On the growth of the number of periodic points for smooth self-maps of a compact manifold

Let be a continuous self-map of a smooth compact connected and simply-connected manifold of dimension . We show that in the homotopy class of there is a map with less then periodic points, up to any given fixed period .

     

A microarray study of gene and protein regulation in human and rat brain following middle cerebral artery occlusion

Background

Our goal was to examine the spatiotemporal integration of tactile information in the hand representation of human primary somatosensory cortex (anterior parietal somatosensory areas 3b and 1), secondary somatosensory cortex (S2), and the parietal ventral area (PV), using high-resolution whole-head magnetoencephalography (MEG). To examine representational overlap and adaptation in bilateral somatosensory cortices, we used an oddball paradigm to characterize the representation of the index finger (D2; deviant stimulus) as a function of the location of the standard stimulus in both right- and left-handed subjects.

Results

We found that responses to deviant stimuli presented in the context of standard stimuli with an interstimulus interval (ISI) of 0.33s were significantly and bilaterally attenuated compared to deviant stimulation alone in S2/PV, but not in anterior parietal cortex. This attenuation was dependent upon the distance between the deviant and standard stimuli: greater attenuation was found when the standard was immediately adjacent to the deviant (D3 and D2 respectively), with attenuation decreasing for non-adjacent fingers (D4 and opposite D2). We also found that cutaneous mechanical stimulation consistently elicited not only a strong early contralateral cortical response but also a weak ipsilateral response in anterior parietal cortex. This ipsilateral response appeared an average of 10.7 ± 6.1 ms later than the early contralateral response. In addition, no hemispheric differences either in response amplitude, response latencies or oddball responses were found, independent of handedness.

Conclusion

Our findings are consistent with the large receptive fields and long neuronal recovery cycles that have been described in S2/PV, and suggest that this expression of spatiotemporal integration underlies the complex functions associated with this region. The early ipsilateral response suggests that anterior parietal fields also receive tactile input from the ipsilateral hand. The lack of a hemispheric difference in responses to digit stimulation supports a lack of any functional asymmetry in human somatosensory cortex.     

Determination of fluoride in toothpaste using headspace solid-phase microextraction and gas chromatography-flame ionization detection

A new method for determination of fluoride in toothpaste employing the headspace solid-phase microextraction (HS-SPME) followed by gas chromatography/flame ionization detection (GC/FID) has been proposed. It is a development of the method for determination of fluoride using trimethylchlorosilane (TMCS) as the derivatization reagent to form trimethylfluorosilane (TMFS), with the liquid/liquid extraction (LLE) step replaced by HS-SPME. To introduce the latter, it was necessary to determine the conditions of the reaction and to optimize the two stages of the SPME procedure: extraction and desorption. The parameters of the SPME analysis using carboxen/polydimethylsiloxane (CAR/PDMS) fiber were defined and compared with the corresponding ones for the LLE method, used as a reference. Also, these two methods were compared with respect to their linearity, precision, and accuracy. Results from toothpaste analyses using these two methods were highly correlated, indicating the potential to use the SPME extraction as an inexpensive and solventfree alternative to the LLE method.     

Lanthanide complexes of the chiral hexaaza macrocycle and its meso-type isomer: solvent-controlled helicity inversion

Lanthanide(III) complexes of the enantiopure chiral hexaaza tetraamine macrocycle L, 2(R),7(R),18(R),23(R)-1,8,15,17,24,31-hexaazatricyclo[25.3.1.1.0.0]-dotriaconta-10,12,14,26,28,30-hexaene, as well as of its meso-type 2(R),7(R),18(S),23(S)-isomeric macrocycle L1, have been synthesized and characterized by spectroscopic methods. The 2D NMR spectra confirm the identity of these complexes and indicate C2 symmetry of the [LnL]3+ and Cs symmetry of the [LnL1]3+ complexes. The crystal structures of the [PrL(NO3)(H2O)2](NO3)2, [EuL(NO3)(H2O)2](NO3)2, [DyL(NO3)2]2[Dy(NO3)5] x 5CH3CN, [YbL(NO3)2]2[Yb(NO3)5] x 5CH3CN, [YbL(H2O)2](NO3)3 x H2O, and [EuL1(NO3)(H2O)2]0.52[EuL1(NO3)2]0.48(NO3)1.52 x 0.48H2O complexes have been determined by single-crystal X-ray diffraction. In all complexes, the lanthanide(III) ions are coordinated by six nitrogen atoms of the macrocycle L or L1, but for each type of complex, the conformation of the macrocycle and the axial ligation are different. The crystallographic, NMR, and CD data show that the [YbL]3+ complex exists in two stable forms. Both forms of the Yb(III) complex have been isolated, and their interconversion was studied in various solvents. The two forms of [YbL]3+ complex correspond to two diastereomers of ligand L, which differ in the sense of the helical twist and the configuration at the stereogenic amine nitrogen atoms. In one of the stereoisomers, the macrocycle L of (RRRR) configuration at the stereogenic cyclohexane carbon atoms adopts the (RSRS) configuration at the amine nitrogen atoms, while in the other stereoisomer, the macrocycle L of (RRRR) configuration at the stereogenic cyclohexane carbon atoms adopts the (SSSS) configuration at the amine nitrogen atoms. The (RRRR)(RSRS) isomer is quantitatively converting to the (RRRR)(SSSS) isomer in water solution, while the reverse process is observed for an acetonitrile solution, thus representing the rare case of helicity inversion controlled by the solvent.     

