Role of mathematics

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  • Today the United States has the challenge and the opportunity to provide all students with the mathematical knowledge, skills, and confidence they will need in a highly technical world. There is considerable nationwide interest in improving students’ understanding of mathematics, combined with an emerging consensus about the essential elements of mathematics instruction; in addition, research has provided valuable insights into how children learn. Together these factors are opening the way to substantial and enduring progress in school mathematics....

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  • The United States must restructure mathematics education--both what is learned and the way it is taught--if children are to develop the mathematical knowledge and skills they will need to be personally and professionally competent in the twenty-first century. Joining the recent reports that have opened a national dialogue on these issues, Reshaping School Mathematics focuses discussion on essential ideas that transcend details of current curricula or assessment results.

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  • Clearly and elegantly presented, Mathematical Methods in Science and Engineering provides a coherent treatment of mathematical methods, bringing advanced mathematical tools to a multidisciplinary audience. The growing interest in interdisciplinary studies has brought scientists from many disciplines such as physics, mathematics, chemistry, biology, economics, and finance together, which has increased the demand for courses in upper-level mathematical techniques.

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  • The curriculum vitae of Alice Turner Schafer lists two specializations: abstract algebra (group theory) and women in mathematics. As early as her high school years Alice exhibited a love for mathematics and an interest in teaching as a career. As a mathematics educator she championed the full participation of women in mathematics.

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  • We present here the second in a sequence of three papers devoted to the Gromov-Witten theory of nonsingular target curves X. Let ω ∈ H2(X,Q) denote the Poincar´e dual of the point class. In the first paper [24], we considered the stationary sector of the Gromov-Witten theory of X formed by the descendents of ω. The stationary sector was identified in [24] with the Hurwitz theory of X with completed cycle insertions. The target P1 plays a distinguished role in the Gromov-Witten theory of target curves.

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  • In the first two articles of this series, we investigated various higher analogues of Gauss composition, and showed how several algebraic objects involving orders in quadratic and cubic fields could be explicitly parametrized. In particular, a central role in the theory was played by the parametrizations of the quadratic and cubic rings themselves. These parametrizations are beautiful and easy to state.

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  • Dedicated to the memory of Gert Kjærg˚ Pedersen ard Abstract In the process of developing the theory of free probability and free entropy, Voiculescu introduced in 1991 a random matrix model for a free semicircular system. Since then, random matrices have played a key role in von Neumann algebra theory (cf. [V8], [V9]). The main result of this paper is the follow(n) (n) ing extension of Voiculescu’s random matrix result: Let (X1 , . . . , Xr ) be a system of r stochastically independent n × n Gaussian self-adjoint random matrices as in Voiculescu’s random matrix paper...

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  • The purpose of  this report  is  to better understand  the  impact of  international students on  the Australian economy, focusing in particular on the effect of potential reductions in higher  education enrolments.  International education  is an Australian export success story. From a small base  it has now  become Australia’s  third  largest export  sector behind  coal and  iron ore, and  is  the  largest  service  export  sector  in  the  economy, worth  around  $18  billion  in  2009.

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  • Scoring Extended- and Short-Response Items Extended- and short-response items are evaluated according to an established scoring scale, called a rubric, developed from a combination of expectations and a sample of actual student responses. Such rubrics must be particularized by expected work and further developed by examples of student work in developing a guide for scorers. Illinois educators play a substantial role in developing these guides used for the scoring of the short- and extended-response items.

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  • In this paper, materials of ZnS:Cu, ZnS:Mn and ZnO:Co were prepared by ceramic method and co-precipitated method. The presence of transition metals such as Cu2+(3d9), Mn2+(3d5) in ZnS and Co2+(3d7) in ZnO make blue bands at around 476 nm, 486 nm and green band at around 514 nm disappeared. Simultaneously, there are luminescence bands at around 533 nm, 582 nm, 693 nm for bulk samples of ZnS:Cu, ZnS:Mn, ZnO:Co and 603 nm for nanocrystalline sample of ZnS:Mn.

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  • In the next Section II we will describe the nature of the general purpose technol- ogy represented by cloud computing, its genesis and its likely impact on the econo- my and on the structure of many markets. As we will see, the introduction of cloud computing is going to reduce drastically the fixed costs of entry and production, turning part of them into variable costs related to the production necessities. This will have a positive impact on entry and competition in all sectors where fixed ICT spending is crucial.

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  • In this report we present some noncommutative weak and strong laws of large numbers. Two case are considered: a von Neumann algebra with a normal faithful state on it and the algebra of measurable operators with normal faithful trace. 1. Introduction and notations One of the problems occurring in noncommutative probability theory concerns the extension of various results centered around limit theorems to the noncommutative context.

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  • The diffusion behaviour of water and HCl solution at different temperatures and concentrations into a modified polyethylene filled with carbon black used for lining is presented. It has shown the predominant role of nature of environment and carbon black content. In the both environments, an increase of environmental temperature increased the capacity of environmental absorption and the diffusion rate.

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  • Simulation of the diffusion mechanism via microscopic bubbles in amorphous materials is carried out using the statistical relaxation models $Co_{81.5}B_{18.5}$ containing $2\times 10^5$ atoms. The present work is focused on the role of these bubbles for self-diffusion in amorphous solids. It was found that the numbers of the vacancy bubbles in amorphous $Co_{81.5}B_{18.5}$ vary from $1.4\times 10^{-3}$ to $4\times 10^{-3}$ per atom depending on the relaxation degree. The simulation shows the collective character of the atomic movement upon diffusion atoms moving.

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  • .Mathematical Methods in Image Reconstruction .S1AM Monographs on Mathematical Modeling and Computation About the Series In 1997, SIAM began a new series on mathematical modeling and computation.

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  • Software requirements for engineering and scientific applications are almost always computational and possess an advanced mathematical component. However, an application that calls for calculating a statistical function, or performs basic differentiation of integration, cannot be easily developed in C++ or most programming languages. In such a case, the engineer or scientist must assume the role of software developer.

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  • Chemistry plays a key role in conquering diseases, solving energy problems, addressing environmental problems, providing the discoveries that lead to new industries, and developing new materials and technologies for national defense and homeland security. However, the field is currently facing a crucial time of change and is struggling to position itself to meet the needs of the future as it expands beyond its traditional core toward areas related to biology, materials science, and nanotechnology....

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  • The third part of the book is dedicated to analysis of role of DNA methylation in cancer. According to the American Cancer Association, nearly 13% of all deaths worldwide are cancer related. Aberrant DNA methylation patterns is likely to play a causative role in cancer initiation and development. The first chapter is dedicated to investigation of DNA methylation role in the development of hepatocellular carcinoma associated with tyrosinemia.

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  • Two centuries ago, in his celebrated work Disquisitiones Arithmeticae of 1801, Gauss laid down the beautiful law of composition of integral binary quadratic forms which would play such a critical role in number theory in the decades to follow. Even today, two centuries later, this law of composition still remains one of the primary tools for understanding and computing with the class groups of quadratic orders. It is hence only natural to ask whether higher analogues of this composition law exist that could shed light on the structure of other algebraic number rings and fields. ...

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  • Elliptic units, which are obtained by evaluating modular units at quadratic imaginary arguments of the Poincar´e upper half-plane, provide us with a rich source of arithmetic questions and insights. They allow the analytic construction of abelian extensions of imaginary quadratic fields, encode special values of zeta functions through the Kronecker limit formula, and are a prototype for Stark’s conjectural construction of units in abelian extensions of number fields.

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