States on systems of sets that are closed under symmetric difference

We consider extensions of certain states. The states are defined on the systems of sets that are closed under the formation of the symmetric difference (concrete quantum logics). These systems can be viewed as certain set‐representable quantum logics enriched with the symmetric difference. We first show how the compactness argument allows us to extend states on Boolean algebras over such systems of sets. We then observe that the extensions are sometimes possible even for non‐Boolean situations. On the other hand, a difference‐closed system can be constructed such that even two‐valued states do not allow for extensions. Finally, we consider these questions in a σ‐complete setup and find a large class of such systems with rather interesting state properties.     

Infinitesimal 2-braidings and differential crossed modules

We categorify the notion of an infinitesimal braiding in a linear strict symmetric monoidal category, leading to the notion of a (strict) infinitesimal 2-braiding in a linear symmetric strict monoidal 2-category. We describe the associated categorification of the 4-term relations, leading to six categorified relations. We prove that any infinitesimal 2-braiding gives rise to a flat and fake flat 2-connection in the configuration space of n particles in the complex plane, hence to a categorification of the Knizhnik–Zamolodchikov connection. We discuss infinitesimal 2-braidings in a certain monoidal 2-category naturally assigned to every differential crossed module, leading to the notion of a symmetric quasi-invariant tensor in a differential crossed module. Finally, we prove that symmetric quasi-invariant tensors exist in the differential crossed module associated to Wagemann's version of the String Lie-2-algebra. As a corollary, we obtain a more conceptual proof of the flatness of a previously constructed categorified Knizhnik–Zamolodchikov connection with values in the String Lie-2-algebra.     

Sub-Rayleigh imaging via N-photon detection

The Rayleigh diffraction bound sets the minimum separation for two point objects to be distinguishable in a conventional imaging system. We demonstrate sub-Rayleigh resolution by scanning a focused beam--in an arbitrary, object-covering pattern that is unknown to the imager--and using N-photon photodetection implemented with a single-photon avalanche detector array. Experiments show resolution improvement by a factor ～(N-N(max))(?) beyond the Rayleigh bound, where N(max) is the maximum average detected photon number in the image, in good agreement with theory.     

On Bernoulli decompositions for random variables, concentration bounds, and spectral localization

As was noted already by A. N. Kolmogorov, any random variable has a Bernoulli component. This observation provides a tool for the extension of results which are known for Bernoulli random variables to arbitrary distributions. Two applications are provided here: (i) an anti-concentration bound for a class of functions of independent random variables, where probabilistic bounds are extracted from combinatorial results, and (ii) a proof, based on the Bernoulli case, of spectral localization for random Schrödinger operators with arbitrary probability distributions for the single site coupling constants. For a general random variable, the Bernoulli component may be defined so that its conditional variance is uniformly positive. The natural maximization problem is an optimal transport question which is also addressed here.     

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