Range sets and partition sets in connection with congruences and algebraic invariants

With a semigroup of transformationsS, we associate a class of equivalence relations onR(S) (calledclosed under inclusion relations), the set of ranges ofS. We define a new notion of connectedness for semigroups of transformations (calledrange-connectedness). For a range-connectedS, the closed under inclusion relations and the left-zero congruences ofS are dually isomorphic. The ideas above are dualized for the partition sets ofS. We associate withS an ordered pair which measures its range and partition connectedness. We generalize to an arbitrary semigroupT by considering faithful representations ofT by semigroups of transformations. In so doing, we are able to define an algebraic invariant for semigroups.     

Prediction of accidental cancellation of different deformation components and optimum fusion orientations

In view of the role of nuclear deformations in the fusion between spherical and deformed nuclei to form super-heavy elements, we try to understand how a cancellation of the different nuclear deformations could arise. We first investigated the correlation between the orientation variation of the deformed nucleus radius and the orientation Coulomb barrier distribution in presence of the higher order deformation components, β₆ and β₈, in addition to the lower order ones. This correlation has been reported in our previous work (Ismail and Seif, 2010) [1] in presence of the lower order (β₂, β₃ and β₄) deformations. Even if there are higher deformations, we found here that the simple expression which describes the deformed target nucleus can be used to predict with good accuracy the behavior of the fusion Coulomb barrier with both orientation and deformation as well as the optimum (cold or hot) fusion configurations. It can predict the orientations of compact and elongated configurations of the interaction and whether they are equatorial or polar or none of them. The value and sign of the deformation parameters ratios with respect to one of them have been used to classify these configurations. We applied the same correlation to predict successfully the mutual cancellation effects between the different deformation components up to β₈. Illustrative examples are given in which the cancellation, at some orientations, brings the fusion barrier back to the spherical case or keeps only the effect of quadrupole deformation, or the effects of both β₂ and β₄.     

The X (X = C, Si and Ge) doped BN nanotube: A computational study

We have performed density functional theory (DFT) calculations to investigate the influence of X-doping (X = C, Si and Ge) on the properties of the electronic structure of the zigzag boron-nitride nanotubes (BNNTs). A single boron and nitrogen atom in the representative (10, 0) BNNT are doped by the X atoms. Electric field gradient (EFG) tensors have been calculated for the different models of the investigated BNNT and converted to quadrupole coupling constants (CQ) for B-11 and N-14 atoms. Our results indicated that the CQ parameters are changed for N-X bonds more than those for B-X ones. The calculations were carried out using the Gaussian 03 software package.     

A DFT studies of structural and quadrupole coupling constants properties in C-doped BeO nanotubes

In the framework of density functional theory (DFT), we calculated the electronic structures and the quadrupole coupling constants (CQ) in the pristine and carbon doped (C-doped) beryllium oxide nanotubes (BeONTs) for the first time. The pristine and C-doped forms of representative (10, 0) zigzag and (5, 5) armchair models of BeONTs were considered in this study. The structures are allowed to relax by performing all atomic optimization. Formation energies indicate that C-doping of Be atom (CBe form) could be more favorable than C-doping of O atom (CO form) in both zigzag and armchair BeONTs. Gap energies and dipole moments detected the effects of dopant in the (5, 5) armchair models; however, those parameters did not detect any significant changes in the C-doped (10, 0) zigzag BeONT models. The calculated nuclear quadrupole coupling constant for the Be and O nuclei reveal that the pristine models can be divided into layers of nuclei with an equivalent electrostatic environment such that those nuclei at the ends of tubes end up in a strong electrostatic environment when compared to the other nuclei along the length of tubes. Comparison with the available data on the pristine BeONTs reveals the influence of C-doping on the CQ parameters of Be and O atoms in the C-doped structures. For most lattice sites, the degree of influence on the CQ parameters of the zigzag model is larger than that of the armchair model. The calculations were performed based on the B3LYP DFT method and 6-31G^∗ standard basis sets using the Gaussian 09 program package.     

