Mathematical Fundamentals Research Articles

Early Numerical Competencies and Students with Mathematics Difficulty

Children start elementary school with variable mathematics ski11s. Some childrenunderstand the fundamentals of numbers and mathematics, while others struggle with basic counting, number recognition, understanding of symbols, quantity discrimination, and concepts of addition and subtraction. Often, this set of early numerical competencies is referred to as number sense or early numeracy competencies. Students need to establish and understand these competencies before moving on to more complex mathematical tasks. This article describes important early num erical competencies and provides a description of how these competencies can be taught to students who struggle with mathematics.

Early Numerical Competencies and Students with Mathematics Difficulty

Children start elementary school with variable mathematics ski11s. Some childrenunderstand the fundamentals of numbers and mathematics, while others struggle with basic counting, number recognition, understanding of symbols, quantity discrimination, and concepts of addition and subtraction. Often, this set of early numerical competencies is referred to as number sense or early numeracy competencies. Students need to establish and understand these competencies before moving on to more complex mathematical tasks. This article describes important early num erical competencies and provides a description of how these competencies can be taught to students who struggle with mathematics.

State of the Art on Permeability Characterization of Fibrous Reinforcements used in Resin Transfer Molding Process

The physical and mathematical fundamentals that are required for the measurement of permeability of fibrous reinforcement used in Resin Transfer Molding (RTM) and to interpret correctly the results of those experiments are considered in this article. The basic concepts of fluid dynamics through porous media applied to the analysis of the impregnation phenomena in fibre preforms are discussed. The principal assumptions to simplify the governing equations into the Darcy's law are summarized in order to give an idea of some typical features of the permeability tests regarding the injection parameters and types of fluids and preforms used. Three important concepts for determining permeability in any direction for anisotropic preforms are introduced: permeability tensor ( Kij), permeability ellipse and effective permeability ( Keff). This paper also deals with the deduction, from Darcy's law and Laplace Equation, of the basic equations used on the unidirectional and divergent radial permeability tests. The final conclusion remarks the importance of the concepts exposed in this work.

Divergence-Based Vector Quantization

Supervised and unsupervised vector quantization methods for classification and clustering traditionally use dissimilarities, frequently taken as Euclidean distances. In this article, we investigate the applicability of divergences instead, focusing on online learning. We deduce the mathematical fundamentals for its utilization in gradient-based online vector quantization algorithms. It bears on the generalized derivatives of the divergences known as Fréchet derivatives in functional analysis, which reduces in finite-dimensional problems to partial derivatives in a natural way. We demonstrate the application of this methodology for widely applied supervised and unsupervised online vector quantization schemes, including self-organizing maps, neural gas, and learning vector quantization. Additionally, principles for hyperparameter optimization and relevance learning for parameterized divergences in the case of supervised vector quantization are given to achieve improved classification accuracy.

Roots of modern technology: an elegant survey of the basic mathematical and scientific concepts

Explaining Modern Technology.- Explaining Modern Technology.- I: Fundamentals of Mathematics and Logic.- Mathematicians Are Humans Like You and Me - They Count and Arrange.- Mathematicians Are Nothing Special - They Draw and Compare.- When It Helps to Ignore Any Meaning.- About the Methods for Computing the Future.- What Talking and Writing Have in Common.- II: Fundamentals of Natural Sciences.- What the Moon Has to Do with Mechanical Engineering.- How Albert Einstein Disregarded Common Sense.- How a Few Frog Legs Triggered the Origin of Electrical Engineering.- Small, Smaller, Smallest - How the Components of Matter Were Found.- How the Difference between Particles and Waves Disappeared.- How Recipes in the Cells of Living Organisms Were Found and Can Be Rewritten.- III: Fundamentals of Engineering.- Why Engineers Are Playing with Models.- Everything becomes Digital - Really Everything?.

