The Gross–Pitaevskii equation: Bäcklund transformations and admitted solutions

Bäcklund transformations are applied to study the Gross–Pitaevskii equation. Supported by previous results, a class of Bäcklund transformations admitted by this equation are constructed. Schwarzian derivative as well as its invariance properties turn out to represent a key tool in the present investigation. Examples and explicit solutions of the Gross–Pitaevskii equation are obtained.

     

On some combinatorial formulae coming from Hessian Topology

We prove that the fields of asymptotic lines of a real hyperbolic homogeneous polynomial are isotopic to the corresponding fields of its hyperbolic homogeneous part. We also show some combinatorial identities which are related to such isotopy.     

Nonsingular systems of generalized Sylvester equations: An algorithmic approach

We consider the uniqueness of solution (i.e., nonsingularity) of systems of r generalized Sylvester and ?‐Sylvester equations with n×n coefficients. After several reductions, we show that it is sufficient to analyze periodic systems having, at most, one generalized ?‐Sylvester equation. We provide characterizations for the nonsingularity in terms of spectral properties of either matrix pencils or formal matrix products, both constructed from the coefficients of the system. The proposed approach uses the periodic Schur decomposition and leads to a backward stable O(n³r) algorithm for computing the (unique) solution.     

Foliations with persistent singularities

Let ω be a differential q-form defining a foliation of codimension q in a projective variety. In this article we study the singular locus of ω in various settings. We relate a certain type of singularities, which we name persistent, with the unfoldings of ω, generalizing previous work done on foliations of codimension 1 in projective space. We also relate the absence of persistent singularities with the existence of a connection in the sheaf of 1-forms defining the foliation.     

Synthesis of butyrolactones by nickel-catalyzed reductive cyanation of alkynols in water

One-pot catalytic synthesis of butyrolactones from alkynols under mild conditions is described here. The methodology involves the use of the K₂[Ni(CN)₄]/NaBH₄ system in presence of KCN and water. According to the experimental evidences, a possible mechanism pathway is suggested, which involves the nickel-catalyzed reductive cyanation of alkynol, followed by nitrile hydration, reduction of double bond and lactonization.     

Subharmonic generation in physical systems: An interaction-box approach

A so-called “interaction-box” formalism, which has recently been introduced to describe hysteresis in dynamical systems in the case of higher harmonic generation, is further discussed and generalized to describe the phenomenon of subharmonic generation. In this case, the increase in the periodicity of the response is reflected in the formation of multiple loops in the Effect (output) vs. Cause (input) diagrams. Conversely, we show how this type of response represents a sort of “signature” of the system, and can thus be employed to draw general conclusions about the features of the latter. A specific example of a nonlinear system is chosen to illustrate the approach, namely a vibrating cantilever beam with a breathing crack. Effect vs. Cause curves are calculated for this system in the presence of higher harmonics and subharmonics.     

Fast atom bombardment mass spectrometry of carbobenzyloxy-protected amino acids and peptides

The positive fast atom bombardment (FAB) mass spectra of 15 N-carbobenzyloxy derivatives of α-amino acids are presented together with those of some synthetic peptides containing other widely employed protecting groups. The data obtained allow a fragmentation pattern to be established for the N-carbobenzyloxy moiety and to obtain detailed structural information on the main fragment ions. A study of the ion current ratio vs. time pattern shows that important fragments derive from the parent protonated molecule through FAB-induced condensed-phase reactions.     

Carbon-13 magnetic resonance study of lanthanide-substituted muscle calcium binding parvalbumins

High resolution natural abundance carbon-13 NMR has been used previously to examine molecular motions and conformational transitions in the muscle calcium binding parvalbumins isolated from mirror carp. [S. J. Opella, D. J. Nelson, and O. Jardetzky, J. Chem. Phys. 64 , 2533 (1976) and D. J. Nelson, S. J. Opella, and O. Jardetzky, Biochemistry 15 , 5552 (1976).] The carbon-13 NMR spectrum of parvalbumin typically reveals the presence of a number of well-resolved resonances from single-carbon sites in the protein. Since accurate assignment of these resonances to specific carbon atoms in the protein is essential before these resonances can be employed as probes of local conformational events, an investigation of the origin of a number of single-carbon resonances has been performed. Carbon-13 NMR on Tb(III)- and Yb(III)-substituted parvalbumin is the principal spectroscopic technique employed; however, results from terbium fluorescence spectroscopy, γ-ray scintillation spectroscopy, and x-ray difference Fourier analysis all contribute to single-carbon site assignment. The principal conclusions drawn from the combined spectroscopic results are that: (1) the downfield carboxyl resonance at 184.6 ppm, previously attributed to Glu-81, whose carboxyl group is involved in an internal ionic bond, originates rather from a carboxyl function coordinating the solvent exposed metal ion, (2) the carbonyl resonance at 168.9 ppm arises from Lys-96, as was previously suggested; and (3) the 11.2 ppm resonance derives from the δ-methyl carbon of Ile-97, a resonance assignment that could not be made previously.