Co‐Conformational Isomerism in a Neutral Ion‐Paired Supramolecular System

Two different counter‐ion‐free host–guest complexes have been prepared and isolated. These compounds were formed from two equally and opposite doubly‐charged species, the viologen guests 1 a ²⁺ and 1 b ²⁺ and the anti‐disulfodibenzo[24]crown‐8 [ DSDB24C8] ^2? host, which gave rise to the 1:1 neutral complexes [ 1 a?DSDB24C8 ] and [ 1 b?DSDB24C8 ]. These species are held together by hydrogen bonding and π stacking, as well as strong electrostatic interactions. The investigation of these neutral ion‐paired supramolecular systems in solution and in the solid state allowed us to establish their co‐conformational preferences. Compound [ 1 a?DSDB24C8 ], with small methyl groups as substituents on the viologen unit, may adopt three different geometries, 1) an exo nonthreaded, 2) a partially threaded, and 3) a threaded arrangement, depending on the relative spatial orientation between the host and guest: The partially‐threaded structure is preferred in solution and in the solid state. The presence of bulky tert‐butylbenzyl groups in the viologen moiety in compound [ 1 b?DSDB24C8 ] restricts the possible geometrical arrangements to one: The exo nonthreaded arrangement. This structure was confirmed in the solid state by X‐ray crystallography. The stability of the neutral complexes in solution was determined by UV/Vis spectrophotometry. The stoichiometry of the complexes was established by continuous variation experiments, and overall equilibrium constants and ΔG° values were determined on the basis of dilution experiments. The results observed are a consequence of only the intrinsic stability of the complexes as there are no additional contributions from counter ions.     

Copolarity of isometric actions

We introduce a new integral invariant for isometric actions of compact Lie groups, the copolarity. Roughly speaking, it measures how far from being polar the action is. We generalize some results about polar actions in this context. In particular, we develop some of the structural theory of copolarity representations, we classify the irreducible representations of copolarity one, and we relate the copolarity of an isometric action to the concept of variational completeness in the sense of Bott and Samelson.

     

Hybrid model for an enzymatic reactor

Cheese whey proteolysis, carried out by immobilized enzymes, can either change or evidence functional properties of the produced peptides, increasing the potential applications of this byproduct of the dairy industry. Optimization and scale-up of the enzymatic reactor relies on its mathematical model—a set of mass balance equations, with reaction rates usually given by Michaelis-Menten-like kinetics; no information about the distribution of peptides’ molecular sizes is supplied. In this article, a hybrid model of a batch enzymatic reactor is presented, consisting of differential mass balances coupled to a “neural-kinetic model,” which provides the molecular weight distributions of the resulting peptides.     

The vectorial Ribaucour transformation for submanifolds and applications

In this paper we develop the vectorial Ribaucour transformation for Euclidean submanifolds. We prove a general decomposition theorem showing that under appropriate conditions the composition of two or more vectorial Ribaucour transformations is again a vectorial Ribaucour transformation. An immediate consequence of this result is the classical permutability of Ribaucour transformations. Our main application is to provide an explicit local construction of an arbitrary Euclidean -dimensional submanifold with flat normal bundle and codimension by means of a commuting family of Hessian matrices on an open subset of Euclidean space . Actually, this is a particular case of a more general result. Namely, we obtain a similar local construction of all Euclidean submanifolds carrying a parallel flat normal subbundle, in particular of all those that carry a parallel normal vector field. Finally, we describe all submanifolds carrying a Dupin principal curvature normal vector field with integrable conullity, a concept that has proven to be crucial in the study of reducibility of Dupin submanifolds.

     

Decay of solutions for a semilinear system of elastic waves in an exterior domain with damping near infinity

We show that the solutions of a semilinear system of elastic waves in an exterior domain with a localized damping near infinity decay in an algebraic rate to zero. We impose an additional condition on the Lamé coefficients. It seems that this restriction cannot be overcome by using the two-finite-speed propagation of the elastic model, since we do not assume compact support on the initial data and because the dissipation does not have compact support. The decay rates obtained for the total energy of the linear problem and the L²$L^2$-norm of the solution improve previous results. For the semilinear problem the decay rates in this paper seem to be the first contribution, mainly in the context of initial data without compact support and localized dissipation.     

Structural determination of Zn and Cd-DTPA complexes: MS, infrared, (13)C NMR and theoretical investigation

The joint application of MS, infrared and (13)C NMR techniques for the determination of metal-DTPA structures (metal=Zn and Cd; DTPA=diethylenetriaminepentacetic acid) is reported. Mass spectrometry allowed determining the 1:1 stoichiometry of the complexes, while infrared analysis suggested that both nitrogen and carboxyl groups are sites for complexation. The (13)C NMR spectrum for the cadmium-containing complex evidenced the existence of free and complexed carboxyl groups, due to a straight singlet at 179.0 ppm (free carboxylic (13)C) and to two broad singlets or a broad doublet at 178.3 ppm (complexed carboxylic (13)C, (2)J(Cd-C(=O))=45.2 Hz). A similar interpretation might be given for the zinc derivative and, with the aid of DFT calculations, structures for both complexes were then proposed.     

A novel source of atomic hydrogen for passivation of defects in silicon

Palladium membranes have been used for decades for the separation of hydrogen from other gasses. In this letter the use of thin palladium leaves to act as sources of atomic hydrogen for silicon samples is explored. It has been assumed in the past that although hydrogen diffuses through palladium in atomic form, the atoms recombine to form molecular hydrogen at the surface. In this letter it is shown that hydrogen supplied to one surface of a palladium leaf can result in atomic hydrogen being released from the opposite surface at low pressure. This is demonstrated through the use of a palladium leaf in a direct plasma system which allows for atomic hydrogen to be supplied to a sample while avoiding exposure to UV radiation from the plasma and high energy charged particles. This method is shown to provide significant atomic hydrogen to silicon samples and improve passivation of silicon surfaces. Method of Shielded Hydrogen Passivation: Schematic of direct plasma chamber with a shield inserted between the plasma and the silicon sample.     

Scattering Frequencies and a Class of Perturbed Systems of Elastic Waves

We consider the system of elastic waves in three dimensions under the presence of an impurity of the medium which we represent by a real-valued function q(x) (or q(x,t)). The medium is assumed to be isotropic and occupies the whole space Ω = ℝ³. We study the location of the scattering frequencies associated with such phenomenon. We conclude that there is a large region on the complex plane which is free of scattering frequencies. In the remaining region they are discrete provided that q satisfies suitable assumptions concerning its behaviour at infinity.