, Wendy M
2012-01-01
The under-representation of women and ethnic minorities in Science, Technology, Engineering, and Mathematics (STEM) education and professions has resulted in a loss of human capital for the US scientific workforce and spurred the development of myriad STEM educational intervention programs. Increased allocation of resources to such programs begs for a critical, prescriptive, evidence-based review that will enable researchers to develop optimal interventions and administrators to maximize investments. We begin by providing a theoretical backdrop for K-12 STEM programs by reviewing current data on under-representation and developmental research describing individual-level social factors undergirding these data. Next, we review prototypical designs of these programs, highlighting specific programs in the literature as examples of program structures and components currently in use. We then evaluate these interventions in terms of overall effectiveness, as a function of how well they address age-, ethnicity-, or gender-specific factors, suggesting improvements in program design based on these critiques. Finally, program evaluation methods are briefly reviewed and discussed in terms of how their empirical soundness can either enable or limit our ability to delineate effective program components. "Now more than ever, the nation's changing demographics demand that we include all of our citizens in science and engineering education and careers. For the U.S. to benefit from the diverse talents of all its citizens, we must grow the pipeline of qualified, underrepresented minority engineers and scientists to fill positions in industry and academia."-Irving P. McPhail..
Nachaisin, Mali; Teeta, Suminya; Deejing, Konlayut; Pharanat, Wanida
2017-09-01
Instant food is a product produced for convenience for consumer. Qualities are an important attribute of food materials reflecting consumer acceptance. The most problem of instant rice is casehardening during drying process resulted in the longer rehydration time. The objective of this research was to study the qualities of shredded Thai-style instant rice under a combined gas-fired infrared and air convection drying. Additionally, the mathematical models for gas-fired infrared assisted thin-layer drying of shredded Thai-style rice for traditional was investigated. The thin-layer drying of shredded Thai-style rice was carried out under gas-fired infrared intensities of 1000W/m2, air temperatures of 70°C and air velocities of 1 m/s. The drying occurred in the falling rate of drying period. The Page model was found to satisfactorily describe the drying behavior of shredded Thai-style rice, providing the highest R2 (0.997) and the lowest MBE and RMSE (0.01 and 0.18) respectively. A 9 point hedonic test showed in softness and color, but odor and overall acceptance were very similar.
Schwinger-Keldysh formalism. Part II: thermal equivariant cohomology
Haehl, Felix M.; Loganayagam, R.; Rangamani, Mukund
2017-06-01
Causally ordered correlation functions of local operators in near-thermal quantum systems computed using the Schwinger-Keldysh formalism obey a set of Ward identities. These can be understood rather simply as the consequence of a topological (BRST) algebra, called the universal Schwinger-Keldysh superalgebra, as explained in our compan-ion paper [1]. In the present paper we provide a mathematical discussion of this topological algebra. In particular, we argue that the structures can be understood in the language of extended equivariant cohomology. To keep the discussion self-contained, we provide a ba-sic review of the algebraic construction of equivariant cohomology and explain how it can be understood in familiar terms as a superspace gauge algebra. We demonstrate how the Schwinger-Keldysh construction can be succinctly encoded in terms a thermal equivariant cohomology algebra which naturally acts on the operator (super)-algebra of the quantum system. The main rationale behind this exploration is to extract symmetry statements which are robust under renormalization group flow and can hence be used to understand low-energy effective field theory of near-thermal physics. To illustrate the general prin-ciples, we focus on Langevin dynamics of a Brownian particle, rephrasing some known results in terms of thermal equivariant cohomology. As described elsewhere, the general framework enables construction of effective actions for dissipative hydrodynamics and could potentially illumine our understanding of black holes.
El Salvador - Formal Technical Education
Millennium Challenge Corporation — With a budget of nearly $20 million, the Formal Technical Education Sub-Activity was designed to strengthen technical and vocational educational institutions in the...
Readings in Formal Epistemology : Sourcebook
Arló-Costa, H.; Hendricks, V.F.; van Benthem, J.
2016-01-01
This volume presents 38 classic texts in formal epistemology, and strengthens the ties between research into this area of philosophy and its neighbouring intellectual disciplines. The editors provide introductions to five subsections: Bayesian Epistemology, Belief Change, Decision Theory,
Formalizing the Process of Constructing Chains of Lexical Units
Directory of Open Access Journals (Sweden)
Grigorij Chetverikov
2015-06-01
Full Text Available Formalizing the Process of Constructing Chains of Lexical Units The paper investigates mathematical aspects of describing the construction of chains of lexical units on the basis of finite-predicate algebra. Analyzing the construction peculiarities is carried out and application of the method of finding the power of linear logical transformation for removing characteristic words of a dictionary entry is given. Analysis and perspectives of the results of the study are provided.
Formal Models of Dilemmas in Social Decision-Making
1974-12-01
34group rationality" ~ have become of increasing interest to both social scientists and laymen. Overpopulation and pollution are two dramatic...Research Institute Paper presented at Human Judgment and Decision Processes Symposium Northern Illinois University October 16, 1974 To appear in... Human Judgment and Decision Processes; Formal and Mathematical Approaches [Kaplan s Schwartz, eds.l /M uMMmMMM —— ^ - ----^ — im I
McConnell, Jennifer A; Schaffner, Donald W
2014-07-01
Temperature is a primary factor in controlling the growth of microorganisms in food. The current U. S. Food and Drug Administration Model Food Code guidelines state that food can be kept out of temperature control for up to 4 h without qualifiers, or up to 6 h, if the food product starts at an initial 41 °F (5 °C) temperature and does not exceed 70 °F (21 °C) at 6 h. This project validates existing ComBase computer models for Salmonella growth under changing temperature conditions modeling scenarios using raw ground beef as a model system. A cocktail of Salmonella serovars isolated from different meat products ( Salmonella Copenhagen, Salmonella Montevideo, Salmonella Typhimurium, Salmonella Saintpaul, and Salmonella Heidelberg) was made rifampin resistant and used for all experiments. Inoculated samples were held in a programmable water bath at 4.4 °C (40 °F) and subjected to linear temperature changes to different final temperatures over various lengths of time and then returned to 4.4 °C (40 °F). Maximum temperatures reached were 15.6, 26.7, or 37.8 °C (60, 80, or 100 °F), and the temperature increases took place over 4, 6, and 8 h, with varying cooling times. Our experiments show that when maximum temperatures were lower (15.6 or 26.7 °C), there was generally good agreement between the ComBase models and experiments: when temperature increases of 15.6 or 26.7 °C occurred over 8 h, experimental data were within 0.13 log CFU of the model predictions. When maximum temperatures were 37 °C, predictive models were fail-safe. Overall bias of the models was 1.11. and accuracy was 2.11. Our experiments show the U.S. Food and Drug Administration Model Food Code guidelines for holding food out of temperature control are quite conservative. Our research also shows that the ComBase models for Salmonella growth are accurate or fail-safe for dynamic temperature conditions as might be observed due to power loss from natural disasters or during transport out of
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
Formal methods for discrete-time dynamical systems
Belta, Calin; Aydin Gol, Ebru
2017-01-01
This book bridges fundamental gaps between control theory and formal methods. Although it focuses on discrete-time linear and piecewise affine systems, it also provides general frameworks for abstraction, analysis, and control of more general models. The book is self-contained, and while some mathematical knowledge is necessary, readers are not expected to have a background in formal methods or control theory. It rigorously defines concepts from formal methods, such as transition systems, temporal logics, model checking and synthesis. It then links these to the infinite state dynamical systems through abstractions that are intuitive and only require basic convex-analysis and control-theory terminology, which is provided in the appendix. Several examples and illustrations help readers understand and visualize the concepts introduced throughout the book.
A Formal Approach to Requirements-Based Programming
Hinchey, Michael G.; Rash, James L.; Rouff, Christopher A.
2005-01-01
No significant general-purpose method is currently available to mechanically transform system requirements into a provably equivalent model. The widespread use of such a method represents a necessary step toward high-dependability system engineering for numerous application domains. Current tools and methods that start with a formal model of a system and mechanically produce a provably equivalent implementation are valuable but not sufficient. The "gap" unfilled by such tools and methods is that the formal models cannot be proven to be equivalent to the requirements. We offer a method for mechanically transforming requirements into a provably equivalent formal model that can be used as the basis for code generation and other transformations. This method is unique in offering full mathematical tractability while using notations and techniques that are well known and well trusted. Finally, we describe further application areas we are investigating for use of the approach.
Herrold, Ardis; Bauer, Amanda, Dr.; Peterson, J. Matt; Large Synoptic Survey Telescope Education and Public Outreach Team
2018-01-01
The Large Synoptic Survey Telescope will usher in a new age of astronomical data exploration for science educators and students. LSST data sets will be large, deep, and dynamic, and will establish a time-domain record that will extend over a decade. They will be used to provide engaging, relevant learning experiences.The EPO Team will develop online investigations using authentic LSST data that offer varying levels of challenge and depth by the start of telescope operations, slated to begin in 2022. The topics will cover common introductory astronomy concepts, and will align with the four science domains of LSST: The Milky Way, the changing sky (transients), solar system (moving) objects, and dark matter and dark energy.Online Jupyter notebooks will make LSST data easily available to access and analyze by students at the advanced middle school through college levels. Using online notebooks will circumvent common obstacles caused by firewalls, bandwidth issues, and the need to download software, as they will be accessible from any computer or tablet with internet access. Although the LSST EPO Jupyter notebooks are Python-based, a knowledge of programming will not be required to use them.Each topical investigation will include teacher and student versions of Jupyter notebooks, instructional videos, and access to a suite of support materials including a forum, and professional development training and tutorial videos.Jupyter notebooks will contain embedded widgets to process data, eliminating the need to use external spreadsheets and plotting software. Students will be able to analyze data by using some of the existing modules already developed for professional astronomers. This will shorten the time needed to conduct investigations and will shift the emphasis to understanding the underlying science themes, which is often lost with novice learners.
Aigner, Martin; Spain, Philip G
2010-01-01
Mathematics is all around us. Often we do not realize it, though. Mathematics Everywhere is a collection of presentations on the role of mathematics in everyday life, through science, technology, and culture. The common theme is the unique position of mathematics as the art of pure thought and at the same time as a universally applicable science. The authors are renowned mathematicians; their presentations cover a wide range of topics. From compact discs to the stock exchange, from computer tomography to traffic routing, from electronic money to climate change, they make the "math inside" unde
Pappas, Theoni
1997-01-01
In this highly readable volume of vignettes of mathematical scandals and gossip, Theoni Pappas assembles 29 fascinating stories of intrigue and the bizarre ? in short, the human background of the history of mathematics. Might a haberdasher have changed Einstein's life? Why was the first woman mathematician murdered? How come there's no Nobel Prize in mathematics?Mathematics is principally about numbers, equations, and solutions, all of them precise and timeless. But, behind this arcane matter lies the sometimes sordid world of real people, whose rivalries and deceptions
Formalization of an environmental model using formal concept analysis - FCA
Bourdon-García, Rubén D.; Burgos-Salcedo, Javier D.
2016-08-01
Nowadays, there is a huge necessity to generate novel strategies for social-ecological systems analyses for resolving global sustainability problems. This paper has as main purpose the application of the formal concept analysis to formalize the theory of Augusto Ángel Maya, who without a doubt, was one of the most important environmental philosophers in South America; Ángel Maya proposed and established that Ecosystem-Culture relations, instead Human-Nature ones, are determinants in our understanding and management of natural resources. Based on this, a concept lattice, formal concepts, subconcept-superconcept relations, partially ordered sets, supremum and infimum of the lattice and implications between attributes (Duquenne-Guigues base), were determined for the ecosystem-culture relations.
Using APOS Theory Framework: Why Did Students Unable To Construct a Formal Proof?
Directory of Open Access Journals (Sweden)
Syamsuri Syamsuri
2017-08-01
Full Text Available Mathematical thinking is necessary in mathematics learning especially in college level. One of activities in undergraduate mathematics learning is proving. This article describes students’ thinking process who unable to construct mathematical formal proof. The description uses APOS Theory to explore students’ mental mechanism and students’ mental structure while they do proving. This research is qualitative research that conducted on students majored in mathematics education in public university in Banten province, Indonesia. Data was obtained through asking students to solve proving-task using think-aloud and then following by interview based task. Results show that the students could not construct a formal proof because they unable to appear encapsulation process. They merely enable to think interiorization and coordination. Based on the results, some suitable learning activities should designed to support the construction of these mental mechanism.
Sedwards, Sean; Mazza, Tommaso
2007-10-15
Compartments and membranes are the basis of cell topology and more than 30% of the human genome codes for membrane proteins. While it is possible to represent compartments and membrane proteins in a nominal way with many mathematical formalisms used in systems biology, few, if any, explicitly model the topology of the membranes themselves. Discrete stochastic simulation potentially offers the most accurate representation of cell dynamics. Since the details of every molecular interaction in a pathway are often not known, the relationship between chemical species in not necessarily best described at the lowest level, i.e. by mass action. Simulation is a form of computer-aided analysis, relying on human interpretation to derive meaning. To improve efficiency and gain meaning in an automatic way, it is necessary to have a formalism based on a model which has decidable properties. We present Cyto-Sim, a stochastic simulator of membrane-enclosed hierarchies of biochemical processes, where the membranes comprise an inner, outer and integral layer. The underlying model is based on formal language theory and has been shown to have decidable properties (Cavaliere and Sedwards, 2006), allowing formal analysis in addition to simulation. The simulator provides variable levels of abstraction via arbitrary chemical kinetics which link to ordinary differential equations. In addition to its compact native syntax, Cyto-Sim currently supports models described as Petri nets, can import all versions of SBML and can export SBML and MATLAB m-files. Cyto-Sim is available free, either as an applet or a stand-alone Java program via the web page (http://www.cosbi.eu/Rpty_Soft_CytoSim.php). Other versions can be made available upon request.
Experimental Mathematics and Mathematical Physics
Energy Technology Data Exchange (ETDEWEB)
Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David; Zudilin, Wadim
2009-06-26
One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values. Recently these techniques have been applied with great success to problems in mathematical physics. Notable among these applications are the identification of some key multi-dimensional integrals that arise in Ising theory, quantum field theory and in magnetic spin theory.
The materiality of mathematics: presenting mathematics at the blackboard.
Greiffenhagen, Christian
2014-09-01
Sociology has been accused of neglecting the importance of material things in human life and the material aspects of social practices. Efforts to correct this have recently been made, with a growing concern to demonstrate the materiality of social organization, not least through attention to objects and the body. As a result, there have been a plethora of studies reporting the social construction and effects of a variety of material objects as well as studies that have explored the material dimensions of a diversity of practices. In different ways these studies have questioned the Cartesian dualism of a strict separation of 'mind' and 'body'. However, it could be argued that the idea of the mind as immaterial has not been entirely banished and lingers when it comes to discussing abstract thinking and reasoning. The aim of this article is to extend the material turn to abstract thought, using mathematics as a paradigmatic example. This paper explores how writing mathematics (on paper, blackboards, or even in the air) is indispensable for doing and thinking mathematics. The paper is based on video recordings of lectures in formal logic and investigates how mathematics is presented at the blackboard. The paper discusses the iconic character of blackboards in mathematics and describes in detail a number of inscription practices of presenting mathematics at the blackboard (such as the use of lines and boxes, the designation of particular regions for specific mathematical purposes, as well as creating an 'architecture' visualizing the overall structure of the proof). The paper argues that doing mathematics really is 'thinking with eyes and hands' (Latour 1986). Thinking in mathematics is inextricably interwoven with writing mathematics. © London School of Economics and Political Science 2014.
Kodaira, Kunihiko
1996-01-01
This is the translation from the Japanese textbook for the grade 11 course, "General Mathematics". It is part of the easier of the three elective courses in mathematics offered at this level and is taken by about 40% of students. The book covers basic notions of probability and statistics, vectors, exponential, logarithmic, and trigonometric functions, and an introduction to differentiation and integration.
Kleene, Stephen Cole
1967-01-01
Undergraduate students with no prior instruction in mathematical logic will benefit from this multi-part text. Part I offers an elementary but thorough overview of mathematical logic of 1st order. Part II introduces some of the newer ideas and the more profound results of logical research in the 20th century. 1967 edition.
Informal work and formal plans
DEFF Research Database (Denmark)
Dalsted, Rikke Juul; Hølge-Hazelton, Bibi; Kousgaard, Marius Brostrøm
2012-01-01
INTRODUCTION: Formal pathways models outline that patients should receive information in order to experience a coherent journey but do not describe an active role for patients or their relatives. The aim of this is paper is to articulate and discuss the active role of patients during their cancer...... trajectories. METHODS AND THEORY: An in-depth case study of patient trajectories at a Danish hospital and surrounding municipality using individual interviews with patients. Theory about trajectory and work by Strauss was included. RESULTS: Patients continuously took initiatives to organize their treatment....... The patients' requests were not sufficiently supported in the professional organisation of work or formal planning. Patients' insertion and use of information in their trajectories challenged professional views and working processes. And the design of the formal pathway models limits the patients' active...
Formal connections in deformation quantization
DEFF Research Database (Denmark)
Masulli, Paolo
product on a Poisson manifold that is in general non-commutative and corresponds to the composition of the quantized observables. While in general it is difficult to express a star product globally on a curved manifold in an explicit way, we consider a case where this is possible, namely that of a Kähler...... terms. This allows us to express the equations determining a trivialization of the formal connection completely in graph terms, and solving them amounts to finding a linear combination of graphs whose derivative is equal to a given expression. We shall also look at another approach to the problem...... that is more calculative. Moreover we use the graph formalism to give a set of recursive equations determining the formal connection for a given family of star products....
