Absence of Solitons for the Defocusing NLS Equation on the Half-line

It has been conjectured that the defocusing nonlinear Schrödinger (NLS) equation on the half-line does not admit solitons. We give a proof of this conjecture.     

Supermacroporous cryogel matrix for integrated protein isolation. Immobilized metal affinity chromatographic purification of urokinase from cell culture broth of a human kidney cell line

A new type of supermacroporous, monolithic, cryogel affinity adsorbent was developed, allowing the specific capture of urokinase from conditioned media of human fibrosarcoma cell line HT1080. The affinity adsorbent was designed with the objective of using it as a capture column in an integrated perfusion/protein separation bioreactor setup. A comparative study between the utility of this novel cryogel based matrix and the conventional Sepharose based affinity matrix for the continuous capture of urokinase in an integrated bioreactor system was performed. Cu(II)-ion was coupled to epoxy activated polyacrylamide cryogel and Sepharose using iminodiacetic acid (IDA) as the chelating ligand. About 27-fold purification of urokinase from the conditioned culture media was achieved with Cu(II)-IDA-polyacrylamide cryogel column giving specific activity of about 814 Plough units (PU)/mg protein and enzyme yields of about 80%. High yields (95%) were obtained with Cu(II)-IDA-Sepharose column by virtue of its high binding capacity. However, the adsorbent showed lower selectivity as compared to cryogel matrix giving specific activity of 161 PU/mg protein and purification factor of 5.3. The high porosity, selectivity and reasonably good binding capacity of Cu(II)-IDA-polyacrylamide cryogel column make it a promising option for use as a protein capture column in integrated perfusion/separation processes. The urokinase peak pool from Cu(II)-IDA-polyacrylamide cryogel column could be further resolved into separate fractions for high and low molecular weight forms of urokinase by gel filtration chromatography on Sephacryl S-200. The selectivity of the cryogel based IMAC matrix for urokinase was found to be higher as compared to that of Cu(II)-IDA-Sepharose column.     

Control structure with disturbance identification for Lagrangian systems

A new control structure for a class of uncertain Lagrangian systems that solves the regulation and tracking control problems is proposed. This structure has good robustness properties, similar to sliding-mode-type controllers; and is free from chattering. The control structure is based on a discontinuous, robust observer, which displays a second-order sliding mode yielding an exponential convergence to the state of the plant in spite of the existence of non-vanishing disturbances and parameter uncertainties. At the same time, with the aid of a low-pass filter, this observer is employed to estimate the perturbations affecting the plant. This disturbance estimation is used to compensate the perturbations acting on the plant, improving the controller robustness. The performance of the proposed control structure is illustrated numerically and experimentally.     

Boundary Value Problems for the Stationary Axisymmetric Einstein Equations: A Disk Rotating Around a Black Hole

We solve a class of boundary value problems for the stationary axisymmetric Einstein equations involving a disk rotating around a central black hole. The solutions are given explicitly in terms of theta functions on a family of hyperelliptic Riemann surfaces of genus 4. In the absence of a disk, they reduce to the Kerr black hole. In the absence of a black hole, they reduce to the Neugebauer-Meinel disk.     

Why Dilated Convolutional Neural Networks: A Proof of Their Optimality

One of the most effective image processing techniques is the use of convolutional neural networks that use convolutional layers. In each such layer, the value of the layer’s output signal at each point is a combination of the layer’s input signals corresponding to several neighboring points. To improve the accuracy, researchers have developed a version of this technique, in which only data from some of the neighboring points is processed. It turns out that the most efficient case—called dilated convolution—is when we select the neighboring points whose differences in both coordinates are divisible by some constant ℓ. In this paper, we explain this empirical efficiency by proving that for all reasonable optimality criteria, dilated convolution is indeed better than possible alternatives.     

