Kakeya-Type Sets Over Cantor Sets of Directions in $$\mathbb {R}^{d+1}$$

Given a Cantor-type subset \(\Omega \) of a smooth curve in \(\mathbb R^{d+1}\), we construct examples of sets that contain unit line segments with directions from \(\Omega \) and exhibit analytical features similar to those of classical Kakeya sets of arbitrarily small \((d+1)\)-dimensional Lebesgue measure. The construction is based on probabilistic methods relying on the tree structure of \(\Omega \), and extends to higher dimensions an analogous planar result of Bateman and Katz (Math Res Lett 15(1):73–81, 2008). In contrast to the planar situation, a significant aspect of our analysis is the classification of intersecting tube tuples relative to their location, and the deduction of intersection probabilities of such tubes generated by a random mechanism. The existence of these Kakeya-type sets implies that the directional maximal operator associated with the direction set \(\Omega \) is unbounded on \(L^p(\mathbb {R}^{d+1})\) for all \(1\le p<\infty \).     

Particle on a torus knot: Constrained dynamics and semi-classical quantization in a magnetic field

Kinematics and dynamics of a particle moving on a torus knot poses an interesting problem as a constrained system. In the first part of the paper we have derived the modified symplectic structure or Dirac brackets of the above model in Dirac’s Hamiltonian framework, both in toroidal and Cartesian coordinate systems. This algebra has been used to study the dynamics, in particular small fluctuations in motion around a specific torus. The spatial symmetries of the system have also been studied.     

Direct Assembly of Mesoporous Silica Functionalized with Polypeptides for Efficient Dye Adsorption

Herein, we introduce a new polypeptide‐functionalized mesoporous silica template fabricated from a biodegradable poly(ethylene oxide‐b‐?‐caprolactone) (PEO‐b‐PCL) diblock copolymer and a poly(tyrosine) (PTyr) biopolymer. The crystallization behavior of the PEO‐b‐PCL diblock copolymer changes after blending, but the secondary structure of PTry remains stable. After selective solvent extraction in THF, the PEO‐b‐PCL is removed, but PTyr remains within the silica matrix due to its different solubility. Fourier‐transform IR spectroscopic analysis (FTIR), thermal gravitometry analysis (TGA), small‐angle X‐ray scattering (SAXS), and X‐ray diffraction (XRD) studies confirm the retention of PTyr to form a polypeptide‐functionalized mesoporous material. The adsorption of methylene blue hydrate (MB) from aqueous solution into the polypeptide‐functionalized mesoporous silica is investigated, thus revealing that the nanocomposite exhibits a high adsorption capacity relative to pure silica due to hydrogen‐bonding interactions between the hydroxy phenolic group of PTyr and the N‐containing aromatic ring from MB.     

Efficient Synthesis of Fully Substituted and Diversely Functionalized Pyrazoles through p-TSA Catalyzed One-Pot Condensation of Cyclic β-Diketones,Arylglyoxals and Arylhydrazones

A one-pot, three-component, and atom economic synthesis of biologically and pharmaceutically important fully substituted and functionalized pyrazole derivatives has been accomplished under metal-catalyst-free benign conditions. The strategy involves early condensation of readily available cyclic β-diketones (dimidone, 4-hydroxycoumarin and 2-hydroxy-1,4-naphthoquinone) and arylglyoxals to generate a chalcone type intermediate which upon acid catalyzed condensation with ambident nucleophile arylhydrazones produces various aryl and cyclic β-diketone substituted pyrazole derivatives. The synthesis embraces high functional group tolerance, broad substrate scope, excellent yield of the products, short reaction time and operationally simple and mild reaction conditions. The synthesis provides an easy opportunity of incorporating biologically important N-diarylsulfide/selenide functionality, various enolisable cyclic β-diketones and other bioactive heterocycles concurrently to pyrazole, which may help in designing and development of pyrazole derivatives of pharmacological significance.     

Magnetic field effect on photoinduced electron transfer between [Cu(phen)2]2+ and DNA

The magnetic field effect (MFE) on the photoinduced electron transfer (PET) reaction between the [Cu(phen)2]2+ complex and DNA has been studied in homogeneous buffer medium and in reverse micelles. The copper complex on photoexcitation can oxidize DNA in a deoxygenated environment. A prominent MFE is found even in a homogeneous aqueous medium for the triplet born radicals. The process of partial intercalation of [Cu(phen)2]2+ complex within DNA is responsible for such a rare observation. In reverse micelles, the MFE is not very much prominent because of the large separation distance between the component radicals of the geminate radical ion pairs generated through PET.     