Optical switching of coupled plasmons of Ag-nanoparticles by photoisomerisation of an azobenzene ligand

The optical switching of coupled plasmons of silver nanoparticles derivatised with a photoisomerisable azobenzene ligand is presented. It is shown that nanoparticle clusters, linked with an azobenzene dithiol molecule, display switchable optical properties. The photoisomerisation of the linker molecule was used to vary the separation between nanoparticles, which was monitored by changes in the UV-Vis-spectra of the plasmon band of adjacent nanoparticles. A red-shift due to the appearance of a coupled longitudinal plasmon band was observed resulting from the formation of nanoparticle clusters. The maximum absorbance wavelength of this secondary plasmon band was altered by isomerisation of the linker and the spectral changes observed were in good agreement with theory and earlier measurements for gold. Evidence of energy transfer between a nanoparticle and an azobenzene terminated monothiol attached to it was also observed in the UV-Vis spectra.     

Tautomerism of acridin-9-amines substituted at the exocyclic nitrogen atom: spectroscopic investigations and theoretical studies

In the ground electronic state, the first two (1 and 2) of the compounds investigated--9-(methoxyamino)acridine (1), 9-hydrazinoacridine (2), N-(2-chloroethyl)acridin-9-amine (3) and N-(5-methylpyridin-2-yl)acridin-9-amine (4)--exist principally in the imino tautomeric form, while the other two (3 and 4) can coexist as amino and imino tautomers in solvents of various polarities and abilities to enter into specific interactions. These features of the molecules are reflected in the experimental absorption spectra and the predicted thermodynamic and spectral data. The predicted thermodynamic characteristics suggest that in the S1 state, the imino tautomers of 1, 2 and 4 and the amino tautomer of 3 are more stable than their tautomeric counterparts. However, the predicted rates of intersystem crossing suggest that the imino tautomers of 1-3 and the amino tautomer of 4 lose excitation energy very rapidly, so that only their counterpart tautomers in fact emit radiation. This explains why 1 and 2 do not fluoresce and why the amino form of 3 and the imino form of 4 are the emitters. 3 and 4 thus represent acridin-9-amines whose imino forms are preferred in the ground state, but whose respective amino and imino forms are preferred in the excited state. Because 3 and 4 are capable of tautomeric transformations in the ground and excited states, and also enter into specific interactions with solvents, these compounds could be potent spectral indicators or probes of environmental properties.     

(18)O/(16)O isotope effect on miscibility of isobutyric acid with water

The miscibility of isobutyric acid with water and the influence of the isotope substitution of oxygen (16O/18O) in water over a broad concentration range are reported. The system exhibits a phase diagram with an upper critical solution temperature (UCST) and a visible isotope effect thereon. The oxygen isotope substitution decreases the UCST, leading to better miscibility of isobutyric acid with water. The isotope shift, DeltaTc = Tc(18O) - Tc(16O), extrapolated to the 100% enrichment in 18O, is equal to -1.15 K; hence it is much smaller and opposite to that found for deuterium substitution. The origin of the observed miscibility isotope effect has been qualitatively discussed in terms of the condensed-phase isotope effect theory.     

Voltammetric determination of catalytic reaction parameters of laccase based on electrooxidation of hydroquinone and ABTS

A convenient method for the measurement of the catalytic activity of laccase is proposed based on the voltammetric determination of catalytic reaction substrates: 2,2'-azinobis-(3-ethylbenzothiazoline-6-sulfonate) diammonium salt (ABTS) and 1,4-benzenediol (hydroquinone). The measurement performed using microelectrodes working under spherical diffusion conditions is both accurate and simple, and allows to monitor parallely the consumption of substrate and formation of product of the catalytic reaction. The method proposed in this paper was compared with the two generally employed procedures based on oxygen measurement by Clark electrode and on spectrophotometry. The procedure described in the present paper was found to be simpler and more reproducible results were obtained than using Clark electrode. Compared to spectrophotometry a larger range of catalytic reaction substrates can be studied including colorless compounds.     

Iso-guanine quintet complexes coordinated by mono valent cations (Na+, K+, Rb+, and Cs+)

The geometric structures, the interaction energies, the vibrational characteristics, and the electronic structures of the complexes of the isoguanine (isoG) quintet coordinated with mono valent cations (Na(+), K(+), Rb(+), and Cs(+)) have been studied based on the nonplanar models. The geometry of the local minimum structure of the Na(+)-isoG quintet complex deviates significantly from the planar structure. The geometric characteristics of the Na(+)-isoG quintet complex support the experimental findings that Na(+) is unlikely to induce the formation of the isoG quintet-based pentaplexes. Similar to the guanine tetraplexes, the ionic selectivity of the isoG quintet-based pentaplexes is largely dominated by the hydration energy of the cations. After hydration correction, the positive value of the free energy difference for the formation of the Na(+)-isoG quintet complex (DeltaG(f)) suggests that the isoG quintet is unable to capture the hydrated Na(+). The negative values of DeltaG(f) for the K(+) and Rb(+) complexes implies that both ions have the tendency to be inserted into the isoG pentaplexes. This study suggests that, to elucidate the high Cs(+) selectivity of isoG pentaplexes, it is necessary to extend the model from the isoG quintet to the isoG decamer.