On the index of Fredholm pairs of idempotents

Using the technique of block-operators, in this note, we prove that if P and Q are idempotents and （P - Q）^2n＋1 is in the trace class, then （P - Q）^2m＋1 is also in the trace class and tr（P - Q）^2m＋1 = dim（k（P） ∩ k（Q）^⊥） -dim（k（P）^⊥ N k（Q））, for all m ≥ n. Moreover, we prove that dim（k（P）∩ k（Q）^⊥） = dim（k（P）^⊥ ∩k（Q）） if and only if there exists a unitary U such that UP = QU and PU = UQ, where k（T） denotes the range of T. Keywords Fredholm, orthogonal projection, positive operator     

Assemblies of a new flexible multicarboxylate ligand and d10 metal centers toward the construction of homochiral helical coordination polymers: structures, luminescence, and NLO-active properties

Hydro(solvo)thermal reactions between a new flexible multicarboxylate ligand of 2,2',3,3'-oxydiphthalic acid (2,2',3,3'-H(4)ODPA) and M(NO(3))(2).xH(2)O (M = Zn, x = 6; M = Cd, x = 4) in the presence of 4,4'-bipyridine (bpy) afford two novel homochiral helical coordination polymers [[Zn(2)(2,2',3,3'-ODPA)(bpy)(H(2)O)(3)].(H(2)O)(2) for 1 and [Cd(2)(2,2',3,3'-ODPA)(bpy)(H(2)O)(3)].(H(2)O)(2) for 2]. Though having almost the same chemical formula, they have different space groups (P2(1)2(1)2(1) for 1 and P2(1) for 2) and different bridging modes of the 2,2',3,3'-ODPA ligand. Two kinds of homochiral helices (right-handed) are found in both 1 and 2, each of which discriminates only one kind of crystallographical nonequivalent metal atom. 1 has a 2D metal-organic framework and can be seen as the unity of two parallel homochiral Zn1 and Zn2 helices, in which the nodes are etheric oxygen atoms. In contrast, 2 has a 3D metal-organic framework and consists of two partially overlapped homochiral Cd1 and Cd2 helices in the two dimensions. Moreover, metal-ODPA helices give a 2D chiral herringbone structural motif in both 1 and 2 in the two dimensions, which are further strengthened by the second ligand of bpy. Bulk materials for 1 and 2 all have good second-harmonic generation activity, approximately 1 and 0.8 times that of urea.     

Densification of silica glass at ambient pressure

We show that densification of silica glass at ambient pressure as observed in irradiation experiments can be attributed to defect generation and subsequent structure relaxation. In our molecular dynamics simulations, defects are created by randomly removing atoms, by displacing atoms from their nominal positions in an otherwise intact glass, and by assigning certain atom excess kinetic energy (simulated ion implantation). The former forms vacancies; displacing atoms and ion implantation produce both vacancies and "interstitials." Appreciable densification is induced by these defects after equilibration of the defective glasses. The structural and vibrational properties of the densified glasses are characterized, displaying resembling features regardless of the means of densification. These results indicate that relaxation of high free-energy defects into metastable amorphous structures enriched in atomic coordination serves as a common mechanism for densification of silica glass at ambient pressure.     

Solvent effect on the aggregate of fluorinated gemini surfactant at silica surface

The aggregate states of partially fluorinated gemini surfactant [(CF3)2CF(CF2)2(CH2)10N(CH3)2]2(CH2)6Br2 (C(F)(5)C10-C6-C10C(F)(5)) on silica surface were investigated with atomic force microscopy (AFM) and water contact angle (CA) measurement by analyzing the effects of bulk concentration and adsorption time on stack state. On surfactant-adsorbed silica surfaces, there was a flat surface layer interspersed with some scattering surfactant aggregates. In the case of short adsorption times, the aggregates would be hemisphere. In the case of long adsorption times, the aggregates would be present in the form of bilayers. With the increase of bulk concentration, the adsorbed amount was enlarged and the surface layer became more compact. The formation of patchy bilayer aggregates indicated the saturation of the surface layer. Furthermore, organic solvent effects on the aggregate state of the surfactant on a silica surface were studied with four organic solvents, including n-hexane, dehydrated ethanol, 1,1,2-trichloro-1,2,2-trifluoroethane, and toluene. With the treatment of different organic solvents, the hemisphere aggregates on the surface layer can rearrange into spherical bilayer, rodlike monolayer, and branched rodlike monolayer aggregates, respectively. The polarity of solvents and affinity of organic solvents for surfactant molecules may have a great impact on the stack state of the fluorinated gemini surfactant molecules.     

