Convergence analysis for Lasserre’s measure-based hierarchy of upper bounds for polynomial optimization

We consider the problem of minimizing a continuous function f over a compact set \({\mathbf {K}}\). We analyze a hierarchy of upper bounds proposed by Lasserre (SIAM J Optim 21(3):864–885, 2011), obtained by searching for an optimal probability density function h on \({\mathbf {K}}\) which is a sum of squares of polynomials, so that the expectation \(\int _{{\mathbf {K}}} f(x)h(x)dx\) is minimized. We show that the rate of convergence is no worse than \(O(1/\sqrt{r})\), where 2r is the degree bound on the density function. This analysis applies to the case when f is Lipschitz continuous and \({\mathbf {K}}\) is a full-dimensional compact set satisfying some boundary condition (which is satisfied, e.g., for convex bodies). The rth upper bound in the hierarchy may be computed using semidefinite programming if f is a polynomial of degree d, and if all moments of order up to \(2r+d\) of the Lebesgue measure on \({\mathbf {K}}\) are known, which holds, for example, if \({\mathbf {K}}\) is a simplex, hypercube, or a Euclidean ball.     

AgNP-decorated SBA-15 for MWCNT Paste Modified Electrode: A Sensor for Simultaneous Voltammetric Determination of Paracetamol and Sulfamethoxazole

A new electrochemical sensor based on a carbon nanotube paste electrode modified with a Santa Barbara Amorphous material (SBA-15) decorated with silver nanoparticles, namely CNT/SBA/Ag-PE, was developed. It was successfully applied for individual and simultaneous determination of both paracetamol (PC) and sulfamethoxazole (SMZ) medicines. The electrode exhibited a linear dynamic range of 0.12–110 μmol L⁻¹ for paracetamol and 0.06–70 μmol L⁻¹ for sulfamethoxazole, and detection limits of 38 and 19 nmol L⁻¹, respectively. The proposed sensor offered high sensitivity, fast response time and the potential for detecting both drugs simultaneously. The CNT/SBA/Ag-PE enabled the simultaneous determination of PC and SMZ in urine samples with high recovery rates.     

Total Synthesis of Albicidin: A Lead Structure from Xanthomonas albilineans for Potent Antibacterial Gyrase Inhibitors

The peptide antibiotic albicidin, which is synthesized by the plant pathogenic bacterium Xanthomonas albilineans, displays remarkable antibacterial activity against various Gram‐positive and Gram‐negative microorganisms. The low amounts of albicidin obtainable from the producing organism or through heterologous expression are limiting factors in providing sufficient material for bioactivity profiling and structure–activity studies. Therefore, we developed a convergent total synthesis route toward albicidin. The unexpectedly difficult formation of amide bonds between the aromatic amino acids was achieved through a triphosgene‐mediated coupling strategy. The herein presented synthesis of albicidin confirms the previously determined chemical structure and underlines the extraordinary antibacterial activity of this compound. The synthetic protocol will provide multigram amounts of albicidin for further profiling of its drug properties.     

Separation of isochromatics and isopachics using a Faraday rotator in dynamic-holographic photoelasticity

A method is presented that allows the simultaneous separation of isochromatic- and isopachic-fringe patterns for transient-plane stress problems. Isopachic fringes are obtained by means of holography with a Faraday cell and a pulsed ruby laser flashing dual pulses. As usual isochromatic whole-order fringes are recorded in a circular-light polariscope. The shock generator (air-gun) and its synchronizing system with the ruby laser is described. The procedure is applied to the recording of the isochromatic- and isopachic-fringe patterns in a disk under radial dynamic loads.     

A Grobman–Hartman Theorem for Control Systems

We consider the problem of locally linearizing a control system via topological transformations. According to [2,3], there is no naive generalization of the classical Grobman–Hartman theorem for ODEs to control systems: a generic control system, when viewed as a set of under-determined differential equations parametrized by the control, cannot be linearized using pointwise transformations on the state and the control values. However, if we allow the transformations to depend on the control at a functional level (open loop transformations), we are able to prove a version of the Grobman–Hartman theorem for control systems.     

Preparation of Chiral Amino Esters by Asymmetric Phase‐Transfer Catalyzed Alkylations of Schiff Bases in a Ball Mill

The asymmetric alkylation of Schiff bases under basic conditions in a ball mill was performed. The starting Schiff bases of glycine were prepared beforehand by milling protected glycine hydrochloride and benzophenone imine, in the absence of solvent. The Schiff base was then reacted with a halogenated derivative in a ball mill in the presence of KOH. By adding a chiral ammonium salt derived from cinchonidine, the reaction proceeded asymmetrically under phase‐transfer catalysis conditions, giving excellent yields and enantiomeric excesses up to 75 %. Because an equimolar amount of starting material was used, purification was greatly simplified.     

New aspects of gold nanorod formation via seed-mediated method

Gold nanorods (AuNRs) were obtained via a wet chemistry technique, in aqueous medium, employing crystallisation seeds. The kinetics of formation, the aspect ratio, and the selectivity of the particles were evaluated according to the parameters of synthesis: the growth-driving agent, seed, and gold precursor concentrations. In 2–4 h, the rod particles attained the expected size and shape under kinetic control, and were stable for at least 2 days. In order to obtain good quality AuNRs in good yields, without enrichment, we suggest keeping the growth-driving agent/gold molar ratio, the Au^I/seed ratio, and the concentration of the reagents in the final solution within specific ranges. For example, even if good molar ratios between the reagents are maintained, relatively highly concentrated reaction solutions lead to AuNRs with lower aspect ratios. The main properties of the prepared colloidal systems and the nanoparticles were evaluated by UV–vis spectroscopy and transmission electron microscopy, respectively.