Parshall, Karen Hunger
2002-01-01
Although today's mathematical research community takes its international character very much for granted, this "global nature" is relatively recent, having evolved over a period of roughly 150 years-from the beginning of the nineteenth century to the middle of the twentieth century. During this time, the practice of mathematics changed from being centered on a collection of disparate national communities to being characterized by an international group of scholars for whom the goal of mathematical research and cooperation transcended national boundaries. Yet, the development of an international community was far from smooth and involved obstacles such as war, political upheaval, and national rivalries. Until now, this evolution has been largely overlooked by historians and mathematicians alike. This book addresses the issue by bringing together essays by twenty experts in the history of mathematics who have investigated the genesis of today's international mathematical community. This includes not only develo...
Logical formalization and the formalization of logic(s)
Czech Academy of Sciences Publication Activity Database
Peregrin, Jaroslav; Svoboda, Vladimír
2016-01-01
Roč. 59, č. 233 (2016), s. 55-80 ISSN 0024-5836 R&D Projects: GA ČR(CZ) GA13-21076S Institutional support: RVO:67985955 Keywords : logical formalization * logical analysis * reflective equilibrium Subject RIV: AA - Philosophy ; Religion
Integrating Semi-formal and Formal Software Specification Techniques
Wieringa, Roelf J.; Dubois, Eric
1998-01-01
In this paper, we report on the integration of informal, semiformal and formal system specification techniques. We present a framework for system specification called TRADE, within which several well-known semiformal specification techniques are placed. TRADE is based on an analysis of structured
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.
Formal Institutions and Subjective Wellbeing
DEFF Research Database (Denmark)
Bjørnskov, Christian; Dreher, Axel; Fischer, Justina A.V.
2010-01-01
A long tradition in economics explores the association between the quality of formal institutions and economic performance. The literature on the relationship between such institutions and happiness is, however, rather limited, and inconclusive. In this paper, we revisit the findings from recent...... cross-country studies on the institution-happiness association. Our findings suggest that their conclusions are qualitatively rather insensitive to the specific measure of 'happiness' used, while the associations between formal institutions and subjective well-being differ among poor and rich countries...
The 1989 progress report: Mathematics
International Nuclear Information System (INIS)
Demazure, M.
1989-01-01
The 1989 progress report of the laboratory of Mathematics of the Polytechnic School (France) is presented. The investigations reported were performed in the following fields: analysis of nonlinear partial differential equations, quantum mechanics, scattering, fluid dynamics and homogenization, equations, varieties with negative curvature, elliptical problems on surfaces, Dirac operator, geometry of algorithms and formal calculus, singularities, Lie groups, dynamics systems. The published papers, the conferences and the Laboratory staff are listed [fr
Problem solving in the borderland between mathematics and physics
DEFF Research Database (Denmark)
Jensen, Jens Højgaard; Niss, Martin; Jankvist, Uffe Thomas
2017-01-01
The article addresses the problématique of where mathematization is taught in the educational system, and who teaches it. Mathematization is usually not a part of mathematics programs at the upper secondary level, but we argue that physics teaching has something to offer in this respect......, if it focuses on solving so-called unformalized problems, where a major challenge is to formalize the problems in mathematics and physics terms. We analyse four concrete examples of unformalized problems for which the formalization involves different order of mathematization and applying physics to the problem......, but all require mathematization. The analysis leads to the formulation of a model by which we attempt to capture the important steps of the process of solving unformalized problems by means of mathematization and physicalization....
Charging transient in polyvinyl formal
Indian Academy of Sciences (India)
Unknown
401–406. © Indian Academy of Sciences. 401. Charging transient in polyvinyl formal. P K KHARE*, P L JAIN† and R K PANDEY‡. Department of Postgraduate Studies & Research in Physics & Electronics, Rani Durgavati University,. Jabalpur 482 001, India. †Department of Physics, Government PG College, Damoh 470 ...
Formal monkey linguistics : The debate
Schlenker, Philippe; Chemla, Emmanuel; Schel, Anne M.; Fuller, James; Gautier, Jean Pierre; Kuhn, Jeremy; Veselinović, Dunja; Arnold, Kate; Cäsar, Cristiane; Keenan, Sumir; Lemasson, Alban; Ouattara, Karim; Ryder, Robin; Zuberbühler, Klaus
2016-01-01
We explain why general techniques from formal linguistics can and should be applied to the analysis of monkey communication - in the areas of syntax and especially semantics. An informed look at our recent proposals shows that such techniques needn't rely excessively on categories of human language:
Rotor and wind turbine formalism
DEFF Research Database (Denmark)
Branlard, Emmanuel Simon Pierre
2017-01-01
The main conventions used in this book for the study of rotors are introduced in this chapter. The main assumptions and notations are provided. The formalism specific to wind turbines is presented. The forces, moments, velocities and dimensionless coefficients used in the study of rotors...
Formalization in Component Based Development
DEFF Research Database (Denmark)
Holmegaard, Jens Peter; Knudsen, John; Makowski, Piotr
2006-01-01
may be specified in a formal language convenient for its purpose and, in principle, unrelated to languages for other aspects. Each aspect forms its own semantic domain, although a semantic domain may be parameterized by values derived from other aspects. The proposed conceptual framework is introduced...
Formal tautologies in Czech language
Bílková, Jana
2006-01-01
The main purpose ofthis work was to describe and classify FT used in the contemporary Czech language and to demonstrate formal and semantic variety and high functional potential of this specific class of sentences. Powered by TCPDF (www.tcpdf.org)
Formal systems for persuasion dialogue
Prakken, Henry
This article reviews formal systems that regulate persuasion dialogues. In such dialogues two or more participants aim to resolve a difference of opinion, each trying to persuade the other participants to adopt their point of view. Systems for persuasion dialogue have found application in various
Automatic Testing with Formal Methods
Tretmans, G.J.; Belinfante, Axel
1999-01-01
The use of formal system specifications makes it possible to automate the derivation of test cases from specifications. This allows to automate the whole testing process, not only the test execution part of it. This paper presents the state of the art and future perspectives in testing based on
DEFF Research Database (Denmark)
Bjørner, Dines; George, Chris W.; Haxthausen, Anne Elisabeth
2004-01-01
these different UML views are unified, integrated, correlated or merely co-located is for others to dispute. We also seek to support multiple views, but are also in no doubt that there must be sound, well defined relations between such views. We thus report on ways and means of integrating formal techniques...
Logan, J David
2013-01-01
Praise for the Third Edition"Future mathematicians, scientists, and engineers should find the book to be an excellent introductory text for coursework or self-study as well as worth its shelf space for reference." -MAA Reviews Applied Mathematics, Fourth Edition is a thoroughly updated and revised edition on the applications of modeling and analyzing natural, social, and technological processes. The book covers a wide range of key topics in mathematical methods and modeling and highlights the connections between mathematics and the applied and nat
Bird, John
2014-01-01
A practical introduction to the core mathematics required for engineering study and practiceNow in its seventh edition, Engineering Mathematics is an established textbook that has helped thousands of students to succeed in their exams.John Bird's approach is based on worked examples and interactive problems. This makes it ideal for students from a wide range of academic backgrounds as the student can work through the material at their own pace. Mathematical theories are explained in a straightforward manner, being supported by practical engineering examples and applications in order to ensure
Handley, Bill
2012-01-01
This new, revised edition of the bestselling Speed Mathematics features new chapters on memorising numbers and general information, calculating statistics and compound interest, square roots, logarithms and easy trig calculations. Written so anyone can understand, this book teaches simple strategies that will enable readers to make lightning-quick calculations. People who excel at mathematics use better strategies than the rest of us; they are not necessarily more intelligent. With Speed Mathematics you'll discover methods to make maths easy and fun. This book is perfect for stud
Energy Technology Data Exchange (ETDEWEB)
Sousa, Tania; Domingos, Tiago [Environment and Energy Section, DEM, Instituto Superior Tecnico, Avenida Rovisco Pais, 1, 1049-001 Lisboa (Portugal)
2006-06-10
The relation between Thermodynamics and Economics is a paramount issue in Ecological Economics. Two different levels can be distinguished when discussing it: formal and substantive. At the formal level, a mathematical framework is used to describe both thermodynamic and economic systems. At the substantive level, thermodynamic laws are applied to economic processes. In Ecological Economics, there is a widespread claim that neoclassical economics has the same mathematical formulation as classical mechanics and is therefore fundamentally flawed because: (1) utility does not obey a conservation law as energy does; (2) an equilibrium theory cannot be used to study irreversible processes. Here, we show that neoclassical economics is based on a wrong formulation of classical mechanics, being in fact formally analogous to equilibrium thermodynamics. The similarity between both formalisms, namely that they are both cases of constrained optimisation, is easily perceived when thermodynamics is looked upon using the Tisza-Callen axiomatisation. In this paper, we take the formal analogy between equilibrium thermodynamics and economic systems far enough to answer the formal criticisms, proving that the formalism of neoclassical economics has irreversibility embedded in it. However, the formal similarity between equilibrium thermodynamics and neoclassical microeconomics does not mean that economic models are in accordance with mass, energy and entropy balance equations. In fact, neoclassical theory suffers from flaws in the substantive integration with thermodynamic laws as has already been fully demonstrated by valuable work done by ecological economists in this field. (author)
Relationship between Mathematics Anxiety and Mathematics ...
African Journals Online (AJOL)
Relationship between Mathematics Anxiety and Mathematics Achievement of Junior Secondary School Students in Maiduguri Metropolis, Borno State, Nigeria. ... Journal of Educational Foundations ... Fear of failure in mathematics test and examination was the main reason why students were anxious of mathematics.
The discursive production of classroom mathematics
Smith, Kim; Hodson, Elaine; Brown, Tony
2013-09-01
School mathematics is a function of its discursive environment where the language being used formats mathematical activity. The paper explores this theme through an extended example in which the conduct of mathematical teaching and learning is restricted by regulative educational policies. It considers how mathematics is discursively produced by student teachers within an employment-based model of teacher education in England where there is a low university input. It is argued that teacher reflections on mathematical learning and teaching within the course are patterned discursively in line with formal curriculum framings, assessment requirements and the local demands of their placement school. Both teachers and students are subject to regulative discourses that shape their actions and as a consequence this regulation influences the forms of mathematical activity that can take place. It is shown how university sessions can provide a limited critical platform from which to interrogate these restrictions and renegotiate them.
Weber, Doug; Jamsek, Damir
1994-01-01
The goal of this task was to investigate how formal methods could be incorporated into a software engineering process for flight-control systems under DO-178B and to demonstrate that process by developing a formal specification for NASA's Guidance and Controls Software (GCS) Experiment. GCS is software to control the descent of a spacecraft onto a planet's surface. The GCS example is simplified from a real example spacecraft, but exhibits the characteristics of realistic spacecraft control software. The formal specification is written in Larch.
First formal ITER negotiations make excellent progress
International Nuclear Information System (INIS)
Barnard, P.
2001-01-01
November 8 and 9 2001 marked the historic beginning of formal negotiations meetings on the ITER project. Delegations from Canada, the European Union, Japan and the Russian Federation met in Toronto, Canada, for the first in a series of Negotiations that is expected to lead, by the end of 2002, to an agreement on the joint implementation of ITER. This agreement will govern, under international law, the construction, operation and decommissioning of ITER. The Negotiations concluded by issuing a joint news release, reflecting a commitment to share the progress reports on the efforts to implement ITER
Entropy Current Formalism for Supersymmetric Theories
Andrianopoli, L; Grassi, P A; Trigiante, M
2015-01-01
The recent developments in fluid/gravity correspondence give a new impulse to the study of fluid dynamics of supersymmetric theories. In that respect, the entropy current formalism requires some modifications in order to be adapted to supersymmetric theories and supergravities. We formulate a new entropy current in superspace with the properties: 1) it is conserved off-shell for non dissipative fluids, 2) it is invariant under rigid supersymmetry transformations 3) it is covariantly closed in local supersymmetric theories 4) it reduces to its bosonic expression on space-time.
Formalized Search Strategies for Human Risk Contributions
DEFF Research Database (Denmark)
Rasmussen, Jens; Pedersen, O. M.
and documentation of the PRA coverage, including the search strategies applied, is discussed and aids are proposed such as plant description in terms of a formal abstraction hierarchy and use of cause-consequence-charts for the documentation of not only the results of PRA but also of its coverage. Typical human...... risk contributions are described on the basis of general plant design features relevant for risk and accident analysis. With this background, search strategies for human risk contributions are treated: Under the designation "work analysis", procedures for the analysis of familiar, well trained, planned...
The mathematics behind PageRank algorithm
Spačal, Gregor
2016-01-01
PageRank is Google's algorithm for ranking web pages by relevance. Pages can then be hierarchically sorted in order to provide better search results. The MSc thesis considers functioning, relevance, general properties of web search and its weaknesses before the appearance of Google. One of the most important questions is, if we can formally explain the mathematics behind PageRank algorithm and what mathematical knowledge is necessary. Finally, we present an example of its implementation i...
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. ...
African Journals Online (AJOL)
The language barrier education in Africa: The challenge of learning and teaching mathematics in a second language · EMAIL FULL TEXT EMAIL FULL TEXT DOWNLOAD FULL TEXT DOWNLOAD FULL TEXT. J Ibe, K Ekpo, O Akpan, UE Uyoata ...
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.
2016-01-01
This book provides a thorough introduction to the challenge of applying mathematics in real-world scenarios. Modelling tasks rarely involve well-defined categories, and they often require multidisciplinary input from mathematics, physics, computer sciences, or engineering. In keeping with this spirit of modelling, the book includes a wealth of cross-references between the chapters and frequently points to the real-world context. The book combines classical approaches to modelling with novel areas such as soft computing methods, inverse problems, and model uncertainty. Attention is also paid to the interaction between models, data and the use of mathematical software. The reader will find a broad selection of theoretical tools for practicing industrial mathematics, including the analysis of continuum models, probabilistic and discrete phenomena, and asymptotic and sensitivity analysis.
Hougardy, Stefan
2016-01-01
Algorithms play an increasingly important role in nearly all fields of mathematics. This book allows readers to develop basic mathematical abilities, in particular those concerning the design and analysis of algorithms as well as their implementation. It presents not only fundamental algorithms like the sieve of Eratosthenes, the Euclidean algorithm, sorting algorithms, algorithms on graphs, and Gaussian elimination, but also discusses elementary data structures, basic graph theory, and numerical questions. In addition, it provides an introduction to programming and demonstrates in detail how to implement algorithms in C++. This textbook is suitable for students who are new to the subject and covers a basic mathematical lecture course, complementing traditional courses on analysis and linear algebra. Both authors have given this "Algorithmic Mathematics" course at the University of Bonn several times in recent years.
DEFF Research Database (Denmark)
Sørensen, John Aasted
2010-01-01
The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18...
DEFF Research Database (Denmark)
Sørensen, John Aasted
2010-01-01
The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15...
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
Pestman, Wiebe R
2009-01-01
This textbook provides a broad and solid introduction to mathematical statistics, including the classical subjects hypothesis testing, normal regression analysis, and normal analysis of variance. In addition, non-parametric statistics and vectorial statistics are considered, as well as applications of stochastic analysis in modern statistics, e.g., Kolmogorov-Smirnov testing, smoothing techniques, robustness and density estimation. For students with some elementary mathematical background. With many exercises. Prerequisites from measure theory and linear algebra are presented.
The motivation of lifelong mathematics learning
Hashim Ali, Siti Aishah
2013-04-01
As adults, we have always learned throughout our life, but this learning is informal. Now, more career-switchers and career-upgraders who are joining universities for further training are becoming the major group of adult learners. This current situation requires formal education in courses with controlled output. Hence, lifelong learning is seen as a necessity and an opportunity for these adult learners. One characteristic of adult education is that the learners tend to bring with them life experience from their past, especially when learning mathematics. Most of them associate mathematics with the school subjects and unable to recognize the mathematics in their daily practice as mathematics. They normally place a high value on learning mathematics because of its prominent role in their prospective careers, but their learning often requires overcoming personal experience and motivating themselves to learn mathematics again. This paper reports on the study conducted on a group of adult learners currently pursuing their study. The aim of this study is to explore (i) the motivation of the adult learners continuing their study; and (ii) the perception and motivation of these learners in learning mathematics. This paper will take this into account when we discuss learners' perception and motivation to learning mathematics, as interrelated phenomena. Finding from this study will provide helpful insights in understanding the learning process and adaption of adult learners to formal education.
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
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.
Formal languages, automata and numeration systems introduction to combinatorics on words
Rigo, Michel
2014-01-01
Formal Languages, Automaton and Numeration Systems presents readers with a review of research related to formal language theory, combinatorics on words or numeration systems, such as Words, DLT (Developments in Language Theory), ICALP, MFCS (Mathematical Foundation of Computer Science), Mons Theoretical Computer Science Days, Numeration, CANT (Combinatorics, Automata and Number Theory). Combinatorics on words deals with problems that can be stated in a non-commutative monoid, such as subword complexity of finite or infinite words, construction and properties of infinite words, unavoidabl
Formal Description of Hybrid Systems
DEFF Research Database (Denmark)
Zhou, Chaochen; Ji, Wang; Ravn, Anders P.
1996-01-01
A language to describe hybrid systems, i.e. networks of communicating discrete and continuous processes, is proposed. A semantics of the language is given in Extended Duration Calculus, a real-time interval logic with a proof system that allows reasoning in mathematical analysis about continuous...
Polynomials formalism of quantum numbers
International Nuclear Information System (INIS)
Kazakov, K.V.
