On the congruence lattice of a Scott-domain

We prove that the congruence lattice of a Scott-domain can be characterized as a complete lattice.Presented by V. Trnkova.The research of the first author was supported by the NSERC of Canada.The research of the second author was supported by the Hungarian National Foundation for Scientific Research, under Grant No. 1903.     

Northcott's theorem on heights I. A general estimate

Given a pointP=(a _o:...:a _n) of projective space ⁿ = ⁿ (A) whereA is the field of algebraic numbers, letd(P) be its degree andH(P) its absolute multiplicative height. Northcott's Theorem says that givend, n andX, there are only finitely many pointsP ⁿ withd(P)d andH(P)X. We will show that there are at mostc(d, n)X ^d(d+n) such points.Supported in part by NSF grant DMS-9108581.     

Die Bestimmung der spezifischen Aktivität trägerarmer Radiojodidlösungen durch papierchromatographische Ermittlung der prozentualen Radioaktivitätsverteilung auf die Jodsubstitutionsproduke von Bromsulfan

Es wird eine neue Methode zur Bestimmung der spezifischen Aktivität trägerarmer Radiojodidlösungen zwischen 5 und 17 Ci/mg (185 bis 630 G Bq/mg) beschrieben, die wesentlich einfacher ist als die bekannten, zum Teil sehr komplizierten Mikroanalysenmethoden und im Prinzip auf eine einfache Trennung eines Radiojodierungsgemisches hinausläuft. Hierzu werden 1 bzw. 2 nmol Bromsulfan (BSP) mit einer exakt zu messenden Menge Na¹²⁵ J bzw. Na¹³¹ J unter Verwendung von Chloramin T radiojodiert. Da die Reaktionsgeschwindigkeitskonstanten der Mono- und Dijodierung des Bromsulfans nicht differierèn, ist es möglich, aus der papierchromatographisch ermittelten prozentualen Radioaktivitätsverteilung das molare Verhältnis der an ein BSP-Molekül gebundenen Jodalome zu berechnen. Bei bekannter BSP-Menge läßt sich daraus die an der Radiojodierung beteiligte Jodmasse ableiten.

Bei der Radiojodierung mit Chloramin T wird jedoch kein 100%iger Jodeinbau erreicht. Die gemessene Aktivitätsmenge muß deshalb durch einen Faktor korrigiert werden, der aus dem Ergebnis der papierchromalographischen Trennung des Reaktionsgemisches abgeleitet wird und der lediglich die auf Mono- und Dijod-BSP entfallenden Radioaktivitätsanteile, nicht dagegen das anorganische Radiojodid berücksichtigt. Die spezifische Aktivität der verwendeten Radiojodidlösung ergibt sich dann als Quotient der korrigierten Radioaktivitätsmenge und der berechneten Radiojodmasse.

Wir haben die erhaltenen Ergebnisse mit den nach einer Referenzmethode gefundenen Werten verglichen. Hierbei wurden die spezifischen Aktivitäten von Na¹²⁵ J aus T3-RIA-Standurdkurven mit ¹²⁵J-T3-Tracern bestimmt, die unter Verwen-dung dieses Na¹²⁵ J präpariert wurden. Es wurde eine Präzision mit einem mittleren Variationskoeffizienlen von ±4% festgestellt.     

Carbon Isotope Analysis in Urea at High 13C-Abundances Using the 13/12CO2-Breath Test Device Fanci2

Abstract

The increasing application of ¹³C-labelled urea in medicine requires simple and reasonable methods for measuring highly enriched ¹³C in urea. The combination: ultimate organic analysis—mass spectrometry so far prescribed is complicated and expensive. For medical diagnosis, however, isotope selective nondispersive infrared spectrometers (NDIRS) have been available for many years. One of these tools is FANci2 which is very reasonable and easily to be operated. By means of such devices also urea highly enriched in ¹³C can be analysed, provided that the samples are first diluted with a defined amount of urea of natural isotopic composition and then transformed into carbon dioxide by means of urease. The relative abundance of ¹³C in this carbon dioxide, measured by nondispersive infrared spectrometry, is then a measure of the ¹³C abundance in the initial urea sample. Comparison of results of such measurements with those attained by mass spectrometry proves that this procedure is feasible and yields precise results.     

Experimental Observations on Superelastic NiTi-Shape Memory Alloys and Suggestions for Modelling

During stress-induced transformation NiTi shows a distinct generation of transformation bands. A simple one-dimensional model for superelastic NiTi wires has been developed to show exemplarily methods to account for these bands in plasticitybased models. To clarify the dependence of the transformation bands on the distribution of latent heat and therefore on the mechanical behaviour, optical and thermographical experiments have been performed. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Ultrafast all-optical modulation on a silicon chip

We experimentally demonstrate ultrafast all-optical modulation using a micrometer-sized silicon photonic integrated device. The device transmission is strongly modulated by photoexcited carriers generated by low-energy pump pulses. A p-i-n junction is integrated on the structure to permit control of the generated carrier lifetimes. When the junction is reverse biased, carriers are extracted from the device in a time as short as 50 ps, permitting greater than 5 Gbit/s modulation of optical signals on a silicon chip.     