Void Fraction as a Function of Depth and Pressure Drops of Packed Beds of Porous Media Formed by Granular Materials

A mathematical equation that describes the void fraction as a function of location, bulk density at the surface, bulk density at the location of interest in the bed, maximum bulk density, bin geometry, friction properties of the grain, and the ratio of lateral to vertical pressures of the grain in a deep packed bed of bulk solids was developed. Variation in the void fraction caused variation in the pressure drop per unit of bed depth. Since bulk density and void fraction are functionally related to each other, the void fraction was expressed as a mathematical function of bed depth, and the model was verified using fundamentals of mathematics. In order to develop the model, Ergun's equation was used and integrated over the bed depth, substituting a void fraction that varied with the bed depth. Model results were compared to Shedd's data. Agreement between Shedd's data and this model was good to a bed depth of 10 m. For bed depths greater than 10 m, results from this model gave much greater pressure drop values than were given by Shedd. The model showed that pressure drop per unit of bed depth increases exponentially with the bed depth.

Condensate system modelling in real time for a training power plant simulator

In this paper, the basis of the models of the condensate water and the air cooled condenser are presented. The models are part of a full scope simulator of a 450 MW combined cycle power plant. The simulator is executed in real time and is intended to be a support for the training of the operators of the Comisian Federal de Electricidad (the Mexican utility company). The simulator is presently in the final acceptance tests stage and is programmed to be in commercial operation in 2010. Here, are included a summary of the modelling methodology used to develop the referred models and the mathematical fundaments used to obtain the main equations. The tendencies of selected variables during a transient are displayed and analysed in order to probe the validity of the new generic models.

The workgroup applied for a mathematics subject

The procedure we are going to present is developed for the graduate programme of Ingeniero Tecnico en Diseno Industrial (Industrial Design Technical Engineering). The subject we study was Fundamentos Matematicos de la Ingenieria (Engineering Mathematical Fundamentals). And the activity is prepared for the practical lessons into the subject which belongs. It consists in a workgroup activity in which students are grouped with the aim of working together in the subject contents along the whole course. We show that the results are amazing.

Measurement-computation converter as a measurement facility

Consideration was given to the elements of the theory of measurement-computation converters (ICC) whose mathematical fundamentals were expounded in the monographs [1,2] oriented to the readers inte...

製品系列展開における共通化・カスタマイゼーション・ラインアップ調整による包括的な最適設計問題に関する研究(機械要素,潤滑,設計,生産加工,生産システムなど)

This research discusses an optimal design problem for product family deployment under a wider perspective throughout commonalization, customization and lineup arrangement. In the discussion, commonalization is viewed as the operation that restricts the feasible region by fixing a set of design variables related to commonalized components or modules, customization is viewed as the operation that adjusts another set of design variables related to reserved freedom, and lineup arrangement toward individual customer's needs is possible within ones that are feasible under commonalization and customization. This paper defines the mathematical fundamentals of the design problem throughout these aspects under the viewpoint of optimal design paradigm. That is, the mathematical formulation is generally defined, its mathematical structure is revealed with a concept of active set strategy, and the modes of the optimal solution are explored toward developing any computational approach for effectively solving such complex design problems. Finally, a case study is demonstrated with a design problem of product family deployment of centrifugal compressors for illustrating the optimality in the throughout design.

Reply to “Comment on ‘Isotope effect in high-Tcsuperconductors’ ”

Our paper on the isotope effect in high-temperature superconductors with cation substitutions presents a comprehensive analysis rooted completely in the experimental evidence. In this Reply we show that pair-breaking disorder, isotope effects, doping-induced variations in Tc and in the magnetic penetration depth, Coulomb's law, and Anderson's theorem are treated with correct physical and mathematical fundamentals. In contrast, the theory fostered in the Comment by Alexandrov and Zhao contradicts several specific experimental facts, eight of which are briefly discussed. Their Comment also uncritically repeats a previously discredited assertion of an isotope effect in the superconducting carrier mass, incorrectly assumes that cation doping continuously varies intrinsic superconducting parameters, unjustifiably assigns importance to data from samples with serious quality problems, and renders a false estimate of the pair-breaking strength.

Teaching and practicing computer science at the university level

Universities offering Computing Science curricula should do so at the university level. Taking pragmatic shortcuts causes stagnation in professional practice. The essential element is the pervasive presence throughout the curriculum of mathematical modelling, which is the role of Formal Methods in its original sense. Mathematical fundamentals and concepts are crucial, software tools are auxiliary and even misleading without the former. Recommendations are given for curriculum structure, specific key courses and attitudes to instil in students and educators. Comparison with other approaches is made. A conclusion is that CS curricula should break outside the limitations caused by conservative policy makers but also self-imposed ones.

