Sharper approximation of extreme points by far points

This research was supported in part by the National Science Foundation, U.S.A.     

Synthesis and characterization of poly(vinyl alcohol)‐graft‐[poly(D,L‐lactide)/poly(D,L‐lactide‐co‐glycolide)] hydrogels

Poly(D ,L ‐lactide) and poly(D ,L ‐lactide‐co‐glycolide) with various composition and with one methacrylate and one carboxylate end group were synthesized and grafted onto poly(vinyl alcohol) (PVA) via the carboxylate group. The graft copolymers were crosslinked via the methacrylate groups using a free radical initiator. The polymer networks were characterized by means of NMR and studied qualitatively by means of IR spectroscopy. The influence of the glycolide content in the polyester grafts and of the number of ester units in the grafts on thermal properties and swellability were studied as well. The high swellability in water is characteristic of all hydrogels. Differential scanning calorimetry (DSC) showed a single glass transition temperature that occurs in the range between 51 and 69 °C. Thermogravimetric analysis (TGA) of the networks showed the main loss in weight in the temperature range between 290 and 370 °C. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4536–4544, 2007     

Review: mass spectrometry of step-growth polymers

For at least two decades different mass spectrometric techniques have been applied for polymer analysis, including the qualitative determination of chemical compositions, end group identification, functionality type distribution and the determination of the cyclisation extend at each degree of polymerisation. Molecular weights exceeding 100 KDa are provable by MALDI-ToF mass spectrometry. Further, molecular weight distributions are determined by MADLI-ToF. However, there are some hints that, there is a discrimination against higher molecular weight species in samples with polydispersity of more than 1.2. Furthermore, pathways for dendritic and hyper-branched polymers, supramolecular polymers and nano condensates are analysed by help of mass spectrometry.     

Far-infrared spectroscopy of CH3OD in highly excited torsional states and the atlas of the Fourier transform spectra in the range 200-350 cm(-1)

The high resolution Fourier transform far-infrared (FIR) spectrum of the torsion rotation band of CH3OD has been analyzed for the highly excited torsion states (n > or = 2) in the vibrational ground state. The spectrum shows splitting of the lines due to strong torsional-rotational-vibrational interactions in the molecule. Assignments were possible for rotational sub-bands in the torsional state as high as n = 4 and for K values up to 8 and J values of up to approximately 30 in most cases, for all the symmetry species. For the third excited torsional state n = 3 assignments were possible to K = 10. The data were analyzed with the help of the energy expansion model, which has been proven very successful in methanol. The state dependent expansion parameters are presented. These molecular parameters were able to reproduce the observed wavenumbers almost to within experimental accuracy of 0.0002 cm(-1) for clean unblended lines. These expansion coefficients should prove valuable in the calculation of precise energy values for excited torsional states up to n = 4, which is way above the torsional barrier. The detailed high-resolution spectral atlas of CH3OD has been presented in the range 200-350 cm(-1). This atlas is an extension of our earlier atlas in the range 20-205 cm(-1). The availability of this atlas in the journal will be very valuable for spectroscopists and astrophysicists seeking information in the infrared (IR) region in the laboratory and in outer space.     

Common supports as fixed points

A family S of sets in R ^d is sundered if for each way of choosing a point from rd+1 members of S, the chosen points form the vertex-set of an (r–1)-simplex. Bisztriczky proved that for each sundered family S of d convex bodies in R ^d , and for each partition (S , S ), of S, there are exactly two hyperplanes each of which supports all the members of S and separates the members of S from the members of S . This note provides an alternate proof by obtaining each of the desired supports as (in effect) a fixed point of a continuous self-mapping of the cartesian product of the bodies.     

Computational complexity of inner and outerj-radii of polytopes in finite-dimensional normed spaces

This paper studies the complexity of computing (or approximating, or bounding) the various inner and outer radii of ann-dimensional convex polytope in the space ⁿ equipped with an _p norm or a polytopal norm. The polytopeP is assumed to be presented as the convex hull of finitely many points with rational coordinates (V-presented) or as the intersection of finitely many closed halfspaces defined by linear inequalities with rational coefficients (-presented). The innerj-radius ofP is the radius of a largestj-ball contained inP; it isP's inradius whenj = n and half ofP's diameter whenj = 1. The outerj-radius measures how wellP can be approximated, in a minimax sense, by an (n — j)-flat; it isP's circumradius whenj = n and half ofP's width whenj = 1. The binary (Turing machine) model of computation is employed. The primary concern is not with finding optimal algorithms, but with establishing polynomial-time computability or NP-hardness. Special attention is paid to the case in whichP is centrally symmetric. When the dimensionn is permitted to vary, the situation is roughly as follows: (a) for general -presented polytopes in _p spaces with 1相似文献   

Metal- and ligand-directed one-pot syntheses,crystal structures,and properties of novel oxo-centered tetra- and hexametallic clusters

