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1.
In this paper we continue to study the spectral norms and their completions ([4]) in the case of the algebraic closure $ \overline {\mathbb Q} $ of ? in ?. Let $ \widetilde{\overline{\mathbb{Q}}} $ be the completion of $ \overline {\mathbb Q} $ relative to the spectral norm. We prove that $ \widetilde{\overline{\mathbb{Q}}} $ can be identified with the R‐subalgebra of all symmetric functions of C(G), where C(G) denotes the ?‐Banach algebra of all continuous functions defined on the absolute Galois group G = Gal$ {\overline {\mathbb Q}} / {\mathbb Q} $. We prove that any compact, closed to conjugation subset of ? is the pseudo‐orbit of a suitable element of $ \widetilde{\overline{\mathbb{Q}}} $. We also prove that the topological closure of any algebraic number field in $ \widetilde{\overline{\mathbb{Q}}} $ is of the form $\widetilde{\mathbb{Q}[x]}$ with x in $ \widetilde{\overline{\mathbb{Q}}} $. 相似文献
2.
The paper presents a new formulation of the integral boundary element method (BEM) using subdomain technique. A continuous approximation of the function and the function derivative in the direction normal to the boundary element (further ‘normal flux’) is introduced for solving the general form of a parabolic diffusion‐convective equation. Double nodes for normal flux approximation are used. The gradient continuity is required at the interior subdomain corners where compatibility and equilibrium interface conditions are prescribed. The obtained system matrix with more equations than unknowns is solved using the fast iterative linear least squares based solver. The robustness and stability of the developed formulation is shown on the cases of a backward‐facing step flow and a square‐driven cavity flow up to the Reynolds number value 50 000. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
3.
Elie Leopold 《Numerical Algorithms》2007,44(4):347-366
In this paper, we give some new explicit relations between two families of polynomials defined by recurrence relations of
all order. These relations allow us to analyze, even in the Sobolev case, how some properties of a family of orthogonal polynomials
are affected when the coefficients of the recurrence relation and the order are perturbed. In a paper we have already given
a method which allows us to study the polynomials defined by a three-term recurrence relation. Also here some generalizations
are given. 相似文献
4.
We investigate function spaces of generalised smoothness of Besov and Triebel–Lizorkin type. Equivalent quasi-norms in terms
of maximal functions and local means are given. An atomic decomposition theorem for this type of spaces is proved.
Mathematics Subject Classification (2000) 46E35 相似文献
5.
Nicolae Tomozeiu 《Applied Surface Science》2006,253(1):376-380
Thin films of a-SiOx (0 < x < 2) were prepared by reactive r.f. magnetron sputtering from a polycrystalline-silicon target in an Ar/O2 gas mixture. The oxygen partial pressure in the deposition chamber was varied so as to obtain films with different values of x. The plasma was monitored, during depositions, by optical emission spectroscopy (OES) system. Energy dispersive X-ray (EDX) measurements and infra-red (IR) spectroscopy were used to study the compositional and structural properties of the deposited layers.Structural modifications of SiOx thin films have been induced by UV photons’ bombardment (wavelength of 248 nm) using a pulsed laser. IR spectroscopy and X-ray photoemission spectroscopy (XPS) were used to investigate the structural changes as a function of x value and incident energy. SiOx phase separation by spinodal decomposition was revealed. The IR peak position shifted towards high wavenumber values when the laser energy is increased. Values corresponding to the SiO2 material (only Si4+) have been found for laser irradiated samples, independently on the original x value. The phase separation process has a threshold energy that is in agreement with theoretical values calculated for the dissociation energy of the investigated material.For high values of the laser energy, crystalline silicon embedded in oxygen-rich silicon oxide was revealed by Raman spectroscopy. 相似文献
6.
Yan B Collins N Wheatley J Irving M Leopold K Chan C Shornikov A Fang L Lee A Stock M Zhao J 《Journal of combinatorial chemistry》2004,6(2):255-261
We have developed a high-throughput purification system to purify combinatorial libraries at a 50-100-mg scale with a throughput of 250 samples/instrument/day. We applied an accelerated retention window method to shorten the purification time and targeted one fraction per injection to simplify data tracking, lower QC workload, and simplify the postpurification processing. First, we determined the accurate retention time and peak height for all compounds using an eight-channel parallel LC/UV/MS system, and calculated the specific preparative HPLC conditions for individual compounds. The preparative HPLC conditions include the compound-specific gradient segment for individual compounds with a fixed gradient slope and the compound-specific UV or ELSD threshold for triggering a fraction collection device. A unique solvent composition or solvent strength was programmed for each compound in the preparative HPLC in order to elute all compounds at the same target time. Considering the possible deviation of the predicted retention time, a 1-min window around the target time was set to collect peaks above a threshold based on UV or ELSD detection. Dual column preparative instruments were used to maximize throughput. We have purified more than 500 000 druglike compounds using this system in the past 3 years. We report various components of this high-throughput purification system and some of our purification results. 相似文献
7.
Microchimica Acta - Eine empfindliche spektrophotometrische Methode zur Bestimmung von Kupfer mit Salicyls~iure wurde beschrieben (Molarextinktion ε = 2,4 · 9 105). Die nachweisbaren... 相似文献
8.
