Exact controllability to trajectories for entropy solutions to scalar conservation laws in several space dimensions

We describe a new method that allows us to obtain a result of exact controllability to trajectories of multidimensional conservation laws in the context of entropy solutions and under a mere non-degeneracy assumption on the flux and a natural geometric condition.     

Local modification of Pythagorean-hodograph quintic spline curves using the B-spline form

The problems of determining the B–spline form of a C ² Pythagorean–hodograph (PH) quintic spline curve interpolating given points, and of using this form to make local modifications, are addressed. To achieve the correct order of continuity, a quintic B–spline basis constructed on a knot sequence in which each (interior) knot is of multiplicity 3 is required. C ² quintic bases on uniform triple knots are constructed for both open and closed C ² curves, and are used to derive simple explicit formulae for the B–spline control points of C ² PH quintic spline curves. These B-spline control points are verified, and generalized to the case of non–uniform knots, by applying a knot removal scheme to the Bézier control points of the individual PH quintic spline segments, associated with a set of six–fold knots. Based on the B–spline form, a scheme for the local modification of planar PH quintic splines, in response to a control point displacement, is proposed. Only two contiguous spline segments are modified, but to preserve the PH nature of the modified segments, the continuity between modified and unmodified segments must be relaxed from C ² to C ¹. A number of computed examples are presented, to compare the shape quality of PH quintic and “ordinary” cubic splines subject to control point modifications.     

Thermodynamics of aqueous solutions of dodecyldimethylethylammonium bromide

The thermodynamic properties of the aqueous solutions of dodecyldimethylethylammonium bromide (DEDAB) were determined as a function of concentration by means of direct methods. Dilution enthalpies at 298 and 313 K, densities and sound velocities at 298 K were measured, allowing the determination of apparent and partial molar enthalpies, volumes, heat capacities and compressibilities. Changes in thermodynamic quantities upon micellization were derived using a pseudo-phase transition approach. These data allow for the determination of the effect of the -CH2- group, when added to the polar head of alkyltrimethylammonium bromides. The properties mainly affected by this addition are the enthalpies and, as a consequence, the entropies. The lowering of the charge density on the quaternary nitrogen due to the inductive effect of the ethyl group, greater than that of the methyl one, raises the plateau value of apparent and molar enthalpy by a quantity similar to that due to the removing of a methylene group from the hydrophobic chain. This effect does not play a great role in the value of the cmc (i.e. on the free energy of micelle formation), since the small decrease in cmc of DEDAB compared to DTAB reflects the increase in the overall hydrophobicity of the molecule. Volumes of DEDAB are greater than those of DTAB by about 15 cm3 mol(-1), both at infinite dilution and at micellar phase, a value in agreement with that generally accepted for a methylene group. The trends of apparent molar heat capacities and compressibilities vs m are the same as for DTAB: in fact, these quantities are related to the number of water molecules involved in the hydrophobic processes in solution, not very greatly affected by the substitution of a methyl group by an ethyl one on the polar head. In summary, this substitution affects to a significant extent the first derivatives of the free energy, but does not affect the second derivatives.     

Discovery of Monoacylglycerol Lipase (MAGL) Inhibitors Based on a Pharmacophore-Guided Virtual Screening Study

Monoacylglycerol lipase (MAGL) is an important enzyme of the endocannabinoid system that catalyzes the degradation of the major endocannabinoid 2-arachidonoylglycerol (2-AG). MAGL is associated with pathological conditions such as pain, inflammation and neurodegenerative diseases like Parkinson’s and Alzheimer’s disease. Furthermore, elevated levels of MAGL have been found in aggressive breast, ovarian and melanoma cancer cells. Due to its different potential therapeutic implications, MAGL is considered as a promising target for drug design and the discovery of novel small-molecule MAGL inhibitors is of great interest in the medicinal chemistry field. In this context, we developed a pharmacophore-based virtual screening protocol combined with molecular docking and molecular dynamics simulations, which showed a final hit rate of 50% validating the reliability of the in silico workflow and led to the identification of two promising and structurally different reversible MAGL inhibitors, VS1 and VS2. These ligands represent a valuable starting point for structure-based hit-optimization studies aimed at identifying new potent MAGL inhibitors.     

The three-hinged arch as an example of piezomechanic passive controlled structure

Although piezoelectric transducers are employed in a variety of fields, their application for vibration control of civil or industrial structures has not yet been fully developed, at the best of authors’ knowledge. Thanks to a new generation of ever more performing piezoceramic materials and to the recent development of scientific proposals based on a very simple technology, this paper presents a step forward to engineering applications for the control of structural systems. A three-hinged arch controlled by piezoelectric stack actuators and passive RL electrical circuits is chosen as a simple structural model that may represent the starting point for a generalization to the most common typologies of civil and industrial engineering structures. Based on the concept of electromechanical analogy, the evolution equations are obtained through a consistent Lagrangian approach. A multimodal vibration suppression is guaranteed by the spectral analogy between the mechanical and electrical components. Preliminary applications related to free oscillations, with one or more actuators on each member, seem to lead to excellent performance in terms of multimodal damping and dissipated energy.     

Mixed Ruthenium–Iridium Carbonyl Cluster Complexes. Synthesis of the Anions [Ru3Ir2(CO)14]2− and [Ru3Ir2(CO)14H]− and Crystal Structures of Their [tetraphenylphosphonium]+ Salts

The reaction of Ru₃(CO)₁₂ and [Ir(CO)₄]^- (as [PPh₄]⁺ or [N(PPh₃)₂]⁺ salts) yields the anion [Ru₃Ir₂(CO)₁₄]^2- (1) which has been found to derive from the intermediate [Ru₃Ir(CO)₁₃]^- anion. Treatment of (1) with acids gives the conjugated hydrido species [Ru₃Ir₂(CO)₁₄H]^- (2). The two anions were characterized by single-crystal X-ray diffraction of their [PPh₄]⁺ salts. [PPh₄]₂[Ru₃Ir₂(CO)₁₄]: space group C2/c, Z=4, a=22.121(5) Å, b=10.546(5) Å, c=25.931(5) Å, =103.870(5)°, R=0.052 and R_w=0.130 for 3128 independent reflections with I>2(I ). [PPh₄][Ru₃Ir₂(CO)₁₄H]: space group P2₁/c, Z=8, a=22.833(5) Å, b=13.893(5) Å, c=25.810(5) Å, =92.650(5)°, R=0.070 and R_w=0.150 for 12141 independent reflections with I>2(I). Both anions 1 and 2 have a trigonal bipyramidal metal frame. There are two independent anions in the asymmetric unit of 2 differing in their ligand stereochemistry.     

A traditional synthetic method, and a new structural motif, for molybdenum-gold clusters: synthesis and solid-state structure of Au8{Mo(CO)5}4(PPh3)4

The neutral cluster [Au8Mo4(CO)20(PPh3)4] was synthesized in low yield from [AuCl(PPh3)] and [Mo2(CO)10]2- in acetonitrile at room temperature. The cluster was characterized by X-ray analysis, IR, and 31P NMR spectroscopy. Its solid-state structure consists of four Au(3)Mo tetrahedral units, fused by four Au atoms in a ring. The average bond lengths are Au-Au 2.77 Angstrom and Mo-Au 2.93 Angstrom. The internal angles of the planar square ring are very close to 90 degrees.