Developing Mathematics Enrichment Workshops for Middle School Students: Philosophy and Sample Workshops

This paper describes our approach to organizing enrichment activities using advanced mathematics topics for diverse audiences of middle school students. We discuss our philosophy and approaches for the structure of these workshops, and then provide sample schedules and resource materials. The workshops cover activities on the following topics: Graphing Calculators; The Chaos Game; Statistical Sampling; CT Scans–the reconstruction problem; The Platonic and Archimedean solids; The Shape of Space; Symmetry; The Binary Number System and the game of NIM; Graph Theory: Proof by Counterexample

Arriving and Belonging: Stories from the St Albans Jewish Community

Helen Singer talks about her parents’ refugee background and her involvement in the creation of the online exhibition: 'Arriving & Belonging: Stories from the St Albans Jewish Community'. Through testimonies, objects and family photographs, the exhibition reveals personal stories of migration and heritage, examining universal themes of sanctuary, courage, compassion and starting a new life in Britain

Cohomological Yang-Mills Theory in Eight Dimensions

We construct nearly topological Yang-Mills theories on eight dimensional manifolds with a special holonomy group. These manifolds are the Joyce manifold with $Spin(7)$ holonomy and the Calabi-Yau manifold with SU(4) holonomy. An invariant closed four form $T_{\mu\nu\rho\sigma}$ on the manifold allows us to define an analogue of the instanton equation, which serves as a topological gauge fixing condition in BRST formalism. The model on the Joyce manifold is related to the eight dimensional supersymmetric Yang-Mills theory. Topological dimensional reduction to four dimensions gives non-abelian Seiberg-Witten equation.Comment: 9 pages, latex, Talk given at APCTP Winter School on Dualities in String Theory, (Sokcho, Korea), February 24-28, 199

Special Quantum Field Theories In Eight And Other Dimensions

We build nearly topological quantum field theories in various dimensions. We give special attention to the case of 8 dimensions for which we first consider theories depending only on Yang-Mills fields. Two classes of gauge functions exist which correspond to the choices of two different holonomy groups in SO(8), namely SU(4) and Spin(7). The choice of SU(4) gives a quantum field theory for a Calabi-Yau fourfold. The expectation values for the observables are formally holomorphic Donaldson invariants. The choice of Spin(7) defines another eight dimensional theory for a Joyce manifold which could be of relevance in M- and F-theories. Relations to the eight dimensional supersymmetric Yang-Mills theory are presented. Then, by dimensional reduction, we obtain other theories, in particular a four dimensional one whose gauge conditions are identical to the non-abelian Seiberg-Witten equations. The latter are thus related to pure Yang-Mills self-duality equations in 8 dimensions as well as to the N=1, D=10 super Yang-Mills theory. We also exhibit a theory that couples 3-form gauge fields to the second Chern class in eight dimensions, and interesting theories in other dimensions.Comment: 36 pages, latex. References have been added together with a not

ULF waves in the solar wind as direct drivers of magnetospheric pulsations

[1] Global magnetospheric ULF pulsations with frequencies in the Pc 5 range (f = 1.7–6.7 mHz) and below have been observed for decades in space and on the Earth. Recent work has shown that in some cases these pulsations appear at discrete frequencies. Global cavity and waveguide modes have been offered as possible sources of such waves. In these models the magnetosphere is presumed to resonate globally at frequencies determined solely by its internal properties such as size, shape, field topology, mass density distribution, etc. We show in this work that upstream solar wind number density and dynamic pressure variations precede and drive compressional magnetic field variations at geosynchronous orbit. Furthermore, spectral analysis shows that wave power spectra in both the solar wind and magnetosphere contain peaks at the same discrete frequencies. Therefore, in contrast to the cavity mode hypothesis, we suggest that discrete ULF pulsations observed within the magnetosphere are at least sometimes directly driven by density oscillations present in the ambient solar wind. Finally, we comment on possible sources for such pulsations observed in the solar wind

Oxidation of basaltic tephras: Influence on reflectance in the 1 micron region

As part of a ongoing study into the products of hydrovolcanism, tuffs were examined from the Cerro Colorado and Pavant Butte tuff cones. The former resides in the northeastern corner of the Pinacate Volcanic Field in Sonara, Mexico and the latter is in the Black Rock Desert of southern Utah. Numerous samples were collected and many of these had their Vis/IR reflectance measured. It seems likely that in the palagonite tuffs there is a combination of nanocrystalline ferric oxide phases contributing to the UV absorption edge, but not to the 1 micron band, plus more crystalline ferric oxides which do contribute to that band as well as ferrous iron within unaltered sideromelane which is skewing the band center to longer wavelengths. This work has implications for the study of Mars. The present work indicates that when ferrous and ferric iron phases are both present, their combined spectral contribution is a single band in the vicinity of 1 micron. The center, depth, and width of that feature has potential to be used to gauge the relative proportions of ferrous and ferric iron phases

Studies of nucleotide sequences in TMV-RNA. II - The action of spleen diesterase

Spleen diesterase action on polynucleotide and ribonucleic acid infectivit

Specific Nature of Hydrolysis of Insulin and Tobacco Mosaic Virus Protein by Thermolysin

Oxidized bovine insulin and tobacco mosaic virus protein used to determine hydrolysis specificity of thermolysi

Internal structure of preformed Cooper pairs

In order to obtain information about the internal structure of the preformed pairs in the pseudogap state of high $T_c$ superconductors, we calculate the propagator of a singlet pair with center of mass coordinate $\mathbf{r}$, and relative distance $\pmb{\rho}$, by solving the Bethe-Salpeter equation, representing the sum over repeated two-particle scattering events due to a distance dependent attraction. We define then a ``pair structure function'' $g_{P}(\mathbf{P},\pmb{\rho})$ that depends on the internal distance $\pmb{\rho}$ between the partners and on the momentum $\mathbf{P}$ of the pair. We calculate this function both for a local potential and $s-$wave symmetry of the order parameter and for a separable potential and $d-$wave symmetry of the order parameter. The influence of the center of mass momentum, strenght of the interaction, temperature, density of particles and of the pseudogap in the one-electron spectrum is studied for both cases.Comment: 12 pages, REVTeX4, 8 EPS figure