Energy transfer of highly vibrationally excited azulene. III. Collisions between azulene and argon

The energy transfer dynamics between highly vibrationally excited azulene molecules (37 582 cm(-1) internal energy) and Ar atoms in a series of collision energies (200, 492, 747, and 983 cm(-1)) was studied using a crossed-beam apparatus along with time-sliced velocity map ion imaging techniques. The angular resolved collisional energy-transfer probability distribution functions were measured directly from the scattering results of highly vibrationally excited azulene. Direct T-VR energy transfer was found to be quite efficient. In some instances, nearly all of the translational energy is transferred to vibrational/rotational energy. On the other hand, only a small fraction of vibrational energy is converted to translational energy (V-T). Significant amount of energy transfer from vibration to translation was observed at large collision energies in backward and sideway directions. The ratios of total cross sections between T-VR and V-T increases as collision energy increases. Formation of azulene-argon complexes during the collision was observed at low enough collision energies. The complexes make only minor contributions to the measured translational to vibrational/rotational (T-VR) energy transfer.     

Raman spectroscopic investigation of carbon nanowalls

Two-dimensional carbon nanowalls (CNWs) were prepared by microwave plasma-enhanced chemical-vapor deposition and scanning electron microscopy was used to observe their morphologies. The Raman observations of different sample orientations and polarizations show that CNWs are well crystallized. Micro-Raman scattering measurements were also carried out with different excitation laser lines (325, 488, 514, 532, and 633 nm). The D band shows a very strong shift of 46.19 cm(-1)eV with excitation laser energy and this has been explained by the double resonance effect. The decreasing intensity ratios IDIG and ID'/IG with increasing laser excitation energy were detected and discussed.     

Structural analysis of κ-carrageenan sulfated oligosaccharides by positive mode Nano-ESI-FTICR-MS and MS/MS by SORI-CID

Structural analysis of sulfated oligosaccharides from kappa-carrageenan of up to ten residues (MW >2 kDa) was successfully carried out by positive mode nano-ESI-FTICR-MS together with MS/MS using sustained off-resonance irradiation-collision induced dissociation (SORI-CID). Glycosidic bond cleavage reactions via the B- and Y-types of fragmentation were observed and enabled complete sequencing of the oligosaccharide samples. The positions of the labile sulfate substituents were observable using SORI-CID, enabling the determination of the sequence of the sulfated residues.     

Protonolysis of the Hg-C bond of chloromethylmercury and dimethylmercury. A DFT and QTAIM study

Possible mechanisms for degrading chloromethylmercury (CH(3)HgCl) and dimethylmercury [(CH3)2Hg] involving thiol and ammonium residues were investigated by DFT and atoms-in-molecules (QTAIM) calculations. Using H2S and HS- as models for thiol and thiolate groups RSH and RS-, respectively, we obtained transition states and energy barriers for possible decomposition routes to Hg(SH)2 based on a model proposed by Moore and Pitts (Moore, M. J.; Distefano, M. D.; Zydowsky, L. D.; Cummings, R. T.; Walsh, C. T. Acc. Chem. Res. 1990, 23, 301. Pitts, K. E.; Summers, A. O. Biochemistry 2002, 41, 10287). Demethylation was found to be a multistep process that involved initial substitution of Cl- by RS-. We found that successive coordination of Hg with thiolates leads to increased negative charge on the methyl group and facilitates the protonolysis of the Hg-C bond by H-SH. This was also found to be the case for (CH3)2Hg. We found that NH4(+) readily protonolyzes the Hg-C bond of these thiolate complexes, suggesting that ammonium residues of protonated amino acids might also act as effective proton donors.     

Simultaneous three-photon-excited violet upconversion luminescence of Ce3+:Lu2Si2O7 single crystals by femtosecond laser irradiation

We found that Ce3+:Lu2Si2O7 single crystals could be excited at 800 nm by using a femtosecond Ti:sapphire laser. The emission spectra of Ce3+:Lu2Si2O7 crystals were the same for one-photon excitation at 267 nm as for excitation at 800 nm. The emission intensity of Ce3+:Lu2Si2O7 crystals was found to depend on the cube of the laser power at 800 nm, consistent with simultaneous absorption of three 800 nm photons. The measured value of the three-photon absorption cross section is sigma'3=2.44x10(-77) cm6 s2.     

Reaction of layered sodium disilicate SKS-6 with calcium chloride solution as revealed by solid state NMR spectroscopy: exploring the calcium ion extracting mechanism of SKS-6

Solid-state 1H, 29Si NMR and 23Na MQMAS NMR spectroscopy combined with X-ray powder diffraction (XRD) technique was used to study the reaction between layered sodium disilicate SKS-6 and calcium chloride solution with different concentrations. Based on the experimental results the calcium ion extracting mechanism of SKS-6 was demonstrated to be via ion replacement, during which calcium ions replace sodium ions and combine with the non-bridging oxygen in SKS-6 for charge compensation, and simultaneously sodium ions leave the interlayer. This ion-replacement process was greatly influenced by the substitution of sodium ions by protons as well as the calcium ions concentration. Increasing calcium ions concentration favors the replacement of sodium ions by calcium ions, but prevents sodium ions from being substituted by protons.