Elliptic Problems with Singular Potential and Double-Power Nonlinearity

We prove the existence of positive symmetric solutions to the semilinear elliptic problem

Lipase-catalyzed solvent-free transesterification of wood sterols

Eighteen commercial lipase preparations, either immobilized or crude enzyme powders, were screened for the transesterification of wood sterols. The reactions were carried out in a solvent-free system, at the optimum temperature of the enzyme preparations as reported by the manufacturer and at the pressure of 2 mbar, with 5 or 10% in weight of the enzyme relative to the wood sterol content of the reacting mixture. Methyl esters of sunflower fatty acids were used as transesterifying agent. Of all the enzymes assayed, only Lipase TL from Pseudomonas stutzeri PL-836 (Meito Sangyo) exhibited any significant transesterifying capacity, 85 and 95% of conversion after 2 and 8 h of reaction, respectively, when 10% in weight of enzyme was used.     

A straightforward synthesis and structure of unprecedented iminium salts of dihydropyrido[3,2-e][1,3]thiazines

Unprecedented 2-iminium chloride salts of 5,8-dihydro-2H-pyrido[3,2-e][1,3]thiazines derivatives (8) were easily synthesized in one step from the corresponding o-chloroformyl-1,4-dihydropyridine (2) and thiourea. The structural study has been carried out by X-ray crystallography and theoretical calculations at the B3LYP/6-31G* levels and reveal that the new salts exhibit appropriate structural features to behave as calcium channel modulators.     

Role of sequence and conformation on the photochemistry and the photophysics of A-T DNA dimers: an experimental and computational approach

The role of base sequence and conformation on the photochemistry and photophysics of thymidylyl (3'-5')-2'-deoxyadenosine sodium salt (TpdA) and 2-deoxyadenylyl (3'-5')-thymidine ammonium salt (dApT) was studied. To this end, nanosecond transient absorption at 266 nm, steady-state irradiation at 254 nm, and quantum chemical calculations were used. The transient absorption spectra show the solvated electron broad band in the visible region for each dinucleotide. In addition, low-intensity absorption bands are observed in the UV region, which are attributed to the deprotonated and protonated neutral radicals of adenine and thymine bases. Photoionization (PI) occurs by one- and two-photon pathways; the latter accounting for approximately 70% of the net PI yield. A diffusion-limited rate constant of 2.0 x 10(10) M(-1) s(-1) was obtained for the reaction of the neutral molecule with the photoejected electron in both sequences. The photodestruction yield, measured from the chromophore loss at 260 nm, decreases in the presence of well-known electron scavengers. This suggests the participation of base radical anions as one of the photodegradation pathways, which is higher in TpdA than in dApT. The intermediacy of a radical ion pair (charge separated state) between the adjacent adenine and thymine bases is proposed in the formation of the [2 + 2] cycloadduct intermediate. The [2 + 2] cycloadduct intermediate is known to be the precursor of the thymine-adenine eight-member ring photoproduct (TA*). Conformational constrains in the radical ion pair are suggested to explain the absence of the TA* photoproduct in dApT. This hypothesis is supported by semiempirical calculations performed on all relevant reactive intermediates proposed to participate in the mechanism of formation of TA*. Altogether, the results show that sequence and conformation profoundly influence the photochemistry and the photophysics of these DNA model systems.     

Pore formation by 6-ketocholestanol in phospholipid monolayers and its interpretation by a general nucleation-and-growth model accounting for the sigmoidal shape of voltage-clamp curves of ion channels

6-Ketocholestanol (KC), a steroid that differs from cholesterol mainly by the presence of a carbonyl group, forms pores inside a dioleoylphosphatidylcholine monolayer self-assembled on mercury by a mechanism similar to that of channel-forming peptides and proteins. The potential steps responsible for pore formation by KC molecules give rise to potentiostatic charge vs time curves whose sigmoidal shape and potential dependence can be quantitatively interpreted on the basis of a mechanism of nucleation and growth of KC clusters. Pore formation by KC allows the penetration of thallous ions across the otherwise impermeable phosphatidylcholine monolayer, while pore disruption taking place at more negative potentials causes a drop in thallous ion permeation. Pore disruption is also accounted for by a mechanism of nucleation and growth of holes inside the KC clusters. The kinetic model of nucleation and growth is general, and accounts quantitatively for the sigmoidal shape and potential dependence of the classical Hodgkin-Huxley voltage-clamp curves of potassium channels in squid giant axon,(1) using a minimum number of free parameters.     

