Size-dependent word frequencies and translational invariance of books

It is shown that a real novel shares many characteristic features with a null model in which the words are randomly distributed throughout the text. Such a common feature is a certain translational invariance of the text. Another is that the functional form of the word-frequency distribution of a novel depends on the length of the text in the same way as the null model. This means that an approximate power-law tail ascribed to the data will have an exponent which changes with the size of the text-section which is analyzed. A further consequence is that a novel cannot be described by text-evolution models such as the Simon model. The size-transformation of a novel is found to be well described by a specific Random Book Transformation. This size transformation in addition enables a more precise determination of the functional form of the word-frequency distribution. The implications of the results are discussed.     

Supersymmetries of the spin-1/2 particle in the field of magnetic vortex, and anyons

The quantum non-relativistic spin-1/2 planar systems in the presence of a perpendicular magnetic field are known to possess the N = 2 supersymmetry. We consider such a system in the field of a magnetic vortex, and find that there are just two self-adjoint extensions of the Hamiltonian that are compatible with the standard N = 2 supersymmetry. We show that only in these two cases one of the subsystems coincides with the original spinless Aharonov-Bohm model and comes accompanied by the super-partner Hamiltonian which allows a singular behavior of the wave functions. We find a family of additional, nonlocal integrals of motion and treat them together with local supercharges in the unifying framework of the tri-supersymmetry. The inclusion of the dynamical conformal symmetries leads to an infinitely generated superalgebra, that contains several representations of the superconformal osp(2∣2) symmetry. We present the application of the results in the framework of the two-body model of identical anyons. The nontrivial contact interaction and the emerging N = 2 linear and nonlinear supersymmetries of the anyons are discussed.     

On the mechanism of the copper-catalyzed enantioselective 1,4-addition of grignard reagents to alpha,beta-unsaturated carbonyl compounds

The mechanism of the enantioselective 1,4-addition of Grignard reagents to alpha,beta-unsaturated carbonyl compounds promoted by copper complexes of chiral ferrocenyl diphosphines is explored through kinetic, spectroscopic, and electrochemical analysis. On the basis of these studies, a structure of the active catalyst is proposed. The roles of the solvent, copper halide, and the Grignard reagent have been examined. Kinetic studies support a reductive elimination as the rate-limiting step in which the chiral catalyst, the substrate, and the Grignard reagent are involved. The thermodynamic activation parameters were determined from the temperature dependence of the reaction rate. The putative active species and the catalytic cycle of the reaction are discussed.     

What can you learn from a molecular probe? New insights on the behavior of C343 in homogeneous solutions and AOT reverse micelles

The behavior of C343, a common molecular probe utilized in solvation dynamics experiments, was studied in homogeneous media and in aqueous and nonaqueous reverse micelles (RMs). In homogeneous media, the Kamlet and Taft solvatochromic comparison method quantified solute-solvent interactions from the absorption and emission bands showing that the solvatochromic behavior of the dye depends not only on the polarity of the medium but also on the hydrogen-bonding properties of the solvent. Specifically, in the ground state the molecule displays a bathochromic shift with the polarity polarizability (pi) and the H-bond acceptor (beta) ability of the solvents and a hypsochromic shift with the hydrogen donor ability (alpha) of the media. The carboxylic acid group causes C343 to display greater sensitivity to the beta than to the pi polarity parameter; this sensitivity increases in the excited state, while the dependence on alpha vanishes. This demonstrates that C343 forms a stable H-bond complex with solvents with high H-bond acceptor ability (high beta) and low H-bond donor character (low alpha). Spectroscopy in nonpolar solvents reveals J-aggregate formation. With information from the Kamlet-Taft analysis, C343 was used to explore RMs composed of water or polar solvents/sodium 1,4-bis-2-ethylhexylsulfosuccinate (AOT)/isooctane using absorption, emission, and time-resolved spectroscopies. Sequestered polar solvents included ethylene glycol (EG), formamide (FA), N,N-dimethylformamide (DMF), and N,N-dimethylacetamide (DMA). Dissolved in the AOT RM systems at low concentration, C343 exists as a monomer, and when introduced to the RM samples in its protonated form, C343 remains protonated driving it to reside in the interface rather than the water pool. The solvathochromic behavior of the dye depends the specific polar solvent encapsulated in the RMs, revealing different types of interactions between the solvents and the surfactant. EG and water H-bond with the AOT sulfonate group destroying their bulk H-bonded structures. While water remains well segregated from the nonpolar regions, EG appears to penetrate into the oil side of the interface. In aqueous AOT RMs, C343 interacts with neither the sulfonate group nor the water, perhaps because of intramolecular H-bonding in the dye. DMF and DMA interact primarily through dipole-dipole forces, and the strong interactions with AOT sodium counterions destroy their bulk structure. FA also interacts with the Na+ counterions but retains its H-bond network present in bulk solvent. Surprisingly, FA appears to be the only polar solvent other than water forming a "polar-solvent pool" with macroscopic properties similar to the bulk.     

