Uniqueness of isometric immersions with the same mean curvature

Motivated by the quasi-local mass problem in general relativity, we study the rigidity of isometric immersions with the same mean curvature into a warped product space. As a corollary of our main result, two star-shaped hypersurfaces in a spatial Schwarzschild or AdS-Schwarzschild manifold with nonzero mass differ only by a rotation if they are isometric and have the same mean curvature. We also prove similar results if the mean curvature condition is replaced by an ${\sigma }_2$-curvature condition.     

Twining Poly(polyoxometalate) Chains into Nanoropes

Organic polymers and inorganic clusters belong to two different disciplines and have completely different properties and structures. When a cluster is attached to the backbone of a polymer as a pendant, the resultant hybrid polymers (polyclusters) exhibit unique behaviours totally different from those of conventional polymers owing to the nanoscale size of the cluster and its particular interactions. Herein, the aggregation of a poly(polyoxometalate)—a polynorbornene backbone with inorganic polyoxometalate cluster pendants—upon addition of a non-solvent to its dilute solution is reported. A three-dimensional network of tangled and snake-like nanothreads was observed. Direct visualisation of individual nanoscale clusters enabled identification of single chains within the nanothreads. These observations suggest that during the process of aggregation, the hybrid polymer forms curved or extended chains as a consequence of an armouring effect in which the collapsed cluster pendants wrap around the backbone. The collapse occurs because they become less soluble in the solvent/non-solvent mixture. The extended chains then become entwined and form nanoropes consisting of multiple chains wound around each other. This study provides a deeper understanding of the nature of polyclusters and should also prove useful for their future development and application.     

Tertiary Amines Differentiated from Primary and Secondary Amines by Active Ester‐Functionalized Hexabenzoperylene in Field Effect Transistors

Herein, we report two novel derivatives of hexabenzoperylene (HBP) that are functionalized with ester groups. Methyl acetate functionalized HBP ( 1 ) in single crystals self‐assembles into a supramolecular nanosheet, which has a two‐dimensional π‐stack of HBP sandwiched between two layers of ester groups. With the same self‐assembly motif, active ester‐functionalized HBP ( 2 ) in field effect transistors has enabled differentiation of tertiary amines from primary and secondary amines, in agreement with the fact that active ester reacts with primary and secondary amines but not with tertiary amines to form amides.     

Thermal Behavior Analysis of Two Synthesized Flavor Precursors of N‐alkylpyrrole Derivatives

To expand the library of pyrrole‐containing flavor precursors, two new flavor precursors—methyl N‐benzyl‐2‐methyl‐5‐formylpyrrole‐3‐carboxylate (NBMF) and methyl N‐butyl‐2‐methyl‐5‐formylpyrrole‐3‐carboxylate (NUMF)—were synthesized by cyclization, oxidation, and alkylation reactions. Thermogravimetry (TG), differential scanning calorimeter, and pyrolysis–gas chromatography/mass spectrometry were utilized to analyze the thermal degradation behavior and thermal degradation products of NBMF and NUMF. The TG‐DTG curve indicated that the maximum mass loss rates of NBMF and NUMF appear at 310 and 268°C, respectively. The largest peaks of NBMF and NUMF showed by the differential scanning calorimeter curve were 315 and 274°C, respectively. Pyrolysis–gas chromatography/mass spectrometry detected small molecule fragrance compounds appeared during thermal degradation, such as 2‐methylpyrrole, 1‐methylpyrrole‐2‐carboxylic acid methyl ester, limonene, and methyl formate. Finally, the thermal degradation mechanism of NBMF and NUMF was discussed, which provided a theoretical basis for their application in tobacco flavoring additives.     

Determination of sulfa antibiotic residues in river and particulate matter by field-amplified sample injection-capillary zone electrophoresis

In the present research, field-amplified sample injection–CZE (FASI–CZE) coupled with a diode array detector was established to determine trace level sulfa antibiotic. Sulfathiazole, sulfadiazine, sulfamethazine, sulfadimethoxine, sulfamethoxazole, and sulfisoxazole were selected as analytes for the experiments. The background electrolyte solution consisted of 70.0 mmol/L borax and 60.0 mmol/L boric acid (including 10% methanol, pH 9.1). The plug was 2.5 mmol/L borax, which was injected into the capillary at a pressure of 0.5 psi for 5 s. Then the sample was injected into the capillary at an injection voltage of –10 kV for 20 s. The electrophoretic separation was carried out under a voltage of +19 kV. The capillary temperature was maintained at 20˚C throughout the analysis, and six sulfonamides were completely separated within 35 min. Compared with pressure injection-CZE, the sensitivity of FASI-CZE was increased by 6.25–10.0 times, and the LODs were reduced from 0.2–0.5 to 0.02–0.05 μg/mL. The method was applied to the determination of sulfonamides in river water and particulate matter samples. The recoveries were 78.59–106.59%. The intraday and interday precisions were 2.89–7.35% and 2.77–7.09%, respectively. This provides a simpler and faster method for the analysis of sulfa antibiotic residues in environmental samples.     

