Hermite‐Hadamard‐type inequalities for interval‐valued coordinated convex functions involving generalized fractional integrals

In this paper, we define interval‐valued left‐sided and right‐sided generalized fractional double integrals. We establish inequalities of Hermite‐Hadamard like for coordinated interval‐valued convex functions by applying our newly defined integrals.     

Ultrahigh Loading Copper Single Atom Catalyst for Palladium-free Wacker Oxidation

Wacker oxidation is an industry-adopted process to transform olefins into value-added epoxides and carbonyls. However, traditional Wacker oxidation involves the use of homogeneous palladium and copper catalysts for the olefin addition and reductive elimination. Here, we demonstrated an ultrahigh loading Cu single atom catalyst(14% Cu, mass fraction) for the palladium-free Wacker oxidation of 4-vinylanisole into the corresponding ketone with N-methylhydroxylamine hydrochloride as an additive under mild conditions. Mechanistic studies by ¹⁸O and deuterium isotope labelling revealed a hydrogen shift mechanism in this palladium-free process using N-methylhydroxylamine hydrochloride as the oxygen source. The reaction scope can be further extended to Kucherov oxidation. Our study paves the way to replace noble metal catalysts in the traditional homogeneous processes with single atom catalysts.     

Theoretical studies of photovoltaic properties of five new silol dithiophene based D2-A-D1-A-D2 donors

Organic solar cell of silol dithiophene based D₂-A-D₁-A-D₂/PC₇₁BM (D: donor part; A: acceptor part; 1 and 2 denote different units) possesses promising power conversion efficiency. Researchers have studied D₂-A-D₁-A-D₂ molecules carefully, including the effects of the different number of terminal thiophenes, the different central moiety (D₁), and the length of the alkyl chain. However, there are few investigations, especially theoretical studies, on the influences of different A (acceptor) units on the properties of D₂-A-D₁-A-D₂ molecule. In the present work, we have designed and modeled five new D₂-A-D₁-A-D₂ (D₂ = bithiophene and D₁ = silol dithiophene) donors by changing A units (A = diketopyrrolopyrrole, naphtho[1,2-c:5,6-c′]bis[1,2,5]thiadiazole, 5-fluoro-2,1,3-benzoselenadiazole, benzobisthiadiazole, and thiazolo[5,4-d]thiazole). We have applied density functional theory (DFT) and time-dependent DFT to predict their ground-state electronic structures and the UV–vis spectra, and the open circuit voltages (Vocs) of organic solar cells of D₂-A-D₁-A-D₂/PC₇₁BM. Based on the calculated results, we find that bithiophene thiazolo[5,4-d]thiazole siloldithiophene (BTTS) (D₂ = bithiophene, A = thiazolo[5,4-d]thiazole, D₁ = silol dithiophene) possesses the highest lowest unoccupied molecular orbital (−2.60 eV) and the lowest highest occupied molecular orbital (−5.33 eV) energies, and the strongest absorption in the visible region. Besides, the solar cell of BTTS/PC₇₁BM has the highest Voc of 1.02 V. These results indicate that it may be a promising donor. In contrast, bithiophene benzobisthiadiazole siloldithiophene (BBBS) (A = benzobisthiadiazole) has low absorption strength in the visible region, which indicates that it may not be a suitable donor material.     

Excitation Dynamics in Chain-Mapped Environments

The chain mapping of structured environments is a most powerful tool for the simulation of open quantum system dynamics. Once the environmental bosonic or fermionic degrees of freedom are unitarily rearranged into a one dimensional structure, the full power of Density Matrix Renormalization Group (DMRG) can be exploited. Beside resulting in efficient and numerically exact simulations of open quantum systems dynamics, chain mapping provides an unique perspective on the environment: the interaction between the system and the environment creates perturbations that travel along the one dimensional environment at a finite speed, thus providing a natural notion of light-, or causal-, cone. In this work we investigate the transport of excitations in a chain-mapped bosonic environment. In particular, we explore the relation between the environmental spectral density shape, parameters and temperature, and the dynamics of excitations along the corresponding linear chains of quantum harmonic oscillators. Our analysis unveils fundamental features of the environment evolution, such as localization, percolation and the onset of stationary currents.     