Thermodynamic behavior of polyelectrolytes with the lower critical solution temperature (LCST) phenomenon

A series of vinyl polymers with L-valine and L-leucine residues, and related copolymers with N-isopropylacrylamide, were studied in aqueous solution at different temperatures (25, 30 and 35°C) and at two ionic strengths (0.01 M and 0.1 M NaCl). The protonation behavior revealed great differences between the polymers that were attributed to the size of the hydrophobic lateral group. Macromolecular shrinkage, occurring above a critical degree of protonation β, was related to hydrophobic forces outweighing the electrostatic repulsions between COO – groups. Low salt concentrations increased the electrostatic potential while high temperatures increased the hydrophobic interaction at lower β. The release of fewer water molecules structured around the polymer chain, responsible for the lower critical solution temperature phenomenon, revealed lower entropy changes at higher temperatures. The reversible configuration of graft polymer chains instantly responded to changes in pH and temperature, modifying the water filtration rates through the pores of cellulose membranes.     

Polygonal heat conductors with a stationary hot spot

We consider a convex polygonal heat conductor whose inscribed circle touches every side of the conductor. Initially, the conductor has constant temperature and, at every time, the temperature of its boundary is kept at zero. The hot spot is the point at which temperature attains its maximum at each given time. It is proved that, if the hot spot is stationary, then the conductor must satisfy two geometric conditions. In particular, we prove that these geometric conditions yield some symmetries provided the conductor is either pentagonal or hexagonal. This research was partially supported by Grants-in-Aid for Scientific Research (B) (# 12440042) and (B) (# 15340047) of Japan Society for the Promotion of Science, and by a Grant of the Italian MURST.     

Displacement measurements in structural elements by optical techniques

Speckle metrology and holographic interferometry (HI) have been used in several civil engineering applications. We present the results obtained by applying speckle photography (SP) to the study of two quadratic shearwalls with different boundary conditions, and the potential of the technique in the study of this kind of structures is described. The analysis of Young's fringes obtained with this technique at certain points on each shearwall provides the whole field of displacement measurements. HI has been used to measure the three components of absolute displacement, verifying that the bulging phenomenon does not affect the in-plane components when the applied load remains on the same plane as the shearwall. A qualitative analysis is carried out following an electronic speckle pattern interferometry (ESPI) technique. The results obtained by optical techniques are compared to the numerical results obtained by the finite element method (FEM), finding good correlation between them in all the cases.     

Photophysics and Photochemistry of z‐Chlorprothixene in Acetonitrile†

Chlorprothixene (CPTX, Taractan^®) is a low potency antipsychotic mainly used for the treatment of psychotic disorders (e.g. schizophrenia) and acute mania occurring as part of bipolar disorders. As in the case of other numerous drugs used in the treatment of psychiatric disorders, CPTX presents geometric isomerism. Therefore, in vitro irradiation induces a rapid Z/E isomerization, which can affect its pharmacokinetic properties. This photoisomerization is not dependent on the oxygen concentration. The Z/E quantum yields determined for zCPTX in acetonitrile are 0.22 and 0.21 in anaerobic and aerobic environments, respectively. In the presence of water, both isomers decompose to produce 2‐chlorothioxanthone (CTX) after prolonged irradiation. This process strongly depends on the water concentration and the irradiation time, i.e. it is autocatalyzed by the CTX through a triplet‐energy transfer mechanism. The protonation state of the terminal amino group, on the other hand, has no effect on the isomerization process, but inhibits the formation of CTX. These results indicate that the phototoxicity of zCPTX is somehow affected by the formation of CTX.     

Operator Correlations and Quantum Regression Theorem in Non-Markovian Lindblad Rate Equations

Non-Markovian Lindblad rate equations arise from alternative microscopic interactions such as quantum systems coupled to composite reservoirs, where extra degrees of freedom mediate the interaction between the system and a Markovian reservoir, as well as from systems coupled to complex structured reservoirs whose action can be well approximated by a direct sum of Markovian sub-reservoirs (Budini in Phys. Rev. A 74:053815 [2006]). The purpose of this paper is two fold. First, for both kinds of interactions we find general expressions for the system operator correlations written in terms of the Lindblad rate propagator. Secondly, we find the conditions under which a quantum regression hypothesis is valid. We show that a non-Markovian quantum regression theorem can only be granted in a stationary regime, being a necessary condition the fulfillment of a detailed balance condition. This result is independent of the underlying microscopic interaction, providing a criterion for the validity of the regression hypothesis in non-Markovian Lindblad-like master equations. As an example, we study the correlations of a two-level system coupled to different kind of reservoirs.