Who Gave You the Cauchy–Weierstrass Tale? The Dual History of Rigorous Calculus

Cauchy’s contribution to the foundations of analysis is often viewed through the lens of developments that occurred some decades later, namely the formalisation of analysis on the basis of the epsilon-delta doctrine in the context of an Archimedean continuum. What does one see if one refrains from viewing Cauchy as if he had read Weierstrass already? One sees, with Felix Klein, a parallel thread for the development of analysis, in the context of an infinitesimal-enriched continuum. One sees, with Emile Borel, the seeds of the theory of rates of growth of functions as developed by Paul du Bois-Reymond. One sees, with E. G. Bj?rling, an infinitesimal definition of the criterion of uniform convergence. Cauchy’s foundational stance is hereby reconsidered.     

A new immunodeficiency disorder in humans involving NK cells

Immunodeficiency disorders have provided much information on the development and interaction of the various B and T lymphoid components in the immune system of man. As the lymphoid system becomes increasingly divided into functional subsets of cells it will be important to find immunodeficiencies affecting newly discovered cell types. Natural killer (NK) cells are a recently described but ill-defined subpopulation of lymphocytes which is thought to play an important part in surveillance against tumour development. Mice homozygous for the beige gene were found to have a selective deficiency in NK function and were more susceptible to transplantation of syngeneic tumours as predicted. We report here that patients carrying the analogous, autosomal recessive Chediak-Higashi (CH) gene have a profound defect in their ability to spontaneously lyse various tumour cells in vitro by either antibody-dependent or independent mechanisms. Since other cell-mediated cytolytic functions were relatively normal, these results suggest that the beige or Chediak-Higashi gene in both man and mouse controls NK function.     

Nachweis von Scilliglaucosidin in den Zwiebeln vonBowiea volubilis Harvey

Summary Hellebrigenin was converted to Scilliglaucosidin-19-ol and 3-Epi-Scilliglaucosidin-19-ol. This proves the correctness of the assumption ofStoll et al. ³ that the aldehydic group of Scilliglaucosidin is in position C-10.Comparison of a reduction product of Nabogenin, a substance isolated earlier from the bulbs ofBowiea volubilis Harvey, with Scilliglaucosidin-19-ol and 3-Epi-Scilliglaucosidin-19-ol showed its identity with the first named compound. This proves that the so called Nabogenin was a mixture consisting mainly of Scilliglaucosidin.

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8. Mitteilung über die Glykoside vonBowiea vocubilis Harvey und 162. Mitteilung über Glykoside und Aglykone.

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7. Mitt.:A. Katz, Helv. chim. Acta38, 1565 (1955).

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161. Mitt.:H. Kündig-Hegedüs undO. Schindler, Helv. chim. Acta39, 904 (1956).     

The dynamics of melt and shear localization in partially molten aggregates

The volcanoes that lie along the Earth's tectonic boundaries are fed by melt generated in the mantle. How this melt is extracted and focused to the volcanoes, however, remains an unresolved question. Here we present new theoretical results with implications for melt focusing beneath mid-ocean ridges. By modelling laboratory experiments, we test a formulation for magma dynamics and provide an explanation for localized bands of high-porosity and concentrated shear deformation observed in experiments. These bands emerge and persist at 15 degrees-25 degrees to the plane of shear. Past theoretical work on this system predicted the emergence of melt bands but at an angle inconsistent with experiments. Our results suggest that the observed band angle results from a balance of porosity-weakening and strain-rate-weakening deformation mechanisms. Lower band angles are predicted for greater strain-rate weakening. From these lower band angles, we estimate the orientation of melt bands beneath mid-ocean ridges and show that they may enhance magma focusing toward the ridge axis.     

A soluble and air-stable organic semiconductor with high electron mobility

Electronic devices based on organic semiconductors offer an attractive alternative to conventional inorganic devices due to potentially lower costs, simpler packaging and compatibility with flexible substrates. As is the case for silicon-based microelectronics, the use of complementary logic elements-requiring n- and p-type semiconductors whose majority charge carriers are electrons and holes, respectively-is expected to be crucial to achieving low-power, high-speed performance. Similarly, the electron-segregating domains of photovoltaic assemblies require both n- and p-type semiconductors. Stable organic p-type semiconductors are known, but practically useful n-type semiconductor materials have proved difficult to develop, reflecting the unfavourable electrochemical properties of known, electron-demanding polymers. Although high electron mobilities have been obtained for organic materials, these values are usually obtained for single crystals at low temperatures, whereas practically useful field-effect transistors (FETs) will have to be made of polycrystalline films that remain functional at room temperature. A few organic n-type semiconductors that can be used in FETs are known, but these suffer from low electron mobility, poor stability in air and/or demanding processing conditions. Here we report a crystallographically engineered naphthalenetetracarboxylic diimide derivative that allows us to fabricate solution-cast n-channel FETs with promising performance at ambient conditions. By integrating our n-channel FETs with solution-deposited p-channel FETs, we are able to produce a complementary inverter circuit whose active layers are deposited entirely from the liquid phase. We expect that other complementary circuit designs can be realized by this approach as well.