This paper explores some of the ambiguities inherent in the notions of generality and genericity, drawing parallels between natural language and mathematics, and thereby obliquely attacking the entrenched view that mathematics is unambiguous. Alternative ways of construing 2N, for example, suggest approaches to some of the difficulties which students find with an algebraic representation of generality. Examples are given to show that confusion of levels is widespread throughout mathematics, but that the very confusion is a source of richness of meaning.

http://bupload.persiangig.com/document/Examples/Generic%20Examples%20Seeing%20the%20General%20in%20the%20Particular.pdf

Generic examples: Seeing the general in the particular

A measurement is presented of the inclusive neutral current e\pm p scattering cross section using data collected by the H1 experiment at HERA during the years 2003 to 2007 with proton beam energies Ep of 920, 575, and 460 GeV. The kinematic range of the measurement covers low absolute four-momentum transfers squared, 1.5 GeV2 < Q2 < 120 GeV2, small values of Bjorken x, 2.9 \cdot 10-5 < x < 0.01, and extends to high inelasticity up to y = 0.85. The structure function FL is measured by combining the new results with previously published H1 data at Ep = 920 GeV and Ep = 820 GeV. The new measurements are used to test several phenomenological and QCD models applicable in this low Q2 and low x kinematic domain.

/pdf/measurement-of-the-inclusive-e-p-scattering-cross-section-at-2pxv1v5sup.pdf

Measurement of the inclusive e ± p scattering cross section at high inelasticity y and of the structure function F L

Introduction 1. Understanding human behavior 2. The incorporation of von Neumann and Morgenstern's behavioral axioms in economics and psychology 3. 'Measurement theory in psychology is behavior theory' 4. Kahneman and Tversky: heuristics, biases, and prospects for psychology and economics 5. Incorporating psychological experiments in economics and the construction of behavioral economics 6. Building and defining behavioral economics Epilogue.

Behavioral Economics: A History

Iris recognition, the ability to recognize and distinguish individuals by their iris pattern, is one of the most reliable biometrics in terms of recognition and identification performance. However, the performance of these systems is affected by poor-quality imaging. In this paper, we extend iris quality assessment research by analyzing the effect of various quality factors such as defocus blur, off-angle, occlusion/specular reflection, lighting, and iris resolution on the performance of a traditional iris recognition system. We further design a fully automated iris image quality evaluation block that estimates defocus blur, motion blur, off-angle, occlusion, lighting, specular reflection, and pixel counts. First, each factor is estimated individually, and then, the second step fuses the estimated factors by using a Dempster-Shafer theory approach to evidential reasoning. The designed block is evaluated on three data sets: Institute of Automation, Chinese Academy of Sciences (CASIA) 3.0 interval subset, West Virginia University (WVU) non-ideal iris, and Iris Challenge Evaluation (ICE) 1.0 dataset made available by National Institute for Standards and Technology (NIST). Considerable improvement in recognition performance is demonstrated when removing poor-quality images selected by our quality metric. The upper bound on computational complexity required to evaluate the quality of a single image is O(n2 log n).

Estimating and Fusing Quality Factors for Iris Biometric Images

There is evidence from earliest historical records that examples play a central role in both the development of mathematics as a discipline and in the teaching of mathematics. It is not surprising therefore that examples have found a place in many theories of learning mathematics. Many would argue that the use of examples is an integral part of the discipline of mathematics and not just an aid for teaching and learning. The forum takes as its background both the variety of ways in which examples are construed within different theories of learning and the contribution that attention to examples can make to the learning and teaching processes. Consequently the forum can be seen as addressing issues at the very heart of mathematics education, both drawing upon and informing many other research topics. We argue that paying attention to examples offers both a practically useful and an important theoretical perspective on the design of teaching activities, on the appreciation of learners’ experiences and on the professional development of mathematics teachers. The importance of these ideas does not actually depend on the framework used for analysing teachers’ intentions, nor on any terms used to describe forms of teaching, such as: ‘analytic-inductive’ or ‘synthetic-deductive’, ‘traditional’ or ‘reform’, ‘rotelearning’ or ‘teaching for understanding’, ‘authentic’ or ‘investigative’. Issues in exemplification are relevant to all kinds of engagement with mathematics. This paper positions exemplification on the research agenda for the community by giving a historical overview of the way examples have been seen in mathematics education; an account of associated literature; an exploration of how exemplification ‘fits’ with various perspectives on learning mathematics; accounts of issues relating to teachers’ and learners’ use of examples; and directions for future research.

/pdf/exemplification-in-mathematics-education-a9u5l23wek.pdf

Exemplification in mathematics education

How commutative can a non-commutative group be?

George Boole: His Life and Work

(1976). Commutativity in Finite Rings. The American Mathematical Monthly: Vol. 83, No. 1, pp. 30-32.

Commutativity in Finite Rings

Groups with automorphisms inverting most elements

We investigate the set of values attained by Pr(R), the probability that a random pair of elements in a nite ring R commute. A key tool is a new notion of isoclinism for rings, and an associated canonical form for rings. In particular, we show that Pr(R) is an isoclinic invariant, and characterize all possible values of Pr(R) 11=32, and the associated isoclinism families.

/pdf/finite-rings-with-many-commuting-pairs-of-elements-4k0y45krgx.pdf

Des MacHale

Papers

How commutative can a non-commutative group be?

George Boole: His Life and Work

Commutativity in Finite Rings

Groups with automorphisms inverting most elements

Finite rings with many commuting pairs of elements