R×R上到R的某类1-1映射的不存在性

In p.32 of [1] the following problem is posed: A problem on Peano mapping Let R be the set of positive rational integers with usual operation a+b≡s(a,b) and a·b≡m(a,b). Every one-to-one(Peano) mapping c=p(a,b) on R×R to all R may serve so associate with s(a,b) and m(a,b) two functions σand μ on R to R by the definitions σ(c)=σ(p(a,b))= s(a,b), and μ(c)=μ(p(a,b))= m(a,b). Does there exist a Peano mapping p(a,b) such that "addition commutes with multiplication" in the sense that σ(μ(c))=μ(σ(c))for all c of R? To illustrate, we note     

Amperometric determination of 6-mercaptopurine on functionalized multi-wall carbon nanotubes modified electrode by liquid chromatography coupled with microdialysis and its application to pharmacokinetics in rabbit

In this paper, multi-wall carbon nanotubes fuctionalized with carboxylic groups modified electrode (MWNT-COOH CME) was fabricated. This chemically modified electrode (CME) can be used as the working electrode in the liquid chromatography for the determination of 6-mercaptopurine (6-MP). The results indicate that the CME exhibits efficiently electrocatalytic oxidation for 6-MP with relatively high sensitivity, stability and long-life. The peak currents of 6-MP are linear to its concentrations ranging from 4.0×10⁻⁷ to 1.0×10⁻⁴ mol l⁻¹ with the calculated detection limit (S/N=3) of 2.0×10⁻⁷ mol l⁻¹. Coupled with microdialysis, the method has been successfully applied to the pharmacokinetic study of 6-MP in rabbit blood. This method provides a fast, sensible and simple technique for the pharmacokinetic study of 6-MP in vivo.     

DNA tile based self-assembly: building complex nanoarchitectures.

DNA tile based self-assembly provides an attractive route to create nanoarchitectures of programmable patterns. It also offers excellent scaffolds for directed self-assembly of nanometer-scale materials, ranging from nanoparticles to proteins, with potential applications in constructing nanoelectronic/nanophotonic devices and protein/ligand nanoarrays. This Review first summarizes the currently available DNA tile toolboxes and further emphasizes recent developments toward self-assembling DNA nanostructures with increasing complexity. Exciting progress using DNA tiles for directed self-assembly of other nanometer scale components is also discussed.     

Synthesis of 6,9-Dipropyl-1,4-Dioxaspiro[4.5] Deca-6,8-Diene-2,10-Dione and its Diels-Alder Reactions with Substituted Acetylenes

The title compound, a masked 3,6-di-n-propyl-o-benzoquinone, was synthesized from 3,6-di-n-propylcatechol in 82% yield. Its Diels-Alder reactions with methyl propiolate, phenylacetylene, 1-octyne, dimethyl acetylenedicarboxylate, diphenylacetylene and 3-hexyne were studied. The yields of the adducts were excellent except for the last two cases in which the unimolecular decomposition of the title compound to generate 3,6-di-n-propylcatechol methylene ether predominates. The regiochemistry of the adducts derived from monosubstituted acetylenes were determined by the correlation of ¹³C chemical shifts of the adducts and the corresponding bicyclo[2.2.2]octa-5,7-diene-2,3-diones obtained from the hydrolysis of the spirolactone ring of the Diels-Alder adducts. Photolysis of these α-diketones gave the corresponding aromatic compounds in high yields. These synthetic sequences provide an effective entry to bicyclo[2.2.2]octa-5,7-diene-2,3-diones and polysubstituted benzene derivatives.     

Preparation of dehydrated powder of hemoglobin vesicles

The carbonyl hemoglobin (CO-Hb), which was used to prevent denaturation (metHb) during the preparation of samples, was encapsulated into lipid vesicles constituted from unsaturated phospholipid, cholesterol and unsaturated fatty acid. Unsaturated components were polymerized by γ-irradiation to enhance the stability of bilayer membrane. An aqueous dispersion of resulting Hb vesicles was freeze-dried in the presence of saccharides (50–200 mM) to obtain a dehydrated powder of Hb vesicles. Change in the vesicle size, the leakage of encapsulated Hb and the oxidation of Hb to metHb were not observed. Therefore, the long-term storage of Hb vesicles can be realized as a dry powder.     