Evidence for pygmy and giant dipole resonances in 130Sn and 132Sn

The dipole strength distribution above the one-neutron separation energy was measured in the unstable 130Sn and the double-magic 132Sn isotopes. The results were deduced from Coulomb dissociation of secondary Sn beams with energies around 500 MeV/nucleon, produced by in-flight fission of a primary 238U beam. In addition to the giant dipole resonance, a resonancelike structure ("pygmy resonance") is observed at a lower excitation energy around 10 MeV exhausting a few percent of the isovector E1 energy-weighted sum rule. The results are discussed in the context of a predicted new dipole mode of excess neutrons oscillating out of phase with the core nucleons.     

Structure of high-Tc superconducting Bi-Sr-Ca-Cu-O films prepared by spray pyrolysis

High-T_c superconducting films of Bi-Sr-Ca-Cu-O have been synthesized by spray pyrolysis of nitrate precursors onto yttria stabilized zirconia (YSZ), followed by rapid annealing at 840°C in air/oxygen. The films are preferentially oriented with c-axis parallel to the plane of the substrate surface. The diffraction patterns of the films correspond to a mixed phase orthorhombic structure, with different c-values of 24.49 Å, 30.78 Å and 37.25 Å. These films exhibit superconductivity at 91 K and zero resistance at 77 K.     

An octahedral nickel(II) complex of a hexadentate N<Subscript>2</Subscript>O<Subscript>2</Subscript>S<Subscript>2</Subscript> thioether ligand: synthesis,characterization, X-ray and electronic structure

A hexadentate dibasic thioether N₂O₂S₂ donor ligand (H ₂ L) and its octahedral nickel(II) complex, [Ni(L)] have been synthesized and characterized by physicochemical and spectroscopic techniques. The structures of both H ₂ L and its nickel complex were confirmed by single-crystal X-ray diffraction studies. The cyclic voltammogram of the complex shows a quasi-reversible Ni(II)/Ni(III) oxidation couple (E _1/2 = 0.88 V) along with a ligand-based reduction (E _1/2 = ?0.83 V). The electronic structures and electrochemical properties have been interpreted with the help of DFT calculations. The electronic transitions as calculated by TDDFT/CPCM method are used to assign the UV–Vis absorption bands.     

Thermally amendable tailor‐made functional polymer by RAFT polymerization and “click reaction”

This investigation reports the preparation and characterization of thermally amendable functional polymer bearing furfuryl functionality via reversible‐addition fragmentation and chain transfer (RAFT) polymerization and Diels‐Alder (DA) reaction. In this case, furfuryl methacrylate (FMA) was polymerized using 4‐cyano‐4‐[(dodecylsulfanylthiocarbonyl)sulfanyl] pentanoic acid as RAFT reagent and 4,4′‐azobis(4‐cyanovaleric acid) as thermal initiator. ¹H NMR, ¹³C NMR, and matrix‐assisted laser desorption ionization time‐of‐flight mass spectrometry analysis showed that furfuryl group in poly(furfuryl methacrylate) (PFMA) was not affected during RAFT polymerization and the tailor‐made polymer had RAFT end group. The DA reaction was successfully carried out between the reactive furfuryl functionality of PFMA and different bismaleimides. The thermoreversible property of these DA polymers was characterized by FT‐IR and DSC analysis. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 3365–3374     

Self-assembled monolayers of Aβ peptides on Au electrodes: an artificial platform for probing the reactivity of redox active metals and cofactors relevant to Alzheimer's disease

The water-soluble hydrophilic part of human Aβ peptide has been extended to include a C-terminal cysteine residue. Utilizing the thiol functionality of this cysteine residue, self-assembled monolayers (SAM) of these peptides are formed on Au electrodes. Atomic force microscopy imaging confirms formation of small Aβ aggregates on the surface of the electrode. These aggregates bind redox active metals like Cu and cofactors like heme, both of which are proposed to generate toxic partially reduced oxygen species (PROS) and play a vital role in Alzheimer's disease. The spectroscopic and electrochemical properties of these Cu and heme bound Aβ SAM are similar to those reported for the soluble Cu and heme bound Aβ peptide. Experiments performed on these Aβ-SAM electrodes clearly demonstrate that (1) heme bound Aβ is kinetically more competent in reducing O(2) than Cu bound Aβ, (2) under physiological conditions the reduced Cu site produces twice as much PROS (measured in situ) than the reduced heme site, and (3) chelators like clioquinol remove Cu from these aggregates, while drugs like methylene blue inhibit O(2) reactivity of the heme cofactor. This artificial construct provides a very easy platform for investigating potential drugs affecting aggregation of human Aβ peptides and PROS generation by its complexes with redox active metals and cofactors.