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1.
Marianne Gerny Burkhard Alpers 《International Journal of Computers for Mathematical Learning》2004,9(1):25-57
In this article we describe a mathematical microworld for investigating car motion on a racing course and its use with a group of grade 12 students. The microworld is concerned with the mathematical construction of courses and functions which describe car motion. It is implemented in the computer algebra system, Maple®, which provides the means to represent courses and functions symbolically and graphically. We describe the learning opportunities offered by the microworld in relation to the research literature on functions. Various facets and layers of the function concept are addressed in the microworld, and we suggest how work in the microworld might help in overcoming some well-known misconceptions.This revised version was published online in September 2005 with corrections to the Cover Date. 相似文献
2.
R. Euler B. Fricke T. Morović W. -D. Sepp A. Rosén 《Zeitschrift für Physik A Hadrons and Nuclei》1980,297(2):101-104
Total energy SCF calculations were performed for noble gas difluorides in a relativistic procedure and compared with analogous non-relativistic calculations. The discrete variational method with numerical basis functions was used. Rather smooth potential energy curves could be obtained. The theoretical Kr-F and Xe-F bond distances were calculated to be 3.5 a.u. and 3.6 a.u. which should be compared with the experimental values of 3.54 a.u. and 3.7 a.u. Although the dissociation energies are off by a factor of about five it was found that ArF2 may be a stable molecule. Theoretical ionization energies for the outer levels reproduce the experimental values for KrF2 and XeF2 to within 2 eV. 相似文献
3.
4.
We prove a general embedding theorem for Sobolev spaces on open manifolds of bounded geometry and infer from this the module structure theorem. Thereafter we apply this to weighted Sobolev spaces. 相似文献
5.
The chemical elements up toZ = 172 are calculated with a relativistic Hartree-Fock-Slater program taking into account the effect of the extended nucleus. Predictions of the binding energies, the X-ray spectra and the number of electrons inside the nuclei are given for the inner electron shells. The predicted chemical behaviour will be discussed for all elements betweenZ = 104-120 and compared with previous known extrapolations. For the elementsZ = 121–172 predictions of their chemistry and a proposal for the continuation of the Periodic Table are given. The eighth chemical period ends withZ = 164 located below Mercury. The ninth period starts with an alkaline and alkaline earth metal and ends immediately similarly to the second and third period with a noble gas atZ = 172.
This work has been supported by the Bundesministerium für Wissenschaft und Bildung and by the Deutsche Forschungsgemeinschaft. 相似文献
Zusammenfassung Mit einem relativistischen Hartree-Fock-Slater Rechenprogramm werden die chemischen Elemente bis zur Ordnungszahl 172 berechnet, wobei der Einfluß des ausgedehnten Kernes berücksichtigt wurde. Für die innersten Elektronenschalen werden Voraussagen über deren Bindungsenergie, das Röntgenspektrum und die Zahl der Elektronen im Kern gemacht. Die voraussichtliche Chemie der Elemente zwischenZ = 104 und 120 wird diskutiert und mit bereits vorhandenen Extrapolationen verglichen. Für die ElementeZ =121–172 wird eine Voraussage über das chemische Verhalten gegeben, sowie ein Vorschlag für die Fortsetzung des Periodensystems gemacht. Die achte chemische Periode endet mit dem Element 164 im Periodensystem unter Quecksilber gelegen. Die neunte Periode beginnt mit einem Alkali- und Erdalkalimetall und endet sofort wieder wie in der zweiten und dritten Periode mit einem Edelgas beiZ = 172.
Resumé Les éléments chimiques jusqu'áZ = 172 sont calculés à l'aide d'un programme Hartree-Fock-Slater relativiste en tenant compte de l'extension du noyau. On fournit des prédictions quant aux énergies de liaison, aux spectres X et au nombre d'électrons dans les noyaux pour les couches électroniques internes. Le comportement chimique prévu est discuté pour tous les éléments entreZ = 104–120 et comparé aux extrapolations connues auparavant. Pour les éléments Z =121–172 on effectue des prévisions de propriétés chimiques et l'on propose un prolongement du Tableau Périodique. La huitième période chimique se termine àZ = 164 sous le mercure. La neuviéme période débute avec un métal alcalin et alcalino-terreux et se termine comme la seconde et la troisième période avec un gaz rare àZ = 172.