A DFT study of carbon nanobuds

In the framework of the density functional theory (DFT) calculations, we present a first time investigation of the properties of four kinds of configurations of carbon nanobuds (CNBs) in which a perfect or defective C60 molecule attaches covalently on the surface of an armchair single-walled carbon nanotube (SWCNT). Chemical shielding (CS) parameters were calculated for the optimized structures. Our results indicate that carbon nanobuds have different values of formation energy, band gap energy, dipole moment, charge transfer and chemical-shielding isotropy (CSI), which result from the many covalent combinations of the fullerenes with the carbon nanotubes. These calculations were carried out using the Gaussian 09 software package.     

Constraints on the nuclear symmetry energy and its density slope from the α decay process

We study the impact of the nuclear symmetry energy and its density dependence on the α-decay process.Within the framework of the preformed cluster model and the energy density formalism, we use different parameterizations of the Skyrme energy density functionals that yield different equations of state(EOS). Each EOS is characterized by a particular symmetryenergy coefficient(a_(sym)) and a corresponding density-slope parameter L. The stepwise trends of the neutron(proton) skin thickness of the involved nuclei with both asym and L do not clarify the oscillating behaviors of the α-decay half-life T_α with these quantities. We find that the change of the skin thickness after α-decay satisfactorily explains these behaviors. The presented results provide constraints on asym centered around an optimum value a_(sym) = 32 MeV, and on L between 41 and 57 MeV. These values of asym and L, which indicate larger reduction of the proton-skin thickness and less increase in the neutron-skin thickness after an α-decay,yield a minimum calculated half-life with the same extracted value of the α-preformation factor inside the parent nucleus.     

Untapped Opportunities of Resin-to-Resin Transfer Reactions (RRTR) for the Convergent Assembly of Multivalent Peptide Conjugates

Handling of the individual fragments remains a bottleneck in the convergent assembly of peptides. Overlooked since the emergence of ligation chemistries during the past two decades, so-called resin-to-resin transfer reactions (RRTR) are here described as a strategic shortcut in this context. Condensation of the involved moieties at an acceptor resin is facilitated by shuttling peptide segments directly from a donor resin in a one-pot fashion. The straightforward synthesis of a sterically constrained 13-mer peptidosteroid model illustrates the utility of this approach, presenting the first successful application of the RRTR methodology in the field of multivalent design and bioconjugation. Relying on established procedures to generate, monitor and isolate intermediates and products, the solid-phase nature of the entire strategy allows for the fast construction of polypeptide adducts and libraries thereof. As such, a rejuvenated use and new opportunities for RRTR are reported.     

A Photoswitchable Agonist for the Histamine H3 Receptor,a Prototypic Family A G‐Protein‐Coupled Receptor

Spatiotemporal control over biochemical signaling processes involving G protein‐coupled receptors (GPCRs) is highly desired for dissecting their complex intracellular signaling. We developed sixteen photoswitchable ligands for the human histamine H₃ receptor (hH₃R). Upon illumination, key compound 65 decreases its affinity for the hH₃R by 8.5‐fold and its potency in hH₃R‐mediated G_i protein activation by over 20‐fold, with the trans and cis isomer both acting as full agonist. In real‐time two‐electrode voltage clamp experiments in Xenopus oocytes, 65 shows rapid light‐induced modulation of hH₃R activity. Ligand 65 shows good binding selectivity amongst the histamine receptor subfamily and has good photolytic stability. In all, 65 (VUF15000) is the first photoswitchable GPCR agonist confirmed to be modulated through its affinity and potency upon photoswitching while maintaining its intrinsic activity, rendering it a new chemical biology tool for spatiotemporal control of GPCR activation.     

Noise power spectra of the inductively coupled plasma

Noise power spectra for the ICP were determined under various conditions, by Fast Fourier Transform (FFT) digital techniques. The major noise types observed were white noise, low frequency noise, and high frequency proportional noise. The high frequency proportional noise increased with concentration of analyte and radio frequency input power. The high frequency proportional noise decreased with increasing nebulizer flow rate and coolant gas flow rate.. The low frequency noise components extended to higher frequencies as the resonance wavelengths of the measured transitions increased. Changing the observation height in the plasma determined which noise types were present in the noise power spectrum. At observation heights near the power coils, all three noise types were present, whereas, low frequency noise predominated at significantly greater heights. Changing the torch design changed the relative amplitudes of the different high frequency proportional noise components, but did not greatly change their respective peak frequencies.