Dual Split Quaternions and Chasles’ Theorem in 3-Dimensional Minkowski Space {\mathbb{E}^{3}_{1}}

In 1831, Michel Chasles proved the existence of a fixed line under a general displacement in ${\mathbb{R}^3}$ . The fixed line called the screw axis of displacement was obtained by McCharthy in [10]. The purpose of this paper is to develop the method which is given for the pure rotation in [14], and thus to obtain the screw axis of spatial displacement in 3-dimensional Minkowski space. Firstly, we give a relation between dual vectors and lines in ${\mathbb{E}^{3}_{1}}$ , characterize the screw axis. Also, we discuss the dual split quaternion representation of a spatial displacement.     

Two-dimensional infrared spectroscopy of antiparallel beta-sheet secondary structure

We investigate the sensitivity of femtosecond Fourier transform two-dimensional infrared spectroscopy to protein secondary structure with a study of antiparallel beta-sheets. The results show that 2D IR spectroscopy is more sensitive to structural differences between proteins than traditional infrared spectroscopy, providing an observable that allows comparison to quantitative models of protein vibrational spectroscopy. 2D IR correlation spectra of the amide I region of poly-l-lysine, concanavalin A, ribonuclease A, and lysozyme show cross-peaks between the IR-active transitions that are characteristic of amide I couplings for polypeptides in antiparallel hydrogen-bonding registry. For poly-l-lysine, the 2D IR spectrum contains the eight-peak structure expected for two dominant vibrations of an extended, ordered antiparallel beta-sheet. In the proteins with antiparallel beta-sheets, interference effects between the diagonal and cross-peaks arising from the sheets, combined with diagonally elongated resonances from additional amide transitions, lead to a characteristic "Z"-shaped pattern for the amide I region in the 2D IR spectrum. We discuss in detail how the number of strands in the sheet, the local configurational disorder in the sheet, the delocalization of the vibrational excitation, and the angle between transition dipole moments affect the position, splitting, amplitude, and line shape of the cross-peaks and diagonal peaks.     

Effective Hamiltonian for non-minimally coupled scalar fields

In the post Newtonian limit, a non-relativistic Hamiltonian is derived for scalar fields with quartic self-interaction and non-minimal coupling to the curvature scalar of the background spacetime. These effects are found to contribute to the non-relativistic Hamiltonian by adding nonlinearities and by modifying the gravitational Darwin term. As we discuss briefly in the text, the impact of these novel structures can be sizable in dense media like neutron star core, and can have observable signatures in phase transitions, for example.     

An Entry into Obtaining Pyrazole‐, Chromone‐, or Oxadiazole‐Substituted 1H‐Pyrazoles via 2,3‐Furandiones

Some new pyrazole‐, chromone‐, or oxadiazole‐substituted 1H‐pyrazoles were obtained via 2,3‐furandiones. Also, we have presented their plausible mechanisms based on rearrangement; one of these rearrangements is Baker–Venkataraman.     

Minimal and Pseudo-Umbilical Rotational Surfaces in Euclidean Space {\mathbb{E}^4}

In this paper we study general rotational surfaces in ${\mathbb{E}^4}$ whose meridian curves lie in two-dimensional planes. We firstly find all minimal general rotational surfaces by solving the differential equation that characterizes minimal general rotational surfaces. Then we determine all pseudo-umbilical general rotational surfaces in ${\mathbb{E}^4}$ .     

IBM-2 calculations of some even-even selenium nuclei

In this study, we determined the most appropriate Hamiltonian that is needed for present calculations of nuclei in the A≅ 80 region by the view of interacting boson model (IBM-2). Using the best-fitted values of parameters in the Hamiltonian, we have calculated energy levels and B(E2) values for a number of transitions in some doubly even Se nuclei. The results were compared with the previous experimental and theoretical data and it is observed that they are in good agreement. The calculations have been extended to Se isotopes with A < 76 for which some B(E2) values are still not known.     

Amino acid‐derived Poly(L‐Lysine) (p(LL)) microgel as a versatile biomaterial: Hydrolytically degradable,drug carrying,chemically modifiable and antimicrobial material

Here, a microgel of poly(_L‐Lysine) (p(LL)) from an amino acid, _L‐Lysine, was synthesized by microemulsion technique using AOT as surfactant in gasoline. The prepared p(LL) microgel was shown to be hydrolytically degradable at pH values of 5.4, 7.4, and 9 in phosphate buffer solution (PBS). The protonated p(LL) microgel was loaded with model drugs such as naproxen and riboflavin and found to release about 80% of loaded naproxen in 180 minutes and 70% of loaded riboflavin in about 120 minutes suggesting the potential of p(LL) microgels to act as fast drug delivery vehicles. Furthermore, p(LL) microgels were chemically modified with 1‐bromoethane (BE), 1‐bromooctane (BO), and 1‐bromoethylamine (BEA) to render antimicrobial capabilities. It was found that protonated p(LL) microgels had 29 ± 1 mm inhibition zone diameter for Pseudomonas aeruginosa ATCC 10145. Furthermore, minimum inhibition concentration (MIC) and minimum bactericidal concentration (MBC) values for Staphylococcus aureus ATCC 6538 were also calculated as 1 and 2.5 mg/mL concentrations, respectively, for protonated p(LL) microgels.     

Synthesis, characterization, DNA interaction and potential applications of gold nanoparticles functionalized with Acridine Orange fluorophores

Two new water-soluble gold nanoparticles (AO-TEG-Au and AO-PEG-Au NPs) are prepared and characterized. They are stabilized by thioalkylated oligoethylene glycols and functionalized with fluorescent Acridine Orange (AO) derivatives. Despite the different core sizes (11.8 and 3.9 nm respectively) and shell composition, they are both well dispersed and are stable in water, even if some self-aggregation is observed in the case of AO-TEG-Au NPs. However, AO-PEG-Au NPs show much lower emission efficiency with respect to AO-TEG-Au NPs. Spectrophotometric and spectrofluorometric experiments indicate that both types of nanoparticle are able to bind to calf thymus DNA, either by external binding or partial intercalation. Preliminary FACS flow cytometry tests seem to indicate that the AO-TEG-Au nanoparticle is able to cross the cell membrane where it is absorbed by Chinese hamster ovary (CHO) cells at the picomolar concentration level.