Diagram Literacy in Preservice Math Teachers, Computer Science Majors, and Typical Undergraduates: The Case of Matrices, Networks, and Hierarchies

According to the National Council of Teachers of Mathematics (2000), children need to learn how to create and use mathematical diagrams to represent and reason about phenomena in the world. The author proposes a model of diagram literacy that includes six types of knowledge required for diagrammatic competence - implicit, construction, similarity, structural, metacognitive, and translational. A study is reported that examined college students' diagram literacy for three interrelated mathematical diagrams - matrices, networks, and hierarchies. Three groups of students participated: preservice, secondary-level, math teachers; computer science majors; and typical undergraduates. The results of the study are reassuring in some ways concerning the level of diagram literacy possessed by students at the culmination of current K through 12 instruction and by teachers of future secondary students. However, the results also point to areas in which preservice math teachers should be better prepared if the goals for students' diagram literacy are to be met.     

Rotational Spectra of Argon Acetone: A Two-Top Internally Rotating Complex

The rotational spectra of the argon acetone weakly bound complex was studied by pulsed jet Fabry-Perot Fourier transform microwave spectroscopy. Over 500 transitions of the complex were measured between 5.5 and 26 GHz from J=2-1 to J=12-11. The two methyl groups undergo hindered internal rotation resulting in four or five internal rotation states. The microwave transitions are within these states, resulting in a splitting of each rotational transition into four and sometimes five distinct transitions. The three-fold barrier to internal rotation is determined to be 260 cm⁻¹, 2% less than the 266 cm⁻¹ barrier in acetone itself. The structure of the complex has the argon atom above the heavy atom plane of the acetone, 3.52 Å from the CO bond and approximately in the C_s plane, which is perpendicular to the CCC plane of acetone.     

Value functions,domination cones and proper efficiency in multicriteria optimization

In the absence of a clear objective value function, it is still possible in many cases to construct a domination cone according to which efficient (nondominated) solutions can be found. The relations between value functions and domination cones and between efficiency and optimality are analyzed here. We show that such cones must be convex, strictly supported and, frequently, closed as well. Furthermore, in most applications potential optimal solutions are equivalent to properly efficient points. These solutions can often be produced by maximizing with respect to a class of concave functions or, under convexity conditions, a class of affine functions.     

The Worpitzky identity for the groups of signed and even-signed permutations

Journal of Algebraic Combinatorics - The well-known Worpitzky identity $$\begin{aligned} (x+1)^n = \sum \limits _{k=0}^{n-1} A_{n,k} {{x+n-k} \atopwithdelims (){n}} \end{aligned}$$ provides a...     

THE 'OPSIN SHIFT' IN BACTERIORHODOPSIN: STUDIES WITH ARTIFICIAL BACTERIORHODOPSINS

Abstract— The difference (in cm⁻¹) in absorption maxima between the protonated Schiff base of retinals and the pigment derived therefrom has been defined as the opsin shift. It represents the influence of the opsin binding site on the chromophore. The analysis of the opsin shifts of a series of dihydrobacteriorhodopsins has led to the external point-charge model, which in addition to a counter anion near the Schiff base ammonium, carries another negative charge in the vicinity of the β-ionone ring. This is in striking contrast to the external point-charge model proposed earlier for the bovine visual pigment. The absorption maxima of rhodopsins formed from bromo- and phenyl retinals support the two models. A retinal carrying a photoaffinity label has yielded a nonbleachable bacteriorhodopsin.     

Spectroscopic techniques in medicine: The future of diagnostics

Spectroscopic techniques have been finding increasing applications in the field of biomedicine especially in the field of disease diagnosis and monitoring in spite of the rapid emergence of several molecular biology based techniques. The significance of spectroscopy techniques and the possibility of using some of the underutilized regions of the electromagnetic radiations are discussed in this review. While previous reviews have already dealt with the potential of Fourier transform infrared spectroscopy-based (FTIR) techniques for clinical applications, the present review addresses the lacunae of the techniques along with its future trends that may make it a technique routinely applied in clinical settings.     

Periodic solitons in nonlocal nonlinear media

We identify periodic solitons in nonlocal nonlinear media: multi-hump soliton solutions propagating in a fully periodic fashion. We also demonstrate recurrences and breathers whose evolution is statistically periodic and discuss why some systems support periodic solitons while others do not.