2005-01-01
Theoretical aspects of the recently suggested perturbation formalism based on the method of quantum number polynomials are considered in the context of the general anharmonicity problem. Using a biatomic molecule by way of example, it is demonstrated how the theory can be extrapolated to the case of vibrational-rotational interactions. As a result, an exact expression for the first coefficient of the Herman-Wallis factor is derived. In addition, the basic notions of the formalism are phenomenologically generalized and expanded to the problem of spin interaction. The concept of magneto-optical anharmonicity is introduced. As a consequence, an exact analogy is drawn with the well-known electro-optical theory of molecules, and a nonlinear dependence of the magnetic dipole moment of the system on the spin and wave variables is established [ru
Contextual approach to quantum formalism
Khrennikov, Andrei
2009-01-01
The aim of this book is to show that the probabilistic formalisms of classical statistical mechanics and quantum mechanics can be unified on the basis of a general contextual probabilistic model. By taking into account the dependence of (classical) probabilities on contexts (i.e. complexes of physical conditions), one can reproduce all distinct features of quantum probabilities such as the interference of probabilities and the violation of Bell’s inequality. Moreover, by starting with a formula for the interference of probabilities (which generalizes the well known classical formula of total probability), one can construct the representation of contextual probabilities by complex probability amplitudes or, in the abstract formalism, by normalized vectors of the complex Hilbert space or its hyperbolic generalization. Thus the Hilbert space representation of probabilities can be naturally derived from classical probabilistic assumptions. An important chapter of the book critically reviews known no-go theorems...
Musical Formalism and Political Performances
Directory of Open Access Journals (Sweden)
Jonathan A. Neufeld
2009-01-01
Full Text Available Musical formalism, which strictly limits the type of thing any description of the music can tell us, is ill-equipped to account for contemporary performance practice. If performative interpretations are in a position to tell us something about musical works—that is if performance is a kind of description, as Peter Kivy argues—then we have to loosen the restrictions on notions of musical relevance to make sense of performance. I argue that musical formalism, which strictly limits the type of thing any description of the music can tell us, is inconsistent with Kivy's quite compelling account of performance. This shows the difficulty that actual performances pose to overly rigid conceptions of music. Daniel Barenboim's unannounced performance of Wagner in Israel in 2001 shows that the problem of the boundaries of musical relevance is no mere philosophical puzzle. It is a pressing problem in the musical public sphere.
Informal work and formal plans
DEFF Research Database (Denmark)
Dalsted, Rikke Juul; Hølge-Hazelton, Bibi; Kousgaard, Marius Brostrøm
2012-01-01
trajectories. METHODS AND THEORY: An in-depth case study of patient trajectories at a Danish hospital and surrounding municipality using individual interviews with patients. Theory about trajectory and work by Strauss was included. RESULTS: Patients continuously took initiatives to organize their treatment...... and care. They initiated processes in the trajectories, and acquired information, which they used to form their trajectories. Patients presented problems to the healthcare professionals in order to get proper help when needed. DISCUSSION: Work done by patients was invisible and not perceived as work....... The patients' requests were not sufficiently supported in the professional organisation of work or formal planning. Patients' insertion and use of information in their trajectories challenged professional views and working processes. And the design of the formal pathway models limits the patients' active...
Formalization of processes in the land relations of Ukraine
Directory of Open Access Journals (Sweden)
K.О. Meteshkin
2017-12-01
Full Text Available The work listed a number of problematic tasks in the sphere of land relations of Ukraine, among which: weak communications between laws, inconsistency interpretations laws and insufficient use of modern information technologies. The relevance of the work is the need to solve problem tasks land relations in Ukraine and absence, proposed in the work, mathematical apparatus for solving these tasks. Analyzed work of scientists, who work in the sphere of land relations and who work in the sphere of formalize of rights. The proposed decision of actual tasks with help create mathematical ensuring for develop decision support system in land relations. The basis of this mathematical ensuring constitute methods of category theory, which provide the formalization of complex tasks. Based on methods of category theory models of land relations are constructed using data Land code of Ukraine. They will become an element of ontology land relations, which will be the structural parts of the knowledge base decision support system in the land management of Ukraine. It should also be noted, what similar models can be used in other subject areas.
DEFF Research Database (Denmark)
Villesèche, Florence; Josserand, Emmanuel
2017-01-01
/organisations and the wider social group of women in business. Research limitations/implications: The authors focus on the distinction between external and internal formal women-only networks while also acknowledging the broader diversity that can characterise such networks. Their review provides the reader with an insight...... member level, the authors suggest that such networks can be of value for organisations and the wider social group of women in management and leadership positions....
Variational formalism for spin particles
International Nuclear Information System (INIS)
Horvathy, P.
1977-11-01
The geometrical formulation of Hamilton's principle presented in a previous paper has been related to the usual one in terms of Lagrangian functions. The exact conditions for their equivalence are obtained and a method is given for the construction of a Lagrangian function. The formalism is extended to spin particles and a local Lagrangian is constructed in this case, too. However, this function cannot be extended to a global one. (D.P.)
Ashtekar formalism with real variables
International Nuclear Information System (INIS)
Kalau, W.; Nationaal Inst. voor Kernfysica en Hoge-Energiefysica
1990-12-01
A new approach to canonical gravity is presented which is based on the Ashtekar formalism. But, in contrast to Ashtekar's variables, this formulation does not need complex quantities nor does it lead to second class constraints. This is achieved using SO(3,1) as a gauge group instead of complexified SO(3). Because of the larger group additional first class constraints are needed which turn out to be cubic and quartic in the momenta. (author). 13 refs
Quantum mechanics formalism for biological evolution
International Nuclear Information System (INIS)
Bianconi, Ginestra; Rahmede, Christoph
2012-01-01
Highlights: ► Biological evolution is an off-equilibrium process described by path integrals over phylogenies. ► The phylogenies are sums of linear lineages for asexual populations. ► For sexual populations, each lineage is a tree and the path integral is given by a sum over these trees. ► Quantum statistics describe the stationary state of biological populations in simple cases. - Abstract: We study the evolution of sexual and asexual populations in fitness landscapes compatible with epistatic interactions. We find intriguing relations between the mathematics of biological evolution and quantum mechanics formalism. We give the general structure of the evolution of sexual and asexual populations which is in general an off-equilibrium process that can be expressed by path integrals over phylogenies. These phylogenies are the sum of linear lineages for asexual populations. For sexual populations, instead, each lineage is a tree of branching ratio two and the path integral describing the evolving population is given by a sum over these trees. Finally we show that the Bose–Einstein and the Fermi–Dirac distributions describe the stationary state of biological populations in simple cases.
Formal and Substantial Irregularity of Procedural Acts in French Law
Directory of Open Access Journals (Sweden)
Hassan Mohseni
2015-12-01
Full Text Available Procedural acts may be invalid because of Formal or Substantial Irregularity. In French Procedural Law we can see a distinction between Invalidity of Instruments owning to Formal Irregularity and Invalidity of Documents by Reason of Essential Defect; a distinction that effects on nature and its plea time and subsequent regularization of document. Formal invalidity must be expressly provided for in Law, except where it is a case of a failure to comply with an important formality or one of public policy but Plea of invalidity based on failure to comply with substantive rules relating to written pleadings shall be admissible without the party raising them having to prove any prejudice to him even where the invalidity does not arise under express provisions.
Understanding visualization: a formal approach using category theory and semiotics.
Vickers, Paul; Faith, Joe; Rossiter, Nick
2013-06-01
This paper combines the vocabulary of semiotics and category theory to provide a formal analysis of visualization. It shows how familiar processes of visualization fit the semiotic frameworks of both Saussure and Peirce, and extends these structures using the tools of category theory to provide a general framework for understanding visualization in practice, including: Relationships between systems, data collected from those systems, renderings of those data in the form of representations, the reading of those representations to create visualizations, and the use of those visualizations to create knowledge and understanding of the system under inspection. The resulting framework is validated by demonstrating how familiar information visualization concepts (such as literalness, sensitivity, redundancy, ambiguity, generalizability, and chart junk) arise naturally from it and can be defined formally and precisely. This paper generalizes previous work on the formal characterization of visualization by, inter alia, Ziemkiewicz and Kosara and allows us to formally distinguish properties of the visualization process that previous work does not.
Jost, Jürgen
2015-01-01
The main intention of this book is to describe and develop the conceptual, structural and abstract thinking of mathematics. Specific mathematical structures are used to illustrate the conceptual approach; providing a deeper insight into mutual relationships and abstract common features. These ideas are carefully motivated, explained and illustrated by examples so that many of the more technical proofs can be omitted. The book can therefore be used: · simply as an overview of the panorama of mathematical structures and the relations between them, to be supplemented by more detailed texts whenever you want to acquire a working knowledge of some structure · by itself as a first introduction to abstract mathematics · together with existing textbooks, to put their results into a more general perspective · to gain a new and hopefully deeper perspective after having studied such textbooks Mathematical Concepts has a broader scope and is less detaile...
Industrial applications of formal methods to model, design and analyze computer systems
Craigen, Dan
1995-01-01
Formal methods are mathematically-based techniques, often supported by reasoning tools, that can offer a rigorous and effective way to model, design and analyze computer systems. The purpose of this study is to evaluate international industrial experience in using formal methods. The cases selected are representative of industrial-grade projects and span a variety of application domains. The study had three main objectives: · To better inform deliberations within industry and government on standards and regulations; · To provide an authoritative record on the practical experience of formal m
Directory of Open Access Journals (Sweden)
I E. Lobanov
2017-01-01
Full Text Available Objectives. The aim of present work was to carry out mathematical modelling of heat transfer with symmetrical heating in flat channels and round pipes with rough walls.Methods. The calculation was carried out using the L'Hôpital-Bernoulli's method. The solution of the problem of intensified heat transfer in a round tube with rough walls was obtained using the Lyon's integral.Results. Different from existing theories, a methodology of theoretical computational heat transfer determination for flat rough channels and round pipes with rough walls is developed on the basis of the principle of full viscosity superposition in a turbulent boundary layer. The analysis of the calculated heat transfer and hydroresistivity values for flat rough channels and round rough pipes shows that the increase in heat transfer is always less than the corresponding increase in hydraulic resistance, which is a disadvantage as compared to channels with turbulators, with all else being equal. The results of calculating the heat transfer for channels with rough walls in an extended range of determinant parameters, which differ significantly from the corresponding data for the channels with turbulators, determine the level of heat exchange intensification.Conclusion. An increase in the calculated values of the relative average heat transfer Nu/NuGL for flat rough channels and rough pipes with very high values of the relative roughness is significantly contributed by both an increase in the relative roughness height and an increase in the Reynolds number Re. In comparison with empirical dependencies, the main advantage of solutions for averaged heat transfer in rough flat channels and round pipes under symmetrical thermal load obtained according to the developed theory is that they allow the calculation of heat exchange in rough pipes to be made in the case of large and very large relative heights of roughness protrusions, including large Reynolds numbers, typical for pipes
Shahzadi, Iqra; Sadaf, Hina; Nadeem, Sohail; Saleem, Anber
2017-02-01
The main objective of this paper is to study the Bio-mathematical analysis for the peristaltic flow of single wall carbon nanotubes under the impact of variable viscosity and wall properties. The right and the left walls of the curved channel possess sinusoidal wave that is travelling along the outer boundary. The features of the peristaltic motion are determined by using long wavelength and low Reynolds number approximation. Exact solutions are determined for the axial velocity and for the temperature profile. Graphical results have been presented for velocity profile, temperature and stream function for various physical parameters of interest. Symmetry of the curved channel is disturbed for smaller values of the curvature parameter. It is found that the altitude of the velocity profile increases for larger values of variable viscosity parameter for both the cases (pure blood as well as single wall carbon nanotubes). It is detected that velocity profile increases with increasing values of rigidity parameter. It is due to the fact that an increase in rigidity parameter decreases tension in the walls of the blood vessels which speeds up the blood flow for pure blood as well as single wall carbon nanotubes. Increase in Grashof number decreases the fluid velocity. This is due to the reason that viscous forces play a prominent role that's why increase in Grashof number decreases the velocity profile. It is also found that temperature drops for increasing values of nanoparticle volume fraction. Basically, higher thermal conductivity of the nanoparticles plays a key role for quick heat dissipation, and this justifies the use of the single wall carbon nanotubes in different situations as a coolant. Exact solutions are calculated for the temperature and the velocity profile. Symmetry of the curved channel is destroyed due to the curvedness for velocity, temperature and contour plots. Addition of single wall carbon nanotubes shows a decrease in fluid temperature. Trapping
Introduction to the foundations of mathematics
Wilder, Raymond L
2012-01-01
This classic undergraduate text by an eminent educator acquaints students with the fundamental concepts and methods of mathematics. In addition to introducing many noteworthy historical figures from the eighteenth through the mid-twentieth centuries, the book examines the axiomatic method, set theory, infinite sets, the linear continuum and the real number system, and groups. Additional topics include the Frege-Russell thesis, intuitionism, formal systems, mathematical logic, and the cultural setting of mathematics. Students and teachers will find that this elegant treatment covers a vast amou
Unity and disunity and other mathematical essays
Davis, Philip J
2015-01-01
This book is a mathematical potpourri. Its material originated in classroom presentations, formal lectures, sections of earlier books, book reviews, or just things written by the author for his own pleasure. Written in a nontechnical fashion, this book expresses the unique vision and attitude of the author towards the role of mathematics in society. It contains observations or incidental remarks on mathematics, its nature, its impacts on education and science and technology, its personalities and philosophies. The book is directed towards the math buffs of the world and, more generally, toward
Computers as medium for mathematical writing
DEFF Research Database (Denmark)
Misfeldt, Morten
2011-01-01
The production of mathematical formalism on state of the art computers is quite different than by pen and paper. In this paper I examine the question of how different media influence the writing of mathematical signs. The examination is based on an investigation of professional mathematicians' use...... of various media for their writing. A model for describing mathematical writing through turntakings is proposed. The model is applied to the ways mathematicians use computers for writing, and especially it is used to understand how interaction with the computer system LaTeX is different in the case...
Does Writing Have Any Effect on Mathematics Success?
Dündar, Sefa
2016-01-01
In this study, the relationship between mathematics success and the formal properties and contents of the notebooks in which students take notes during mathematics classes have been examined. The exploratory model, in which quantitative and qualitative data are used together, has been used in this study. This study consists of 176 students from 3…
Conditional Inference and Advanced Mathematical Study: Further Evidence
Inglis, Matthew; Simpson, Adrian
2009-01-01
In this paper, we examine the support given for the "theory of formal discipline" by Inglis and Simpson (Educational Studies Mathematics 67:187-204, "2008"). This theory, which is widely accepted by mathematicians and curriculum bodies, suggests that the study of advanced mathematics develops general thinking skills and, in particular, conditional…
The Framing Discussion: Connecting Student Experience with Mathematical Knowledge
Henning, John E.; Balong, Megan
2011-01-01
This article introduces the framing discussion, an informal discussion of a mathematical problem that takes place at the beginning of a lesson or unit. The purpose of the framing discussion is to assess student knowledge, motivate student interest, and to serve as a basis for guiding students to more formal mathematical knowledge. The article…
Formal Development and Verification of Railway Control Systems
DEFF Research Database (Denmark)
Vu Hong, Linh; Haxthausen, Anne Elisabeth; Peleska, Jan
standards [2] for railways to use formal (i.e. mathematical) logic and models for the unambiguous description of requirements and designs as well as for exhaustive verification as they give a higher assurance of safety compared to conventional methods. The use of domain-specific methods is another trend...... can be combined and used for an efficient development and verification of new fail-safe systems. The expected result is a methodology for using domain-specific, formal languages, techniques and tools for more efficient development and verification of robust software for railway control systems......This paper presents work package WP4.1 of the RobustRails research project. The work package aims at suggesting a methodology for efficient development and verification of safe and robust railway control systems. 1 Project background and state of the art Over the next 10 years all Danish railway...
Cahill, Kevin
2013-01-01
Unique in its clarity, examples and range, Physical Mathematics explains as simply as possible the mathematics that graduate students and professional physicists need in their courses and research. The author illustrates the mathematics with numerous physical examples drawn from contemporary research. In addition to basic subjects such as linear algebra, Fourier analysis, complex variables, differential equations and Bessel functions, this textbook covers topics such as the singular-value decomposition, Lie algebras, the tensors and forms of general relativity, the central limit theorem and Kolmogorov test of statistics, the Monte Carlo methods of experimental and theoretical physics, the renormalization group of condensed-matter physics and the functional derivatives and Feynman path integrals of quantum field theory.
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...
Hiriart-Urruty, Jean-Baptiste
This book contains a collection of exercises (called “tapas”) at undergraduate level, mainly from the fields of real analysis, calculus, matrices, convexity, and optimization. Most of the problems presented here are non-standard and some require broad knowledge of different mathematical subjects in order to be solved. The author provides some hints and (partial) answers and also puts these carefully chosen exercises into context, presents information on their origins, and comments on possible extensions. With stars marking the levels of difficulty, these tapas show or prove something interesting, challenge the reader to solve and learn, and may have surprising results. This first volume of Mathematical Tapas will appeal to mathematicians, motivated undergraduate students from science-based areas, and those generally interested in mathematics.
Rubin, Andrew
2014-01-01
This book presents concise descriptions and analysis of the classical and modern models used in mathematical biophysics. The authors ask the question "what new information can be provided by the models that cannot be obtained directly from experimental data?" Actively developing fields such as regulatory mechanisms in cells and subcellular systems and electron transport and energy transport in membranes are addressed together with more classical topics such as metabolic processes, nerve conduction and heart activity, chemical kinetics, population dynamics, and photosynthesis. The main approach is to describe biological processes using different mathematical approaches necessary to reveal characteristic features and properties of simulated systems. With the emergence of powerful mathematics software packages such as MAPLE, Mathematica, Mathcad, and MatLab, these methodologies are now accessible to a wide audience. Provides succinct but authoritative coverage of a broad array of biophysical topics and models Wr...