A multi-channel audio system based on the theory of integral equations.

The basics of a multi-channel audio system, which attempts the reproduction of a desired sound field, are presented. The system’s hardware consists of a three-dimensional array of loudspeakers, and can be used in combination with a specially designed microphone array. The mathematical fundamentals on which this technique is grounded consist of the formulation of the problems as an integral equation. The loudspeaker signals are determined from the knowledge of the target sound field on the boundary of a given control volume. The solution to this inverse problem is computed performing a singular value decomposition of the integral operator involved. For some simple array geometries it is possible to calculate an analytical solution to the problem. A regularization method is applied, as required by the ill-posed nature of the inverse problem under consideration. Some insight into the physical meaning of the ill-posedness is given and some analogies to near-field acoustic holography are suggested. The effectiveness of the method proposed has been verified experimentally and some of the experimental results are presented. Finally, it is shown how this technique has been successfully applied to the design of a multi-channel auralization system for room acoustics.

Simulation of processes in natural-circulation circuits of heat-recovery boilers of combined cycle power plants

Mathematical fundamentals of development of models of natural-circulation circuits of heat-recovery boilers are considered. Processes in the high-pressure circuit of a P-96 boiler are described.

Character of the magnetic monopole field

Based upon the Helmholtz decomposition theorem this paper shows that the field of a stationary magnetic monopole, assuming it exists, cannot be represented by a vector potential. Persisting to use vector potential in monopole representation violates fundamentals of mathematics. The importance of this finding is that the vector potential representation was crucial to the original prediction of the quantised value for a magnetic charge.

Fast Dynamics of an Eel-Like Robot—Comparisons With Navier–Stokes Simulations

This paper proposes a dynamic model of the swim of elongated fish suited to the online control of biomimetic eel-like robots. The approach can be considered as an extension of the original reactive ldquolarge elongated body theoryrdquo of Lighthill to the 3-D self-propulsion to which a resistive empirical model has been added. While all the mathematical fundamentals have been detailed by Boyer . (http://www.irccyn.ec-nantes.fr/hebergement/Publications/2007/3721.pdf, 2007), this paper essentially focuses on the numerical validation and calibration of the model and the study of swimming gaits. The proposed model is coupled to an algorithm allowing us to compute the motion of the fish head and the field of internal control torque from the knowledge of the imposed internal strain fields. Based on the Newton-Euler formalism of robot dynamics, this algorithm works faster than real time. As far as precision is concerned, many tests obtained with several planar and 3-D gaits are reported and compared (in the planar case) with a Navier-Stokes solver, which, until today have been devoted to the planar swim. The comparisons obtained are very encouraging since in all the cases we tested, the differences between our simplified and reference simulations do not exceed 10%.

Educating Future Water Resources Managers

Educating Future Water Resources Managers

Fiziko-matematicheskie osnovy mnogoal'ternativnogo raspoznavaniya i identifikatsii gidrolokatsionnykh polei tel slozhnoi geometricheskoi formy

Физико-математические основы многоальтернативного распознавания и идентификации гидролокационных полей тел сложной геометрической формы, Давыдов В.С.

2210 製品系列展開のためのモジュール・カスタマイゼーション・ラインアップの包括的な最適設計に関する考察 : 第1報:包括的設計における最適性とその構造

This research discusses product family design toward its extension to throughtout consideration of commonalization, customization, and lineup arrangement under optimal design paradigm. That is, commonalization is viewed as the operation that restricts the feasible region by fixing a set of design variables related to commonalized components or modules against later customization and final lineup offered to customers. Customization is viewed as the operation that arranges line up by adjusting another set of design variables related to reserved freedom for customer's needs. Their mutual and bi-directional relationship must be matter of optimal design. This paper discusses the mathematical fundamentals of optimal product family design at the view point of throughout design.

MIMO channel orthogonalisations applying universal eigenbasis

Some mathematical fundamentals of the multiple input multiple output (MIMO) channel orthogonalisations using prolate spheroidal wave functions (PSWFs) as a universal basis are presented. In contrast to the Karhunen–Loeve expansion or singular value decomposition, the PSWF basis is ‘invariant’ to the properties of the MIMO channel covariance matrix and provides an almost minimum set of eigenfunctions that allow the channel to be represented with a predefined accuracy.