Synthesis of 3,4-Bis(Butylselanyl)Selenophenes and 4-Alkoxyselenophenes Promoted by Oxone®

We describe herein an alternative transition-metal-free procedure to access 3,4-bis(butylselanyl)selenophenes and the so far unprecedented 3-(butylselanyl)-4-alkoxyselenophenes. The protocol involves the 5-endo-dig electrophilic cyclization of 1,3-diynes promoted by electrophilic organoselenium species, generated in situ through the oxidative cleavage of the Se-Se bond of dibutyl diselenide using Oxone^® as a green oxidant. The selective formation of the title products was achieved by controlling the solvent identity and the amount of dibutyl diselenide. By using 4.0 equiv of dibutyl diselenide and acetonitrile as solvent at 80 °C, four examples of 3,4-bis(butylselanyl)selenophenes were obtained in moderate to good yields (40–78%). When 3.0 equiv of dibutyl diselenide were used, in the presence of aliphatic alcohols as solvent/nucleophiles under reflux, 10 3-(butylselanyl)-4-alkoxyselenophenes were selectively obtained in low to good yields (15–80%).     

Liquid–liquid phase equilibrium of methanol + ethylbenzene + isooctane + ethanol system at 303 K

The phase equilibrium data for methanol + ethanol + isooctane systems were obtained at 303.15 K. Data for methanol + ethylbenzene + isooctane system were taken from literature. The effect of ethanol addition on the system equilibrium was investigated at the same temperature. The distribution curves for ternary and quaternary system was analyzed. The experimental results for ternary systems were correlated with UNIQUAC and NRTL equations. For the ternary systems studied here, the NRTL equation is more accurate than the UNIQUAC. The equilibrium data for the three ternary systems were used to determine interactions parameters for the UNIQUAC equation. For the quaternary system, the experimental data can be fitted more accurately to UNIQUAC equation than by the UNIFAC method.     

Capillary electrophoresis-mass spectrometry of proteins at medium pH using bilayer-coated capillaries

The feasibility of using noncovalently bilayer-coated capillaries for capillary electrophoresis-mass spectrometry (CE-MS) of acidic proteins was investigated using background electrolytes (BGEs) of medium pH. The capillary was coated by successively rinsing the capillary with solutions of the oppositely charged polymers polybrene (PB) and poly(vinyl sulfonic acid) (PVS). Volatile BGEs containing ammonium formate and/or N-methyl morpholine were tested at pH 7.5 and 8.5. Overall, these BGEs provided relatively fast protein separations (analysis times of ca. 12 min) and showed high efficiencies (70,000-300,000 plates) when the ionic strength was sufficiently high. Migration-time reproducibilities were very favorable with RSDs of less than 1.0%. Infusion experiments showed satisfactory MS responses for studied proteins dissolved in ammonium formate (pH 8.5), however, high concentrations of N-methyl morpholine appeared to seriously suppress the MS protein signals. Evaluation of the CE-MS system was performed by analyzing a mixture of intact proteins yielding efficient separations and good-quality mass spectra. CE-MS analysis of a reconstituted formulation of the biopharmaceutical recombinant human growth hormone (rhGH) which was stored for a prolonged time, revealed one degradation product which was provisionally identified as desamido rhGH. Based on the MS responses the amount of degradation was estimated to be ca. 25%.     

The Hunter-Saxton System and the Geodesics on a Pseudosphere

We show that the two-component Hunter-Saxton system with negative coupling constant describes the geodesic flow on an infinite-dimensional pseudosphere. This approach yields explicit solution formulae for the Hunter-Saxton system. Using this geometric intuition, we conclude by constructing global weak solutions. The main novelty compared with similar previous studies is that the metric is indefinite.     

Classification of Traveling Waves for a Class of Nonlinear Wave Equations

We classify the weak traveling wave solutions for a class of one-dimensional non-linear shallow water wave models. The equations are shown to admit smooth, peaked, and cusped solutions, as well as more exotic waves such as stumpons and composite waves. We also explain how some previously studied traveling wave solutions of the models fit into this classification.