Formalized search strategies for human risk contributions
International Nuclear Information System (INIS)
Rasmussen, J.; Pedersen, O.M.
1982-07-01
For risk management, the results of a probabilistic risk analysis (PRA) as well as the underlying assumptions can be used as references in a closed-loop risk control; and the analyses of operational experiences as a means of feedback. In this context, the need for explicit definition and documentation of the PRA coverage, including the search strategies applied, is discussed and aids are proposed such as plant description in terms of a formal abstraction hierarchy and use of cause-consequence-charts for the documentation of not only the results of PRA but also of its coverage. Typical human risk contributions are described on the basis of general plant design features relevant for risk and accident analysis. With this background, search strategies for human risk contributions are treated: Under the designation ''work analysis'', procedures for the analysis of familiar, well trained, planned tasks are proposed. Strategies for identifying human risk contributions outside this category are outlined. (author)
Concepts of modern mathematics
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
Insights into teaching mathematics
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
Applied mathematics made simple
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
Mathematical Building-Blocks in Engineering Mechanics
Boyajian, David M.
2007-01-01
A gamut of mathematical subjects and concepts are taught within a handful of courses formally required of the typical engineering student who so often questions the relevancy of being bound to certain lower-division prerequisites. Basic classes at the undergraduate level, in this context, include: Integral and Differential Calculus, Differential…
Foundation and Mathematical Uses of Higher Types
DEFF Research Database (Denmark)
Kohlenbach, Ulrich
2002-01-01
This paper addresses `1),' to which S. Feferman has contributed so profoundly. We study mathematical strong, but nevertheless PRA-reducible, systems in all finite types, emphasizing the need of third order variables already for a faithful formalization of continuous functions between Polish spaces...
Bartocci, Claudio; Guerraggio, Angelo; Lucchetti, Roberto; Williams, Kim
2011-01-01
Steps forward in mathematics often reverberate in other scientific disciplines, and give rise to innovative conceptual developments or find surprising technological applications. This volume brings to the forefront some of the proponents of the mathematics of the twentieth century, who have put at our disposal new and powerful instruments for investigating the reality around us. The portraits present people who have impressive charisma and wide-ranging cultural interests, who are passionate about defending the importance of their own research, are sensitive to beauty, and attentive to the soci
Green, George
2005-01-01
An almost entirely self-taught mathematical genius, George Green (1793 -1841) is best known for Green's theorem, which is used in almost all computer codes that solve partial differential equations. He also published influential essays, or papers, in the fields of hydrodynamics, electricity, and magnetism. This collection comprises his most significant works.The first paper, ""An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism,"" which is also the longest and perhaps the most Important, appeared In 1828. It introduced the term potential as desig
DEFF Research Database (Denmark)
Sørensen, John Aasted
2011-01-01
The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able....... Having completed this the student is able to carry out the following: Expressions and sets: Define a set; define a logic expression; negate a logic expression; combine logic expressions; construct a truth table for a logic expression; apply reduction rules for logic expressions. Apply these concepts...
Aubin, J.-P.
1983-01-01
Mathematics seems to be treated at IIASA as if it were some sort of shameful disease, carefully hidden away in departments labelled with trendy but unrevealing names. Any debate about the role of mathematics and mathematicians at IIASA appears fated to be confused by the introduction of many seemingly unrelated issues, by the fact that many of the protagonists have their own vested interests to protect, and by the fact--why not admit it--that there are many dark fears of the more "esoteric" s...
Simpson, Amber; Haltiwanger, Leigh
2017-01-01
This mixed methods study investigates the ways in which secondary mathematics prospective teachers acquire skills needed to attend to, interpret, and respond to students' mathematical thinking and the ways in which their perceived strengths and weaknesses influence their skills when this type of formalized training is not part of their program.…
FORMAL MODELS OF LANGUAGE SYSTEMS
Directory of Open Access Journals (Sweden)
G. Chetverikov
2009-01-01
Full Text Available The basic construction concepts of unifying two-digit and multi-valued means of processing symbolic data are considered. The present approach is based upon a single methodological and special purpose principle by applying the proposed methods of the intelligence theory for mathematical input/output data and their intermediate transformations by an appropriate AFP-structure of the third grade.
Formal Housing Sector Reform in Neoliberal Nigeria
Directory of Open Access Journals (Sweden)
Maren Mallo Daniel
2016-09-01
Full Text Available In the past two decades, Nigeria has deployed neoliberal principles in the provision of formal housing. This approach was adopted on the assumption that the implementation of enabling reforms would enhance the role of the private sector and equally promote the development of a formal housing system in Nigeria. This has not occurred; the neoliberal housing approach has brought fewer results than the reform promised. The study therefore aims to explore the agency and actions of Nigerian authorities in response to this neoliberal agenda. To achieve this aim, the following objectives are pursued: The first objective analyses why neoliberalism failed to effectively change the housing market in Nigeria; the second examines the impact of neoliberal restructuring process on housing provision in Nigeria; and the last analyses the success of legislative reform that were carried to support housing provision under Nigeria’s neoliberalism. To achieve these objectives, the paper adopts a documentary method and in accordance with this, a wide range of documentary evidence was collected for a content analysis. The findings of the analysis suggest that economic recession, political instability and changing ideological stances of successive governments affected the consistency of neoliberal reforms. Furthermore, the reforms implemented were seen to be progressive but the events occurred rather slowly, haphazardly and uncoordinated. A time lag is also observed in the reform processes and the sequence of events shows a lack of consideration of the interdependency of legislation and action. This policy review concludes that the neoliberal approach has the potential to improve the delivery of formal housing; however the authorities need to be consistent with the reforms while at the same time aligning legislation and action.
Principles of mathematical modeling
Dym, Clive
2004-01-01
Science and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and "own" the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation techniques. The second half demonstrates the latest applications for these tools to a broad variety of subjects, including exponential growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, an...
Measuring the effect of formalization
International Nuclear Information System (INIS)
Stoelen, K.; Mohn, P.
1998-01-01
We present an ongoing research activity concerned with measuring the effect of an increased level of formalization in software development. We summarize the experiences from a first experimental development. Based on these experiences, we discuss a number of technical issues; in particular, problems connected to metrics based on fault reports. First of all, what is a fault? Secondly, how should the fault counting be integrated in the development process? Thirdly, any reasonable definition of fault depends on a notion of satisfaction. Hence, we must address the question: What does it mean for a specification or an implementation to satisfy a requirement imposed by a more high-level specification? (author)
Directory of Open Access Journals (Sweden)
Carlos Coimbra-Araujo
2017-08-01
Full Text Available For several reasons, the Exact Sciences have been shown as one of the areas of scientific knowledge that most demand actions in non-formal spaces of education. One of the main reasons lies in the fact that Mathematics, Physics, Chemistry and Astronomy are traditionally addressed, within the school environment and in the formal curriculum, unrelated to the student reality. Such subjects are often seen as a set of inflexible and incomprehensible principles. In this aspect, the present work reviews the main problems surrounding the teaching of the mentioned scientific areas, highlighting non-formal tools for the teaching of Mathematics, Physics, Chemistry, Astronomy and, in particular, the modern virtual environments of teaching modeled by Computing Science. Other historical difficulties that the formal education of Exact Sciences has suffered in Brazil are also presented, as well some of the main non-formal resources sought to complement the curriculum that is usually presented in the classroom.
Talking about teaching and learning mathematics in indigenous schools
Directory of Open Access Journals (Sweden)
Lucélida de Fátima Maia da Costa
2012-09-01
Full Text Available To teach and to learn mathematics are not always conjugated concomitantly, particularly in the context of formal indigenous schools. This article puts in discussion some facts about the role of schools in indigenous communities, often mistakenly called Indian schools, as well as questions about the meaning of teaching mathematics in those contexts. Based on the concepts of ethnomathematics, it shows that a dialogue is possible between the traditional mathematical knowledge of various ethnic groups of the Amazon and the knowledge disseminated by formal school teaching practice.
Philosophy of mathematics set theory, measuring theories, and nominalism
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.
Fujita, Shinsaku
2015-01-01
Chirality and stereogenicity are closely related concepts and their differentiation and description is still a challenge in chemoinformatics. A new stereoisogram approach, developed by the author, is introduced in this book, providing a theoretical framework for mathematical aspects of modern stereochemistry. The discussion covers point-groups and permutation symmetry and exemplifies the concepts using organic molecules and inorganic complexes.
Weaver, Nik
2001-01-01
With a unique approach and presenting an array of new and intriguing topics, Mathematical Quantization offers a survey of operator algebras and related structures from the point of view that these objects are quantizations of classical mathematical structures. This approach makes possible, with minimal mathematical detail, a unified treatment of a variety of topics.Detailed here for the first time, the fundamental idea of mathematical quantization is that sets are replaced by Hilbert spaces. Building on this idea, and most importantly on the fact that scalar-valued functions on a set correspond to operators on a Hilbert space, one can determine quantum analogs of a variety of classical structures. In particular, because topologies and measure classes on a set can be treated in terms of scalar-valued functions, we can transfer these constructions to the quantum realm, giving rise to C*- and von Neumann algebras.In the first half of the book, the author quickly builds the operator algebra setting. He uses this ...
Kennard, Jackie
2007-01-01
One of the most interesting developments in teaching has been the growing importance of the outdoor environment. Whether it be playground, garden or field, the outdoors offers a range of challenging experiences, especially in the delivery of early mathematics. Oral feedback to parents, together with photographic displays, can show them that…
Kepner, Gordon R
2014-08-27
This study uses dimensional analysis to derive the general second-order differential equation that underlies numerous physical and natural phenomena described by common mathematical functions. It eschews assumptions about empirical constants and mechanisms. It relies only on the data plot's mathematical properties to provide the conditions and constraints needed to specify a second-order differential equation that is free of empirical constants for each phenomenon. A practical example of each function is analyzed using the general form of the underlying differential equation and the observable unique mathematical properties of each data plot, including boundary conditions. This yields a differential equation that describes the relationship among the physical variables governing the phenomenon's behavior. Complex phenomena such as the Standard Normal Distribution, the Logistic Growth Function, and Hill Ligand binding, which are characterized by data plots of distinctly different sigmoidal character, are readily analyzed by this approach. It provides an alternative, simple, unifying basis for analyzing each of these varied phenomena from a common perspective that ties them together and offers new insights into the appropriate empirical constants for describing each phenomenon.
A survey of formal languages for contracts
DEFF Research Database (Denmark)
Hvitved, Tom
2010-01-01
In this short paper we present the current status on formal languages and models for contracts. By a formal model is meant an unambiguous and rigorous representation of contracts, in order to enable their automatic validation, execution, and analysis — activates that are collectively referred...... to as contract lifecycle management (CLM). We present a set of formalism requirements, which represent features that any ideal contract model should support, based on which we present a comparative survey of existing contract formalisms....
2010-04-01
... 19 Customs Duties 1 2010-04-01 2010-04-01 false Formal entry. 4.9 Section 4.9 Customs Duties U.S... FOREIGN AND DOMESTIC TRADES Arrival and Entry of Vessels § 4.9 Formal entry. (a) General. Section 4.3 provides which vessels are subject to formal entry and where and when entry must be made. The formal entry...
Formalizing the concept phase of product development
Schuts, M.; Hooman, J.
2015-01-01
We discuss the use of formal techniques to improve the concept phase of product realisation. As an industrial application, a new concept of interventional X-ray systems has been formalized, using model checking techniques and the simulation of formal models. cop. Springer International Publishing
Formal Testing of Correspondence Carrying Software
Bujorianu, M.C.; Bujorianu, L.M.; Maharaj, S.
2008-01-01
Nowadays formal software development is characterised by use of multitude formal specification languages. Test case generation from formal specifications depends in general on a specific language, and, moreover, there are competing methods for each language. There is a need for a generic approach to
Computational experiment approach to advanced secondary mathematics curriculum
Abramovich, Sergei
2014-01-01
This book promotes the experimental mathematics approach in the context of secondary mathematics curriculum by exploring mathematical models depending on parameters that were typically considered advanced in the pre-digital education era. This approach, by drawing on the power of computers to perform numerical computations and graphical constructions, stimulates formal learning of mathematics through making sense of a computational experiment. It allows one (in the spirit of Freudenthal) to bridge serious mathematical content and contemporary teaching practice. In other words, the notion of teaching experiment can be extended to include a true mathematical experiment. When used appropriately, the approach creates conditions for collateral learning (in the spirit of Dewey) to occur including the development of skills important for engineering applications of mathematics. In the context of a mathematics teacher education program, this book addresses a call for the preparation of teachers capable of utilizing mo...
The language of mathematics telling mathematical tales
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.
New method of contour image processing based on the formalism of spiral light beams
Energy Technology Data Exchange (ETDEWEB)
Volostnikov, Vladimir G; Kishkin, S A; Kotova, S P [Samara Branch of the P.N. Lebedev Physical Institute, Russian Academy of Sciences, Samara (Russian Federation)
2013-07-31
The possibility of applying the mathematical formalism of spiral light beams to the problems of contour image recognition is theoretically studied. The advantages and disadvantages of the proposed approach are evaluated; the results of numerical modelling are presented. (optical image processing)
Weber, Keith
2009-01-01
This paper presents a case study of a highly successful student whose exploration of an advanced mathematical concept relies predominantly on syntactic reasoning, such as developing formal representations of mathematical ideas and making logical deductions. This student is observed as he learns a new mathematical concept and then completes…
Sierpinska, Anna
1994-01-01
The concept of understanding in mathematics with regard to mathematics education is considered in this volume, the main problem for mathematics teachers being how to facilitate their students'' understanding of the mathematics being taught.
Formal algorithmic elimination for PDEs
Robertz, Daniel
2014-01-01
Investigating the correspondence between systems of partial differential equations and their analytic solutions using a formal approach, this monograph presents algorithms to determine the set of analytic solutions of such a system and conversely to find differential equations whose set of solutions coincides with a given parametrized set of analytic functions. After giving a detailed introduction to Janet bases and Thomas decomposition, the problem of finding an implicit description of certain sets of analytic functions in terms of differential equations is addressed. Effective methods of varying generality are developed to solve the differential elimination problems that arise in this context. In particular, it is demonstrated how the symbolic solution of partial differential equations profits from the study of the implicitization problem. For instance, certain families of exact solutions of the Navier-Stokes equations can be computed.
International Nuclear Information System (INIS)
Nedelec, J.C.
1988-01-01
The 1988 progress report of the Applied Mathematics center (Polytechnic School, France), is presented. The research fields of the Center are the scientific calculus, the probabilities and statistics and the video image synthesis. The research topics developed are: the analysis of numerical methods, the mathematical analysis of the physics and mechanics fundamental models, the numerical solution of complex models related to the industrial problems, the stochastic calculus and the brownian movement, the stochastic partial differential equations, the identification of the adaptive filtering parameters, the discrete element systems, statistics, the stochastic control and the development, the image synthesis techniques for education and research programs. The published papers, the congress communications and the thesis are listed [fr
Driessche, Pauline; Wu, Jianhong
2008-01-01
Based on lecture notes of two summer schools with a mixed audience from mathematical sciences, epidemiology and public health, this volume offers a comprehensive introduction to basic ideas and techniques in modeling infectious diseases, for the comparison of strategies to plan for an anticipated epidemic or pandemic, and to deal with a disease outbreak in real time. It covers detailed case studies for diseases including pandemic influenza, West Nile virus, and childhood diseases. Models for other diseases including Severe Acute Respiratory Syndrome, fox rabies, and sexually transmitted infections are included as applications. Its chapters are coherent and complementary independent units. In order to accustom students to look at the current literature and to experience different perspectives, no attempt has been made to achieve united writing style or unified notation. Notes on some mathematical background (calculus, matrix algebra, differential equations, and probability) have been prepared and may be downlo...
Intuitions and Competence in Formal Semantics
Directory of Open Access Journals (Sweden)
Martin Stokhof
2010-12-01
Full Text Available In formal semantics intuition plays a key role, in two ways. Intuitions about semantic properties of expressions are the primary data, and intuitions of the semanticists are the main access to these data. The paper investigates how this dual role is related to the concept of competence and the role that this concept plays in semantics. And it inquires whether the self-reflexive role of intuitions has consequences for the methodology of semantics as an empirical discipline.ReferencesBaggio, Giosuè, van Lambalgen, Michiel & Hagoort, Peter. 2008. ‘Computing and recomputing discourse models: an ERP study of the semantics of temporal connectives’. Journal of Memory and Language 59, no. 1: 36–53.http://dx.doi.org/10.1016/j.jml.2008.02.005Chierchia, Gennaro & McConnell-Ginet, Sally. 2000. Meaning and Grammar. second ed. Cambridge, Mass.: MIT Press.Chomsky, Noam. 1965. Aspects of the Theory of Syntax. Cambridge, Mass.: MIT Press.Cresswell, Max J. 1978. ‘Semantic competence’. In F. Guenthner & M. Guenther-Reutter (eds. ‘Meaning and Translation’, 9–27. Duckworth, London. de Swart, Henriëtte. 1998. Introduction to Natural Language Semantics. Stanford: CSLI.Dowty, David, Wall, Robert & Peters, Stanley. 1981. Introduction to Montague Semantics. Dordrecht: Reidel.Heim, Irene & Kratzer, Angelika. 1998. Semantics in Generative Grammar. Oxford: Blackwell.Larson, Richard & Segal, Gabriel. 1995. Knowledge of Meaning. Cambridge, Mass.: MIT Press.Lewis, David K. 1975. ‘Languages and Language’. In Keith Gunderson (ed. ‘Language, Mind and Knowledge’, 3–35. Minneapolis: University of Minnesota Press.Montague, Richard. 1970. ‘Universal Grammar’. Theoria 36: 373–98.http://dx.doi.org/10.1111/j.1755-2567.1970.tb00434.xPartee, Barbara H. 1979. ‘Semantics – Mathematics or Psychology?’ In Rainer Bäuerle, Urs Egli & Arnim von Stechow (eds. ‘Semantics from Different Points of View’, 1–14. Berlin: Springer.Partee, Barbara H. 1980.
