Stability of Critical Points with Interval Persistence

Scalar functions defined on a topological space are at the core of many applications such as shape matching, visualization and physical simulations. Topological persistence is an approach to characterizing these functions. It measures how long topological structures in the sub-level sets persist as c changes. Recently it was shown that the critical values defining a topological structure with relatively large persistence remain almost unaffected by small perturbations. This result suggests that topological persistence is a good measure for matching and comparing scalar functions. We extend these results to critical points in the domain by redefining persistence and critical points and replacing sub-level sets with interval sets . With these modifications we establish a stability result for critical points. This result is strengthened for maxima that can be used for matching two scalar functions.     

Excitation wavelength dependence of solvation dynamics in a supramolecular assembly: PEO-PPO-PEO triblock copolymer and SDS

The triblock copolymer (PEO)20-(PPO)70-(PEO)20 (P123) forms a supramolecular aggregate with sodium dodecyl sulfate (SDS). The solvation dynamics and anisotropy decay of coumarin 480 (C480) in different regions of a P123-SDS aggregate are studied through variation of the excitation wavelength (lambdaex) using femtosecond upconversion. In a P123 micelle, because of the drastic differences in polarity between the hydrophilic corona region (PEO block) and the hydrophobic PPO core, C480 exhibits a pronounced red edge excitation shift (REES) of emission maximum by 24 nm. In the P123-SDS aggregate, SDS penetrates the core of the P123 micelle. This increases the polarity of the core and reduces the difference in the polarity between the core and the corona region. In a P123-SDS aggregate, the REES is much smaller (5 nm) which suggests a reduced difference between the core and the corona. Solvation dynamics in a P123 micelle displays a bulklike ultrafast component (<0.3 and 1 ps) in the PEO corona region, a 200 ps component arising from dynamics of polymer segments, and a very long component (5000 or 3000 ps) due to the highly restricted PPO core. In a P123-SDS aggregate, at lambdaex = 375 and 405 nm, the solvation dynamics is found to be faster than that in P123 micelle. In this case, the component (3000 ps) arising from the core region is faster than that (5000 ps) in P123 micelle. In both P123 micelle and P123-SDS aggregate, the relative contribution of the core region decreases and that of the corona region increases with an increase in lambdaex. At lambdaex = 435 nm, which probes the hydrophilic corona, the solvation dynamics for both P123 micelle and P123-SDS aggregate are almost similar.     

Femtosecond ligand/core dynamics of microwave-assisted synthesized silicon quantum dots in aqueous solution

A microwave-assisted reaction has been developed to produce hydrogen-terminated silicon quantum dots (QDs). The Si QDs were passivated for water solubility via two different methods: hydrosilylation produced 3-aminopropenyl-terminated Si QDs, and a modified St?ber process produced silica-encapsulated Si QDs. Both methods produce water-soluble QDs with maximum emission at 414 nm, and after purification, the QDs exhibit intrinsic fluorescence quantum yield efficiencies of 15 and 23%, respectively. Even though the QDs have different surfaces, they exhibit nearly identical absorption and fluorescence spectra. Femtosecond transient absorption spectroscopy was used for temporal resolution of the photoexcited carrier dynamics between the QDs and ligand. The transient dynamics of the 3-aminopropenyl-terminated Si QDs is interpreted as a formation and decay of a charge-transfer (CT) excited state between the delocalized π electrons of the carbon linker and the Si core excitons. This CT state is stable for ~4 ns before reverting back to a more stable, long-living species. The silica-encapsulated Si QDs show a simpler spectrum without CT dynamics.     

Restriction theorems for Higgs principal bundles

We prove analogues of Grauert–Mülich and Flenner?s restriction theorems for semistable principal Higgs bundle over any smooth complex projective variety.     

Substituent effects in halogen bonding complexes between aromatic donors and acceptors: a comprehensive ab initio study

Substituent effects in halogen bonding complexes involving aromatic rings are investigated. We have analyzed how the interaction energy (the RI-MP2/aug-cc-pVDZ level of theory) is affected by the substitution in both halogen bond donor and acceptor aromatic moieties. In addition, we have used two different aromatic electron donor molecules pyridine and cyanobenzene, which allow us to study the effect of having the electron donor nitrogen atom forming part of the ring or outside the ring (-CN). Interestingly, the effect of the substituents on the interaction energies is similar in both cases. We have obtained the Hammett's plots for four combinations of aromatic donors and acceptors and in all cases we have obtained good regression plots (interaction energies vs. Hammett's σ parameter). We have also studied and compared bifurcated halogen bonds using both possible combinations, that is two donors and one acceptor and vice versa. In addition, we have analyzed the effect of the solvent on the interaction energies using COSMO. Finally, we have used Bader's theory of "atoms-in-molecules" to demonstrate that the electron density computed at the bond critical point that emerges upon complexation can be used as a measure of bond order in this noncovalent interaction.     

