Lovelock tensor as generalized Einstein tensor

We show that the splitting feature of the Einstein tensor, as the first term of the Lovelock tensor, into two parts, namely the Ricci tensor and the term proportional to the curvature scalar, with the trace relation between them is a common feature of any other homogeneous terms in the Lovelock tensor. Motivated by the principle of general invariance, we find that this property can be generalized, with the aid of a generalized trace operator which we define, for any inhomogeneous Euler–Lagrange expression that can be spanned linearly in terms of homogeneous tensors. Then, through an application of this generalized trace operator, we demonstrate that the Lovelock tensor analogizes the mathematical form of the Einstein tensor, hence, it represents a generalized Einstein tensor. Finally, we apply this technique to the scalar Gauss–Bonnet gravity as an another version of string–inspired gravity. This work was partially supported by a grant from the MSRT/Iran.     

On Dynamics of Brans–Dicke Theory of Gravitation

We study longstanding problem of cosmological clock in the context of Brans–Dicke theory of gravitation. We present the Hamiltonian formulation of the theory for a class of spatially homogeneous cosmological models. Then, we show that formulation of the Brans–Dicke theory in the Einstein frame allows how an identification of an appropriate cosmological time variable, as a function of the scalar field in the theory, can be emerged in quantum cosmology. The classical and quantum results are applied to the Friedmann–Robertson–Walker cosmological models.     

Sub-Angstrom oscillation amplitude non-contact atomic force microscopy for lateral force gradient measurement

We report the first results from novel sub-Angstrom oscillation amplitude non-contact atomic force microscopy developed for lateral force gradient measurements. Quantitative lateral force gradients between a tungsten tip and Si(1 1 1)-(7 × 7) surface can be measured using this microscope. Simultaneous lateral force gradient and scanning tunnelling microscope images of single and multi atomic steps are obtained. In our measurement, tunnel current is used as feedback. The lateral stiffness contrast has been observed to be 2.5 N/m at single atomic step, in contrast to 13 N/m at multi atomic step on Si(1 1 1) surface. We also carried out a series of lateral stiffness-distance spectroscopy. We observed lateral stiffness-distance curves exhibit sharp increase in the stiffness as the sample is approached towards the surface. We usually observed positive stiffness and sometimes going into slightly negative region.     

Grafting of temperature sensitive PNIPAAm on hydrophilised polysulfone UF membranes

Poly(N-isopropyl acrylamide) (PNIPAAm) was grafted on a polysulfone UF membrane. The changes of permeability as well as retention of PEG (35 kg/mol) and Dextran (500 kg/mol) between 23 and 60 °C were determined for both grafted and unmodified membranes. The results showed that the viscosity corrected water permeability and solute retention were almost constant for the unmodified membranes within the measured temperature range, the permeability of the grafted membranes increased and the retention of Dextran and PEG decreased with temperature. The variation of changes was most obvious in the temperature range 27–37 °C for the modified membranes due to the lower critical solution temperature (LCST) of PNIPAAm. The location and profile of PNIPAAm inside and on the surface of the membrane were analysed by SEM and FTIR. Depth profile calculation for FTIR spectra showed that PNIPAAm was mostly placed inside the membrane (at a depth of 1.06–1.10 μm from the surface) rather than on the surface. The amount of grafted PNIPAAm was low and did not significantly affect the morphology of the membrane. Therefore, a difference in SEM pictures of modified and unmodified membranes could not be seen. The modified membrane exhibited a clearly different thermal response compared to the unmodified one.     

The use of 6-carboxynaphthofluorescein phosphoramidite in the automated synthesis of quencher-dye oligonucleotide probes (QDOPs)

Real-time detection and quantitation of specific amplicons have been achieved using quencher and dye-labeled oligonucleotides such as molecular beacons. The molecular beacon molecule has a fluorescent reporter dye at the 5′-end and a quencher at the 3′-end. When the closed molecular beacon is excited by irradiation, the reporter fluorescence is greatly reduced by quenching through the process of fluorescence resonance energy transfer. When the molecular beacon hybridizes to the target, the stem loop opens making the fluorophore and quencher spatially distinct, thus increasing the reporter dye fluorescence intensity. Labeling of dyes to 5′-end of oligonucleotides has been done typically using manual methods, it is possible to do manual coupling at the milligram scale. Described here is the development of a scalable process for oligonucleotide labeling, which is robust, and has been achieved for 6-carboxynaphthofluorescein by connecting it to a corresponding phosphoramidite [Theisen, P.; McCollum, C.; Upadhya, K.; Jacobson. K.; Vu, H.; Andrus, A.; Tetrahedron Lett.1992, 33, 5033-5036].     

Analytical treatments of the space–time fractional coupled nonlinear Schrödinger equations

Under investigation in this work is a (\(2+1\))-dimensional the space–time fractional coupled nonlinear Schrödinger equations, which describes the amplitudes of circularly-polarized waves in a nonlinear optical fiber. With the aid of conformable fractional derivative and the fractional wave transformation, we derive the analytical soliton solutions in the form of rational soliton, periodic soliton, hyperbolic soliton solutions by four integration method, namely, the extended trial equation method, the \(\exp (-\,\Omega (\eta ))\)-expansion method and the improved \(\tan (\phi (\eta )/2)\)-expansion method and semi-inverse variational principle method. Based on the the extended trial equation method, we derive the several types of solutions including singular, kink-singular, bright, solitary wave, compacton and elliptic function solutions. Under certain condition, the 1-soliton, bright, singular solutions are driven by semi-inverse variational principle method. Based on the analytical methods, we find that the solutions give birth to the dark solitons, the bright solitons, combine dark-singular, kink, kink-singular solutions with fractional order for nonlinear fractional partial differential equations arise in nonlinear optics.