Formalization of the Integral Calculus in the PVS Theorem Prover
Directory of Open Access Journals (Sweden)
Ricky Wayne Butler
2009-04-01
Full Text Available The PVS Theorem prover is a widely used formal verification tool used for the analysis of safetycritical systems. The PVS prover, though fully equipped to support deduction in a very general logic framework, namely higher-order logic, it must nevertheless, be augmented with the definitions and associated theorems for every branch of mathematics and Computer Science that is used in a verification. This is a formidable task, ultimately requiring the contributions of researchers and developers all over the world. This paper reports on the formalization of the integral calculus in the PVS theorem prover. All of the basic definitions and theorems covered in a first course on integral calculus have been completed.The theory and proofs were based on Rosenlicht’s classic text on real analysis and follow the traditional epsilon-delta method. The goal of this work was to provide a practical set of PVS theories that could be used for verification of hybrid systems that arise in air traffic management systems and other aerospace applications. All of the basic linearity, integrability, boundedness, and continuity properties of the integral calculus were proved. The work culminated in the proof of the Fundamental Theorem Of Calculus. There is a brief discussion about why mechanically checked proofs are so much longer than standard mathematics textbook proofs.
Dilemma in Teaching Mathematics
Md Kamaruddin, Nafisah Kamariah; Md Amin, Zulkarnain
2012-01-01
The challenge in mathematics education is finding the best way to teach mathematics. When students learn the reasoning and proving in mathematics, they will be proficient in mathematics. Students must know mathematics before they can apply it. Symbolism and logic is the key to both the learning of mathematics and its effective application to…
15 CFR 971.901 - Formal hearing procedures.
2010-01-01
... precedence over 15 CFR part 904, subpart C, to the extent there is a conflict. (2) Hearings held under this... held by order of the Administrator; (iii) The issues in dispute which are to be resolved in the formal... (3) Require at or prior to any hearing, the submission and exchange of evidence. (e) Argument. At the...
Framing the Adoption of Serious Games in Formal Education
Arnab, Sylvester; Berta, Riccardo; Earp, Jeffrey; de Freitas, Sara; Popescu, Maria; Romero, Margarida; Stanescu, Ioana; Usart, Mireia
2012-01-01
Nowadays formal education systems are under increasing pressure to respond and adapt to rapid technological innovation and associated changes in the way we work and live. As well as accommodation of technology in its ever-diversifying forms, there is a fundamental need to enhance learning processes through evolution in pedagogical approaches, so…
Lectures on formally real fields
Prestel, Alexander
1984-01-01
Absolute values and their completions - like the p-adic number fields- play an important role in number theory. Krull's generalization of absolute values to valuations made applications in other branches of mathematics, such as algebraic geometry, possible. In valuation theory, the notion of a completion has to be replaced by that of the so-called Henselization. In this book, the theory of valuations as well as of Henselizations is developed. The presentation is based on the knowledge aquired in a standard graduate course in algebra. The last chapter presents three applications of the general theory -as to Artin's Conjecture on the p-adic number fields- that could not be obtained by the use of absolute values only.
Mathematical sense-making in quantum mechanics: An initial peek
Dreyfus, Benjamin W.; Elby, Andrew; Gupta, Ayush; Sohr, Erin Ronayne
2017-12-01
Mathematical sense-making—looking for coherence between the structure of the mathematical formalism and causal or functional relations in the world—is a core component of physics expertise. Some physics education research studies have explored what mathematical sense-making looks like at the introductory physics level, while some historians and "science studies" have explored how expert physicists engage in it. What is largely missing, with a few exceptions, is theoretical and empirical work at the intermediate level—upper division physics students—especially when they are learning difficult new mathematical formalism. In this paper, we present analysis of a segment of video-recorded discussion between two students grappling with a quantum mechanics question to illustrate what mathematical sense-making can look like in quantum mechanics. We claim that mathematical sense-making is possible and productive for learning and problem solving in quantum mechanics. Mathematical sense-making in quantum mechanics is continuous in many ways with mathematical sense-making in introductory physics. However, in the context of quantum mechanics, the connections between formalism, intuitive conceptual schema, and the physical world become more compound (nested) and indirect. We illustrate these similarities and differences in part by proposing a new symbolic form, eigenvector eigenvalue, which is composed of multiple primitive symbolic forms.
Doing Mathematics with Purpose: Mathematical Text Types
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'…
Teachers' Mathematics as Mathematics-at-Work
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…
Teaching Mathematical Modeling in Mathematics Education
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…
Freedom and enforcement in action a study in formal action theory
Czelakowski, Janusz
2015-01-01
Action theory is the object of growing attention in a variety of scientific disciplines, and this is the first volume to offer a synthetic view of the range of approaches possible in the topic. The volume focuses on the nexus of formal action theory with a startlingly diverse set of subjects, which range from logic, linguistics, artificial intelligence, and automata theory to jurisprudence, deontology, and economics. It covers semantic, mathematical and logical aspects of action, showing how the problem of action breaks the boundaries of traditional branches of logic located in syntactics and semantics and now lies on lies on the borderline between logical pragmatics and praxeology. The chapters here focus on specialized tasks in formal action theory, beginning with a thorough description and formalization of the language of action, and moving through material on the differing models of action theory to focus on probabilistic models, the relations of formal action theory to deontic logic, and its key appl...
Formal models of grammar: The Minimalist Program and constraint-based grammars – HPSG and LFG
Directory of Open Access Journals (Sweden)
Érica dos S. Rodrigues
2009-06-01
Full Text Available This paper aims at briefly presenting the main tendencies associated with the most productive formal models of grammar currently under scrutiny: the Minimalist Program, a recent version of generative linguistics; Lexical Functional Grammar; and Head- Driven Phrase Structure Grammar. A basic picture of the main concerns of these formal models of language emerges from the comparison and contrast between their main objectives, the formal mechanisms they adopt and the kind of research tendency each model represents.
Teaching Undergraduate Mathematics Using CAS Technology: Issues and Prospects
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…
Applications of the Decoherence Formalism
Brun, Todd Andrew
In this work the decoherence formalism of quantum mechanics is explored and applied to a number of interesting problems in quantum physics. The boundary between quantum and classical physics is examined, and demonstration made that quantum histories corresponding to classical equations of motion become more probable for a broad class of models, including linear and nonlinear models of Brownian motion. The link between noise, dissipation, and decoherence is studied. This work is then applied to systems which classically exhibit dissipative chaotic dynamics. A theory is explicated for treating these systems, and the ideas are applied to a particular model of the forced, damped Duffing oscillator, which is chaotic for certain parameter values. Differences between classical and quantum chaos are examined, particularly differences arising in the structure of fractal strange attractors, and the conceptual difficulties in framing standard notions of chaos in a quantum system. A brief discussion of previous work on quantum chaos is included, and the differences between Hamiltonian and dissipative chaos pointed out; a somewhat different interpretation of quantum chaos from the standard one is suggested. A class of histories for quantum systems, in phase space rather than configuration space, is studied. Different ways of representing projections in phase space are discussed, and expressions for the probability of phase space histories are derived; conditions for such histories to decohere are also estimated in the semiclassical limit.
A Formal Description of Problem Frames
Souleymane KOUSSOUBE; Roger NOUSSI; Balira O. KONFE
2014-01-01
Michael Jackson defines a Problem Frame as a mean to describe and classify software development problems. The initial description of problem Frames is essentially graphical. A weakness of this proposal is the lack of formal specification allowing efficient reasoning tools. This paper deals with Problem Frames’ formal specification with Description Logics. We first propose a formal terminology of Problem Frames leading to the specification of a Problem Frames’ TBOX and a specific problem’s ABO...
Survey of Existing Tools for Formal Verification.
Energy Technology Data Exchange (ETDEWEB)
Punnoose, Ratish J.; Armstrong, Robert C.; Wong, Matthew H.; Jackson, Mayo
2014-12-01
Formal methods have come into wide use because of their effectiveness in verifying "safety and security" requirements of digital systems; a set of requirements for which testing is mostly ineffective. Formal methods are routinely used in the design and verification of high-consequence digital systems in industry. This report outlines our work in assessing the capabilities of commercial and open source formal tools and the ways in which they can be leveraged in digital design workflows.
What Determines Firms’ Decisions to Formalize?
Neil McCulloch; Günther G. Schulze; Janina Voss
2010-01-01
In this paper we analyze the decision of small and micro firms to formalize, i.e. to obtain business and other licenses in rural Indonesia. We use the rural investment climate survey (RICS) that consists of non-farm rural enterprises, most of them microenterprises, and analyze the effect of formalization on tax payments, corruption, access to credit and revenue, taking into account the endogeneity of the formalization decision to such benefits and costs. We show, contrary to most of the liter...
Formal Semantics: Origins, Issues, Early Impact
Directory of Open Access Journals (Sweden)
Barbara H. Partee
2010-12-01
. J. Hintikka & P. Suppes (eds. ‘Approaches to Natural Language’, 221–242. Dordrecht: Reidel. Reprinted in Montague (1974, 247–270; Reprinted in Portner and Partee, eds., 2002, 17–34http://newstar.rinet.ru/~goga/biblio/essential-readings/01-Montague-The.Proper.Treatment.of.Quantification.in.OrdinarMontague, R. 1974. Formal Philosophy. Selected Papers of Richard Montague. New Haven/London: Yale University Press. Edited and with an introduction by Richmond H. Thomason. Newmeyer, F. J. 1980. Linguistic Theory in America: The First Quarter Century of Transformational Generative Grammar. New York: Academic Press.Parsons, T. 1968. ‘A semantics for English’. Ms.Parsons, T. 1972. ‘An Outline of a Semantics of English’. Ms. University of Massachusetts, Amherst.Partee, B. H. 1971. ‘On the requirement that transformations preserve meaning’. In C. J. Fillmore & D. T. Langendoen (eds. ‘Studies in Linguistic Semantics’, 1–21. Holt, Rinehart, and Winston.Partee, B. H. 1973a. ‘The semantics of belief-sentences’. In J. M. E. Moravcsik K. J. J. Hintikka & P. Suppes (eds. ‘Approaches to Natural Language’, 309–336. Dordrecht: Reidel.Partee, B. H. 1973b. ‘Some transformational extensions of Montague grammar’. Journal of Philosophical Logic 2: 509–534. Reprinted in Partee (1976, pp. 51–76.http://semanticsarchive.net/Archive/TEwODQ3Z/.Partee, B. H. 1973c. ‘Comments on Montague’s paper’. In J. M. E. Moravcsik K. J. J. Hintikka & P. Suppes (eds. ‘Approaches to Natural Language’, 243–258. Dordrecht: Reidel.Partee, B. H. 1975. ‘Montague grammar and transformational grammar’. Linguistic Inquiry 6: 203–300.Partee, B. H. (ed.. 1976. Montague Grammar. New York: Academic Press.Partee, B. H. 1979. ‘Semantics - mathematics or psychology?’ In R. Bäuerle, U. Egli & A. von Stechow (eds. ‘Semantics from Different Points of View’, 1–14. Berlin: Springer-Verlag.Partee, B. H. 1982. ‘Belief-sentences and the limits of semantics
DEFF Research Database (Denmark)
Mogensen, Arne; Georgiev, Vladimir; Ulovec, Andreas
To encourage many more young people to appreciate the real nature and spirit of mathematics and possibly to be enrolled in mathematics study it is important to involve them in doing mathematics (not just learning about mathematics). This goal could be achieved if mathematics teachers are prepared...... to identify and work with mathematically gifted students (without loosing the rest). The book offers chapters on gifted students, mathematical competences and other issues....
Directory of Open Access Journals (Sweden)
Michael Christie
Full Text Available Abstract Participation rates of women in Science, Technology, Engineering and Mathematics (STEM is comparatively low and their attrition rates high. An obvious solution is to attract more women to study such subjects. In 2016 the authors undertook research to find out why so few women enrolled in STEM subjects and investigate ways of increasing their recruitment and retention in this area. The informants in our study were enrolled in a tertiary preparation course as well as nursing and education programs. A critique of the literature was used to develop a survey that informed focus group and interview schedules which were used in collecting data. Our study found that many of the factors that hindered women from applying for STEM courses twenty years ago still apply today and recommends actions that can help increase recruitment of women into STEM and assist their retention and graduation in those areas of tertiary education.
Non-linear wave equations:Mathematical techniques
International Nuclear Information System (INIS)
1978-01-01
An account of certain well-established mathematical methods, which prove useful to deal with non-linear partial differential equations is presented. Within the strict framework of Functional Analysis, it describes Semigroup Techniques in Banach Spaces as well as variational approaches towards critical points. Detailed proofs are given of the existence of local and global solutions of the Cauchy problem and of the stability of stationary solutions. The formal approach based upon invariance under Lie transformations deserves attention due to its wide range of applicability, even if the explicit solutions thus obtained do not allow for a deep analysis of the equations. A compre ensive introduction to the inverse scattering approach and to the solution concept for certain non-linear equations of physical interest are also presented. A detailed discussion is made about certain convergence and stability problems which arise in importance need not be emphasized. (author) [es
Familial aggregation patterns in mathematical ability.
Wijsman, Ellen M; Robinson, Nancy M; Ainsworth, Kathryn H; Rosenthal, Elisabeth A; Holzman, Ted; Raskind, Wendy H
2004-01-01
Mathematical talent is an asset in modern society both at an individual and a societal level. Environmental factors such as quality of mathematics education undoubtedly affect an individual's performance, and there is some evidence that genetic factors also may play a role. The current study was performed to investigate the feasibility of undertaking genetics studies on mathematical ability. Because the etiology of low ability in mathematics is likely to be multifactorial and heterogeneous, we evaluated families ascertained through a proband with high mathematical performance in grade 7 on the SAT to eliminate, to some degree, adverse environmental factors. Families of sex-matched probands, selected for high verbal performance on the SAT, served as the comparison group. We evaluated a number of proxy measures for their usefulness in the study of clustering of mathematical talent. Given the difficulty of testing mathematics performance across developmental ages, especially with the added complexity of decreasing exposure to formal mathematics concepts post schooling, we also devised a semiquantitative scale that incorporated educational, occupational, and avocational information as a surrogate for an academic mathematics measure. Whereas several proxy measures showed no evidence of a genetic basis, we found that the semiquantitative scale of mathematical talent showed strong evidence of a genetic basis, with a differential response as a function of the performance measure used to select the proband. This observation suggests that there may be a genetic basis to specific mathematical talent, and that specific, as opposed to proxy, investigative measures that are designed to measure such talent in family members could be of benefit for this purpose.
Formal language constrained path problems
Energy Technology Data Exchange (ETDEWEB)
Barrett, C.; Jacob, R.; Marathe, M.
1997-07-08
In many path finding problems arising in practice, certain patterns of edge/vertex labels in the labeled graph being traversed are allowed/preferred, while others are disallowed. Motivated by such applications as intermodal transportation planning, the authors investigate the complexity of finding feasible paths in a labeled network, where the mode choice for each traveler is specified by a formal language. The main contributions of this paper include the following: (1) the authors show that the problem of finding a shortest path between a source and destination for a traveler whose mode choice is specified as a context free language is solvable efficiently in polynomial time, when the mode choice is specified as a regular language they provide algorithms with improved space and time bounds; (2) in contrast, they show that the problem of finding simple paths between a source and a given destination is NP-hard, even when restricted to very simple regular expressions and/or very simple graphs; (3) for the class of treewidth bounded graphs, they show that (i) the problem of finding a regular language constrained simple path between source and a destination is solvable in polynomial time and (ii) the extension to finding context free language constrained simple paths is NP-complete. Several extensions of these results are presented in the context of finding shortest paths with additional constraints. These results significantly extend the results in [MW95]. As a corollary of the results, they obtain a polynomial time algorithm for the BEST k-SIMILAR PATH problem studied in [SJB97]. The previous best algorithm was given by [SJB97] and takes exponential time in the worst case.
Skolem and pessimism about proof in mathematics.
Cohen, Paul J
2005-10-15
Attitudes towards formalization and proof have gone through large swings during the last 150 years. We sketch the development from Frege's first formalization, to the debates over intuitionism and other schools, through Hilbert's program and the decisive blow of the Gödel Incompleteness Theorem. A critical role is played by the Skolem-Lowenheim Theorem, which showed that no first-order axiom system can characterize a unique infinite model. Skolem himself regarded this as a body blow to the belief that mathematics can be reliably founded only on formal axiomatic systems. In a remarkably prescient paper, he even sketches the possibility of interesting new models for set theory itself, something later realized by the method of forcing. This is in contrast to Hilbert's belief that mathematics could resolve all its questions. We discuss the role of new axioms for set theory, questions in set theory itself, and their relevance for number theory. We then look in detail at what the methods of the predicate calculus, i.e. mathematical reasoning, really entail. The conclusion is that there is no reasonable basis for Hilbert's assumption. The vast majority of questions even in elementary number theory, of reasonable complexity, are beyond the reach of any such reasoning. Of course this cannot be proved and we present only plausibility arguments. The great success of mathematics comes from considering 'natural problems', those which are related to previous work and offer a good chance of being solved. The great glories of human reasoning, beginning with the Greek discovery of geometry, are in no way diminished by this pessimistic view. We end by wishing good health to present-day mathematics and the mathematics of many centuries to come.
