Fundamental asymmetries between spatial and temporal boundaries in electromagnetics

Time-varying materials bring an extra degree of design freedom compared to their conventional time-invariant counterparts. However, few discussions have focused on the underlying physical difference between spatial and temporal boundaries. In this letter, we thoroughly investigate those differences from the perspective of conservation laws. By doing so, the building blocks of optics and electromagnetics such as the reflection law, Snell's law, and Fresnel's equations can be analogously derived in a temporal context, but with completely different interpretations. Furthermore, we study the unique features of temporal boundaries, such as their nonconformance to energy conservation and causality

System response analysis in wavenumber domain for linear space-invariant time-varying problems

Being a powerful tool for linear time-invariant (LTI) systems, system response analysis can also be applied to the so-called linear space-invariant (LSI) but time-varying systems, which is a dual of the conventional LTI problems. In this paper, we propose a system response analysis method for LSI problems by conducting Fourier transform of the field distribution on the space instead of time coordinate. Specifically, input and output signals can be expressed in the wavenumber (spatial frequency) domain. In this way, the system function in wavenumber domain can also be obtained for LSI systems. Given an arbitrary input and temporal profile of the medium, the output can be easily predicted using the system function. Moreover, for a complex temporal system, the proposed method allows for decomposing it into multiple simpler subsystems that appear in sequence in time. The system function of the whole system can be efficiently calculated by multiplying those of the individual subsystems

An Efficient Ullmann-Type C−O Bond Formation Catalyzed by an Air-Stable Copper(I)−Bipyridyl Complex

An efficient O-arylation of phenols and aliphatic alcohols with aryl halides was developed that uses an air-stable copper(I) complex as the catalyst. This arylation reaction can be performed in good yield in the absence of Cs2CO3. A variety of functional groups are compatible with these reaction conditions with low catalyst loading levels

An Efficient Ullmann-Type C−O Bond Formation Catalyzed by an Air-Stable Copper(I)−Bipyridyl Complex

An efficient O-arylation of phenols and aliphatic alcohols with aryl halides was developed that uses an air-stable copper(I) complex as the catalyst. This arylation reaction can be performed in good yield in the absence of Cs2CO3. A variety of functional groups are compatible with these reaction conditions with low catalyst loading levels

An Efficient Ullmann-Type C−O Bond Formation Catalyzed by an Air-Stable Copper(I)−Bipyridyl Complex

An efficient O-arylation of phenols and aliphatic alcohols with aryl halides was developed that uses an air-stable copper(I) complex as the catalyst. This arylation reaction can be performed in good yield in the absence of Cs2CO3. A variety of functional groups are compatible with these reaction conditions with low catalyst loading levels

An Efficient Ullmann-Type C−O Bond Formation Catalyzed by an Air-Stable Copper(I)−Bipyridyl Complex

An efficient O-arylation of phenols and aliphatic alcohols with aryl halides was developed that uses an air-stable copper(I) complex as the catalyst. This arylation reaction can be performed in good yield in the absence of Cs2CO3. A variety of functional groups are compatible with these reaction conditions with low catalyst loading levels

Copper(I)-Catalyzed Aryl Bromides To Form Intermolecular and Intramolecular Carbon−Oxygen Bonds

A highly efficient Cu-catalyzed C−O bond-forming reaction of alcohol and aryl bromides has been developed. This transformation was realized through the use of copper(I) iodide as a catalyst, 8-hydroxyquinoline as a ligand, and K3PO4 as a base. A variety of functionalized substrates were found to react under these reaction conditions to provide products in good to excellent yields

Additional file 1 of Identification of the cuproptosis-related molecular subtypes and an immunotherapy prognostic model in hepatocellular carcinoma

Additional file1. Fig S1: The flow chart of this study. HCC, hepatocellular carcinoma. TMB, tumor mutation burden. TME, tumor microenvironment. GSVA, gene set variation analysis. GO, Gene Ontology. KEGG, Kyoto Encyclopedia

Investigations on Ferroelectric Liquid Crystal by High Resolution TEM and Solid State ¹³C NMR

In order to investigate the structural and dynamical properties of ferroelectric liquid crystal (FLC) in different phases a model compound [4-(3)-(S)-methyl-2-(S)-chloropentanoyloxy)]-4′-nonyloxy-biphenyl (3M2CPNOB) is synthesized. High resolution transmission electron microscopy (HR-TEM) is applied to observe the morphology of 3M2CPNOB and temperature-dependent solid state 13C NMR to record 13C chemical shifts at different phases. A liquid nitrogen quenching method is used to maintain the conformation of the mesophases for HR-TEM experiments. TEM images show that all the smectic A (SmA), smectic C* (SmC*) and crystalline phases have lamellar morphology. The interplanar distances in the crystalline phase are smaller than those in SmA and SmC* phases because of denser arrangement of the molecules. Both 13C chemical shifts and line shape vary with different phases. The experimental results suggest that SmC* phase as an intermediate occurs in the anisotropy transition process from SmA to crystalline phase, the helical structure of the SmC* phase unwinds in the magnetic field and the conformations of the SmA and isotropic phase are very similar

Non-centrosymmetric Hollow BiOCl Nanocaps with Tailored Openings for the Photocatalytic Degradation of Rhodamine B

Micelles of surfactants have been employed as a powerful tool for the synthesis of hollow nanostructures. Nonetheless, it is still challenging to use micelles to direct the growth of hollow nanostructures with open interiors, especially for crystalline materials. Herein, we report a versatile method to precisely synthesize non-centrosymmetric hollow BiOCl nanocaps with open interiors for the first time. The growth mechanism of the hollow BiOCl nanocaps is elucidated, and the openings of BiOCl nanocaps can be precisely controlled by fine tuning their growth conditions. The non-centrosymmetric BiOCl nanocaps yield a pseudo-first-order degradation kinetic rate constant of up to 0.1217 min–1 in the photodegradation of rhodamine-B, 7.8 times higher than that of common BiOCl nanoplates. This suggests that BiOCl nanocaps show excellent photocatalytic performance to degrade colored rhodamine B. Furthermore, the BiOCl nanocaps can be also extended in the photodegradation of colorless contaminants in industrial wastewater. More importantly, the micelle-directed growth strategy can be generalized to synthesize non-centrosymmetric BiOCl0.5Br0.5 and BiOBr hollow nanocaps. This synthetic strategy heralds a paradigm for designing non-centrosymmetric hollow nanostructures with micelles and may open up an avenue for unique hollow nanomaterials with tailorable structures and properties