Explicit formula for the optimal government debt ceiling

Motivated by the current debt crisis in the world, we develop a stochastic debt control model to study the optimal government debt ceiling, or equivalently the optimal ceiling for government debt. We consider a government that wants to control its debt by imposing an upper bound or ceiling on its debt-to-GDP ratio. We assume that debt generates a cost for the country, and this cost is an increasing and convex function of debt ratio. The government can intervene to reduce its debt ratio, but there is a cost generated by this reduction. The goal of the government is to find the optimal control that minimizes the expected total cost. We obtain an explicit solution for the government debt problem, that gives an explicit formula for optimal government debt ceiling. Moreover, we derive a rule for optimal debt policy in terms of the optimal government debt ceiling. In an extension of the model, we find that countries with a strong positive link between debt and economic growth should have a high optimal debt ceiling. This paper provides the first theoretical model for the optimal government debt ceiling.     

Selective Ruthenium‐Catalyzed Reductive Alkoxylation and Amination of Cyclic Imides

Reported herein, for the first time, is the selective ruthenium‐catalyzed reductive alkoxylation and amination of phthalimides/succinimides. Notably, this novel methodology avoids hydrogenation of the aromatic ring and allows methoxylation of substituted imides with good to excellent selectivity for one of the carbonyl groups. The reported method opens the door to the development of new processes for the selective synthesis of various functionalized N‐heterocyclic compounds. As an example, intramolecular reductive couplings to afford tricyclic compounds are presented for the first time.     

Remarks on a Strongly Nonlinear Model for Two‐Layer Flows with a Top Free Surface

We revisit in this paper the strongly nonlinear long wave model for large amplitude internal waves in two‐layer flows with a free surface proposed by Choi and Camassa [1] and Barros et al. [2]. Its solitary‐wave solutions were the object of the work by Barros and Gavrilyuk [3], who proved that such solutions are governed by a Hamiltonian system with two degrees of freedom. A detailed analysis of the critical points of the system is presented here, leading to some new results. It is shown that conjugate states for the long wave model are the same as those predicted by the fully nonlinear Euler equations. Some emphasis will be given to the baroclinic mode, where interfacial waves are known to change polarity according to different values of density and depth ratios. A critical depth ratio separates these two regimes and its analytical expression is derived directly from the model. In addition, we prove that such waves cannot exist throughout the whole range of speeds.     

QTAIM N-center delocalization indices as descriptors of aromaticity in mono and poly heterocycles

The implementation of the n-center electron delocalization indices, n-DIs, and n-order electron localization indices, n-LIs, within the framework of the quantum theory of atoms in molecules, QTAIM, is performed. n-DIs are shown to be very useful to study the local aromaticity in monocyclic and polycyclic compounds. Total and pi n-DIs from n=4 to 7 were computed for a series of typical 4, 5, 6, and 7-center aromatic and antiaromatic rings. For n>or=5 the pi n-DI accounts for the 95% of the total n-DI and can be employed alone to measure the aromaticity. A scaling factor on the n-DIs is required in order to compare the aromaticity of [5c-6e] and [6c-6e] rings, the same correction allows to estimate the relative aromatic stabilization of polycyclic compounds using the sum of its values for individual rings. This is called Effective Scaled Electron Delocalization, ESED. The comparison with other aromaticity indices reflects a good correlation between ESED and both resonance energies, and HOMA indices. The most important differences between scaled pi n-DIs and NICS(0) indices are found for compounds that contain rings with different number of centers or pi electrons.     

Spectroscopic characterization and Langmuir-Blodgett films of a novel azopolymer material

Spectroscopic characterization and fabrication of Langmuir and Langmuir-Blodgett (LB) films of an azopolymer-pyridine (PAzPy) are reported. UV-visible absorption and fluorescence spectra, Fourier transform infrared (FTIR) spectra, and Raman spectra were recorded. The vibrational assignment of the observed spectra is supported by a complete geometry optimization, followed by vibrational frequency and intensity computations of both the trans and cis forms of the monomer (AzPy) using density functional theory at the B3LYP 6-31G(d,p) level of theory. Langmuir monolayers of the polymer (PAzPy) were formed at the water-air interface, and LB films of high quality were formed onto solid substrates. The polymer LB films were investigated by surface-enhanced Raman scattering.     