Mathematics, the Computer, and the Impact on Mathematics Education.
Tooke, D. James
2001-01-01
Discusses the connection between mathematics and the computer; mathematics curriculum; mathematics instruction, including teachers learning to use computers; and the impact of the computer on learning mathematics. (LRW)
Formal representation of complex SNOMED CT expressions
Directory of Open Access Journals (Sweden)
Markó Kornél
2008-10-01
Full Text Available Abstract Background Definitory expressions about clinical procedures, findings and diseases constitute a major benefit of a formally founded clinical reference terminology which is ontologically sound and suited for formal reasoning. SNOMED CT claims to support formal reasoning by description-logic based concept definitions. Methods On the basis of formal ontology criteria we analyze complex SNOMED CT concepts, such as "Concussion of Brain with(out Loss of Consciousness", using alternatively full first order logics and the description logic ℰℒ MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaWenfgDOvwBHrxAJfwnHbqeg0uy0HwzTfgDPnwy1aaceaGae8hmHuKae8NeHWeaaa@37B1@. Results Typical complex SNOMED CT concepts, including negations or not, can be expressed in full first-order logics. Negations cannot be properly expressed in the description logic ℰℒ MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaWenfgDOvwBHrxAJfwnHbqeg0uy0HwzTfgDPnwy1aaceaGae8hmHuKae8NeHWeaaa@37B1@ underlying SNOMED CT. All concepts concepts the meaning of which implies a temporal scope may be subject to diverging interpretations, which are often unclear in SNOMED CT as their contextual determinants are not made explicit. Conclusion The description of complex medical occurrents is ambiguous, as the same situations can be described as (i a complex occurrent C that has A and B as temporal parts, (ii a simple occurrent A' defined as a kind of A followed by some B, or (iii a simple occurrent B' defined as a kind of B preceded by some A. As negative statements in SNOMED CT cannot be exactly represented without
Authenticity of Mathematical Modeling
Tran, Dung; Dougherty, Barbara J.
2014-01-01
Some students leave high school never quite sure of the relevancy of the mathematics they have learned. They fail to see links between school mathematics and the mathematics of everyday life that requires thoughtful decision making and often complex problem solving. Is it possible to bridge the gap between school mathematics and the mathematics in…
Formal Computer Validation of the Quantum Phase Estimation Algorithm
Witzel, Wayne; Rudinger, Kenneth; Sarovar, Mohan; Carr, Robert
While peer review and scientific consensus provide some assurance to the validity of ideas, people do make mistakes that can slip through the cracks. A plethora of formal methods tools exist and are in use in a variety of settings where high assurance is demanded. Existing tools, however, require a great deal of expertise and lack versatility, demanding a non-trivial translation between a high-level description of a problem and the formal system. Our software, called Prove-It, allows a nearly direct translation between human-recognizable formulations and the underlying formal system. While Prove-It is not designed for particularly efficient automation, a primary goal of other formal methods tools, it is extremely flexible in following a desired line of reasoning (proof structure). This approach is particularly valuable for validating proofs that are already known. We will demonstrate a validation of the Quantum Phase Estimation Algorithm using Prove-It. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under Contract DE-AC04-94AL85000. This work was supported by the Laboratory Directed Research and Development program at Sandia National Laboratories.
The normative structure of mathematization in systematic biology.
Sterner, Beckett; Lidgard, Scott
2014-06-01
We argue that the mathematization of science should be understood as a normative activity of advocating for a particular methodology with its own criteria for evaluating good research. As a case study, we examine the mathematization of taxonomic classification in systematic biology. We show how mathematization is a normative activity by contrasting its distinctive features in numerical taxonomy in the 1960s with an earlier reform advocated by Ernst Mayr starting in the 1940s. Both Mayr and the numerical taxonomists sought to formalize the work of classification, but Mayr introduced a qualitative formalism based on human judgment for determining the taxonomic rank of populations, while the numerical taxonomists introduced a quantitative formalism based on automated procedures for computing classifications. The key contrast between Mayr and the numerical taxonomists is how they conceptualized the temporal structure of the workflow of classification, specifically where they allowed meta-level discourse about difficulties in producing the classification. Copyright © 2014. Published by Elsevier Ltd.
29 CFR 1690.306 - Formal submission in absence of consultation.
2010-07-01
... 29 Labor 4 2010-07-01 2010-07-01 false Formal submission in absence of consultation. 1690.306... § 1690.306 Formal submission in absence of consultation. If an initiating agency has an issuance which was already under development on or before July 1, 1978, when Executive Order 12067 became effective...
A Conceptual Formalization of Crosscutting in AOSD
van den Berg, Klaas; Conejero, J.M.
2005-01-01
We propose a formalization of crosscutting based on a conceptual framework for AOSD. Crosscutting is clearly distinguished from the related concepts scattering and tangling. The definitions of these concepts are formalized and visualized with matrices and matrix operations. This allows more precise
Formalizing Evaluation in Music Information Retrieval
DEFF Research Database (Denmark)
Sturm, Bob L.
2013-01-01
We develop a formalism to disambiguate the evaluation of music information retrieval systems. We define a ``system,'' what it means to ``analyze'' one, and make clear the aims, parts, design, execution, interpretation, and assumptions of its ``evaluation.'' We apply this formalism to discuss...
Applicability of four parameter formalisms in interpreting ...
Indian Academy of Sciences (India)
terms of applicability of the three well known four-parameter formalisms for the representation of the thermody- namic properties of binary systems. The study indicates that the derived values of the infinite dilution parameters based on the formalisms compare favourably with the computed data available in the literature.
Hamiltonian path integral formalism with higher derivatives
Energy Technology Data Exchange (ETDEWEB)
Barcelos-Neto, J.; Natividade, C.P. (Rio de Janeiro Univ. (Brazil). Inst. de Fisica)
1991-07-01
We study the Hamiltonian path integral formalism for systems containing higher derivatives. First we show the consistency of the formalism in applications involving only scalar fields. Later we use the Maxwell electromagnetic theory with a higher order regularization term to show that the Batalin-Fradkin-Vilkovisky (BFV) theory can also be consistently described. (orig.).
DNA expressions - A formal notation for DNA
Vliet, Rudy van
2015-01-01
We describe a formal notation for DNA molecules that may contain nicks and gaps. The resulting DNA expressions denote formal DNA molecules. Different DNA expressions may denote the same molecule. Such DNA expressions are called equivalent. We examine which DNA expressions are minimal, which
Formal balancing of chemical reaction networks
van der Schaft, Abraham; Rao, S.; Jayawardhana, B.
2016-01-01
In this paper we recall and extend the main results of Van der Schaft, Rao, Jayawardhana (2015) concerning the use of Kirchhoff’s Matrix Tree theorem in the explicit characterization of complex-balanced reaction networks and the notion of formal balancing. The notion of formal balancing corresponds
Restorative Practices as Formal and Informal Education
Carter, Candice C.
2013-01-01
This article reviews restorative practices (RP) as education in formal and informal contexts of learning that are fertile sites for cultivating peace. Formal practices involve instruction about response to conflict, while informal learning occurs beyond academic lessons. The research incorporated content analysis and a critical examination of the…
Formal Engineering Hybrid Systems: Semantic Underpinnings
Bujorianu, M.C.; Bujorianu, L.M.
2008-01-01
In this work we investigate some issues in applying formal methods to hybrid system development and develop a categorical framework. We study the themes of stochastic reasoning, heterogeneous formal specification and retrenchment. Hybrid systems raise a rich pallets of aspects that need to be
Industrial Practice in Formal Methods : A Review
DEFF Research Database (Denmark)
Bicarregui, Juan C.; Fitzgerald, John; Larsen, Peter Gorm
2009-01-01
We examine the the industrial application of formal methods using data gathered in a review of 62 projects taking place over the last 25 years. The review suggests that formal methods are being applied in a wide range of application domains, with increasingly strong tool support. Significant chal...
Formal Analysis of a Fair Payment Protocol
Cederquist, J.G.; Dashti, Muhammad Torabi; Dimitrakos, Theo; Martinelli, Fabio
We formally specify a payment protocol described by Vogt et al. This protocol is intended for fair exchange of time-sensitive data. Here the mCRL language is used to formalize the protocol. Fair exchange properties are expressed in the regular alternation-free mu-calculus. These properties are then
The simplest formal argument for fitness optimization
Indian Academy of Sciences (India)
2008-12-23
Dec 23, 2008 ... The Formal Darwinism Project aims to provide a formal argument linking population genetics to fitness optimization, which of necessity includes defining fitness. This bridges the gulf between those biologists who assume that natural selection leads to something close to fitness optimization and those ...
The simplest formal argument for fitness optimization
Indian Academy of Sciences (India)
The Formal Darwinism Project aims to provide a formal argument linking population genetics to fitness optimization, which of necessity includes defining fitness. This bridges the gulf between those biologists who assume that natural selection leads to something close to fitness optimization and those biologists who believe ...
The origin of the logic of symbolic mathematics Edmund Husserl and Jacob Klein
Hopkins, Burt C
2011-01-01
Burt C. Hopkins presents the first in-depth study of the work of Edmund Husserl and Jacob Klein on the philosophical foundations of the logic of modern symbolic mathematics. Accounts of the philosophical origins of formalized concepts-especially mathematical concepts and the process of mathematical abstraction that generates them-have been paramount to the development of phenomenology. Both Husserl and Klein independently concluded that it is impossible to separate the historical origin of the thought that generates the basic concepts of mathematics from their philosophical meanings. Hopkins explores how Husserl and Klein arrived at their conclusion and its philosophical implications for the modern project of formalizing all knowledge.
Multiscale mathematical modeling of the hypothalamo-pituitary-gonadal axis.
Clément, Frédérique
2016-07-01
Although the fields of systems and integrative biology are in full expansion, few teams are involved worldwide into the study of reproductive function from the mathematical modeling viewpoint. This may be due to the fact that the reproductive function is not compulsory for individual organism survival, even if it is for species survival. Alternatively, the complexity of reproductive physiology may be discouraging. Indeed, the hypothalamo-pituitary-gonadal (HPG) axis involves not only several organs and tissues but also intricate time (from the neuronal millisecond timescale to circannual rhythmicity) and space (from molecules to organs) scales. Yet, mathematical modeling, and especially multiscale modeling, can renew our approaches of the molecular, cellular, and physiological processes underlying the control of reproductive functions. In turn, the remarkable dynamic features exhibited by the HPG axis raise intriguing and challenging questions to modelers and applied mathematicians. In this article, we draw a panoramic review of some mathematical models designed in the framework of the female HPG, with a special focus on the gonadal and central control of follicular development. On the gonadal side, the modeling of follicular development calls to the generic formalism of structured cell populations, that allows one to make mechanistic links between the control of cell fate (proliferation, differentiation, or apoptosis) and that of the follicle fate (ovulation or degeneration) or to investigate how the functional interactions between the oocyte and its surrounding cells shape the follicle morphogenesis. On the central, mainly hypothalamic side, models based on dynamical systems with multiple timescales allow one to represent within a single framework both the pulsatile and surge patterns of the neurohormone GnRH. Beyond their interest in basic research investigations, mathematical models can also be at the source of useful tools to study the encoding and decoding of
Enhancing System Realisation in Formal Model Development
DEFF Research Database (Denmark)
Tran-Jørgensen, Peter Würtz Vinther
– a formal methods tool that supports the Vienna Development Method. The development of the code generation infrastructure has involved the re-design of the software architecture of Overture. The new architecture brings forth the reuse and extensibility features of Overture to take into account the needs......Software for mission-critical systems is sometimes analysed using formal specification to increase the chances of the system behaving as intended. When sufficient insights into the system have been obtained from the formal analysis, the formal specification is realised in the form of a software...... implementation. One way to realise the system’s software is by automatically generating it from the formal specification – a technique referred to as code generation. However, in general it is difficult to make guarantees about the correctness of the generated code – especially while requiring automation...
The mathematics of elections and voting
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 Formal Analysis of the Web Services Atomic Transaction Protocol with UPPAAL
DEFF Research Database (Denmark)
Ravn, Anders Peter; Srba, Jiri; Vighio, Saleem
2010-01-01
We present a formal analysis of the Web Services Atomic Transaction (WS-AT) protocol. WS-AT is a part of the WS-Coordination framework and describes an algorithm for reaching agreement on the outcome of a distributed transaction. The protocol is modelled and verified using the model checker UPPAAL....... Our model is based on an already available formalization using the mathematical language TLA+ where the protocol was verified using the model checker TLC. We discuss the key aspects of these two approaches, including the characteristics of the specification languages, the performances of the tools...
Exhibition - Mathematics, A Beautiful Elsewhere
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...
A mathematical model of embodied consciousness.
Rudrauf, David; Bennequin, Daniel; Granic, Isabela; Landini, Gregory; Friston, Karl; Williford, Kenneth
2017-09-07
We introduce a mathematical model of embodied consciousness, the Projective Consciousness Model (PCM), which is based on the hypothesis that the spatial field of consciousness (FoC) is structured by a projective geometry and under the control of a process of active inference. The FoC in the PCM combines multisensory evidence with prior beliefs in memory and frames them by selecting points of view and perspectives according to preferences. The choice of projective frames governs how expectations are transformed by consciousness. Violations of expectation are encoded as free energy. Free energy minimization drives perspective taking, and controls the switch between perception, imagination and action. In the PCM, consciousness functions as an algorithm for the maximization of resilience, using projective perspective taking and imagination in order to escape local minima of free energy. The PCM can account for a variety of psychological phenomena: the characteristic spatial phenomenology of subjective experience, the distinctions and integral relationships between perception, imagination and action, the role of affective processes in intentionality, but also perceptual phenomena such as the dynamics of bistable figures and body swap illusions in virtual reality. It relates phenomenology to function, showing the computational advantages of consciousness. It suggests that changes of brain states from unconscious to conscious reflect the action of projective transformations and suggests specific neurophenomenological hypotheses about the brain, guidelines for designing artificial systems, and formal principles for psychology. Copyright © 2017 Elsevier Ltd. All rights reserved.
Figures of thought mathematics and mathematical texts
Reed, David
2003-01-01
Examines the ways in which mathematical works can be read as texts, examines their textual strategiesand demonstrates that such readings provide a rich source of philosophical debate regarding mathematics.
Mathematics for Life: Sustainable Mathematics Education
Renert, Moshe
2011-01-01
Ecological sustainability has not been a major focus of mathematics education research, even though it has attracted considerable attention in other areas of educational research in the past decade. The connections between mathematics education and ecological sustainability are not readily apparent. This paper explores how mathematics educators…
Mathematical Modelling Approach in Mathematics Education
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…
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
Recovering the quantum formalism from physically realist axioms
Auffèves, Alexia; Grangier, Philippe
2017-03-01
We present a heuristic derivation of Born’s rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantization. This approach naturally leads to the usual quantum formalism, within a new realistic conceptual framework that is discussed in details. Physically, the structure of Quantum Mechanics appears as a result of the interplay between the quantized number of “modalities” accessible to a quantum system, and the continuum of “contexts” that are required to define these modalities. Mathematically, the Hilbert space structure appears as a consequence of a specific “extra-contextuality” of modalities, closely related to the hypothesis of Gleason’s theorem, and consistent with its conclusions.
A dynamic subgrid scale model for Large Eddy Simulations based on the Mori-Zwanzig formalism
Parish, Eric J.; Duraisamy, Karthik
2017-11-01
The development of reduced models for complex multiscale problems remains one of the principal challenges in computational physics. The optimal prediction framework of Chorin et al. [1], which is a reformulation of the Mori-Zwanzig (M-Z) formalism of non-equilibrium statistical mechanics, provides a framework for the development of mathematically-derived reduced models of dynamical systems. Several promising models have emerged from the optimal prediction community and have found application in molecular dynamics and turbulent flows. In this work, a new M-Z-based closure model that addresses some of the deficiencies of existing methods is developed. The model is constructed by exploiting similarities between two levels of coarse-graining via the Germano identity of fluid mechanics and by assuming that memory effects have a finite temporal support. The appeal of the proposed model, which will be referred to as the 'dynamic-MZ-τ' model, is that it is parameter-free and has a structural form imposed by the mathematics of the coarse-graining process (rather than the phenomenological assumptions made by the modeler, such as in classical subgrid scale models). To promote the applicability of M-Z models in general, two procedures are presented to compute the resulting model form, helping to bypass the tedious error-prone algebra that has proven to be a hindrance to the construction of M-Z-based models for complex dynamical systems. While the new formulation is applicable to the solution of general partial differential equations, demonstrations are presented in the context of Large Eddy Simulation closures for the Burgers equation, decaying homogeneous turbulence, and turbulent channel flow. The performance of the model and validity of the underlying assumptions are investigated in detail.
González-Castro, Paloma; Cueli, Marisol; Areces, Débora; Rodríguez, Celestino; Sideridis, Georgios
2016-01-01
Problem solving represents a salient deficit in students with mathematical learning difficulties (MLD) primarily caused by difficulties with informal and formal mathematical competencies. This study proposes a computerized intervention tool, the integrated dynamic representation (IDR), for enhancing the early learning of basic mathematical…
On Fitting a Formal Method into Practice
DEFF Research Database (Denmark)
Gmehlich, Rainer; Grau, Katrin; Hallerstede, Stefan
2011-01-01
of industrial use. We report on where Event-B and its tools have succeeded, where they have not. We also report on advances that were inspired by the case study. Interestingly, the case study was not a pure formal methods problem. In addition to Event-B, it used Problem Frames for capturing requirements....... The interaction between the two proved to be crucial for the success of the case study. The heart of the problem was tracing informal requirements from Problem Frames descriptions to formal Event-B models. To a large degree, this issue dictated the approach that had to be used for formal modelling. A dedicated...
