Rhodamine-Based Cu2+ -Selective Fluorosensor: Synthesis, Mechanism, and Application in Living Cells

A rhodamine B-based fluorescence probe (1) for the sensitive and selective detection of Cu²⁺ ion has been designed and synthesized using pyridine moiety. The optical properties of this compound have been investigated in acetonitrile-water binary solution (7:3 v/v). Compound 1 is found to be an excellent sensor for a biologically/physiologically very important transition metal ion (Cu²⁺) using only the two very different modes of measurements (absorption and emission); one case displayed intensity enhancement whereas in other case showed intensity depletion (quenching). A mechanistic investigation has been performed to explore the static nature of quenching process. The sensor has been found to be very effective in sensing Cu²⁺ ion inside living cells also.     

Torsion and entropy driven denaturation of DNA

A unified theory of the denaturation transition having torsion energy as the control parameter has been formulated here in the framework of the mapping of a DNA molecule onto a Heisenberg spin system. The torsion energy incorporates the torque, tension and temperature, the latter being associated with the twist angle. The denaturation transition can be mapped onto the quantum phase transition induced by a quench when the temperature effect is incorporated in the quench time and torsion takes the role of the external field. The denaturation transition occurs when the entanglement entropy of the spin system vanishes.     

Dielectric permittivity studies of nematogenic compounds and their binary mixtures showing induced smectic Ad phase

The binary mixture of 4-n-pentyl phenyl 4-n′-hexyloxy benzoate (ME6O.5) and p-cyanophenyl trans-4-pentyl cyclohexane carboxylate (CPPCC) shows the presence of induced Smectic A_d phase. In the present work the phase diagram as well as static dielectric permittivity measurements of different mixtures throughout the composition range, are reported. The observed variation of dielectric anisotropy with molar concentration in the nematic and smectic phases is explained, assuming the formation of both homo- and hetero-dimers in the mixture.     

Analytical determination of optimal luminosity for τ mass scan

Resorting to Hessian matrix, the analytical formula is obtained to determine the optimal luminosity proportion for the experiment of τ mass scan. Comparison of numerical results indicate the consistency between the present analytical evaluation and the previous computation based on the sampling technique.     

Semiprimality and Nilpotency of Nonassociative Rings Satisfying x(yz) = y(zx)

In this article we study nonassociative rings satisfying the polynomial identity x(yz) = y(zx), which we call “cyclic rings.” We prove that every semiprime cyclic ring is associative and commutative and that every cyclic right-nilring is solvable. Moreover, we find sufficient conditions for the nilpotency of cyclic right-nilrings and apply these results to obtain sufficient conditions for the nilpotency of cyclic right-nilalgebras.     

On Isolated Submodules

Let R be a ring with identity and let M be a unital left R-module. A proper submodule L of M is radical if L is an intersection of prime submodules of M. Moreover, a submodule L of M is isolated if, for each proper submodule N of L, there exists a prime submodule K of M such that N ? K but L ? K. It is proved that every proper submodule of M is radical (and hence every submodule of M is isolated) if and only if N ∩ IM = IN for every submodule N of M and every (left primitive) ideal I of R. In case, R/P is an Artinian ring for every left primitive ideal P of R it is proved that a finitely generated submodule N of a nonzero left R-module M is isolated if and only if PN = N ∩ PM for every left primitive ideal P of R. If R is a commutative ring, then a finitely generated submodule N of a projective R-module M is isolated if and only if N is a direct summand of M.     

The non-commutative oscillator, symmetry and the Landau problem

The isotropic oscillator on a plane is discussed where the coordinate and momentum space are both considered to be non-commutative. We also discuss the symmetry properties of the oscillator for three separate cases when the non-commutative parameters Θ and for x and p-space, respectively, satisfy specific relations. We compare the Landau problem with the isotropic oscillator on non-commutative space and obtain a relation between the two non-commutative parameters and the magnetic field of the Landau problem.     

Optical and structural properties of lead iodide thin films prepared by vacuum evaporation method

Thermally processed lead iodide (PbI₂) thin films were prepared by the vacuum evaporation method in a constant ambient. Measured thickness of the film was verified analytically from the optical transmittance data in a wavelength range between 300 and 1600 nm. From the Tauc relation for the non‐direct inter band transition, the optical band gap of the film was found to be 2.58 eV for film thickness 300 nm. X‐ray diffraction analysis confirmed that PbI₂ films are polycrystalline, having hexagonal structure. The low fluctuation in Urbach energy indicates that the grain size is quite small. The present findings are in agreement with the other results. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Expansion dynamics of an array of high density Bose-Einstein condensates produced in a 1D CO<Subscript>2</Subscript> laser optical lattice

We discuss the expansion dynamics under mean-field repulsion of an array of ⁸⁷Rb Bose-Einstein condensates produced in an all-optical scheme involving 1D lattice with nearly 10⁵ atoms, after fast evaporative cooling of just about 1 s. Single site occupation exceeds 2 × 10⁴ in our experiments. The possibility of transition to two-dimensionality was also investigated. The expansion behavior of the high density multiple micro-condensates produced directly in the CO₂ laser 1D optical lattice, with a lattice spacing of 5.3 μm, agrees well with a numerical simulation based on the mean-field theory.