Proof without Words: On Sums of Squares and Triangles

author's final draft post-referee and pre-publication copySummary. We visually display a relationship between sums of squares and the sum of an even number of triangular numbers. Connections to some proofs without words appearing in the literature are briefly discussed.Ye

Growth Kinetics of Vitamin C Crystals in a Batch L(+)-Ascorbic Acid – Methanol – Ethanol – Water System: Size Independent Growth Model Approach

The experimental data concerning growth kinetics of vitamin C (L(+)-ascorbic acid, LAA) crystals in a seeded and cooling batch mass crystallization process realized in a four–compound: L(+)-ascorbic acid–methanol–ethanol–water system are reported. Influences of initial composition of solution and its linear cooling rate on “average, effective” values of crystal linear growth rate were examined. Small divergences between LAA crystal size distributions (CSDs) data from granulometric analysis and Coulter counter were interpreted theoretically and discussed. Linear growth rates of crystals in a batch crystallizer were acquired with a proposed by Nývlt indirect method, based on the analysis of population density n(L) data in a MSMPR (mixed suspension mixed product removal) crystallizer. Size–independent growth (SIG) kinetics was assumed. It can be concluded, that the largest and the most uniform particles of purified, crystalline vitamin C correspond to higher initial concentration of L(+)-ascorbic acid in a solution and lower cooling rate applied

Connecting Inquiry, Research, and Technology: The Multigenre Digital Inquiry Project

This article describes research on a Multigenre Digital Inquiry Project (MDIP), a technology-infused project designed to provide an opportunity for students to inquire about a topic of interest and share their research using 21st century technologies. Instead of composing a research paper or literature review, students designed a website with pieces written in multiple genres to share their learning, including at least two pieces created using digital tools. In this article, the authors share the design of the MDIP and how it was implemented in three teacher education courses. Data analysis aimed to understand how pre-service teachers engaged in this project and reflected on their learning. Using themes from the analysis of students’ end-of-semester reflections and memos written about the pieces included in the projects, the authors share how students valued support in various areas including technology, how they expanded their views of writing and genre, and how their experiences illustrated academic, personal, and pedagogical growth. Ultimately, students learned from this challenging, yet rewarding experience. Finally, the authors share suggestions for others interested in incorporating a MDIP in their work

Conformal lattice of magnetic bubble domains in garnet film

We report experimental observations of magnetic bubble domain arrays with no apparent translational symmetry. Additionally the results of comparative numerical studies are discussed. Our goal is to present experimental evidence for natural occurence of conformal structures.Comment: 7 pages, 2 figures, LaTeX2e, accepted as paper E090 at JEMS'01 (Joint European Magnetic Symposia, formerly EMMA + MRM), August 28th to September 1st, 2001, Grenoble, Franc

Differentiation of the facial-vestibulocochlear ganglionic complex in human embryos of developmental stages 13–15

A study was made on 18 embryos of developmental stages 13–15 (5th week). Serial sections made in horizontal, frontal, and sagittal planes were stained with routine histological methods and some of them were treated with silver. In embryos of stage 13, the otic vesicle is at the rhombomere 5, and close to the vesicle is the facial-vestibulocochlear ganglionic complex in which the geniculate, vestibular, and cochlear ganglion may be discerned. These ganglia are well demarcated in embryos of stage 14. In the last investigated stage (15th) the nerve fibres of the ganglia reach the common afferent tract

Quaternary climate modulation of Pb isotopes in the deep Indian Ocean linked to the Himalayan chemical weathering

We use reductive sediment leaching to extract lead (Pb) from the authigenic fraction of marine sediments and reconstruct the Pb isotope evolution of the deep central Indian Ocean over the past 250 thousand years at ∼3 kyr resolution. Temporal variations define a binary mixing line that is consistent with data from ferromanganese nodules and which records mixing between two well-defined endmembers through time. The unradiogenic endmember appears to represent a widely-distributed Pb source, from mid-ocean ridges or possibly volcanic aerosols, while the radiogenic endmember coincides with the composition of Ganges–Brahmaputra river sediments that are indicative of the Himalayan weathering inputs. Glacial–interglacial Pb isotope variations are striking and can be explained by an enhancement of Himalayan contributions by two to three times during interglacial periods, indicating that climate modulates the supply of dissolved elements to the ocean. While these changes could accurately record variations in the continental chemical weathering flux in response to warmer and wetter conditions during interglacials, the relative proportions of Pb derived from the Ganges and Brahmaputra appear to have been constant through time. This observation may point towards particulate-dissolved interactions in the estuary or pro-delta as a buffer of short timescale variability in the composition (and potentially flux) of the fluvial inputs. In addition, the changes are recorded at 3800 m water depth, and with the lack of deep water formation in the Bay of Bengal, a mechanism to transfer such a signature into the deep ocean could either be reversible scavenging of dissolved Pb inputs and/or boundary exchange on the deep sea fan. Unless the mechanism transferring the Pb isotope signature into the deep ocean was itself highly sensitive to global climate cycles, and with the absence of a precessional signal in our Pb isotope data, we suggest that the Indian climate and its influence on basin-scale chemical weathering were strongly modulated by glacial versus interglacial boundary conditions