Encapsulation of trivalent phosphate anion within a rigidified π-stacked dimeric capsular assembly of tripodal receptor

The tris(thiourea) receptor, L, in the presence of excess H(2)PO(4)(-) has been found to encapsulate a trivalent phosphate ion within a π-stacked dimeric capsular assembly of the receptor with twelve strong H-bonds via deprotonation, as evident from the origin of a new set of signals in the (1)H NMR titration experiments.     

An in vitro and in vivo study of a novel zinc complex, zinc N-(2-hydroxyacetophenone)glycinate to overcome multidrug resistance in cancer

Multiple drug resistance (MDR) remains a major clinical challenge for cancer treatment. P-glycoprotein is the major contributor and they exceed their role in the chemotherapy resistance of most of the malignancies. Attempts in several preclinical and clinical studies to reverse the MDR phenomenon by using MDR modulators have not yet generated promising results. In the present study, a co-ordination complex of zinc viz., Zn N-(2-hydroxyacetophenone)glycinate (ZnNG) has been synthesized, characterized and its antitumour activity was tested in vitro against drug sensitive and resistant human T-lymphoblastic leukemic cell lines (CCRF/CEM and CEM/ADR5000 respectively) and in vivo against Ehrlich ascites carcinoma (EAC) implanted in female Swiss albino mice. To evaluate the cytotoxic potential of ZnNG, we used sensitive CCRF/CEM and drug resistant CEM/ADR 5000 cell lines in vitro. Moreover, ZnNG also has the potential ability to reverse the multidrug resistance phenotype in drug resistant CEM/ADR 5000 cell line and induces apoptosis in combination with vinblastine. ZnNG remarkably increases the life span of Swiss albino mice bearing sensitive and doxorubicin resistant subline of EAC in presence and in absence of doxorubicin. In addition, intraperitoneal application of ZnNG in mice does not show any systemic toxicity in preliminary trials in normal mice. To conclude, a novel metal chelate of zinc viz., ZnNG, may be a promising therapeutic agent against sensitive as well as drug resistant cancers.     

Influence of heterogeneity of confined water on photophysical behavior of acridine with amines: a time-resolved fluorescence and laser flash photolysis study

The photophysical behavior of acridine (Acr) shows facilitated water-assisted protonation equilibrium between its deprotonted (Acr* ～ 10 ns) and protonated forms (AcrH(+*) ～ 28 ns) within confined region of ordered water molecules inside AOT/H(2)O/n-heptane reverse micelles (RMs). The time-resolved-area-normalized-emission spectra confirm both Acr* and AcrH(+*), while time-resolved-emission spectra depict time evolution between them. Quenching of AcrH(+*) with N,N-dimethylaniline (DMA) is a purely diffusion-controlled bimolecular quenching with linear Stern-Volmer (S-V) plot, while nonlinearity arises with triethylamine (TEA) that forms ground state complex with AcrH(+) (AcrH(+)··H(2)O··TEA) indicating both static and dynamic quenching. Transient intermediates, DMA(?+) and AcrH(?) infer photoinduced electron transfer from DMA to Acr, while those from AcrH(+)··H(2)O··TEA complex suggest water mediated excited-state proton transfer (ESPT) between AcrH(+) and TEA. The ESPT becomes faster in larger RMs due to enhanced mobility of hydronium ions in AcrH(+)··H(2)O··TEA, which reduces in smaller RMs as water becomes much more constrained owing to stronger complexation by excess confinement.     

Unexpected nonadditivity effects in anion-π complexes

Several complexes of fluorine-substituted ethyne, ethene, butadiene, benzene, and [n]radialenes (n = 3-5) with two anions have been optimized at the RI-MP2/aug-cc-pVTZ level of theory. The additivity of the anion-π interaction was studied depending on the number of double bonds and fluorine atoms. Interesting nonadditivity effects were observed in the aromatic and antiaromatic complexes, which were analyzed by partitioning the total interaction energy into individual components, using Bader's theory of "atoms in molecules" and changes in the aromatic character of the ring upon complexation.     

Layer-by-layer electrostatic assembly with a control over orientation of molecules: anisotropy of electrical conductivity and dielectric properties

While forming layer-by-layer (LbL) electrostatic assembly of a magnetic organic molecule, namely, nickel phthalocyanine (NiPc), we apply a magnetic field. The field orients the magnetic moment of the molecules on a monolayer along the direction of magnetic field. Such an orientation of the molecules is then electrostatically immobilized with a monolayer of a polycation. By repeating the dipping cycle, we form LbL films with planar NiPc molecules facing a particular direction. With NiPc's moment perpendicular to the molecular plane, two types of LbL films were formed: (a) NiPc's molecular plane parallel to the substrate (moment is perpendicular) and (b) molecules perpendicular to the substrate and facing one particular direction, the direction of magnetic field. Such films, with the molecules lying either (a) parallel or (b) perpendicular to the substrate, provide unique systems to study anisotropy of optical, dielectric, and electrical characteristics in these planar organic molecules. The latter film responds to the polarization of incident beam in electronic absorption spectroscopy. Here we show methods to obtain an orientation of molecules in LbL films and study anisotropy of dielectric constant and conductivity of the molecules in ultrathin films.