A new Finite Element Method for magneto-dynamical problems: two-dimensional results

A mixed Lagrange finite element technique is used to solve the Maxwell equations in the magneto-hydrodynamic (MHD) limit in an hybrid domain composed of vacuum and conducting regions. The originality of the approach is that no artificial boundary condition is enforced at the interface between the conducting and the insulating regions and the non-conducting medium is not approximated by a weakly conducting medium as is frequently done in the literature. As a first evaluation of the performance of the method, we study two-dimensional (2D) configurations, where the flow streamlines of the conducting fluid are planar, i.e., invariant in one direction, and either the magnetic field (“magnetic scalar” case) or the electric field (“electric scalar” case) is parallel to the invariant direction. Induction heating, eddy current generation, and magnetic field stretching are investigated showing the usefulness of finite element methods to solve magneto-dynamical problems with complex insulating boundaries.     

A Class of Rational Arithmetical Functions with Combinatorial Meanings

ＡＣｌａｓｏｆＲａｔｉｏｎａｌＡｒｉｔｈｍｅｔｉｃａｌＦｕｎｃｔｉｏｎｓｗｉｔｈＣｏｍｂｉｎａｔｏｒｉａｌＭｅａｎｉｎｇｓＰｅｎｔｉＨａｕｋｋａｎｅｎ（Ｄｅｐｔ．ｏｆＭａｔｈ．Ｓｃｉｓ．，Ｕｎｉｖ．ｏｆＴａｍｐｅｒｅ，Ｐ．Ｏ．Ｂｏｘ６０７，ＦＩＮ－...     

Different aspects of the monotonicity of a function

In this paper, we investigate which aspects are overriding in the concept images of monotonicity of Finnish tertiary mathematics students, i.e., on which aspects of monotonicity they base their argument in different types of exercises related to that concept. Further, we examine the relationship between the quality of principal aspects and the success in solving monotonicity exercises and a few other standard problems in calculus. Our findings indicate that a mathematics student's conception about monotone functions is often restricted to continuous or differentiable functions and the algebraic aspect – the nearest one to the formal definition of monotonicity – is rare.     

Die Einheitlichkeit des 2,4-Dinitrophenylosazons des Glyoxals

Zusammenfassung Aus Glyoxal wurden mit salzsaurer 2,4-Dinitrophenylhydrazinlösung Hydrazone dargestellt. Als Ausgangssubstanz kamen das Mono- und Polyglyoxal sowie die Hydrogensulfitverbindung des Glyoxals und dessen Tetraäthylacetal zur Anwendung. Bei Einhaltung einer genügend langen Fällungsdauer erhielt man als Reaktionsprodukt in allen Fällen dieselbe Verbindung, das Osazon des Monoglyoxals, das bei der Reduktion mit Zinn und Salzsäure in 1,2-Diaminoäthan überging. Bei zu kurzer Fällungsdauer wurde als Reaktionsprodukt — unabhängig von der zugegebenen Reagensmenge — ein Gemisch der Mono- und Bishydrazone des Monoglyoxals erhalten. Die Komponenten wurden sowohl papierals auch dünnschichtchromatographisch getrennt. Bei Behandlung mit alkalischem Äthanol wurde das Monohydrazon orange und das Bishydrazon, das Osazon, blau gefärbt. Die von uns früher geäußerte Auffassung^18,19, daß sich das Osazon des Glyoxals mit alkalischem Äthanol blau färbt, erwies sich somit als stichhaltig.

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Summary Hydrazones of glyoxal were prepared from mono- and polyglyoxal, from the bisulfite derivative of glyoxal and the tetraethyl acetal with 2,4-dinitrophenylhydrazine in hydrochloric acid solution. When sufficient time was used for precipitation the same compound, monoglyoxal osazone, was obtained in all cases. Reduction of the monoglyoxal osazone with tin and hydrochloric acid gave diaminoethane. If the precipitation time was too short, a mixture of the mono- and bishydrazones of monoglyoxal was obtained-independently of the amount of reagent added. The components were separated by paper and thin-layer chromatography. The monohydrazone gave an orange colour with alkaline ethanol, while the bishydrazone, osazone, gave a blue one. Thus our previous opinion^18,19 that the osazone of glyoxal gives a blue colour with alkaline ethanol has been confirmed.

     

Electron ionization mass spectrometric study of monomeric models of O-polysaccharides of Vibrio cholerae O:1, serotypes Ogawa and Inaba

Fragmentation mechanisms of electron ionization (EI) mass spectrometry of the title compounds have been elucidated by high-resolution (HR) mass spectrometric measurements of the elemental composition and measurements of the metastable transitions (B(2)/E, CID). The experimental results were interpreted with the help of Mass Frontier 3.0 software, which aided the elucidation of fragmentation mechanisms and helped to deduce structures of the ions formed. Characteristic under the conditions of EI-MS measurement was the production of protonated adducts. Three distinct pathways observed include the formation of oxonium type ions, the conjugated transfer of electrons in the pyranose ring, and cleavage of the acylamide side chains. By applying the results obtained, the molecular mass, as well as the structures of both the saccharide and acylamide side chain involved in related substances, can be determined.     

A Further Combinatorial Number-Theoretic Extension of Euler's Totient

ＡＦｕｒｔｈｅｒＣｏｍｂｉｎａｔｏｒｉａｌＮｕｍｂｅｒ┐ＴｈｅｏｒｅｔｉｃＥｘｔｅｎｓｉｏｎｏｆＥｕｌｅｒ′ｓＴｏｔｉｅｎｔＰｅｎｔｉＨａｕｋｋａｎｅｎ（Ｄｅｐｔ．ｏｆＭａｔｈ．Ｓｃｉｓ．，ＵｎｉｖｅｒｓｉｔｙｏｆＴａｍｐｅｒｅ，Ｐ．Ｏ．Ｂｏｘ６０...     

Second fundamental form of a map

Summary This paper is devoted to the study of the 2, fundamental form of a map, which generalizes this notion, well known for isometric immersions. We generalize results by Vilms, Yano, and Ishihara, and study in detail projective and umbilical maps.