Observation of abruptly autofocusing waves

We report on the experimental observation of abruptly autofocusing waves. This interesting family of wave packets has been realized by using a radially symmetric Airy intensity distribution. As demonstrated in our experiments, these waves can exhibit unusual features, such as the ability to autofocus by following a parabolic trajectory toward their focus.     

Pre-engineered abruptly autofocusing beams

We introduce a new family of (2+1)D light beams with pre-engineered abruptly autofocusing properties. These beams have a circularly symmetric input profile that develops outward of a dark disk and oscillates radially as a sublinear-chirp signal, creating a series of concentric intensity rings with gradually decreasing width. The light rays involved in this process form a caustic surface of revolution that bends toward the beam axis at an acceleration rate that is determined by the radial chirp itself. The collapse of the caustic on the axis leads to a large intensity buildup right before the intended focus. This ray-optics interpretation provides valuable insight into the dynamics of abruptly autofocusing waves.     

A new weighted Bellman function

We give sharp in p and w estimates of operator norms of Riesz transforms in the $L^p(w\mathrm{d}x)$ spaces, when the $A_p$ characteristic of the weight is close to 1 (flat case). This is done by proving the existence of a certain Bellman function.     

On resonant Neumann problems: Multiplicity of solutions

We consider a semilinear Neumann problem with an asymptotically linear reaction term. We assume that resonance occurs at infinity. Using variational methods based on the critical point theory, together with the reduction technique and Morse theory, we show that the problem has at least four nontrivial smooth solutions.     

An analytical method for the simultaneous trace determination of acidic pharmaceuticals and phenolic endocrine disrupting chemicals in wastewater and sewage sludge by gas chromatography-mass spectrometry

This article presents an analytical method based on solid-phase extraction (SPE) and gas chromatography coupled with mass spectrometry for the simultaneous determination of the most frequently used acidic pharmaceutical residues, ibuprofen, diclofenac, naproxen and ketoprofen (KFN), and phenolic endocrine disruptors, bisphenol (BPA), triclosan (TCS), nonylphenol, nonylphenol monoethoxylate and nonylphenol diethoxylate, in wastewater and sewage sludge samples. In the first phase of the study, each compound has been characterized individually and afterwards in mixture as a trimethylsilyl derivative in order to identify the characteristic ions (m/z ratio) constituting the mass spectrum and to choose the ions for quantification and confirmation. Subsequently, derivatization was evaluated by testing different variables such as the volume of the derivatization solvent bis(trimethylsilyl)trifluoroacetamide and the effect of each catalyst, pyridine and 1% trimethyl chlorosilane, in the derivatized solution. For the analysis of wastewater samples, two commercial SPE cartridges, C18 and Oasis HLB, were compared for their extraction efficiency of the target compounds. The key parameter of extraction procedure included the effect of pH (2.5, 5.3 and 7) of the loading solution. For solid samples, parameters such as the extracted biomass, the volume of the extraction organic solvent and the effect of matrix interferences in chromatographic analysis were evaluated. By using C18 cartridges as purification procedure and ultrasound sonication, satisfactory mean relative recoveries with BPA-d16 and meclofenamic acid as surrogates were obtained ranging from 91% to 117% for wastewater and 84% to 107% for sewage sludge samples. Nine-point calibration of the standard mixture was performed by linear regression analysis with a correlation coefficient >0.99 for all the tested compounds. Limits of detection for the developed methods were established between 0.3 (KFN) and 14.8 (BPA) ng L⁻¹, and 15.0 (TCS) and 32.9 (BPA) ng g⁻¹ for wastewater and sewage sludge, respectively. Application to real samples of the wastewater treatment plant in Athens, the capital of Greece, demonstrated the presence of all tested compounds in most of the samples.     

Aryl-O reductive elimination from reaction of well-defined aryl-Cu(III) species with phenolates: the importance of ligand reactivity

Well-defined aryl-Cu(III) species undergo rapid reductive elimination upon reaction with phenolates (PhO(-)), to form aryl-OPh cross-coupling products. Kinetic studies show that the reaction follows a different mechanistic pathway compared to the reaction with phenols. The pH active cyclized pincer-like ligand undergoes an initial amine deprotonation that triggers a faster reactivity at room temperature. A mechanistic proposal for the enhanced reactivity and the role of EPR-detected Cu(II) species will be discussed in detail.     

Strong agostic-type interactions in ruthenium benzylidene complexes containing 7-azaindole based scorpionate ligands

The complexes [Ru(Tai)Cl{=C(H)Ph}(PCy(3))] (4) and [Ru((Ph)Bai)Cl{=C(H)Ph}(PCy(3))] (5) [where Tai = HB(7-azaindolyl)(3) and (Ph)Bai = Ph(H)B(7-azaindolyl)(2)] have been prepared and structurally characterised. The borohydride unit is located in the coordination site trans to the chloride ligand in both complexes. The degree of interaction between the borohydride group and the metal centre was found to be significantly large in both cases. Thermolysis reactions involving complex 4 led to a dehydrogenation reaction forming [Ru(Tai)Cl{PCy(2)(η(2)-C(6)H(9))}] (6) where the benzylidene group acts as a hydrogen acceptor.     

Preserving closedness of operators under summation

We give a sufficient condition for the sum of two closed operators to be closed. In particular, we study the sum of two sectorial operators with the sum of their sectoriality angles greater than π  . We show that if one of the operators admits bounded H^∞$H^{\infty }$-calculus and the resolvent of the other operator satisfies a boundedness condition stronger than the standard sectoriality, but weaker than the bounded imaginary powers property in the case of UMD spaces, then the sum is closed. We apply the result to the abstract parabolic problem and give a sufficient condition for L^p$L^p$-maximal regularity.     

A sort synthesis of polyhydroxylated pyrrolizidines via sequential 1,3-dipolar cycloaddition and reductive amination

Polyhydroxylated pyrrolizidines bearing a methyl group at C-5 have been synthesized by 1,3-dipolar cycloaddition of five membered cyclic nitrones with methyl vinyl ketone followed by a N–O reductive cleavage and in situ intramolecular reductive amination. The stereochemistry of the obtained compounds is examined in relation to the reactions mechanism.