New insights on the behavior of PRODAN in homogeneous media and in large unilamellar vesicles

The behavior of 6-propionyl-2-dimethylaminonaphthalene (PRODAN) was studied in homogeneous media and in large unilamellar vesicles (LUVs) of the phospholipid 1,2-di-oleoyl-sn-glycero-3-phosphatidylcholine (DOPC), using absorption, emission, depolarization, and time-resolved spectroscopies. In homogeneous media, the Kamlet and Taft solvatochromic comparison method quantified solute-solvent interactions from the absorption and emission PRODAN bands. These studies demonstrate that the absorption band is sensitive to the polarity-polarizability (pi) and the hydrogen bond donor ability (alpha) parameters of the media. PRODAN in the excited state is even more sensitive to these parameters and to the hydrogen bond acceptor ability (beta) of the media. The transition energy (expressed in kcal/mol) for both absorption and emission bands gives a linear correlation with the well-known polarity parameter E(T30). The results from the absorption and emission bands also reveal that PRODAN aggregates in water. The monomer has two fluorescence lifetimes, 2.27 and 0.65 ns, while the aggregate has a lifetime of 14.6 ns. Using steady-state anisotropy measurements, the calculated volumes of the aggregate and the monomer are 5590 and 222 mL mol(-1), respectively. In DOPC LUVs, PRODAN undergoes a partition process between the water bulk and the DOPC bilayer. We show that the partition constant (K(p)) value is large enough that only at [DOPC] below 0.15 mg/mL PRODAN in water can be detected. PRODAN dissolved in LUVs at [DOPC] > 1 mg/mL exists completely incorporated in its monomer form and senses two different microenvironments within the bilayer: a polar region in the interface near the water and a less polar and also less viscous environment, between the phospholipid tails. These environments were characterized by their fluorescence lifetimes (tau), showing that PRODAN in the polar microenvironment has a tau value of approximately 4 ns while in the less polar region gives a value of 1.2 ns. Moreover, this probe also senses the micropolarity of these two different regions of the bilayer and yields values similar to that of methanol and tetrahydrofuran.     

99mTc generator with hydrated MnO2 as adsorbent of 99Mo

An ^99mTc generator with MnO₂ as adsorbent of ⁹⁹Mo was investigated. Through batch experiments the retention of ⁹⁹Mo onto MnO₂was studied as a function of the shaking time and the pH value of the ⁹⁹Mo solution. It was found that ⁹⁹Mo showed a retention of 100% onto MnO₂ at the pH range from 3 to 11, and the equilibrium distribution was reached in less than 10 minutes. In column experiments the retention of ⁹⁹Mo onto MnO₂ was also high: 99.72%. In this case, the pH of the utilized ⁹⁹Mo solution was 5. The ^99mTc could be eluted from the MnO₂-⁹⁹Mo column by using either distilled water with a pH of 5 or an aqueous solution of 0.9% NaCl. With the saline solution, the ^99mTc elution yields were higher than 80%, and only one aliquot of 5 ml was needed to get these yields. The best results were obtained when the column was packed with 1 g of MnO₂. The water and the saline solution were passed through the column at a rate of 1.25 ml/min.     

First-Order Phase Transformation at Constant Volume: A Continuous Transition?

We describe a first-order phase transition of a simple system in a process where the volume is kept constant. We show that, unlike what happens when the pressure is constant, (i) the transformation extends over a finite temperature (and pressure) range, (ii) each and every extensive potential (internal energy U, enthalpy H, Helmholtz energy F, and Gibbs energy G), and the entropy S is continuous across the transition, and (iii) the constant-volume heat capacity does not diverge during the transition and only exhibits discrete jumps. These non-intuitive results highlight the importance of controlling the correct variables in order to distinguish between continuous and discontinuous transitions. We apply our results to describe the transition between ice VI and liquid water using thermodynamic information available in the literature and also to show that a first-order phase transition driven in isochoric condition can be used as the operating principle of a mechanical actuator.     

Electromagnetic simulation of a 32-GHz, TE021 gyrotron

A simulation study with experimental parameters of a 32-GHz gyrotron operating in the TE₀₂₁ mode is presented. Beam electrons with typical energy of 40 keV and transverse-to-axial velocity ratio ranging from α=0.8 to α=2.0 are injected into the cavity to drive electromagnetic oscillations from noise. On the basis of an electromagnetic particle-in-cell (PIC) code, a parameterization study is carried out to determine the dependence of output power upon pitch ratio and beam current. A comparison of the PIC simulation results with the predictions of the fixed-field approximation on considering Gaussian and asymmetric profiles has indicated close agreement between field parameters and conversion efficiency corresponding to both approaches     

Design,synthesis, molecular docking and in vitro evaluation of benzothiazole derivatives as 11β-hydroxysteroid dehydrogenase type 1 inhibitors

Molecular Diversity - 11-Beta hydroxysteroid dehydrogenase type 1 (11β-HSD1) regulates cortisol levels mainly in adipose, hepatic and brain tissues. There is a relationship between the high...