This work has been supported by the Bundesministerium für Wissenschaft und Bildung and by the Deutsche Forschungsgemeinschaft. 相似文献
6.
7.
Mihlbachler K Fricke J Yun T Seidel-Morgenster A Schmidt-Traub H Guiochon G 《Journal of chromatography. A》2001,908(1-2):49-70
Although it is impossible to manufacture identical columns for use in a simulated moving bed (SMB) process, theoretical studies assume that all the columns in an SMB unit have identical characteristics. In practice, calculations in modeling and optimization studies are made with the average values of each column parameter set. In this report, the effects on SMB process performance caused by column-to-column fluctuations of the parameters are discussed. As a first step, we show how the differences in porosity of the columns may be taken into account with a revised set of separation conditions. Reductions in the purity of the extract and the raffinate streams are quantitatively related to the column-to-column fluctuations of the retention times of the two components arising from these porosity differences. For the sake of simplicity, the discussion first addresses the case of a four-column SMB operating under linear conditions. Then, the scope is extended to the cases of SMB units incorporating several columns in each section and to SMB units operating under nonlinear conditions. 相似文献
8.
Prostaglandin D2 synthase (PGDS) (beta-trace protein) is a highly abundant cerebrospinal fluid (CSF) glycoprotein. A number of studies have been performed to determine the potential value of this protein for the diagnosis of various neurological disorders. The measurement of total PGDS levels in CSF has proved marginally useful for this purpose, but promising results were obtained while investigating changes in the posttranslational modifications (PTM) pattern. Using 2-DE analysis, we previously showed that PGDS is differentially expressed in ante- and post mortem CSF samples. In the present study, we examined whether the PGDS isoforms may help to distinguish stroke and neurodegenerative disease patients from healthy subjects. The pattern of PGDS PTM was analyzed in CSF from patients with various neurological disorders (n = 44) using IEF/immunoblotting techniques. Strong alterations of this pattern were detected in patients with different forms of degenerative dementia. These findings are consistent with PGDS being altered in some neurological diseases and provide new opportunities for clinical applications. 相似文献
9.
K. Rashid B. Fricke J. H. Blanke J. P. Desclaux 《Zeitschrift für Physik D Atoms, Molecules and Clusters》1988,11(2):99-103
The ground state (J=0) electronic correlation energy of the 4-electron Be-sequence is calculated in the Multi-Configuration Dirac-Fock approximation forZ=4–20. The 4 electrons were distributed over the configurations arising from the 1s, 2s, 2p, 3s, 3p and 3d orbitals. Theoretical values obtained here are in good agreement with experimental correlation energies. 相似文献
10.
Burkhard Schmidt Ingo Franke Franz-Josef Witteler Michael Binder 《Helvetica chimica acta》1983,66(8):2564-2571
The novel cannabinoids (6aR, 10aR)-N-ethyl-Δ8-tetrahydrocannabinol-18-amide (15) and (6aR, 10aR, 17 RS)-N-ethyl-17-methyl-Δ8- tetrahydrocannabinol-18-amide (16) , designed as cannabinoid affinity ligands, were synthesized from the corresponding acids 11 and 12 via the N-hydroxysuccinimide esters. Amide 16 was tested in the rat and was generalized to Δ9-tetrahydrocannabinol, being 5 times less potent than the training drug. An improved synthesis of (6aR, 10aR)-17,18-didehydro-Δ8-tetrahydrocannabinol (23) is reported. As model reaction for the preparation of a tritiated Δ8-tetrahydrocannabinol, compound 23 was selectively deuterated at C(17) and C(18) in benzene/Et3N using [(C6H5)3P]3RuCl2 as catalyst. 相似文献