Zusammenfassung In der vorliegenden Arbeit wird das Sedimentationsgleichgewicht der Systeme Na6[H2W12O40]—NaCI—H2O und Na6[H2W12O40]—NaClO4— H2O untersucht. Die scheinbare molare Masse Mapp des Natriummetawolframats wird in beiden Systemen als Funktion der Natriummetawolfrarnat-Anfangspartialdichte
0
PX
z gemessen. Durch lineare Extrapolation der Funktion Mapp = Mapp (PP,, ) auf die Polymerelektrolyt-Anfangspartialdichte Null können die Grenzwerte der scheinbaren molaren Masse (Mapp)o ermittelt werden. Aus den (Mapp)o-Werten wird die Abhängigkeit der Größe (ln
PXz
/m
BX
)
mPXz von der NaCI- bzw. NaClO4-Molalität berechnet.Die Bestimmung der molaren Masse und der (stöchiometrischen) Ladungszahl eines Polymerelektrolyten aus den experimentell ermittelten (Mapp)o-Werten unter Anwendung der Lamm-Williams-Gleichung wird diskutiert. Zur Ermittlung der beiden Größen müssen mehrere Versuchsreihen mit zwei verschiedenen Fremdelektrolyten durchgeführt werden. Externe Messungen sind nicht erforderlich.Man erhält auf diese Weise verläßliche Werte so-wohl der molaren Masse als auch der (stächiometrischen) Ladungszahl.
Mit 5 Abbildungen und 3 Tabellen 相似文献
Summary The sedimentation equilibria of the systems sodium metatungstate-sodium chloride-water and sodium metatungstate-sodium perchlorate-water are investiated. In both systems the apparent molecular mass Mapp of sodium metatungstate (PX z) is measured in dependence on partial density 0 PX z before centrifugation. By linear extrapolation of the function Mapp = Mapp ( 0 PX z the limiting value (Mapp)o for 0 PX z = 0 is obtained. The variation with sodium chloride and sodium perchlorate molality of the quantity (ln PX z m BX )mPXz is calculated from (Mapp)o data.The determination of the molecular mass and the algebraic valency of a polymeric ion by means of the (Mapp)o values calculated by Lamm-Williams equation is discussed. In order to obtain these two quantities at least two series of experiments are required, each of which using a different supporting electrolyte. External measurements are not necessary. In this way reliable values for the molecular mass as well as for the stoichiometric valency are obtained.
Mit 5 Abbildungen und 3 Tabellen 相似文献
9.
Boron-doped diamond (BDD) electrodes were used to investigate the possibility of detecting aniline by linear-sweep cathodic stripping voltammetry. It was found that the dimeric species (p-aminodiphenylamine and benzidine) formed by anodic oxidation of aniline during the accumulation period are involved in electrochemically reversible redox processes and, in acidic media, the shape of the stripping voltammetric response is suitable for aniline detection in the micromolar concentration range. The low background current of conductive diamond is an advantage compared to other electrode materials and allows a detection limit of 1 μM. Weak adsorption properties and the extreme electrochemical stability are additional advantages of BDD and it was found that, even after long-time measurements, the electrode surface can regain its initial activity by an anodic polarization in the potential region of water decomposition. 相似文献
10.
Zusammenfassung In der vorliegenden Arbeit wird das Sedimentations-gleichgewicht des Systems Na6[H2W12O40]-NaClO4-H2O bei 25 °C untersucht. Die scheinbare Ladungszahl des Natriummetawolframats wird als Funktion der NaClO4-MolalitätmNaClO4 ermittelt. Aus dieser Abhängigkeit kann für die summarische Dissoziation des NatriummetawolframatsNa2[H2W12O4o] 6Na+ + [H2W12O40]6– die DissoziationskonstanteK in Gegenwart von NaClO4 als Fremdelektrolyt zuK=0,08 mol6·kg–6 bestimmt werden.Der Kreuzdifferentialquotient
(
PXz
, ist der Trace-Aktivitätskoeffizient des Natriummetawolframats) wird ebenfalls als Funktion der NaClO4-Molalität ermittelt.Die Konzentrationsabhängigkeit des Trace-Aktivitätskoeffizienten zeigt einen Verlauf, wie er unseres Wissens nach noch nicht von anderen Autoren beobachtet wurde.
Mit 5 Abbildungen und 1 Tabelle 相似文献
Summary An ultracentrifugal study of the sedimentation equilibrium of the system Na2[H2W12O40]-NaClO4-H2Oat 25 °C is presented. The dependency of the apparent charge of the sodium metatungstate on NaClO4-molality is investigated. From these data the dissociation constant for the dissociation of the sodium metatungstate in the presence of NaClO4 according to the equationNa[H2W12O40] 6Na+ + [H2W12O40]6– is calculated toK=0.08 mol6·kg–6. The cross differential quotient ( PXz is the trace activity coefficient of the sodium metatungstate) shows a behavior in its dependence on NaClO4-molality which to our knowledge has not yet been reported by other authors.
Mit 5 Abbildungen und 1 Tabelle 相似文献