Starting from closely related metal-ligand combinations, completely different oligomeric metal clusters are synthesized. Whereas, picoline-tetrazolylamide HL(1) (1) and zinc or nickel acetate afforded [2x2] grids [M(4)(L(1))(8)] (2), slightly different N-(2-methylthiazole-5-yl)-thiazole-2-carboxamide HL(2) (5 a) and nickel acetate yielded the monometallic complex [Ni(L(2))(2)(OH(2))(2)] (6). In contrast, reaction of 5 a with zinc acetate produced the tetrametallic zinc cluster [Zn(4)O(L(2))(4)(OAc)(2)] (7). Even more surprising, when 3-methyl-substituted HL(3) (5 b) instead of 2-methyl-substituted HL(2) (5 a) was allowed to react under identical conditions with zinc acetate, the cluster [Zn(4)O(L(3))(4)Cl(2)] (8) crystallized from dichloromethane. Clusters 7 and 8 are isostructural. As for 7, in 8 two of the edges of the tetrahedron of zinc ions are doubly bridged, two are singly bridged, and the other two are nonbridged. On the other hand, when iron(II) acetate under aerobic conditions was allowed to react with 5 a, the unprecedented complex [[Fe(3)O(L(2))(2)(OAc)(4)](2)O] (9) was isolated. Cluster 9 is composed of two trimetallic, triangular mu(3)-O(2-)-centered [Fe(3)O(L(2))(2)(OAc)(4)](+) modules, linked by an almost linear mu(2)-O(2-) bridge. The M?ssbauer spectrum together with cyclic voltammetric and square-wave voltammetric measurements of 9 are reported, and 6-9 were characterized unequivocally by single-crystal X-ray structure analyses.     

Mono- and dinuclear molybdenum complexes with sterically demanding cycloheptatrienyl ligands

Sterically demanding cycloheptatrienylium (tropylium) salts of the type (1,3,5-C7H4R3)BF4 [R = t-Bu, (3a)BF4; R = SiMe3, (3b)BF4] have been prepared from the corresponding 1,3,5-trisubstituted benzene derivatives 1 by ring expansion with diazomethane followed by hydride abstraction with triphenylcarbenium tetrafluoroborate, (Ph3C)BF4. Complexation can be achieved by arene exchange and Mo(CO)3 group transfer employing [(eta6-p-xylene)Mo(CO)3] (4) to yield the cationic complexes (5)BF4. In refluxing mesitylene, [(eta7-C7H4t-Bu3)Mo(CO)3]BF4, (5a)BF4, undergoes CO substitution to furnish the mesitylene sandwich complex (6a)BF4. A cyclic voltammetric study reveals that this complex exhibits a reversible one-electron oxidation to the dicationic 17e complex 6a2+, which can also be accessed by chemical oxidation with AgBF4. On the contrary, the reduction of 6a+ is irreversible and does not yield a stable 19e complex 6a. To study the fate of the reduced 19e form, (5a)BF4 was treated with Na2Hg to diastereoselectively afford the C-C coupled bicycloheptatriene complex 7a. Paramagnetic, dinuclear complexes of the type [(eta7-C7H4R3)Mo(mu-Cl)3Mo(eta7-C7H4R3)] (8) have been obtained from the reaction of (5)BF4 with Me3SiCl. These can be regarded as mixed-valence Mo(0)/Mo(+I) compounds with a metal-metal bond order of 0.5. Cyclic voltammetric studies reveal that both complexes 8a and 8b undergo reversible one-electron oxidation as well as reduction. Treatment with one equivalent of ferrocenium hexafluorophosphate leads to removal of the unpaired electron and formation of the diamagnetic complexes (8)PF6. Theoretical DFT calculations have been carried out to further elucidate the bonding in these systems. In addition, the X-ray crystal structures of (5b)BF4, (6a)BF4 x CH2Cl2, (6a)(BF4)2 x (acetone)2, 7a x CH2Cl2, 8a x 0.5C6H14, and (8a)PF6 x Et2O are reported.     

Activity of AC electrokinetically immobilized horseradish peroxidase

Dielectrophoresis (DEP) is an AC electrokinetic effect mainly used to manipulate cells. Smaller particles, like virions, antibodies, enzymes, and even dye molecules can be immobilized by DEP as well. In principle, it was shown that enzymes are active after immobilization by DEP, but no quantification of the retained activity was reported so far. In this study, the activity of the enzyme horseradish peroxidase (HRP) is quantified after immobilization by DEP. For this, HRP is immobilized on regular arrays of titanium nitride ring electrodes of 500 nm diameter and 20 nm widths. The activity of HRP on the electrode chip is measured with a limit of detection of 60 fg HRP by observing the enzymatic turnover of Amplex Red and H₂O₂ to fluorescent resorufin by fluorescence microscopy. The initial activity of the permanently immobilized HRP equals up to 45% of the activity that can be expected for an ideal monolayer of HRP molecules on all electrodes of the array. Localization of the immobilizate on the electrodes is accomplished by staining with the fluorescent product of the enzyme reaction. The high residual activity of enzymes after AC field induced immobilization shows the method's suitability for biosensing and research applications.     

Metal/Metal Redox Isomerism Governed by Configuration

A pair of diastereomeric dinuclear complexes, [Tp′(CO)BrW{μ-η²-C,C′-κ²-S,P-C₂(PPh₂)S}Ru(η⁵-C₅H₅)(PPh₃)], in which W and Ru are bridged by a phosphinyl(thiolato)alkyne in a side-on carbon P,S-chelate coordination mode, were synthesized, separated and fully characterized. Even though the isomers are similar in their spectroscopic properties and redox potentials, the like-isomer is oxidized at W while the unlike-isomer is oxidized at Ru, which is proven by IR, NIR and EPR-spectroscopy supported by spectro-electrochemistry and computational methods. The second oxidation of the complexes was shown to take place at the metal left unaffected in the first redox step. Finally, the tipping point could be realized in the unlike isomer of the electronically tuned thiophenolate congener [Tp′(CO)(PhS)W{μ-η²-C,C′-κ²-S,P-C₂(PPh₂)S}Ru(η⁵-C₅H₅)-(PPh₃)], in which valence trapped W^III/Ru^II and W^II/Ru^III cationic species are at equilibrium.