Discrete Uncertainty Principles and Sparse Signal Processing

We develop new discrete uncertainty principles in terms of numerical sparsity, which is a continuous proxy for the 0-norm. Unlike traditional sparsity, the continuity of numerical sparsity naturally accommodates functions which are nearly sparse. After studying these principles and the functions that achieve exact or near equality in them, we identify certain consequences in a number of sparse signal processing applications.     

Synthesis,Mechanism Elucidation and Biological Insights of Tellurium(IV)-Containing Heterocycles

Inspired by the synthetic and biological potential of organotellurium substances, a series of five- and six-membered ring organotelluranes containing a Te−O bond were synthesized and characterized. Theoretical calculations elucidated the mechanism for the oxidation-cyclization processes involved in the formation of the heterocycles, consistent with chlorine transfer to hydroxy telluride, followed by a cyclization step with simultaneous formation of the new Te−O bond and deprotonation of the OH group. Moreover, theoretical calculations also indicated anti-diastereoisomers to be major products for two chirality center–containing compounds. Antileishmanial assays against Leishmania amazonensis promastigotes disclosed 1,2λ⁴-oxatellurane LQ50 (IC₅₀=4.1±1.0; SI=12), 1,2λ⁴-oxatellurolane LQ04 (IC₅₀=7.0±1.3; SI=7) and 1,2λ⁴-benzoxatellurole LQ56 (IC₅₀=5.7±0.3; SI=6) as more powerful and more selective compounds than the reference, being up to four times more active. A stability study supported by ¹²⁵Te NMR analyses showed that these heterocycles do not suffer structural modifications in aqueous-organic media or at temperatures up to 65 °C.     

Phosphinothiolates as Ligands for Polyhydrido Copper Nanoclusters

The reaction of [CuI(HSC₆H₄PPh₂)]₂ with NaBH₄ in CH₂Cl₂/EtOH led to air‐ and moisture‐stable copper hydride nanoparticles (CuNPs) containing phosphinothiolates as new ligands, one of which was isolated by crystallization. The X‐ray crystal structure of [Cu₁₈H₇L₁₀I] (L=^?S(C₆H₄)PPh₂) shows unprecedented features in its 28‐atom framework (18 Cu and 10 S atoms). Seven hydrogen atoms, in hydride form, are needed for charge balance and were located by density functional theory methods. H₂ was released from the copper hydride nanoparticles by thermolysis and visible light irradiation.     

Polynuclear Gold [AuI]4, [AuI]8, and Bimetallic [AuI4AgI] Complexes: C−H Functionalization of Carbonyl Compounds and Homogeneous Carbonylation of Amines

The synthesis of tetranuclear gold complexes, a structurally unprecedented octanuclear complex with a planar [Au^I₈] core, and pentanuclear [Au^I₄M^I] (M=Cu, Ag) complexes is presented. The linear [Au^I₄] complex undergoes C?H functionalization of carbonyl compounds under mild reaction conditions. In addition, [Au^I₄Ag^I] catalyzes the carbonylation of primary amines to form ureas under homogeneous conditions with efficiencies higher than those achieved by gold nanoparticles.     

Tightness of the maximum likelihood semidefinite relaxation for angular synchronization

Motivated by stochastic 0–1 integer programming problems with an expected utility objective, we study the mixed-integer nonlinear set: \(P = \big \{(w,x)\in \mathbb {R}\times \left\{ 0,1\right\} ^N: w \le f(a'x + d), b'x \le B\big \}\) where N is a positive integer, \(f:\mathbb {R}\mapsto \mathbb {R}\) is a concave function, \(a, b \in \mathbb {R}^N\) are nonnegative vectors, d is a real number and B is a positive real number. We propose a family of inequalities for the convex hull of P by exploiting submodularity of the function \(f(a'x + d)\) over \(\{0,1\}^N\) and the knapsack constraint \(b'x \le B\). Computational effectiveness of the proposed inequalities within a branch-and-cut framework is illustrated using instances of an expected utility capital budgeting problem.     

Open photoacoustic cell x-ray detection

A simple open-cell configuration photoacoustic x-ray detector is experimentally demonstrated. The front air chamber of a commercial electret microphone is used as the transducer medium of conventional photoacoustics. The observed signal is well described by the thermal diffusion model for the photoacoustic signal.     

Can five-membered Te<Subscript>2</Subscript>N<Subscript>2</Subscript>S rings be considered aromatic?

The structures and molecular properties of three cyclic tellurium species [Te₂N₂S]²⁺ (1 ²⁺ ), [Te₂N₂SCl]⁺ (1 ⁺ ), and Te₂N₂SCl₂ (1) were studied using Density Functional Theory (DFT) with the aim of analyzing and quantifying the degree of electron delocalization in the rings. The structural data for the AsF₆⁻ salt of the cation 1 ⁺ , as well as the experimental vibrational frequencies of 1 and 1 ⁺ , were compared to calculated structures and vibrational modes. While only the five-membered ring of 1 ²⁺ obeys the classic Hückel aromaticity criteria, reflected in the nature of the π orbitals and natural resonance structures, all the three species are magnetic aromatic according to nucleus-independent chemical shift (NICS). However, the out-of-plane component of the NICS tensor (NICS_zz) is able to provide a reliable characterization of the π aromatic character, by showing that successive binding of two chlorine atoms to the same tellurium atom disrupts the π electron delocalization, and that total NICS cannot always be trusted as an aromaticity indicator.     

Electropolymerization of <Emphasis Type="Italic">trans</Emphasis>-[RuCl<Subscript>2</Subscript>(vpy)<Subscript>4</Subscript>] complex—EQCM and Raman studies

The electropolymerization of trans-[RuCl₂(vpy)₄] (vpy=4-vinylpyridine) on Au or Pt electrodes was studied by cyclic voltammetry, electrochemical quartz crystal microbalance (EQCM) technique, and Raman spectroscopy. Cyclic voltammetry of the monomer at a microelectrode shows the typical Ru(III/II) and Ru(IV/III) waves, together with the vinyl reduction waves at −1.5 and −2.45 V and adsorption wave at −0.8 V. Electrodeposition on EQCM technique performed under potential cycling between −0.9 and −2.0 V revealed that the polymerization proceeded well in advance of the vinyl reduction waves. At potentials more positive than −0.9 V, soluble oligomers were deposited irreversibly on the electrode during the oxidative sweep. The film also showed reversible mass changes due to the oxidation and accompanying ingress of charge-balancing anions and solvent into the film. In contrast, potentiostatic growth of the polymer at −1.6 V was slower because the oligomeric material was lost completely from the electrode. Unreacted vinyl groups were detected by in situ Raman spectroscopy for films grown at −0.7, −0.9, and −1.6 V but were absent when the polymerization was carried out at −2.9 V vs Ag/Ag⁺.