2]Catenane assembly from calix[4]arene crown ethers [In Process Citation

A variety of novel calix[4]arene-incorporating crown ethers with or without intramolecular hydrogen bonding have been prepared by two efficient methods and utilized as donor rings to assemble calix[4]arene [2]catenanes based on pi-stacking interaction between hydroquinone and bipyridinium units. Treatment of calix[4]arene crown ethers 4, 10a, or 10b, whose cone conformation was fixed by intramolecular hydrogen bonding within the calix[4]arene moiety, with dicationic salt 15 x 2PF6 and dibromide 16 afforded the corresponding [2]catenanes 17a x 4PF6, 17b x 4PF6, and 17c x 4PF6 in 20%, 53%, and 55% yields, respectively, whereas from the reactions of 15 x 2PF6 and dibromide 16 in the presence of conformationally flexible 11 or 12 with a cone conformation kept by two propyl groups, [2]catenanes 18 x 4PF6 and 19 x 4PF6 were obtained in 12% and 6% yields. [2]Catenanes 21a x 4Cl, 21b x 4Cl, and 21c x 4Cl, incorporating calix[4]arene in both the donor and acceptor rings, were also successfully assembled from 10a or 10b, 16, and dicationic salts 20a x 2PF6 or 20b x 2PF6. The dynamic 1H NMR and absorption spectra of the [2]catenanes have been investigated, which revealed a strongest donor-acceptor interaction in 17a x 4PF6 and that the cone [2]catenanes 17a-c x 4PF6 can isomerize to the partial cone isomer at high temperature. The difference of the dynamic properties of these catenanes was discussed. The results demonstrate that catenation is one new general method to change the conformational distributions of calix[4]arenes.     

Controlled synthesis and magnetic properties of 2D and 3D iron azide networks infinity2[Fe(N3)2(4,4'-bpy)] and infinity3[Fe(N3)2(4,4'-bpy)

Controlled synthesis of transition metal complexes with mixed ligands has led to two new compounds with the same empirical formula [Fe(N3)2(4,4'-bpy)] (4,4'-bpy=4,4'- bipyridine). The compound 2D-[Fe(N3)2(4,4'-bpy)] (I) contains end-on (EO) bridging azido ligands. It crystallizes in the orthorhombic crystal system, space group Cmmm (No. 65): a=11.444(2) A, b=15.181(3) A, c=3.458(1) A, V=600.8(2) A(3), and Z=2. The compound 3D-[Fe(N3)2(4,4'-bpy)] (II) contains end-to-end (EE) azido bridges. It belongs to the tetragonal crystal system, space group P4(1)2(1)2 (No. 92): a=8.132(1) A, b=8.132(1) A, c=16.708(3) A, V=1104.9(5) A(3), and Z=4. Crystals of I and II have been grown by the diffusion method. Phase-pure samples of both compounds have been obtained by means of an optimal solution synthesis. Spontaneous long-range magnetic ordering was found in both I and II, with I being a metamagnet, and II being a ferromagnet. For I, in the low-field region, multiple transitions at TN1=20 K and TN2=5 K were observed, and these indicated the existence of Fe moment reorientation. Heat capacity measurements on II confirmed ferromagnetic transition at TC=20 K.     

A chiral porous 3D metal-organic framework with an unprecedented 4-connected network topology

A novel homochiral 3D metal-organic framework [CdL2(H2O)2][ClO4]2.2DMF.3EtOH.5/3H2O, 1, (L =(R)-6,6-dichloro-2,2-diethoxy-1,1-binaphthyl-4,4-bipyridine) exhibits an unprecedented 4-connected network topology owing to the cis- configuration of the Cd coordination and possesses permanent porosity as demonstrated by TGA, XRPD, and CO2 adsorption isotherm studies.     

Reactivity of [CpCr(CO)3]2 towards thione (CS) moieties in some sulfur-containing substrates

The reaction of [CpCr(CO)₃]₂ (Cp = η⁵-C₅H₅) (1) with 1 mol equivalent of 2,5-dimercapto-1,3,4-thiadiazole (DMcTH₂) at ambient temperature led to the isolation of a reddish-brown crystalline solid of CpCr(CO)₃(η¹-DMcTH) (5) and a green solid of CpCr(CO)₃H (2) in yields of ca. 28% and 30%, respectively, along with some [CpCr(CO)₂]₂ (3) and [CpCr(CO)₂]₂S (4). The reaction of 1 with 1 mol equivalent of vinylene trithiocarbonate (SCS(CH)₂S) (VTTC) at 90 °C led to the isolation of a red crystalline solid of CpCr(CO)₂(η²-SCHSC₂H₂) (6) in ca. 15% yield while the reaction of 1 with isopropylxanthic disulfide ((CH₃)₂CHOCS₂)₂ resulted in the formation of CpCr(CO)₂(η²-S₂COCH(CH₃)₂) (8) in ca. 80% yield. The complexes 5, 6 and 8 have been determined by single crystal X-ray diffraction analysis.     

Laser action of C,N, O,F, Cl,and Br in hollow cathode discharges

C, N, O, F, Cl, and Br red and infrared laser emission was investigated using hollow cathode discharges in gas mixtures of helium and molecules containing the corresponding atoms. A total of 33 laser lines with wavelengths from 0.7 to 2.0m was observed. Three laser lines of atomic C, five laser lines of atomic N, two laser lines of atomic Cl and five laser lines of atomic Br were observed for the first time. Dissociation charge transfer and dissociative excitation transfer are suggested as being responsible for populating the upper laser levels.