A Metal–Organic Framework Based Methane Nano‐trap for the Capture of Coal‐Mine Methane

As a major greenhouse gas, methane, which is directly vented from the coal‐mine to the atmosphere, has not yet drawn sufficient attention. To address this problem, we report a methane nano‐trap that features oppositely adjacent open metal sites and dense alkyl groups in a metal–organic framework (MOF). The alkyl MOF‐based methane nano‐trap exhibits a record‐high methane uptake and CH₄/N₂ selectivity at 298 K and 1 bar. The methane molecules trapped within the alkyl MOF were crystalographically identified by single‐crystal X‐ray diffraction experiments, which in combination with molecular simulation studies unveiled the methane adsorption mechanism within the MOF‐based nano‐trap. The IAST calculations and the breakthrough experiments revealed that the alkyl MOF‐based methane nano‐trap is a new benchmark for CH₄/N₂ separation, thereby providing a new perspective for capturing methane from coal‐mine methane to recover fuel and reduce greenhouse gas emissions.     

Development of sample preparation technique to characterize chemical structure of humin by synchrotron-radiation–based X-ray photoelectron spectroscopy

Carbon-binding state of humin (HM, a non-conductive insoluble organo-mineral humic substance) was successfully characterized for the first time by synchrotron-radiation–based X-ray photoelectron spectroscopy (XPS). Four sample preparation techniques—HM on double-sided carbon tape, indium sheet, copper mesh, and in pellet formed from the mixture of HM and copper powder (Cu) at different mixing ratios (1:1, 1:2, and 1:6 v/v)—were compared. The results show that HM samples prepared using the first three methods had significant charge buildup, which made the interpretation of the XPS spectra impossible because of the shifts in the binding energy of C 1s XPS spectra. Pellets of HM:Cu mixture enhanced the electrical conductivity and reduced charge buildup on the sample surface. Pellets prepared with HM:Cu ratio of 1:1 (v/v) provided the minimum charge buildup and high sensitivity with difference in C 1s spectra regardless of the observing position. The C 1s spectra, estimated by the subtraction of the carbon contamination in Cu, showed the resolution of CC (284.0 eV), C C/C H (285.1 eV), C O (286.3 eV), CO (287.3 eV), and OC O (288.3 eV) and three additional peaks of CF (289.3 eV), CF₂ (290.2 eV), and CF₃ (291.4 eV). Soft X-ray absorption spectroscopic (XAS) analysis further proved the existence of fluoride (F 1s) in HM structure. The detection of fluorinated carbon in HM showed a great advancement of XPS compared with other conventional analyses. X-ray with the incident angle of 0° provided the smallest (nearly negligible) energy shift in the C 1s spectra of HM and did not damage the surface of the sample.     

A Pfaffian formula for the monomer–dimer model on surface graphs

We consider the monomer–dimer model on weighted graphs embedded in surfaces with boundary, with the restriction that only monomers located on the boundary are allowed. We give a Pfaffian formula for the corresponding partition function, which generalises the one obtained by Giuliani et al. (J Stat Phys 163(2):211–238, 2016) for graphs embedded in the disc. Our proof is based on an extension of a bijective method mentioned in Giuliani et al. (2016), together with the Pfaffian formula for the dimer partition function of Cimasoni–Reshetikhin (Commun Math Phys 275(1):187–208, 2007).     

Theoretical investigation of hot electron cooling process in GaAs/AlAs cylindrical quantum wire under the influence of an intense electromagnetic wave

Hot electrons cooling by phonons in GaAs/AlAs cylindrical quantum wire (CQW), under the influence of an intense electromagnetic wave (EMW), is studied theoretically. Analytic expression for the electron cooling power (CP) is derived from the quantum transport equation for phonons, using the Hamiltonian of interacting electron–optical phonon system. Both photon absorption and emission processes are considered. Numerical results show that the CP reaches maximum when the energy difference between electronic subbands equals the energy of an optical phonon plus the photon energy. Under the influence of the EMW, the negative CP is observed showing that electrons gain energy from phonon and photon instead of losing their energy. Also, the CP increases with increasing the EMW amplitude. Our results theoretically clarify the mechanism of the electron cooling process by phonons in the GaAs/AlAs CQW under the EMW, which is of significance for designing and fabricating high-speed nanoelectronic devices based on this material.     

Stability Property in Bifunction-Set Optimization

This paper gives sufficient conditions for the lower and upper semicontinuities of the solution mapping of a model, called the parametric bifunction-set optimization problem, which provides a bridge between several parametric set optimization problems and parametric generalized vector Ky Fan inequality problems. Our main theorems, applied to the just mentioned problems, give some new or sharper results.     

Irreducible characters of 3′-degree of finite symmetric,general linear and unitary groups

Let G be a finite symmetric, general linear, or general unitary group defined over a field of characteristic coprime to 3. We construct a canonical correspondence between irreducible characters of degree coprime to 3 of G and those of ${\mathbf{N}}_G(P)$, where P is a Sylow 3-subgroup of G. Since our bijections commute with the action of the absolute Galois group over the rationals, we conclude that fields of values of character correspondents are the same.     

Convergence of proximal algorithms with stepsize controls for non-linear inverse problems and application to sparse non-negative matrix factorization

Numerical Algorithms - We consider a general ill-posed inverse problem in a Hilbert space setting by minimizing a misfit functional coupling with a multi-penalty regularization for stabilization....     

Piezoelectric textured ceramics: Effective properties and application to ultrasonic transducers

Piezoelectric textured ceramics obtained by homo-template grain growth (HTGG) were recently demonstrated. A simple model with several assumptions has been used to calculate effective parameters of these new materials. Different connectivities have been simulated to show that spatial arrangements between the considered phases have little influence on the effective parameters, even through the 3-0 connectivity delivers the highest electromechanical thickness factor. A transducer based on a textured ceramic sample has been fabricated and characterised to show the efficiency of these piezoelectric materials. Finally, in a single element transducer configuration, simulation shows an improvement of 2 dB sensitivity for a transducer made with textured ceramic in comparison with a similar transducer design based on standard soft PZT (at equivalent bandwidths).     

Characters of -degree with cyclotomic field of values

If is a prime number and is a finite group, we show that has an irreducible complex character of degree not divisible by with values in the cyclotomic field .

     

Iterative Regularization Methods for the Multiple-Sets Split Feasibility Problem in Hilbert Spaces

In this paper, we introduce iterative regularization methods for solving the multiple-sets split feasibility problem, that is to find a point closest to a family of closed convex subsets in one space such that its image under a bounded linear mapping will be closest to another family of closed convex subsets in the image space. We consider the cases, when the families are either finite or infinite. We also give two numerical examples for illustrating our main method.