Determining all Nash equilibria in a (bi-linear) inspection game

This paper addresses a “game” between an inspection agency and multiple inspectees that are subject to random inspections by that agency. We provide explicit (easily computable) expressions for all possible Nash equilibria and verify that none is left out. In particular, our results characterize situations when there exists a unique Nash equilibrium. We also explore special features of the Nash equilibria and the solution of the problem the inspection agency faces in a non-strategic environment.     

Verifiable conditions of <Emphasis Type="Italic">ℓ</Emphasis><Subscript>1</Subscript>-recovery for sparse signals with sign restrictions

We propose necessary and sufficient conditions for a sensing matrix to be “s-semigood” – to allow for exact ℓ ₁-recovery of sparse signals with at most s nonzero entries under sign restrictions on part of the entries. We express error bounds for imperfect ℓ ₁-recovery in terms of the characteristics underlying these conditions. These characteristics, although difficult to evaluate, lead to verifiable sufficient conditions for exact sparse ℓ ₁-recovery and thus efficiently computable upper bounds on those s for which a given sensing matrix is s-semigood. We examine the properties of proposed verifiable sufficient conditions, describe their limits of performance and provide numerical examples comparing them with other verifiable conditions from the literature.     

Stepwise Metal–Ligand Cooperation by a Reversible Aromatization/Deconjugation Sequence in Ruthenium Complexes with a Tetradentate Phenanthroline‐Based Ligand

The synthesis and reactivity of ruthenium complexes containing the tetradentate phenanthroline‐based phosphine ligand 2,9‐bis((di‐tert‐butylphosphino)methyl)‐1,10‐phenanthroline (PPhenP) is described. The hydrido chloro complex [RuHCl(PPhenP)] ( 2 ) undergoes facile dearomatization upon deprotonation of the benzylic position, to give [RuH(PPhenP‐H)] ( 4 ). Addition of dihydrogen to 4 causes rearomatization of the phenanthroline moiety to trans‐[Ru(H)₂(PPhenP)] ( 5 ), followed by hydrogenation of an aromatic heterocycle in the ligand backbone, to give a new dearomatized and deconjugated complex [RuH(PPhenP*‐H)] ( 6 ). These aromatization/deconjugation steps of the coordinated ligand were demonstrated to be reversible and operative in the dehydrogenation of primary alcohols without the need for a hydrogen acceptor. This aromatization/deconjugation sequence constitutes an unprecedented mode of a stepwise cooperation between the metal center and the coordinated ligand.     

Quantification of water compartmentation in cell suspensions by diffusion-weighted and T(2)-weighted MRI

When studying water diffusion in biological systems, any specific signal attenuation curve may be reproduced by a broad range of mathematical functions. Our goals were to quantify the diffusion and T₂ relaxation properties of water in a simple biological system and to study the changes that occur in osmotically stressed cells.     

DFT Calculations and Synthesis Reveal: Key Intermediates,Omitted Mechanisms,and Unsymmetrical Bimane Products

Theoretical and experimental mixed approaches are complementary and valuable. Our DFT calculations support the mechanism suggested by Kosower, adding to it a key diaziridine intermediate that determines the relative product distribution of this reaction. Our results are consistent with the formation of the diazoketene intermediate as the rate-limiting step. Based on curve fittings, first or second-order kinetics cannot be ruled out. This may indicate that more than one mechanism is simultaneously at play in this transformation. This unexpected outcome led us to study an alternative cyclopropenone intermediate. Although cyclopropenone is not likely to be formed under thermal conditions, adding it to the reaction mixture results in bimane structures. The most staggering finding from this investigation was the unanticipated generation of the unsymmetrical anti-(Me,Me)(Ph,Ph)bimane. The optimization of this route towards unsymmetrical bimanes will require additional investigation.     

Dual Role of Silicon-based Matrices in Electron Exchange Matrices for Waste Treatment

Para chloro aniline (PCA) is a common toxic pollutant found in pharmaceutical wastewater. Our study suggests a novel PCA treatment method based on a heterogeneous advanced oxidation process (AOP) that proceeds in an electron exchange matrix (EEM) prepared by the incorporation of redox-active specie in silica matrices using the sol-gel synthesis route. The results, which are supported by DFT calculations, show that the silicon skeleton of the EEM has two important roles, both as a porous matrix that hosts the redox species and as an oxidant species involved in the AOP. The calculations indicate that the formation of a radical on the nitrogen is favored. The suggested mechanism could shed light on the AOP, which proceeds in a heterogenous system, and on its application inside the understudied EEMs that, until now, have been a virtual black box. A better understanding of the mechanism could lead to improved control over the heterogeneous processes that can play a critical role in industries with the need to treat small amounts of toxic compounds at low concentrations, such as in the pharmaceutical industry.