Effect of Environment on the Scattering of Electrons by a Junction of Different Topological Materials

The studies of electron transport through a junction of topological materials in the literature so far ignore the coupling of a topological material to its surrounding environment. Here, the dynamics of an open system through a stochastic Hamiltonian are simulated to investigate the influence of the environment on the scattering of electrons by a junction of different topological materials, such as a Dirac–Weyl magnetic junction and a topological insulator. It is found that, although the detrimental effect of the environment is inevitable, the Landauer conductance can be enhanced via adjusting the system–environment coupling strength. This result supplies the possibilty of changing the transport feature of topological materials by modulating the surrounded environment. It is also demonstrated that a non-Hermitian Hamiltonian can be used to replace the stochastic Hamiltonian for this study, when the system and the environment coupling are weak.     

Measuring fluorescence to track a quantum emitter's state: a theory review

We review the continuous monitoring of a qubit through its spontaneous emission, at an introductory level. Contemporary experiments have been able to collect the fluorescence of an artificial atom in a cavity and transmission line, and then make measurements of that emission to obtain diffusive quantum trajectories in the qubit's state. We give a straightforward theoretical overview of such scenarios, using a framework based on Kraus operators derived from a Bayesian update concept; we apply this flexible framework across common types of measurements including photodetection, homodyne, and heterodyne monitoring and illustrate its equivalence to the stochastic master equation formalism throughout. Special emphasis is given to homodyne (phase-sensitive) monitoring of fluorescence. The examples we develop are used to illustrate basic methods in quantum trajectories, but also to introduce some more advanced topics of contemporary interest, including the arrow of time in quantum measurement, and trajectories following optimal measurement records derived from a variational principle. The derivations we perform lead directly from the development of a simple model to an understanding of recent experimental results.     

材料表征方法理论与实践课程的改革与建设*

通过与超星专业慕课制作团队合作搭建网络教学平台,将线上慕课教学与线下实验教学相结合,对材料表征方法理论与实践课程进行了全方位的改革。与传统实验教学相比,改革后的课程不仅能够激发学生的学习兴趣,实现时间空间的相对自由,还可以完善考核机制,提升教学质量,从而为高校化学研究生实验课程的改革提供一定的借鉴意义。     

On the Lipschitz equivalence of self‐affine sets

Recently Lipschitz equivalence of self‐similar sets on has been studied extensively in the literature. However for self‐affine sets the problem is more awkward and there are very few results. In this paper, we introduce a w‐Lipschitz equivalence by repacing the Euclidean norm with a pseudo‐norm w. Under the open set condition, we prove that any two totally disconnected integral self‐affine sets with a common matrix are w‐Lipschitz equivalent if and only if their digit sets have equal cardinality. The main methods used are the technique of pseudo‐norm and Gromov hyperbolic graph theory on iterated function systems.     

Isomorphisms of spaces with large distortion

Let K and S be locally compact Hausdorff spaces and let X be a strictly convex Banach space of finite dimension at least 2. In this paper, we prove that if there exists an isomorphism T from onto satisfying then K and S are homeomorphic. Here denotes the Schäffer constant of X. Even for the classical cases , and , this result is the X‐valued Banach–Stone theorem via isomorphism with the largest distortion that is known so far, namely . On the other hand, it is well known that this result is not true for , even though K and S are compact Hausdorff spaces.     

Separation of antipyretic analgesics by open tubular capillary electrochromatography with homopolymer coatings

This study developed an open‐tubular capillary electrochromatography protocol for the analysis of antipyretic analgesic drugs, which used a multifunctional homopolymer as coating. A controlled/living radical polymerization strategy was adopted to obtain poly(N‐acryloxysuccinimide) with a tunable chain‐length. The homopolymer coating enhanced the separation performance by contributing to the hydrophobic and hydrogen‐bonding interactions between the analytes and the homopolymer. The effect of polymer chain‐length and buffer pH and concentration on the separation efficiency was evaluated. In this approach, baseline separation of the three test drugs was achieved within 15 min. The repeatability of the prepared homopolymer coating was investigated, with the relative standard deviations < 2.88% observed in intra‐ and interday runs. Good linearity in the 5–800 µM range (R² ≥ 0.998) demonstrates that accurate quantitative analysis of real samples was achieved. Moreover, the proposed assay was used to quantify the three drugs (aminopyrine, 4‐aminoantipyrine, and phenacetin) in urine samples, achieving recovery rates between 92.1 and 108.7%. This promising methodology may be used for the analysis of drugs in real bio‐samples and for the development of unique homopolymer coatings for open‐tubular capillary electrochromatography systems.