Sharp bounds for multiplicities of Bianchi modular forms

We prove a degree-one saving bound for the dimension of the space of cohomological automorphic forms of fixed level and growing weight on $\mathrm{SL}_2$ over any number field that is not totally real. In particular, we establish a sharp bound on the growth of cuspidal Bianchi modular forms. We transfer our problem into a question over the completed universal enveloping algebras by applying an algebraic microlocalisation of Ardakov and Wadsley to the completed homology. We prove finitely generated Iwasawa modules under the microlocalisation are generic, solving the representation theoretic question by estimating growth of Poincar\'e-Birkhoff-Witt filtrations on such modules.Comment: 25 pages. To appear in Annals of Mathematic

Fault diagnosis for rotating machinery based on multi-differential empirical mode decomposition

The fault diagnosis of rotating machinery has crucial significance for the safety of modern industry, and the fault feature extraction is the key link of the diagnosis process. As an effective time-frequency method, Empirical Mode Decomposition (EMD) has been widely used in signal processing and feature extraction. However, the mode mixing phenomenon may lead to confusion in the identification of multi frequency signals and restricts the applications of EMD. In this paper, a novel method based on Multi-Differential Empirical Mode Decomposition (MDEMD) was proposed to extract the energy distribution characteristics of fault signals. Firstly, multi-order differential signals were deduced and decomposed by EMD. Then, their energy distribution characteristics were extracted and utilized to construct the feature matrix. Finally, taking the feature matrix as input, the classifiers were applied to diagnosis the existence and severity of rotating machinery faults. Simulative and practical experiments were implemented respectively, and the results demonstrated that the proposed method, i.e. MDEMD, is able to eliminate the mode mixing effectively, and the feature matrix extracted by MDEMD has high separability and universality, furthermore, the fault diagnosis based on MDEMD can be accomplished more effectively and efficiently with satisfactory accuracy

Antibiotics and antibiotic resistance genes in global lakes:A review and meta-analysis

Lakes are an important source of freshwater, containing nearly 90% of the liquid surface fresh water worldwide. Long retention times in lakes mean pollutants from discharges slowly circulate around the lakes and may lead to high ecological risk for ecosystem and human health. In recent decades, antibiotics and antibiotic resistance genes (ARGs) have been regarded as emerging pollutants. The occurrence and distribution of antibiotics and ARGs in global freshwater lakes are summarized to show the pollution level of antibiotics and ARGs and to identify some of the potential risks to ecosystem and human health. Fifty-seven antibiotics were reported at least once in the studied lakes. Our meta-analysis shows that sulfamethoxazole, sulfamerazine, sulfameter, tetracycline, oxytetracycline, erythromycin, and roxithromycin were found at high concentrations in both lake water and lake sediment. There is no significant difference in the concentration of sulfonamides in lake water from China and that from other countries worldwide; however, there was a significant difference in quinolones. Erythromycin had the lowest predicted hazardous concentration for 5% of the species (HC5) and the highest ecological risk in lakes. There was no significant difference in the concentration of sulfonamide resistance genes (sul1 and sul2) in lake water and river water. There is surprisingly limited research on the role of aquatic biota in propagation of ARGs in freshwater lakes. As an environment that is susceptible to cumulative build-up of pollutants, lakes provide an important environment to study the fate of antibiotics and transport of ARGs with a broad range of niches including bacterial community, aquatic plants and animals

SIRT1 protects against myocardial ischemia–reperfusion injury via activating eNOS in diabetic rats

BACKGROUND: Diabetic patients are more sensitive to myocardial ischemic injury than non-diabetic patients. Silent information regulator 1 (SIRT1) is a nicotinamide adenine dinucleotide-dependent histone deacetylase making the heart more resistant to ischemic injury. As SIRT1 expression is considered to be reduced in diabetic heart, we therefore hypothesized that up-regulation of SIRT1 in the diabetic heart may overcome its increased susceptibility to ischemic injury. METHODS: Male Sprague–Dawley rats were fed with high-fat diet and injected with streptozotocin once to induce diabetes. Diabetic rats received injections of adenoviral vectors encoding SIRT1 (Ad-SIRT1) at five myocardial sites. Four days after adenoviral injection, the rats were subjected to myocardial ischemia and reperfusion (MI/R). Outcome measures included left ventricular function, infarct size, cellular death and oxidative stress. RESULTS: Delivery of Ad-SIRT1 into the hearts of diabetic rats markedly increased SIRT1 expression. Up-regulation of SIRT1 in diabetic hearts improved cardiac function and reduced infarct size to the extent as in non-diabetic animals following MI/R, which was associated with reduced serum creatine kinase-MB, lactate dehydrogenase activities and cardiomyocyte apoptosis. Moreover, Ad-SIRT1 reduced the increase in the superoxide generation and malonaldialdehyde content and simultaneously increased the antioxidant capability. Furthermore, Ad-SIRT1 increased eNOS phosphorylation and reduced eNOS acetylation in diabetic hearts. NOS inhibitor L-NAME inhibited SIRT1-enhanced eNOS phosphorylation, and blunted SIRT1-mediated anti-apoptotic and anti-oxidative effects and cardioprotection. CONCLUSIONS: Overexpression of SIRT1 reduces diabetes-exacerbated MI/R injury and oxidative stress via activating eNOS in diabetic rats. The findings suggest SIRT1 may be a promising novel therapeutic target for diabetic cardiac complications

Electrochemical Investigation of Calcium Substituted Monoclinic Li3_3 V2_2(PO4_4)3_3 Negative Electrode Materials for Sodium‐ and Potassium‐Ion Batteries

Herein, the electrochemical properties and reaction mechanism of Li$_{3‒2x}$Ca$_x$V$_2$(PO$_4$)$_3$/C (x = 0, 0.5, 1, and 1.5) as negative electrode materials for sodium-ion/potassium-ion batteries (SIBs/PIBs) are investigated. All samples undergo a mixed contribution of diffusion-controlled and pseudocapacitive-type processes in SIBs and PIBs via Trasatti Differentiation Method, while the latter increases with Ca content increase. Among them, Li$_3$V$_2$(PO$_4$)$_3$/C exhibits the highest reversible capacity in SIBs and PIBs, while Ca$_{1.5}$V$_2$(PO$_4$)$_3$/C shows the best rate performance with a capacity retention of 46% at 20 C in SIBs and 47% at 10 C in PIBs. This study demonstrates that the specific capacity of this type of material in SIBs and PIBs does not increase with the Ca-content as previously observed in lithium-ion system, but the stability and performance at a high C-rate can be improved by replacing Li$^+$ with Ca$^{2+}$. This indicates that the insertion of different monovalent cations (Na$^+$/K$^+$) can strongly influence the redox reaction and structure evolution of the host materials, due to the larger ion size of Na$^+$ and K$^+$ and their different kinetic properties with respect to Li$^+$. Furthermore, the working mechanism of both LVP/C and Ca$_{1.5}$V$_2$(PO$_4$)$_3$/C in SIBs are elucidated via in operando synchrotron diffraction and in operando X-ray absorption spectroscopy