Towards Formal Implementation of PUS Standard
Ilić, D.
2009-05-01
As an effort to promote the reuse of on-board and ground systems ESA developed a standard for packet telemetry and telecommand - PUS. It defines a set of standard service models with the corresponding structures of the associated telemetry and telecommand packets. Various missions then can choose to implement those standard PUS services that best conform to their specific requirements. In this paper we propose a formal development (based on the Event-B method) of reusable service patterns, which can be instantiated for concrete application. Our formal models allow us to formally express and verify specific service properties including various telecommand and telemetry packet structure validation.
Review of the helicity formalism; Revision del formalismo de helicidad
Energy Technology Data Exchange (ETDEWEB)
Barreiro, F.; Cerrada, M.; Fernandez, E.
1972-07-01
Our purpose in these notes has been to present a brief and general review of the helicity formalism. We begin by discussing Lorentz invariance, spin and helicity ideas, in section 1 . In section 2 we deal with the construction of relativistic states and scattering amplitudes in the helicity basis and we study their transformation properties under discrete symmetries. Finally we present some more sophisticated topics like kinematical singularities of helicity amplitudes, kinematical constraints and crossing relations 3, 4, 5 respectively. (Author) 8 refs.
A note on the locus and function of formal gender
Picallo, M. Carme
2017-01-01
This paper examines some aspects of nominal inflection. It focuses in particular on noun classification with evidence drawn mainly from Spanish where noun classification surfaces as formal Gender. Under a minimalist lens, this feature is a puzzling grammatical element because it seems uncongenial to the idea of optimal design. I examine some syntactic evidence to assess the syntactic locus of Gender features in nominal structures, and conjecture that noun classification simply externalizes so...
Mathematical modelling in science and mathematics education
Teodoro, Vítor Duarte; Neves, Rui Gomes
2011-01-01
Scientific research involves mathematical modelling in the context of an interactive balance between theory, experiment and computation. However, computational methods and tools are still far from being appropriately integrated in the high school and university curricula in science and mathematics. In this paper, it is discussed the relevance of mathematical modelling and illustrated how a computer modelling tool (Modellus, a free tool available on the Internet and developed at FCTUNL) can be used to embed modelling in high school and undergraduate courses. Modellus allows students to create and explore mathematical models using functions, differential and iterative equations, and visualize the behaviour of mathematical objects.
Artificial grammar learning meets formal language theory: an overview
Fitch, W. Tecumseh; Friederici, Angela D.
2012-01-01
Formal language theory (FLT), part of the broader mathematical theory of computation, provides a systematic terminology and set of conventions for describing rules and the structures they generate, along with a rich body of discoveries and theorems concerning generative rule systems. Despite its name, FLT is not limited to human language, but is equally applicable to computer programs, music, visual patterns, animal vocalizations, RNA structure and even dance. In the last decade, this theory has been profitably used to frame hypotheses and to design brain imaging and animal-learning experiments, mostly using the ‘artificial grammar-learning’ paradigm. We offer a brief, non-technical introduction to FLT and then a more detailed analysis of empirical research based on this theory. We suggest that progress has been hampered by a pervasive conflation of distinct issues, including hierarchy, dependency, complexity and recursion. We offer clarifications of several relevant hypotheses and the experimental designs necessary to test them. We finally review the recent brain imaging literature, using formal languages, identifying areas of convergence and outstanding debates. We conclude that FLT has much to offer scientists who are interested in rigorous empirical investigations of human cognition from a neuroscientific and comparative perspective. PMID:22688631
Artificial grammar learning meets formal language theory: an overview.
Fitch, W Tecumseh; Friederici, Angela D
2012-07-19
Formal language theory (FLT), part of the broader mathematical theory of computation, provides a systematic terminology and set of conventions for describing rules and the structures they generate, along with a rich body of discoveries and theorems concerning generative rule systems. Despite its name, FLT is not limited to human language, but is equally applicable to computer programs, music, visual patterns, animal vocalizations, RNA structure and even dance. In the last decade, this theory has been profitably used to frame hypotheses and to design brain imaging and animal-learning experiments, mostly using the 'artificial grammar-learning' paradigm. We offer a brief, non-technical introduction to FLT and then a more detailed analysis of empirical research based on this theory. We suggest that progress has been hampered by a pervasive conflation of distinct issues, including hierarchy, dependency, complexity and recursion. We offer clarifications of several relevant hypotheses and the experimental designs necessary to test them. We finally review the recent brain imaging literature, using formal languages, identifying areas of convergence and outstanding debates. We conclude that FLT has much to offer scientists who are interested in rigorous empirical investigations of human cognition from a neuroscientific and comparative perspective.
Ethnomathematics in non-formal educational settings
DEFF Research Database (Denmark)
Pais, Alexandre; Mesquita, Monica
The push to marry off local and school knowledge has been a growing concern within educational sciences, particularly in mathematics education where a field of studies by the name of ethnomathematics has been producing research around the uses people do of mathematics outside school’s walls...... the inconsistencies of schooling, and the promotion of a non-scholarized ethnomathematics....
The Intersituational Generality of Formal Thought
Stone, Mary Ann; Ausubel, David P.
1969-01-01
Shows that, contrary to Piagetian Theory, formal thought in a variety of subject matters is not possible until sufficient requisite concrete background experience in each content area involved has been attained. (MH)
Graphical And Textual Notations In Formal Specification
Energy Technology Data Exchange (ETDEWEB)
Bove, Rocco; Dipoppa, Giovanni; Groven, Arne-Kristian; Sivertsen, Terje
1996-07-01
The present report describes the current status of the co-operative project between ENEA and the OECD Halden Reactor Project on graphical and formal methods for software specification. The aim of this project is to contribute to a clarification of the relationship between graphical descriptions and formal specifications, and to provide guidelines for how they can be combined in order to utilize the strengths of' each approach. The overall aim of such a combination is to improve the formal basis of graphical descriptions and make formal specifications more generally comprehensible. The research reported includes the application of the IPTES technology on the APRM case example, an approach to the translation of Petri nets into algebraic specification, and the specification of real-time distributed systems using time-extended LOTOS. (author)
El Salvador - Non-Formal Skills Development
Millennium Challenge Corporation — The Non-Formal Skills Development Sub-Activity had a budget of $5 million (USD) to provide short-term training to vulnerable populations in El Salvador's Northern...
Transitions from Formal Education to the Workplace
Olson, Joann S.
2014-01-01
This chapter frames the transition to adulthood in the context of the moving from formal educational settings to the often less-structured learning that occurs in workplace settings. Although schooling may end, learning continues.
Regla formal de justicia, valores y principios
López Ruiz, Francisco
1995-01-01
SUMARIO: 1. Racionalidad y regla formal de justicia. 2. Las diferencias estructurales entre normas y principios. 3. Clases de principios. 4. Funciones de los principios. 5. Principios y racionalidad material del Derecho. Publicado
Formal specification of human-computer interfaces
Auernheimer, Brent
1990-01-01
A high-level formal specification of a human computer interface is described. Previous work is reviewed and the ASLAN specification language is described. Top-level specifications written in ASLAN for a library and a multiwindow interface are discussed.
Formalisms for reuse and systems integration
Rubin, Stuart
2015-01-01
Reuse and integration are defined as synergistic concepts, where reuse addresses how to minimize redundancy in the creation of components; while, integration focuses on component composition. Integration supports reuse and vice versa. These related concepts support the design of software and systems for maximizing performance while minimizing cost. Knowledge, like data, is subject to reuse; and, each can be interpreted as the other. This means that inherent complexity, a measure of the potential utility of a system, is directly proportional to the extent to which it maximizes reuse and integration. Formal methods can provide an appropriate context for the rigorous handling of these synergistic concepts. Furthermore, formal languages allow for non ambiguous model specification; and, formal verification techniques provide support for insuring the validity of reuse and integration mechanisms. This edited book includes 12 high quality research papers written by experts in formal aspects of reuse and integratio...
Toward a formal ontology for narrative
Directory of Open Access Journals (Sweden)
Ciotti, Fabio
2016-03-01
Full Text Available In this paper the rationale and the first draft of a formal ontology for modeling narrative texts are presented. Building on the semiotic and structuralist narratology, and on the work carried out in the late 1980s by Giuseppe Gigliozzi in Italy, the focus of my research are the concepts of character and of narrative world/space. This formal model is expressed in the OWL 2 ontology language. The main reason to adopt a formal modeling approach is that I consider the purely probabilistic-quantitative methods (now widespread in digital literary studies inadequate. An ontology, on one hand provides a tool for the analysis of strictly literary texts. On the other hand (though beyond the scope of the present work, its formalization can also represent a significant contribution towards grounding the application of storytelling methods outside of scholarly contexts.
Statistical Survey of Non-Formal Education
Directory of Open Access Journals (Sweden)
Ondřej Nývlt
2012-12-01
Full Text Available focused on a programme within a regular education system. Labour market flexibility and new requirements on employees create a new domain of education called non-formal education. Is there a reliable statistical source with a good methodological definition for the Czech Republic? Labour Force Survey (LFS has been the basic statistical source for time comparison of non-formal education for the last ten years. Furthermore, a special Adult Education Survey (AES in 2011 was focused on individual components of non-formal education in a detailed way. In general, the goal of the EU is to use data from both internationally comparable surveys for analyses of the particular fields of lifelong learning in the way, that annual LFS data could be enlarged by detailed information from AES in five years periods. This article describes reliability of statistical data aboutnon-formal education. This analysis is usually connected with sampling and non-sampling errors.
Directory of Open Access Journals (Sweden)
Nancy Chitera
2016-11-01
Full Text Available In this article, we present a discussion about the type of mathematical discourse that is being produced in classrooms where the language of learning and teaching is local languages. We also further explore the tensions in the mathematical discourse being produced. The study sample was 4 mathematics teachers from a semi-urban primary school in Malawi. The methods of data collection included classroom observations, pre-observation focus group discussions and reflective interviews. The results show that even though both students and teachers were able to communicate freely in local languages in the mathematics classroom, the mathematical discourse that came was distorted. This is mainly caused by lack of a well-developed mathematical discourse in local languages, which in turn takes away the confidence of mathematics teachers in the classroom. As a result, the mathematics classrooms are still being characterized by teachers not being creative, use of word by word from books, focus more on procedural than conceptual and thus teacher centered is still dominant in these classrooms. Furthermore, it is found that there are tensions between the formal and informal mathematical language in local languages. These results in turn have promoted a more in-depth understanding to the teaching and learning of mathematics when local language is the language of learning and teaching. Therefore, this article argues for a well-balanced approach when it comes to teaching and learning of mathematics rather than just focusing on the use of local languages.
Approaches to Formal Verification of Security Protocols
Lal, Suvansh; Jain, Mohit; Chaplot, Vikrant
2011-01-01
In recent times, many protocols have been proposed to provide security for various information and communication systems. Such protocols must be tested for their functional correctness before they are used in practice. Application of formal methods for verification of security protocols would enhance their reliability thereby, increasing the usability of systems that employ them. Thus, formal verification of security protocols has become a key issue in computer and communications security. In...
Improved formalism for precision Higgs coupling fits
International Nuclear Information System (INIS)
Barklow, Tim; Peskin, Michael E.; Jung, Sunghoon; Tian, Junping
2017-08-01
Future e + e - colliders give the promise of model-independent determinations of the couplings of the Higgs boson. In this paper, we present an improved formalism for extracting Higgs boson couplings from e + e - data, based on the Effective Field Theory description of corrections to the Standard Model. We apply this formalism to give projections of Higgs coupling accuracies for stages of the International Linear Collider and for other proposed e + e - colliders.
Towards a Formal Model of Context Awareness
DEFF Research Database (Denmark)
Kjærgaard, Mikkel Baun; Bunde-Pedersen, Jonathan
2006-01-01
There is a definite lack of formal support for modeling realistic context-awareness in pervasive computing applications. The CONAWA calculus presented in this paper provides mechanisms for modeling complex and interwoven sets of context-information by extending ambient calculus with new constructs...... and capabilities. The calculus is a step in the direction of making formal methods applicable in the area of pervasive computing....
Towards a Formal Notion of Trust
DEFF Research Database (Denmark)
Nielsen, Mogens; Krukow, Karl Kristian
2003-01-01
Trust management systems have been proposed as an alternative to traditional security mechanisms in Global Computing. We present some challenges in establishing a formal foundation for the notion of trust, and some preliminary ideas towards a category of trust models.......Trust management systems have been proposed as an alternative to traditional security mechanisms in Global Computing. We present some challenges in establishing a formal foundation for the notion of trust, and some preliminary ideas towards a category of trust models....
Improved formalism for precision Higgs coupling fits
Barklow, Tim; Fujii, Keisuke; Jung, Sunghoon; Karl, Robert; List, Jenny; Ogawa, Tomohisa; Peskin, Michael E.; Tian, Junping
2018-03-01
Future e+e- colliders give the promise of model-independent determinations of the couplings of the Higgs boson. In this paper, we present an improved formalism for extracting Higgs boson couplings from e+e- data, based on the effective field theory description of corrections to the Standard Model. We apply this formalism to give projections of Higgs coupling accuracies for stages of the International Linear Collider and for other proposed e+e- colliders.
Formalization of Many-Valued Logics
DEFF Research Database (Denmark)
Villadsen, Jørgen; Schlichtkrull, Anders
2017-01-01
Partiality is a key challenge for computational approaches to artificial intelligence in general and natural language in particular. Various extensions of classical two-valued logic to many-valued logics have been investigated in order to meet this challenge. We use the proof assistant Isabelle...... to formalize the syntax and semantics of many-valued logics with determinate as well as indeterminate truth values. The formalization allows for a concise presentation and makes automated verification possible....
Formal System Verification for Trustworthy Embedded Systems
2011-04-19
step is for the first time formal and machine-checked. Contemporary OS verification projects include Verisoft, Verisoft XT, and Verve . The Verisoft...tens of thousands lines of code. The Verve kernel [22] shows that type and memory safety properties can be established on the assembly level via type...systems and therefore with much lower cost. Verve contains a formally verified runtime system, in particular a garbage collector that the type system
Reshetnyak, A. A.
2003-01-01
In the framework of started in Ref.[1] construction procedure of the general superfield quantization method for gauge theories in Lagrangian formalism the rules for Hamiltonian formulation of general superfield theory of fields (GSTF) are introduced and are on the whole considered. Mathematical means developed in [1] for Lagrangian formulation of GSTF are extended to use in Hamiltonian one. Hamiltonization for Lagrangian formulation of GSTF via Legendre transform of superfunction $S_{L}\\bigl(...
Directory of Open Access Journals (Sweden)
Emma Emanuilova Yandybaeva
2015-03-01
Full Text Available The methods of information subjects and objects interaction rules formalization in the electronic trading platform system has been developed. They are based on mathematical model of mandatory role-based access control. As a result of the work we have defined set of user roles and constructed roles hierarchy. For the roles hierarchy restrictions have been imposed to ensure the safety of the information system.
Simulators for teaching formal languages and automata theory: a comparative survey
Chesñevar, Carlos Iván; Cobo, María Laura
2002-01-01
Formal languages and automata theory (FL&AT) are central subjects in the CS curricula which are usually diffcult both to teach and to learn. This situation has motivated the development of a number of computer simulators as educational tools which allow the student to implement and `bring to life' many topics which traditionally were studied and analyzed mathematically rather than algorithmically. This paper discusses the main features of several educational software tools currently availa...
Formal and physical equivalence in two cases in contemporary quantum physics
Fraser, Doreen
2017-08-01
The application of analytic continuation in quantum field theory (QFT) is juxtaposed to T-duality and mirror symmetry in string theory. Analytic continuation-a mathematical transformation that takes the time variable t to negative imaginary time-it-was initially used as a mathematical technique for solving perturbative Feynman diagrams, and was subsequently the basis for the Euclidean approaches within mainstream QFT (e.g., Wilsonian renormalization group methods, lattice gauge theories) and the Euclidean field theory program for rigorously constructing non-perturbative models of interacting QFTs. A crucial difference between theories related by duality transformations and those related by analytic continuation is that the former are judged to be physically equivalent while the latter are regarded as physically inequivalent. There are other similarities between the two cases that make comparing and contrasting them a useful exercise for clarifying the type of argument that is needed to support the conclusion that dual theories are physically equivalent. In particular, T-duality and analytic continuation in QFT share the criterion for predictive equivalence that two theories agree on the complete set of expectation values and the mass spectra and the criterion for formal equivalence that there is a "translation manual" between the physically significant algebras of observables and sets of states in the two theories. The analytic continuation case study illustrates how predictive and formal equivalence are compatible with physical inequivalence, but not in the manner of standard underdetermination cases. Arguments for the physical equivalence of dual theories must cite considerations beyond predictive and formal equivalence. The analytic continuation case study is an instance of the strategy of developing a physical theory by extending the formal or mathematical equivalence with another physical theory as far as possible. That this strategy has resulted in
Mathematics Connection: Editorial Policies
African Journals Online (AJOL)
MATHEMATICS CONNECTION aims at providing a forum to promote the development of Mathematics Education in Ghana. Articles that seek to enhance the teaching and/or learning of mathematics ... Faculty of Social Sciences, Methodist University, Accra Prof. B. K. Gordor, Department of Mathematics (UCC), Cape Coast ...
DEFF Research Database (Denmark)
Hansen, Vagn Lundsgaard
2005-01-01
A brief tour through the history of mathematics from the very beginnings to modern times, with an emphasis on the main contributions and important periods of mathematics in various civilizations.......A brief tour through the history of mathematics from the very beginnings to modern times, with an emphasis on the main contributions and important periods of mathematics in various civilizations....
