Dressing for a Novel Integrable Generalization of the Nonlinear Schrödinger Equation

We implement the dressing method for a novel integrable generalization of the nonlinear Schrödinger equation. As an application, explicit formulas for the N-soliton solutions are derived. As a by-product of the analysis, we find a simplification of the formulas for the N-solitons of the derivative nonlinear Schrödinger equation given by Huang and Chen.     

Efficient and reproducible analysis of peptides by capillary electrophoresis using noncovalently bilayer-coated capillaries

The usefulness of a noncovalent capillary coating consisting of two layers of oppositely charged polymers for the separation of peptides with capillary electrophoresis (CE) was studied. Capillaries were coated simply by subsequently flushing with solutions of 1% m/v Polybrene and 1% v/v poly(vinylsulfonate) (PVS) forming a bilayer, which showed to produce a strong and highly reproducible electroosmotic flow (EOF) at low pH. Using this coating in combination with a background electrolyte (BGE) containing sodium phosphate (pH 2.5) and 0.01% v/v PVS, initially broadened and overlapping peaks were obtained for some test peptides. By omitting the PVS from the BGE, the peak width and shape of the peptides improved resulting in baseline separation. A systematic study of the influence of the BGE composition showed that considerable further enhancement of the separation efficiency was achieved by increasing the ionic strength of the BGE. Using a BGE of 200 mM tris(hydroxymethyl)aminomethane (Tris)-phosphate (pH 2.5) plate numbers for the peptides were in the 300 000-600 000 range and the relative standard deviation of the peptide migration times was less then 0.3% (n = 5). The use of Tris-phosphate instead of sodium phosphate allowed the current to stay within acceptable limits when 30 kV was used as separation voltage. Overall, the bilayer coating showed a remarkable EOF repeatability, as well as long-term stability. Compared to bare fused-silica capillaries the intraday and interday repeatability of migration times was very favorable and coated capillaries could be used for over a month performing analyses with low and high ionic strength BGEs without any performance deterioration. The usefulness of the bilayer-coated capillaries for the analysis of positively charged peptides was demonstrated by the fast and efficient separation of various closely related enkephalins and the baseline separation of an isomeric peptide/peptoid couple exhibiting efficiencies of over 550 000 plates.     

Simplex maximization of the correlation coefficient for DNA sizing analysis by capillary electrophoresis

The separation of DNA molecules in polymeric solution by capillary electrophoresis involves the optimization of several variables, such as polymer solution concentration, electric field separation, temperature, etc. The optimization of each variable individually usually is a time-consuming process and the results may reach a false optimum point. Chemometric methods are suitable to be applied in such cases in which a number of variables can be optimized simultaneously. The simplex is a chemometric method that can perform such a task easily and efficiently. In this study, a simplex method was carried out to maximize the correlation coefficient (r(2)) of a logarithmic plot of mobility (mu) vs. base pair (bp), which was obtained from the separation of DNA fragments of size between 75 and 4072 bp. The simplex showed three vertexes with r(2) > 0.98 and the vertex 21 showing the highest resolution. For the fragments between 201 and 2036 bp, the r(2) increased to 0.992 with and relative standard deviation (RSD) lower than 0.2% (inter- and intra-day variation). The precision of the method in determining the size of a PCR DNA fragment was carried out using a 1 kbp DNA ladder. With the addition of an internal standard to the sample, the precision could be further improved.     

Transmetallation versus β-hydride elimination: the role of 1,4-benzoquinone in chelation-controlled arylation reactions with arylboronic acids

The formation of an atypical, saturated, diarylated, Heck/Suzuki, domino product produced under oxidative Heck reaction conditions, employing arylboronic acids and a chelating vinyl ether, has been investigated by DFT calculations. The calculations highlight the crucial role of 1,4-benzoquinone (BQ) in the reaction. In addition to its role as an oxidant of palladium, which is necessary to complete the catalytic cycle, this electron-deficient alkene opens up a low-energy reaction pathway from the post-insertion σ-alkyl complex. The association of BQ lowers the free-energy barrier for transmetallation of the σ-alkyl complex to create a pathway that is energetically lower than the oxidative Heck reaction pathway. Furthermore, the calculations showed that the reaction is made viable by BQ-mediated reductive elimination and leads to the saturated diarylated product.     

Transmetallation Versus β‐Hydride Elimination: The Role of 1,4‐Benzoquinone in Chelation‐Controlled Arylation Reactions with Arylboronic Acids

The formation of an atypical, saturated, diarylated, Heck/Suzuki, domino product produced under oxidative Heck reaction conditions, employing arylboronic acids and a chelating vinyl ether, has been investigated by DFT calculations. The calculations highlight the crucial role of 1,4‐benzoquinone (BQ) in the reaction. In addition to its role as an oxidant of palladium, which is necessary to complete the catalytic cycle, this electron‐deficient alkene opens up a low‐energy reaction pathway from the post‐insertion σ‐alkyl complex. The association of BQ lowers the free‐energy barrier for transmetallation of the σ‐alkyl complex to create a pathway that is energetically lower than the oxidative Heck reaction pathway. Furthermore, the calculations showed that the reaction is made viable by BQ‐mediated reductive elimination and leads to the saturated diarylated product.     

Rigidity and Bifurcation Results for CMC Hypersurfaces in Warped Product Spaces

In this paper, we deduce some rigidity results in warped product spaces under normal variations of CMC hypersurfaces. In particular, we prove the existence of one-parameter families locally rigid on the spatial fiber of Anti-de Sitter Schwarzschild spacetime and one-parameter families with bifurcation points on the spatial fiber of de Sitter Schwarzschild spacetime.