Computing equilibria of Cournot oligopoly models with mixed-integer quantities

We consider Cournot oligopoly models in which some variables represent indivisible quantities. These models can be addressed by computing equilibria of Nash equilibrium problems in which the players solve mixed-integer nonlinear problems. In the literature there are no methods to compute equilibria of this type of Nash games. We propose a Jacobi-type method for computing solutions of Nash equilibrium problems with mixed-integer variables. This algorithm is a generalization of a recently proposed method for the solution of discrete so-called “2-groups partitionable” Nash equilibrium problems. We prove that our algorithm converges in a finite number of iterations to approximate equilibria under reasonable conditions. Moreover, we give conditions for the existence of approximate equilibria. Finally, we give numerical results to show the effectiveness of the proposed method.     

Rate coefficients for reactions of OH radicals with CH3D,CH2D2, CHD3, and CD4

Fourier transform infrared (FTIR) smog chamber techniques were used to investigate the atmospheric chemistry of the isotopologues of methane. Relative rate measurements were performed to determine the kinetics of the reaction of the isotopologues of methane with OH radicals in cm³ molecule⁻¹ s⁻¹ units: k(CH₃D + OH) = (5.19 ± 0.90) × 10⁻¹⁵, k(CH₂D₂ + OH) = (4.11 ± 0.74) × 10⁻¹⁵, k(CHD₃ + OH) = (2.14 ± 0.43) × 10⁻¹⁵, and k(CD₄ + OH) = (1.17 ± 0.19) × 10⁻¹⁵ in 700 Torr of air diluent at 296 ± 2 K. Using the determined OH rate coefficients, the atmospheric lifetimes for CH_4–xD_x (x = 1–4) were estimated to be 6.1, 7.7, 14.8, and 27.0 years, respectively. The results are discussed in relation to previous measurements of these rate coefficients.     

Reducing the computational cost of NMR crystallography of organic powders at natural isotopic abundance with the help of 13C-13C dipolar couplings

Structure determination of functional organic compounds remains a formidable challenge when the sample exists as a powder. Nuclear magnetic resonance crystallography approaches based on the comparison of experimental and Density Functional Theory (DFT)-computed ¹H chemical shifts have already demonstrated great potential for structure determination of organic powders, but limitations still persist. In this study, we discuss the possibility of using ¹³C-¹³C dipolar couplings quantified on powdered theophylline at natural isotopic abundance with the help of dynamic nuclear polarization, to realize a DFT-free, rapid screening of a pool of structures predicted by ab initio random structure search. We show that although ¹³C-¹³C dipolar couplings can identify structures possessing long range structural motifs and unit cell parameters close to those of the true structure, it must be complemented with other data to recover information about the presence and the chemical nature of the supramolecular interactions.     

q value and parent energy optimization using a low-voltage ionization approach increases resolution in linear ion trap mass spectrometry

In this work, the isolation step in the linear ion trap was performed using different “q values” conditions at a low collision-induced dissociation (CID) energy leading to the parent ion resolution improvements, reasonably due to better ion energy distribution. According to the results, we obtained a greater resolution and mass accuracy operating in both traditional electrospray and low voltage ionization near the q value = 0.778 and with a CID energy of 10%. This effect was evaluated with low-molecular-mass compounds (skatole and arginine). The proposed optimization yielded a superior instrument performance without adding technological complexity to mass spectrometry analyses.     

Reactive uptake of NO3, N2O5, NO2, HNO3, and O3 on three types of polycyclic aromatic hydrocarbon surfaces

We investigated the reactive uptake of NO3, N2O5, NO2, HNO3, and O3 on three types of solid polycyclic aromatic hydrocarbons (PAHs) using a coated wall flow tube reactor coupled to a chemical ionization mass spectrometer. The PAH surfaces studied were the 4-ring systems pyrene, benz[a]anthracene, and fluoranthene. Reaction of NO3 radicals with all three PAHs was observed to be very fast with the reactive uptake coefficient, gamma, ranging from 0.059 (+0.11/-0.049) for benz[a]anthracene at 273 K to 0.79 (+0.21/-0.67) for pyrene at room temperature. In contrast to the NO3 reactions, reactions of the different PAHs with the other gas-phase species (N2O5, NO2, HNO3, and O3) were at or below the detection limit (gamma 相似文献   

Photochemical Bromination of 2,5-Dimethylbenzoic Acid as Key Step of an Improved Alkyne-Functionalized Blue Box Synthesis**

Cyclobis(paraquat-p-phenylene), also known as “blue box”, is a highly electron-deficient macrocycle, widely used as a molecular receptor for small electron-rich molecules. Inserting a reactive functional group onto the molecular structure of this cyclophane is paramount for its inclusion into complex architectures. To this aim, including an alkyne moiety would be ideal, because it can participate in click reactions. However, the synthesis of such alkyne-functionalized cyclophane suffers from several drawbacks: the use of toxic and expensive CCl₄, the need for high-pressure reactors, and overall low yield. We have revised the existing synthesis of this cyclophane derivative bearing an alkyne moiety, to overcome all these limitations. In particular, photochemical radical bromination is adopted to obtain a sensitive intermediate. We demonstrated that the synthesized host molecule can be functionalized via click reactions and take part in radical-radical interactions. Our work makes a key functionalized paraquat macrocycle more accessible, facilitating the development of novel redox-responsive systems.     

Coronaviruses Use ACE2 Monomers as Entry-Receptors

The angiotensin-converting enzyme 2 (ACE2) has been identified as entry receptor on cells enabling binding and infection with the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) via trimeric spike (S) proteins protruding from the viral surface. It has been suggested that trimeric S proteins preferably bind to plasma membrane areas with high concentrations of possibly multimeric ACE2 receptors to achieve a higher binding and infection efficiency. Here we used direct stochastic optical reconstruction microscopy (dSTORM) in combination with different labeling approaches to visualize the distribution and quantify the expression of ACE2 on different cells. Our results reveal that endogenous ACE2 receptors are present as monomers in the plasma membrane with densities of only 1–2 receptors μm⁻². In addition, binding of trimeric S proteins does not induce the formation of ACE2 oligomers in the plasma membrane. Supported by infection studies using vesicular stomatitis virus (VSV) particles bearing S proteins our data demonstrate that a single S protein interaction per virus particle with a monomeric ACE2 receptor is sufficient for infection, which provides SARS-CoV-2 a high infectivity.     

Effect of a reduced mobility layer on the interplay between molecular relaxations and diffusion-limited crystallization rate in ultrathin polymer films

In ultrathin polymer films, the coupling between the segmental mobility, precursor of the molecular diffusion, and the crystallization rate is broken down because of interfacial interactions. In particular, in the presence of a reduced mobility layer at the interface with the substrate, the crystallization kinetics slow down at a length scale bigger than the one connected with the deviation from bulk behavior of the structural relaxation. By modeling the influence of the substrate interactions on the parameters governing the temperature evolution of the main relaxation time, it was possible to reproduce the effect of geometrical confinement on the quantities connected to the diffusion-limited crystallization rate. Upon reduction of the thickness or increasing of the substrate interaction, the films show an apparent higher glass stability in terms of an increase of the cold crystallization temperature and of the crystallization time. The deviations from bulk behavior were found to vanish above a crossover temperature as already observed for the phenomena connected to the glass transition.