Half-sandwich rhodium (and iridium) complexes as enantioselective catalysts for the 1,3-dipolar cycloaddition of 3,4-dihydroisoquinoline N-oxide to methacrylonitrile

Cationic half-sandwich complexes containing the [(eta(5)-C(5)Me(5))M(Diphos*)] moiety (M=Rh, Ir; Diphos*=chiral diphosphine ligand) catalyze the cycloaddition of the nitrone 3,4-dihydroisoquinoline N-oxide (A) to methacrylonitrile (B) with excellent regio and endo selectivity and low-to-moderate enantioselectivity. The most active and selective catalyst, (S(Rh),R(C))-[(eta(5)-C(5)Me(5))Rh{(R)-Prophos)} (NC(Me)C==CH(2))](SbF(6))(2), has been isolated and fully characterized including the determination of the molecular structure by X-ray diffraction. The R-at-metal epimers of the complexes [(eta(5)-C(5)Me(5))M{(R)-Prophos)}(NC(Me)C==CH(2))](SbF(6))(2) (M=Rh, Ir) isomerize to the corresponding S-at-metal diastereomers. The stoichiometric cycloaddition of A with B is catalyzed by diastereopure (S(M),R(C))-[(eta(5)-C(5)Me(5))M{(R)-Prophos)}(NC(Me)C==CH(2))](SbF(6))(2) with perfect regio and endo selectivity and very good (up to 95 %) ee. The catalyst can be recycled up to nine times without significant loss of either activity or selectivity.     

Designing nanosensors based on charged derivatives of gramicidin A

Detection of chemical processes on a single molecule scale is the ultimate goal of sensitive analytical assays. We recently reported the possibility to detect chemical modifications on individual molecules by monitoring a change in the single ion channel conductance of derivatives of gramicidin A (gA) upon reaction with analytes in solution. These peptide-based nanosensors detect reaction-induced changes in the charge of gA derivatives that were engineered to carry specific functional groups near their C-terminus.1 Here, we discuss five key design parameters to optimize the performance of such chemomodulated ion channel sensors. In order to realize an effective sensor that measures changes in charge of groups attached to the C-terminus of a gA pore, the following conditions should be fulfilled: (1) the change in charge should occur as close to the entrance of the pore as possible; (2) the charge before and after reaction should be well-defined within the operational pH range; (3) the ionic strength of the recording buffer should be as low as possible while maintaining a detectable flow of ions through the pore; (4) the applied transmembrane voltage should be as high as possible while maintaining a stable membrane; (5) the lipids in the supporting membrane should either be zwitterionic or charged differently than the derivative of gA. We show that under the condition of high applied transmembrane potential (>100 mV) and low ionic strength of the recording buffer (< or =0.10 M), a change in charge at the entrance of the pore is the dominant requirement to distinguish between two differently charged derivatives of gA; the conductance of the heterodimeric gA pore reported here does not depend on a difference in charge at the exit of the pore. We provide a simple explanation for this asymmetric characteristic based on charge-induced local changes in the concentration of cations near the lipid bilayer membrane. Charge-based ion channel sensors offer tremendous potential for ultrasensitive functional detection since a single chemical modification of each individual sensing element can lead to readily detectable changes in channel conductance.     

Revisiting the calculation of condensed Fukui functions using the quantum theory of atoms in molecules

The analysis of previously reported shortcomings of the condensed Fukui functions obtained making use of the quantum theory of atoms in molecules indicates these drawbacks are due to the inadequacy of the definition employed to compute them and not to the partitioning. A new procedure, which respects the mathematical definition and solves these problems, is presented for the calculation of condensed Fukui functions for atomic basins defined according to the quantum theory of atoms in molecules. It is tested in a set of 18 molecules, which includes the most controversial reported cases.     

Explosion of electron bubbles attached to quantized vortices in liquid 4He

Electron bubbles in superfluid (4)He have been recently observed in low-temperature cavitation measurements under experimental conditions where quantized vortices are also present in the liquid, and which might be attached to the bubbles. We have calculated, within density functional theory, the structure and energetics of electron bubbles pinned to linear vortices in liquid (4)He at low temperature, and the pressure at which such structures become mechanically unstable. Our results are in semiquantitative agreement with the experiments. We discuss dynamical effects not included in the theoretical model used in the present calculations, and which could explain some discrepancies between our results and the experimental data.     

Evaluation of mitochondrial respiratory chain activity in wound healing by low-level laser therapy

Laser therapy is used in many biomedical sciences to promote tissue regeneration. Many studies involving low-level laser therapy have shown that the healing process is enhanced by such therapy. In this work, we evaluated mitochondrial respiratory chain complexes II and IV and succinate dehydrogenase activities in wounds after irradiation with low-level laser. The animals were divided into two groups: group 1, the animals had no local nor systemic treatment and were considered as control wounds; group 2, the wounds were treated immediately after they were made and every day after with a low-level laser (AsGa, wavelength of 904 nm) for 10 days. The results showed that low-level laser therapy improved wound healing. Besides, our results showed that low-level laser therapy significantly increased the activities of complexes II and IV but did not affect succinate dehydrogenase activity. These findings are in accordance to other works, where cytochrome c oxidase (complex IV) seems to be activated by low-level laser therapy. Besides, we showed, for the first time, that complex II activity was also activated. More studies are being carried out in order to evaluate other mitochondrial enzymes activities after different doses and irradiation time of low-level laser.