On fractal measures and diophantine approximation

We study diophantine properties of a typical point with respect to measures on Namely, we identify geometric conditions on a measure on guaranteeing that -almost every is not very well multiplicatively approximable by rationals. Measures satisfying our conditions are called friendly. Examples include smooth measures on nondegenerate manifolds; thus this paper generalizes the main result of [KM]. Another class of examples is given by measures supported on self-similar sets satisfying the open set condition, as well as their products and pushforwards by certain smooth maps.     

Fuzzy turnover rate chance constraints portfolio model

One concern of many investors is to own the assets which can be liquidated easily. Thus, in this paper, we incorporate portfolio liquidity in our proposed model. Liquidity is measured by an index called turnover rate. Since the return of an asset is uncertain, we present it as a trapezoidal fuzzy number and its turnover rate is measured by fuzzy credibility theory. The desired portfolio turnover rate is controlled through a fuzzy chance constraint. Furthermore, to manage the portfolios with asymmetric investment return, other than mean and variance, we also utilize the third central moment, the skewness of portfolio return. In fact, we propose a fuzzy portfolio mean–variance–skewness model with cardinality constraint which combines assets limitations with liquidity requirement. To solve the model, we also develop a hybrid algorithm which is the combination of cardinality constraint, genetic algorithm, and fuzzy simulation, called FCTPM.     

Band structure for some Nb3X compounds

The tight binding method is used to calculate band structure for a number of Nb₃X compounds. The 4d band of the niobium, as well as the s-p bands of the X-atoms, are considered. The transfer and overlap integrals are calculated using tabulated atomic orbitals. The crystal field parameters (CFP) are estimated more carefully, taking into account deviations from a muffin-tin potential. We employ here the independent band approximation in which no interband interaction is considered. This approximation has been proved successful for the V₃Ga case, and it is estimated here that interband interaction may shift some levels up or down by 50 mRy or so, but the overall band-structure does not change. The Fermi level is found to lie in the neighbourhood of three peaks; one belongs to the δ₂(d_xy) band and the two others belong to the π(d_xz, d_yz) band.     

Fluorescence multicolor hologram recorded by using a macrolens array

We present a new efficient method for obtaining multicolor digital Fresnel holograms of three-dimensional (3-D) objects emitting incoherent fluorescent light. For each emitted fluorescent light wavelength, a single monochromatic digital modified Fresnel hologram of the 3-D scene is generated. Using a macrolens array, only nine projections of the 3-D scene are captured in a single camera shot and are then digitally processed to yield the hologram. The 3-D reconstructed images from all the monochromatic holograms are composed into a single multicolor image of the 3-D scene. The proposed holographic technique is demonstrated by experiments.     

Supramolecular Translation of Enzymatically Triggered Disassembly of Micelles into Tunable Fluorescent Responses

The need for advanced fluorescent imaging and delivery platforms has motivated the development of smart probes that change their fluorescence in response to external stimuli. Here a new molecular design of fluorescently labeled PEG–dendron hybrids that self‐assemble into enzyme‐responsive micelles with tunable fluorescent responses is reported. In the assembled state, the fluorescence of the dyes is quenched or shifted due to intermolecular interactions. Upon enzymatic cleavage of the hydrophobic end‐groups, the labeled polymeric hybrids become hydrophilic, and the micelles disassemble. This supramolecular change is translated into a spectral response as the dye–dye interactions are eliminated and the intrinsic fluorescence is regained. We demonstrate the utilization of this molecular design to generate both Turn‐On and spectral shift responses by adjusting the type of the labeling dye. This approach enables transformation of non‐responsive labeling dyes into smart fluorescent probes.     

NaNO2/I2 as an alternative reagent for the synthesis of 1,2,3-benzotriazin-4(3H)-ones from 2-aminobenzamides

An efficient transformation of 2-aminobenzamides to 1,2,3-benzotriazin-4(3H)-ones in the presence of sodium nitrite (NaNO₂) and Iodine (I₂) is described. The reaction is proposed to proceed via formation of nitrosyl halide that induces nitrosylation of the amino group of 2-aminobenzamide leading to diazotization followed by intramolecular cyclization.     

Nonlinear interactions with an ultrahigh flux of broadband entangled photons

We experimentally demonstrate sum-frequency generation with entangled photon pairs, generating as many as 40,000 photons per second, visible even to the naked eye. The nonclassical nature of the interaction is exhibited by a linear intensity dependence of the nonlinear process. The key element in our scheme is the generation of an ultrahigh flux of entangled photons while maintaining their nonclassical properties. This is made possible by generating the down-converted photons as broadband as possible, orders of magnitude wider than the pump. This approach can be applied to other nonlinear interactions, and may become useful for various quantum-measurement tasks.     

Divergent trajectories and ℚ-rank

The author proves a conjecture of the author: IfG is a semisimple real algebraic defined over ℚ, Γ is an arithmetic subgroup (with respect to the given ℚ-structure) andA is a diagonalizable subgroup admitting a divergent trajectory inG/Γ, then dimA≤ rank_ℚ G.     

Probing conformational variations at the ATPase site of the RNA helicase DbpA by high-field electron-nuclear double resonance spectroscopy

The RNA helicase DbpA promotes RNA remodeling coupled to ATP hydrolysis. It is unique because of its specificity to hairpin 92 of 23S rRNA (HP92). Although DbpA kinetic pathways leading to ATP hydrolysis and RNA unwinding have been recently elucidated, the molecular (atomic) basis for the coupling of ATP hydrolysis to RNA remodeling remains unclear. This is, in part, due to the lack of detailed structural information on the ATPase site in the presence and absence of RNA in solution. We used high-field pulse ENDOR (electron-nuclear double resonance) spectroscopy to detect and analyze fine conformational changes in the protein's ATPase site in solution. Specifically, we substituted the essential Mg(2+) cofactor in the ATPase active site for paramagnetic Mn(2+) and determined its close environment with different nucleotides (ADP, ATP, and the ATP analogues ATPγS and AMPPnP) in complex with single- and double-stranded RNA. We monitored the Mn(2+) interactions with the nucleotide phosphates through the (31)P hyperfine couplings and the coordination by protein residues through (13)C hyperfine coupling from (13)C-enriched DbpA. We observed that the nucleotide binding site of DbpA adopts different conformational states upon binding of different nucleotides. The ENDOR spectra revealed a clear distinction between hydrolyzable and nonhydrolyzable nucleotides prior to RNA binding. Furthermore, both the (13)C and the (31)P ENDOR spectra were found to be highly sensitive to changes in the local environment of the Mn(2+) ion induced by the hydrolysis. More specifically, ATPγS was efficiently hydrolyzed upon binding of RNA, similar to ATP. Importantly, the Mn(2+) cofactor remains bound to a single protein side chain and to one or two nucleotide phosphates in all complexes, whereas the remaining metal coordination positions are occupied by water. The conformational changes in the protein's ATPase active site associated with the different DbpA states occur in remote coordination shells of the Mn(2+) ion. Finally, a competitive Mn(2+) binding site was found for single-stranded RNA construct.