Synergistic therapeutic effects of Duzhong Jiangya Tablets and amlodipine besylate combination in spontaneously hypertensive rats using 1H-NMR- and MS-based metabolomics

Duzhong Jiangya Tablet (DJT) composed of Eucommia ulmoides Oliv. and several other traditional Chinese medicines is a Chinese herbal compound, which is clinically used to treat hypertension. The aim of this study was to evaluate the antihypertensive effect of DJT and amlodipine besylate (AB) on the synergistic treatment of spontaneously hypertensive rats (SHRs), and to explore its antihypertensive mechanism. The synergistic therapeutic effect of DJT in combination with AB on SHR was studied using two metabolomics methods based on mass spectrum (MS) and nuclear magnetic resonance. Metabolomics analysis of plasma, urine, liver, and kidney and the combination of orthogonal partial least squares discriminant analysis was performed to expose potential biomarkers. Then, the overall metabolic characteristics and related abnormal metabolic pathways in hypertensive rats were constructed. Blood pressure measurements showed that DJT combined with AB has better effects in treating hypertension than it being alone. A total of 30 biomarkers were identified, indicating that hypertension disrupted the balance of multiple metabolic pathways in the body, and that combined administration restored metabolite levels better than their administration alone. The changes of biomarkers revealed the synergistic therapeutic mechanism of DJT combined with AB, which provided a reference for the combination of Chinese and Western medicines.     

Comparative Study of the Supercapacitive Performance of Three Ferrocene-Based Structures: Targeted Design of a Conductive Ferrocene-Functionalized Coordination Polymer as a Supercapacitor Electrode

As redox-active based supercapacitors are known as highly desirable next-generation supercapacitor electrodes, the targeted design of two ferrocene-functionalized (Fc(COOH)₂) clusters based on coinage metals, [(PPh₃)₂AgO₂CFcCO₂Ag(PPh₃)₂]₂ ⋅ 7 CH₃OH (SC₁: super capacitor) and [(PPh₃)₃CuO₂CFcCO₂Cu(PPh₃)₃] ⋅ 3 CH₃OH (SC₂), is reported. Both structures are fully characterized by various techniques. The structures are utilized as energy storage electrode materials, giving 130 F g⁻¹ and 210 F g⁻¹ specific capacitance at 1.5 A g⁻¹ in Na₂SO₄ electrolyte, respectively. The obtained results show that the presence of Cu^I instead of Ag^I improves the supercapacitive performance of the cluster. Further, to improve the conductivity, the PSC₂ ([(PPh₃)₂CuO₂CFcCO₂]_∞), a polymeric structure of SC₂, was synthesized and used as an energy storage electrode. PSC₂ displays high conductivity and gives 455 F g⁻¹ capacitance at 3 A g⁻¹. The PSC₂ as a supercapacitor electrode presents a high power density (2416 W kg⁻¹), high energy density (161 Wh kg⁻¹), and long cycle life over 4000 cycles (93 %). These results could lead to the amplification of high-performance supercapacitors in new areas to develop real applications and stimulate the use of the targeted design of coordination polymers without hybridization or compositions with additive materials.     

Enantioselective Total Synthesis of Pseudopteroxazole and Ileabethoxazole

Enantioselective total syntheses of pseudopteroxazole ( 1 ) and ileabethoxazole ( 2 ) are presented. The two original stereocenters were constructed in excellent enantioselectivity and good diastereoselectivity through Carreira's asymmetric dual catalytic allylation, which shows potential for accessing diastereoisomers at C2 and C3 of 1 and 2 . Cationic cyclizations of 13 and 24 demonstrated an effective pathway for the construction of the opposite configurations at C1 in 1 and 2 . Additionally, an approach for the introduction of methyl at C4 is a feasible solution for structural modifications at C4 in 1 and 2 .