InP(001)-(2 x 1) surface: a hydrogen stabilized structure

The InP(001)(2 x 1) surface has been reported to consist of a semiconducting monolayer of buckled phosphorus dimers. This apparent violation of the electron counting principle was explained by effects of strong electron correlation. Combining first-principles calculations with reflectance anisotropy spectroscopy and LEED experiments, we find that the (2 x 1) reconstruction is not at all a clean surface: it is induced by hydrogen adsorbed in an alternating sequence on the buckled P dimers. Thus, the microscopic structure of the InP growth plane relevant to standard gas phase epitaxy conditions is resolved and shown to obey the electron counting rule.     

Silver: a novel growth catalyst for Ge nanoislands on Si(113)

The impact of silver pre‐adsorption on germanium growth on Si(113) was investigated using in‐situ low‐energy electron microscopy (LEEM) as well as low‐energy electron diffraction (LEED). The adsorption of silver leads to the formation of a regular pattern of nanofacets along the [1 0] direction. The periodicity of this pattern in [33 ] direction was determined to (44 ± 4) nm. From LEED series at different energies the facets were identified to be of (111) and (115) orientation. While the (111) facets show a (√3 × √3)‐R30° reconstruction, the (115) facets exhibit a (2 × n) superstructure. The subsequent growth of Ge results in the formation of nanoislands that are aligned along the facets. These Ge islands have an anisotropic shape with typical sizes of about 100 nm in [33 ] direction and 400 nm in [1 0] direction. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Construction of relative difference sets and Hadamard groups

‘There exist normal \((2m,2,2m,m)\) relative difference sets and thus Hadamard groups of order \(4m\) for all \(m\) of the form $$\begin{aligned} m= x2^{a+t+u+w+\delta -\epsilon +1}6^b 9^c 10^d 22^e 26^f \prod _{i=1}^s p_i^{4a_i} \prod _{i=1}^t q_i^2 \prod _{i=1}^u \left( (r_i+1)/2)r_i^{v_i}\right) \prod _{i=1}^w s_i \end{aligned}$$ under the following conditions: \(a,b,c,d,e,f,s,t,u,w\) are nonnegative integers, \(a_1,\ldots ,a_r\) and \(v_1,\ldots ,v_u\) are positive integers, \(p_1,\ldots ,p_s\) are odd primes, \(q_1,\ldots ,q_t\) and \(r_1,\ldots ,r_u\) are prime powers with \(q_i\equiv 1\ (\mathrm{mod}\ 4)\) and \(r_i\equiv 1\ (\mathrm{mod}\ 4)\) for all \(i, s_1,\ldots ,s_w\) are integers with \(1\le s_i \le 33\) or \(s_i\in \{39,43\}\) for all \(i, x\) is a positive integer such that \(2x-1\) or \(4x-1\) is a prime power. Moreover, \(\delta =1\) if \(x>1\) and \(c+s>0, \delta =0\) otherwise, \(\epsilon =1\) if \(x=1, c+s=0\) , and \(t+u+w>0, \epsilon =0\) otherwise. We also obtain some necessary conditions for the existence of \((2m,2,2m,m)\) relative difference sets in partial semidirect products of \(\mathbb{Z }_4\) with abelian groups, and provide a table cases for which \(m\le 100\) and the existence of such relative difference sets is open.     

Experimental characterization of bi-directional terahertz emission from gold-coated nanogratings

The THz radiation emission of Au-coated nanogratings (fused silica substrate, 30?nm Au layer thickness, 500?nm grating constant) upon fs laser irradiation (785?nm, 150?fs, 1?kHz,???1?mJ/pulse) is observed in both directions along the laser beam axis (forward and backward) and for both, illumination of the Au/air or the Au/silica interface. THz radiation along the laser beam propagation is emitted in a narrow solid angle of about 15°?fwhm independent on the laser pulse fluence, the angle of incidence and the nanograting profile. The bar width and groove depth of the nanograting as well as the angle of laser beam incidence strongly affect the THz radiation yield. The energy of single THz light pulses is measured absolutely (2?fJ in the 0.3?C0.38?THz range) using a highly sensitive and fast superconducting transition edge sensor. The bi-directional emission of THz radiation is in agreement with the model assumption of surface plasmon polaritons propagating simultaneously on both Au layer interfaces (Au/air and Au/silica).