DEFF Research Database (Denmark)
Hansen, Vagn Lundsgaard
A brief tour through the history of mathematics from the very beginnings to modern times, with an emphasis on the main contributions and important periods of mathematics in various civilizations.......A brief tour through the history of mathematics from the very beginnings to modern times, with an emphasis on the main contributions and important periods of mathematics in various civilizations....
Indian Academy of Sciences (India)
2001-08-10
World Mathematical Year 2000. (July 23 to August 10, 2001) at Indian Institute of Science, Bangalore 560 012 sponsored by National Board for Higher Mathematics, organised by Department of Mathematics and. TIFR Centre, Indian Institute of Science. Prof. J L Bona, Department of Mathematics, University of Texas at ...
Chanting as mathematical enculturation
Directory of Open Access Journals (Sweden)
Anne Watson
2004-10-01
Full Text Available Unison response is a major teaching strategy in mathematics throughout the world. The spoken word is the dominant source of mathematical stimulus, the dominant shaper of the mathematical environment in which school learners construct mathematical meaning. The teachers’ utterances are intended to be expert, and the creation of learner responses is intended to involve learning of some kind.
Tegmark, Max
2014-02-01
The world can be described using mathematical equations and numbers, but why does maths do it so well? In his new book Our Mathematical Universe, a section of which is abridged and edited here, Max Tegmark makes the radical proposal that our reality isn't just described by mathematics - it is mathematics.
Formality of the Chinese collective leadership.
Li, Haiying; Graesser, Arthur C
2016-09-01
We investigated the linguistic patterns in the discourse of four generations of the collective leadership of the Communist Party of China (CPC) from 1921 to 2012. The texts of Mao Zedong, Deng Xiaoping, Jiang Zemin, and Hu Jintao were analyzed using computational linguistic techniques (a Chinese formality score) to explore the persuasive linguistic features of the leaders in the contexts of power phase, the nation's education level, power duration, and age. The study was guided by the elaboration likelihood model of persuasion, which includes a central route (represented by formal discourse) versus a peripheral route (represented by informal discourse) to persuasion. The results revealed that these leaders adopted the formal, central route more when they were in power than before they came into power. The nation's education level was a significant factor in the leaders' adoption of the persuasion strategy. The leaders' formality also decreased with their increasing age and in-power times. However, the predictability of these factors for formality had subtle differences among the different types of leaders. These results enhance our understanding of the Chinese collective leadership and the role of formality in politically persuasive messages.
Application of Formal Methods in Software Engineering
Directory of Open Access Journals (Sweden)
Adriana Morales
2011-12-01
Full Text Available The purpose of this research work is to examine: (1 why are necessary the formal methods for software systems today, (2 high integrity systems through the methodology C-by-C –Correctness-by-Construction–, and (3 an affordable methodology to apply formal methods in software engineering. The research process included reviews of the literature through Internet, in publications and presentations in events. Among the Research results found that: (1 there is increasing the dependence that the nations have, the companies and people of software systems, (2 there is growing demand for software Engineering to increase social trust in the software systems, (3 exist methodologies, as C-by-C, that can provide that level of trust, (4 Formal Methods constitute a principle of computer science that can be applied software engineering to perform reliable process in software development, (5 software users have the responsibility to demand reliable software products, and (6 software engineers have the responsibility to develop reliable software products. Furthermore, it is concluded that: (1 it takes more research to identify and analyze other methodologies and tools that provide process to apply the Formal Software Engineering methods, (2 Formal Methods provide an unprecedented ability to increase the trust in the exactitude of the software products and (3 by development of new methodologies and tools is being achieved costs are not more a disadvantage for application of formal methods.
Towards a Formal Semantics of Flight Plans and Trajectories
Hagen, George E.; Butler, Ricky W.
2014-01-01
In the National Airspace System, ight plans are often used only as a planning tool by air trac controllers and aircraft operators. These plans are implicitly translated into trajectories by the pilot or by the ight management system, and subsequently own by the aircraft. This translation process inevitably introduces di erences between the plan and the trajectory. However, given the current intended usage, exact correspondence between the plan and the trajectory is not needed. To achieve greater capacity and eciency, future air trac management concepts are being designed around the use of trajectories where predictability is extremely important. In this paper, a mathematical relationship between ight plans and trajectories is explored with the goal of making feasible, highly accurate predictions of future positions and velocities of aircraft. The goal here is to describe, in mathematically precise detail, a formal language of trajectories, whereby all receivers of the trajectory information will be able to arrive at precisely the same trajectory predication and to do this without having aircraft broadcast a large amount of data. Although even a four-dimensional ight plan is simple in structure, this paper will show that it is inherently ambiguous and will explore these issues in detail. In e ect, we propose that a rigorous semantics for ight plans can be developed and this will serve as an important stepping stone towards trajectory-based operations in the National Airspace System.
From Religion to Dialectics and Mathematics
Directory of Open Access Journals (Sweden)
Achtner Wolfgang
2016-03-01
Full Text Available Hermann Grassmann is known to be the founder of modern vector and tensor calculus. Having as a theologian no formal education in mathematics at a university he got his basic ideas for this mathematical innovation at least to some extent from listening to Schleiermacher’s lectures on Dialectics and, together with his brother Robert, reading its publication in 1839. The paper shows how the idea of unity and various levels of reality first formulated in Schleiermacher’s talks about religion in 1799 were transformed by him into a philosophical system in his dialectics and then were picked up by Grassmann and operationalized in his philosophical-mathematical treatise on the extension theory (German: Ausdehnungslehre in 1844.
Curci-Ferrari-type condition in Hamiltonian formalism: A free spinning relativistic particle
Shukla, A.; Bhanja, T.; Malik, R. P.
2013-03-01
The Curci-Ferrari (CF)-type restriction emerges in the description of a free spinning relativistic particle within the framework of the Becchi-Rouet-Stora-Tyutin (BRST) formalism when the off-shell nilpotent and absolutely anticommuting (anti-)BRST symmetry transformations for this system are derived from the application of the horizontality condition (HC) and its supersymmetric generalization (SUSY-HC) within the framework of the superfield formalism. We show that the above CF condition, which turns out to be the secondary constraint of our present theory, remains time-evolution invariant within the framework of Hamiltonian formalism. This time-evolution invariance i) physically justifies the imposition of the (anti-)BRST invariant CF-type condition on this system, and ii) mathematically implies the linear independence of BRST and anti-BRST symmetries of our present theory.
Computer Vision and Mathematical Morphology
Roerdink, J.B.T.M.; Kropratsch, W.; Klette, R.; Albrecht, R.
1996-01-01
Mathematical morphology is a theory of set mappings, modeling binary image transformations, which are invariant under the group of Euclidean translations. This framework turns out to be too restricted for many applications, in particular for computer vision where group theoretical considerations
AdS/CFT correspondence in operator formalism
Terashima, Seiji
2018-02-01
In this paper we study the AdS/CFT correspondence in the operator formalism without assuming the GKPW relation. We explicitly show that the low energy spectrum of the large N limit of CFT, which is realized by a strong coupling gauge theory, is identical to the spectrum of the free gravitational theory in the global AdS spacetime under some assumptions which are expected to be valid. Thus, two theories are equivalent for the low energy region under the assumptions. Using this equivalence, the bulk local field is constructed and the GKPW relation is derived.
Mathematical modeling in realistic mathematics education
Riyanto, B.; Zulkardi; Putri, R. I. I.; Darmawijoyo
2017-12-01
The purpose of this paper is to produce Mathematical modelling in Realistics Mathematics Education of Junior High School. This study used development research consisting of 3 stages, namely analysis, design and evaluation. The success criteria of this study were obtained in the form of local instruction theory for school mathematical modelling learning which was valid and practical for students. The data were analyzed using descriptive analysis method as follows: (1) walk through, analysis based on the expert comments in the expert review to get Hypothetical Learning Trajectory for valid mathematical modelling learning; (2) analyzing the results of the review in one to one and small group to gain practicality. Based on the expert validation and students’ opinion and answers, the obtained mathematical modeling problem in Realistics Mathematics Education was valid and practical.
Directory of Open Access Journals (Sweden)
A. V. Masloboev
2015-01-01
Full Text Available The paper deals with development of methods and tools for mathematical and computer modeling of the multilevel network-centric control systems of regional security. This research is carried out under development strategy implementation of the Arctic zone of the Russian Federation and national safeguarding for the period before 2020 in the Murmansk region territory. Creation of unified interdepartmental multilevel computer-aided system is proposed intended for decision-making information support and socio-economic security monitoring of the Arctic regions of Russia. The distinctive features of the investigated system class are openness, self-organization, decentralization of management functions and decision-making, weak hierarchy in the decision-making circuit and goal generation capability inside itself. Research techniques include functional-target approach, mathematical apparatus of multilevel hierarchical system theory and principles of network-centric control of distributed systems with pro-active components and variable structure. The work considers network-centric management local decisions coordination problem-solving within the multilevel distributed systems intended for information support of regional security. The coordination problem-solving approach and problem formalization in the multilevel network-centric control systems of regional security have been proposed based on developed multilevel recurrent hierarchical model of regional socio-economic system complex security. The model provides coordination of regional security indexes, optimized by the different elements of multilevel control systems, subject to decentralized decision-making. The model specificity consists in application of functional-target technology and mathematical apparatus of multilevel hierarchical system theory for coordination procedures implementation of the network-centric management local decisions. The work-out and research results can find further
Why formal learning theory matters for cognitive science.
Fulop, Sean; Chater, Nick
2013-01-01
This article reviews a number of different areas in the foundations of formal learning theory. After outlining the general framework for formal models of learning, the Bayesian approach to learning is summarized. This leads to a discussion of Solomonoff's Universal Prior Distribution for Bayesian learning. Gold's model of identification in the limit is also outlined. We next discuss a number of aspects of learning theory raised in contributed papers, related to both computational and representational complexity. The article concludes with a description of how semi-supervised learning can be applied to the study of cognitive learning models. Throughout this overview, the specific points raised by our contributing authors are connected to the models and methods under review. Copyright © 2013 Cognitive Science Society, Inc.
Formal Model-Driven Engineering: Generating Data and Behavioural Components
Directory of Open Access Journals (Sweden)
Chen-Wei Wang
2012-12-01
Full Text Available Model-driven engineering is the automatic production of software artefacts from abstract models of structure and functionality. By targeting a specific class of system, it is possible to automate aspects of the development process, using model transformations and code generators that encode domain knowledge and implementation strategies. Using this approach, questions of correctness for a complex, software system may be answered through analysis of abstract models of lower complexity, under the assumption that the transformations and generators employed are themselves correct. This paper shows how formal techniques can be used to establish the correctness of model transformations used in the generation of software components from precise object models. The source language is based upon existing, formal techniques; the target language is the widely-used SQL notation for database programming. Correctness is established by giving comparable, relational semantics to both languages, and checking that the transformations are semantics-preserving.
The Stages of Student Mathematical Imagination in Solving Mathematical Problems
Wibowo, Teguh; Sutawidjaja, Akbar; As'ari, Abdur Rahman; Sulandra, I. Made
2017-01-01
This research is a qualitative study that aimed to describe the stages of students mathematical imagination in solving mathematical problems. There are three kinds of mathematical imagination in solving mathematical problems, namely sensory mathematical imagination, creative mathematical imagination and recreative mathematical imagination.…
Informal Content and Student Note-Taking in Advanced Mathematics Classes
Fukawa-Connelly, Timothy; Weber, Keith; Mejía-Ramos, Juan Pablo
2017-01-01
This study investigates 3 hypotheses about proof-based mathematics instruction: (a) that lectures include informal content (ways of thinking and reasoning about advanced mathematics that are not captured by formal symbolic statements), (b) that informal content is usually presented orally but not written on the board, and (c) that students do not…
Semantic Contamination and Mathematical Proof: Can a Non-Proof Prove?
Mejia-Ramos, Juan Pablo; Inglis, Matthew
2011-01-01
The way words are used in natural language can influence how the same words are understood by students in formal educational contexts. Here we argue that this so-called semantic contamination effect plays a role in determining how students engage with mathematical proof, a fundamental aspect of learning mathematics. Analyses of responses to…
Huseyin, Aksu Hasan
2015-01-01
The aim of this study is to determine elementary mathematics teachers' thoughts and feelings on the courses of school-experience and teacher-practice. In this study was used the qualitative research method. Those involved in the study were 20 mathematics teachers employed in formal/government primary schools in the Province of Giresun and in the…
Developing the Practice of Teacher Questioning through a K-2 Elementary Mathematics Field Experience
Schwartz, Catherine
2015-01-01
This article presents findings from research on a field experience designed to help elementary preservice teachers learn the practice of teacher questioning during formal and informal interviews to analyze student mathematical thinking in K-2 classrooms. The practice of teacher questioning is framed as choosing a mathematical goal, analyzing…
Surya, Edy; Sabandar, Jozua; Kusumah, Yaya S.; Darhim
2013-01-01
The students' difficulty which was found is in the problem of understanding, drawing diagrams, reading the charts correctly, conceptual formal mathematical understanding, and mathematical problem solving. The appropriate problem representation is the basic way in order to understand the problem itself and make a plan to solve it. This research was…
Mathematics without boundaries surveys in pure mathematics
Pardalos, Panos
2014-01-01
The contributions in this volume have been written by eminent scientists from the international mathematical community and present significant advances in several theories, methods and problems of Mathematical Analysis, Discrete Mathematics, Geometry and their Applications. The chapters focus on both old and recent developments in Functional Analysis, Harmonic Analysis, Complex Analysis, Operator Theory, Combinatorics, Functional Equations, Differential Equations as well as a variety of Applications. The book also contains some review works, which could prove particularly useful for a broader audience of readers in Mathematical Sciences, and especially to graduate students looking for the latest information.
Mathematical Rigor in Introductory Physics
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.
Three essays in mathematical finance
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.
Construction of Formal Ontology on Computer
Directory of Open Access Journals (Sweden)
Yelda FIRAT
2013-01-01
Full Text Available From a general point of view, the defined reality models by using a formal language are called formal ontology. These general purposeful models can be also used in the special fields of application. Because ontologies are large-scale by their nature, they have the potential of hosting errors and deficiencies in case they are generated by human labor. Besides, an ontology formed such a way will be difficult to be adapted to a application specific. In this study, an application of a computerized formal ontology formation saved from probable problems which are likely to arise using human labor will be introduced. In the application, semantic analysis of Turkish has been targetted as a special application field using corpus-based marking method in the framework of formal concept analysis. Beside the applications of these kinds of natural language processing formal ontologies are used considerably in the field of education as they present the information in the way of semantic structures clearly and meaningfully. The most important reasons of this are the use of the information technologies such as expansion of constructivist approach and the concept maps used for educational reasons.
Mathematical modelling as basis for efficient enterprise management
Directory of Open Access Journals (Sweden)
Kalmykova Svetlana
2017-01-01
Full Text Available The choice of the most effective HR- management style at the enterprise is based on modeling various socio-economic situations. The article describes the formalization of the managing processes aimed at the interaction between the allocated management subsystems. The mathematical modelling tools are used to determine the time spent on recruiting personnel for key positions in the management hierarchy selection.
Programming-Languages as a Conceptual Framework for Teaching Mathematics
Feurzeig, Wallace; Papert, Seymour A.
2011-01-01
Formal mathematical methods remain, for most high school students, mysterious, artificial and not a part of their regular intuitive thinking. The authors develop some themes that could lead to a radically new approach. According to this thesis, the teaching of programming languages as a regular part of academic progress can contribute effectively…
The Mathematics of Dispatchability Revisited
Morris, Paul
2016-01-01
Dispatchability is an important property for the efficient execution of temporal plans where the temporal constraints are represented as a Simple Temporal Network (STN). It has been shown that every STN may be reformulated as a dispatchable STN, and dispatchability ensures that the temporal constraints need only be satisfied locally during execution. Recently it has also been shown that Simple Temporal Networks with Uncertainty, augmented with wait edges, are Dynamically Controllable provided every projection is dispatchable. Thus, the dispatchability property has both theoretical and practical interest. One thing that hampers further work in this area is the underdeveloped theory. The existing definitions are expressed in terms of algorithms, and are less suitable for mathematical proofs. In this paper, we develop a new formal theory of dispatchability in terms of execution sequences. We exploit this to prove a characterization of dispatchability involving the structural properties of the STN graph. This facilitates the potential application of the theory to uncertainty reasoning.
Classical mechanics Hamiltonian and Lagrangian formalism
Deriglazov, Alexei
2016-01-01
This account of the fundamentals of Hamiltonian mechanics also covers related topics such as integral invariants and the Noether theorem. With just the elementary mathematical methods used for exposition, the book is suitable for novices as well as graduates.
First order formalism for quantum gravity
International Nuclear Information System (INIS)
Gleiser, M.; Holman, R.; Neto, N.P.
1987-05-01
We develop a first order formalism for the quantization of gravity. We take as canonical variables both the induced metric and the extrinsic curvature of the (d - 1) -dimensional hypersurfaces obtained by the foliation of the d - dimensional spacetime. After solving the constraint algebra we use the Dirac formalism to quantize the theory and obtain a new representation for the Wheeler-DeWitt equation, defined in the functional space of the extrinsic curvature. We also show how to obtain several different representations of the Wheeler-DeWitt equation by considering actions differing by a total divergence. In particular, the intrinsic and extrinsic time approaches appear in a natural way, as do equivalent representations obtained by functional Fourier transforms of appropriate variables. We conclude with some remarks about the construction of the Hilbert space within the first order formalism. 10 refs