Al Multiple-Quantum MAS NMR of Mechanically Treated Bayerite (α-Al(OH)3) and Silica Mixtures

Two-dimensional ²⁷Al multiple-quantum magic angle spinning (MQMAS) NMR experiments are used to study mixtures of bayerite (α-Al(OH)₃) with either silicic acid (SiO₂.nH₂O) or silica gel (SiO₂) that have been ground together for varying lengths of time. This mechanical treatment produces changes in the ²⁷Al MAS and MQMAS NMR spectra that correspond to the formation of new Al species. Mean values of the quadrupolar interaction (P_Q) and isotropic chemical shift (δ_CS) are extracted from the two-dimensional ²⁷Al NMR spectra for each of these species. The presence of significant distributions of both ²⁷Al quadrupolar and chemical shift parameters is demonstrated and the effect of grinding duration on the magnitudes of these distributions is discussed.     

Students Talk About Prime: What We Heard About Definitions

This study examines data from college students who worked in pairs to make decisions about a list of potential definitions of prime number. Analysis focused on the evidence each student pair cited when they decided whether or not a statement could be used as a definition for prime number. The purpose of this paper is to describe patterns in the ways students used the evidence they cited. Findings suggest that students attend to important features of mathematical definitions, with some students giving preference to usability and others giving preference to definitions that are unambiguous.     

Diagnostic assessment of preparedness of level one sports science students for biomechanics modules

The primary objective of this study was to investigate the use of a diagnostic test to assess the prepardness of level one students for a sports biomechanics module. During their first week at university, a cohort of 108 students completed a diagnostic test at the end of their first lecture in sports biomechanics, with no prior notice. Upon completion of the 12-week module, the students sat the same diagnostic test, again with no prior notice. The results from the initial test were used to identify areas that required emphasis and additional resources during delivery of the module. The comparison of test results from the two sittings was used as a measure of the level of success of the module in increasing the level of student understanding. It is concluded that the design of a diagnostic test specific to a module can be used both to inform subsequent teaching and to assess success of teaching methods.     

Characterizing algebraic stacks

We extend the notion of algebraic stack to an arbitrary subcanonical site . If the topology on is local on the target and satisfies descent for morphisms, we show that algebraic stacks are precisely those which are weakly equivalent to representable presheaves of groupoids whose domain map is a cover. This leads naturally to a definition of algebraic -stacks. We also compare different sites naturally associated to a stack.

     

Shifting algorithms for tree partitioning with general weighting functions

Recently two shifting algorithms were designed for two optimum tree partitioning problems: The problem of max-min q-partition [4] and the problem of min-max q-partition [1]. In this work we investigate the applicability of these two algorithms to max-min and min-max partitioning of a tree for various different weighting functions. We define the families of basic and invariant weighting functions. It is shown that the first shifting algorithm yields a max-min q-partition for every basic weighting function. The second shifting algorithm yields a min-max q-partition for every invariant weighting function. In addition a modification of the second algorithm yields a min-max q-partition for the noninvariant diameter weighting function.     

Bivariate interpolation based on univariate subdivision schemes

The paper presents a bivariate subdivision scheme interpolating data consisting of univariate functions along equidistant parallel lines by repeated refinements. This method can be applied to the construction of a surface passing through a given set of parametric curves. Following the methodology of polysplines and tension surfaces, we define a local interpolator of four consecutive univariate functions, from which we sample a univariate function at the mid-point. This refinement step is the basis to an extension of the 4-point subdivision scheme to our setting. The bivariate subdivision scheme can be reduced to a countable number of univariate, interpolatory, non-stationary subdivision schemes. Properties of the generated interpolant are derived, such as continuity, smoothness and approximation order.