Formula 1 – A Mathematical Microworld with CAS: Analysis of Learning Opportunities and Experiences with Students

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.     

Fluorinated tellurium(IV) azides and their precursors

The perfluoroaryl tellurolates C₆F₅TeLi (1) and 4-CF₃C₆F₄TeLi (2) were prepared. These intermediates were identified by NMR spectroscopy and may form, depending on the reaction conditions, either the corresponding ditellanes C₆F₅TeTeC₆F₅ (3) and CF₃C₆F₄TeTeC₆F₄CF₃ (4) by subsequent oxidation, or in the case of 1, a telluranthrene (C₆F₄Te)₂ (5) by reaction with itself. The halogenation products of 5, ( C₆F₄Te)₂F₄ (6), (C₆F₄Te)₂Cl₄ (7), (C₆F₄Te)₂Br₄ (8), as well as the azidation product (C₆F₄Te)₂(N₃)₄ (9) were synthesized. Furthermore, in pursuit of our recent work on tellurium azides, the syntheses and properties of R₂Te(N₃)₂ (R=CF₃ (10), C₆F₂H₃ (11)) and RTe(N₃)₃ (R=CF₃ (12) and C₆F₅ (13)) are reported. The crystal structures of CF₃C₆F₄TeTeC₆F₄CF₃ (4), (C₆F₄Te)₂Br₄ (8), and (C₆F₂H₃)₂Te(N₃)₂ (11) were determined.     

Prostaglandin D2 synthase and its post-translational modifications in neurological disorders

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.     

Synthesis of Cannabinoid Model Compounds. Part 3. (6aR, 10aR)-N-ethyl-Δ8-tetrahydrocannabinol-18-amide, (6aR, 10aR, 17 RS)-N-ethyl-17-methyl-Δ8- tetrahydrocannabinol-18-amide and (6aR, 10aR)-17,18-didehydro-Δ8-tetrahydrocannabinol

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.     

Synthesis and structure of a stabilized 10-membered cyclic enediyne

The synthesis and structure of an acetal protected 10-membered cyclic enediyne-1,2-diol rac-10 is reported. The conformational constrain of the unsaturated macrocycle by the acetal protection group prevents the thermal cyclization reaction of the endiyne during synthesis and purification.     

A liquid chromatography-mass spectrometry method for the quantification of both etoricoxib and valdecoxib in human plasma

A practicable and selective liquid chromatography-mass spectrometry assay for the determination of two cyclooxygenase-2 inhibitors, etoricoxib and valdecoxib, in human plasma is presented. The analytical technique is based on reversed-phase high-performance liquid chromatography (HPLC) coupled to atmospheric pressure chemical ionisation (APCI) mass spectrometry (Finnigan Mat LCQ ion trap). Mass analysis was performed in the positive ion mode. The ion trap was operated in the tandem MS mode (MS2) and the transitions of etoricoxib (m/z 359.2 --> 280.3) and valdecoxib (m/z 315.1 --> 235.1) were followed by selected reaction monitoring. Retention times of etoricoxib and valdecoxib were 1.05 and 1.08 min, respectively. The method was validated over a linear range 10-2500 and 5-1000 microg/L using the other substrate as internal standard. After validation, the method was used to study the pharmacokinetic pro fi le of etoricoxib or valdecoxib in a healthy volunteer after administration of a single oral dose (valdecoxib, 20 mg; etoricoxib, 90 mg). The presented method was suf fi cient to cover more than 90% of the area under the plasma concentration time curve.     

α-Substituierte phosphonate—38: 1-dimethylamino-1-cyano-methanphosphonsäurediethylester,ein neues edukt zur darstellung von carbonsäuren, 1-cyanoenaminen und homoenolaten

Alkylation of 1-dimethylamino-1-cyanomethanephosphonic acid diethyl ester (8), easily obtainable from diethyl phosphite and the 0,N-acetal 9, yields 1-alkyl derivatives 14. Elimination of HCN converts 14 into 1-phosphonoenamines 6. Carbonyl compounds react with 8 to give 1-cyanoenamines 15 which may be hydrolyzed to from the homologous carboxylic acid. Alternatively, deprotonation of 15 yields the homoenolate anions 17 which can be alkylated or hydroxyalkylated, permitting chain extension of carbonyl compounds through introduction of an α-carboxyl and a β-alkyl group. Acid catalyzed hydrolysis of 8 results in cleavage of the PC bond, leading to the corresponding α-dimethylamino alkanoic acids. A phosphonic acid 11 can be obtained from 8 by application of the silylester method. An unambigous assignment of E/Z-isomers of the cyanoenamines 15 has been derived from ¹³C-NMR spectroscopy.     

1,2‐Dithioquadratato‐ und 1,2‐Dithiooxalatoindate(III)

Indium(III) chloride forms in water with potassium 1,2‐dithiooxalate (dto) and potassium 1,2‐dithiosquarate (dtsq) stable coordination compounds. Due to the higher bridging ability of the 1,2‐dithiooxalate ligand in all cases only thiooxalate bridged binuclear complexes were found. From 1,2‐dithioquadratate with an identical donor atom set mononuclear trischelates could be isolated. Five crystalline complexes, (BzlMe₃N)₄[(dto)₂In(dto)In(dto)₂] ( 1 ), (BzlPh₃P)₄[(dto)₂In(dto)In(dto)₂] ( 2 ), (BzlMe₃N)₃[In(dtsq)₃] ( 3 ), (Bu₄N)₃[In(dtsq)₃] ( 4 ) and (Ph₄P)[In(dtsq)₂(DMF)₂] ( 5 ), have been isolated and characterized by X‐ray analyses. Due to the type of the complex and the cations involved these compounds crystallize in different space groups with the following parameters: 1 , monoclinic in P2₁/c with a = 14.4035(5) Å, b = 10.8141(5) Å, c = 23.3698(9) Å, β = 124.664(2)°, and Z = 2; 2 , triclinic in P with a = 11.3872(7) Å, b = 13.6669(9) Å, c = 17.4296(10) Å, α = 88.883(5)°, β = 96.763(1)°, γ = 74.587(5)°, and Z = 1; 3 , hexagonal in R3 with a = 20.6501(16) Å, b = 20.6501(16) Å, c = 19.0706(13) Å and Z = 6; 4 , monoclinic in P2₁/c with a = 22.7650(15) Å, b = 20.4656(10) Å, c = 14.4770(9) Å, β = 101.095(5)°, and Z = 4; 5 , triclinic in P with a = 9.2227(6) Å, b = 15.3876(9) Å, c = 15.5298(9) Å, α = 110.526(1)°, β = 100.138(1)°, γ = 101.003(1)°, and Z = 2.