Infinitely many homoclinic solutions for perturbed second-order Hamiltonian systems with subquadratic potentials

In this paper, we consider the following perturbed second-order Hamiltonian system $$-\ddot{u}(t)+L(t)u=\nabla W(t,u(t))+\nabla G(t,u(t)), \qquad \forall \ t\in \mathbb{R},$$ where $W(t,u)$ is subquadratic near origin with respect to $u$; the perturbation term $G(t,u)$ is only locally defined near the origin and may not be even in $u$. By using the variant Rabinowitz's perturbation method, we establish a new criterion for guaranteeing that this perturbed second-order Hamiltonian system has infinitely many homoclinic solutions under broken symmetry situations. Our result improves some related results in the literature

Homoclinic orbits for periodic second order Hamiltonian systems with superlinear terms

We obtain the existence of nontrivial homoclinic orbits for nonautonomous second order Hamiltonian systems by using critical point theory under some different superlinear conditions from those previously used in Hamiltonian systems. In particular, an example is given to illustrate our result

Infinitely many homoclinic solutions for perturbed second-order Hamiltonian systems with subquadratic potentials

In this paper, we consider the following perturbed second-order Hamiltonian system −u¨(t) + L(t)u = ∇W(t, u(t)) + ∇G(t, u(t)), ∀ t ∈ R, where W(t, u) is subquadratic near origin with respect to u; the perturbation term G(t, u) is only locally defined near the origin and may not be even in u. By using the variant Rabinowitz’s perturbation method, we establish a new criterion for guaranteeing that this perturbed second-order Hamiltonian system has infinitely many homoclinic solutions under broken symmetry situations. Our result improves some related results in the literature

Microlens arrays with adjustable aspect ratio fabricated by electrowetting and their application to correlated color temperature tunable light-emitting diodes

We develop a facile, fast, and cost-effective method based on the electrowetting effect to fabricate concave microlens arrays (MLA) with a tunable height-to-radius ratio, namely aspect ratio (AR). The electric parameters including voltage and frequency are demonstrated to play an important role in the MLA forming process. With the optimized frequency of 5 Hz, the AR of MLA are tuned from 0.057 to 0.693 for an increasing voltage from 0 V to 180 V. The optical properties of the MLA, including their transmittance and light diffusion capability, are investigated by spectroscopic measurements and ray-tracing simulations. We show that the overall transmittance can be maintained above around 90% over the whole visible range, and that an AR exceeding 0.366 is required to sufficiently broaden the transmitted light angular distribution. These properties enable to apply the developed MLA films to correlated-color-temperature (CCT)-tunable light-emitting-diodes (LEDs) to enhance their angular color uniformity (ACU). Our results show that the ACU of CCT-tunable LEDs is significantly improved while preserving almost the same lumen output, and that the MLA with the highest AR exhibits the best ACU performance

Simple transanal total mesorectal resection versus laparoscopic transabdominal total mesorectal resection for the treatment of low rectal cancer: a single-center retrospective case-control study

AimTo evaluate the efficacy and safety of simple TaTNE in the treatment of low rectal cancer compared with laparoscopic transabdominal TME.MethodsWe collected patients with low rectal cancer admitted to our hospital between January 2019 and November 2021 who received simple TaTME or laparoscopic transabdominal TME. The main outcome was the integrity of the TME specimen. Secondary outcomes were the number of lymph nodes dissected, intraoperative blood loss, operative time, surgical conversion rate, Specimen resection length, circumferential margin (CRM), and distal resection margin (DRM), complication rate. In addition, the Wexner score and LARS score of fecal incontinence were performed in postoperative follow-up.ResultsPathological tissues were successfully resected in all patients. all circumferential margins of the specimen were negative. Specimen resection length was not statistically significant (9.94 ± 2.85 vs. 8.90 ± 2.49, P > 0.05). The incidence of postoperative complications in group A (n = 0) was significantly lower than that in group B (n = 3) (P > 0.05). There was no significant difference in operation time between group A and group B (296 ± 60.36 vs. 305 ± 58.28, P > 0.05). Among the patients with follow-up time less than 1 year, there was no significant difference in Wexner score and LARS score between group A and group B (P > 0.05). However, in patients who were followed up for more than 1 year, the Wexner score in group A (9.25 ± 2.73) was significantly lower than that in group B (17.36 ± 10.95) and was statistically significant (P < 0.05).ConclusionFor radical resection of low rectal cancer, Simple TaTME resection may be as safe and effective as laparoscopic transabdominal TME, and the long-term prognosis may be better

Protecting Intestinal Microenvironment Alleviates Acute Graft-Versus-Host Disease

Acute gut graft-versus-host disease (aGVHD) is a leading threat to the survival of allogeneic hematopoietic stem cell transplantation (allo-HSCT) recipients. Abnormal gut microbiota is correlated with poor prognosis in allo-HSCT recipients. A disrupted intestinal microenvironment exacerbates dysbiosis in GVHD patients. We hypothesized that maintaining the integrity of the intestinal barrier may protect gut microbiota and attenuate aGVHD. This hypothesis was tested in a murine aGVHD model and an in vitro intestinal epithelial culture. Millipore cytokine array was utilized to determine the expression of proinflammatory cytokines in the serum. The 16S rRNA sequencing was used to determine the abundance and diversity of gut microbiota. Combining Xuebijing injection (XBJ) with a reduced dose of cyclosporine A (CsA) is superior to CsA alone in improving the survival of aGVHD mice and delayed aGVHD progression. This regimen also reduced interleukin 6 (IL-6) and IL-12 levels in the peripheral blood. 16S rRNA analysis revealed the combination treatment protected gut microbiota in aGVHD mice by reversing the dysbiosis at the phylum, genus, and species level. It inhibited enterococcal expansion, a hallmark of GVHD progression. It inhibited enterococcal expansion, a hallmark of GVHD progression. Furthermore, Escherichia coli expansion was inhibited by this regimen. Pathology analysis revealed that the combination treatment improved the integrity of the intestinal tissue of aGVHD mice. It also reduced the intestinal permeability in aGVHD mice. Besides, XBJ ameliorated doxorubicin-induced intestinal epithelial death in CCK-8 assay. Overall, combining XBJ with CsA protected the intestinal microenvironment to prevent aGVHD. Our findings suggested that protecting the intestinal microenvironment could be a novel strategy to manage aGVHD. Combining XBJ with CsA may reduce the side effects of current aGVHD prevention regimens and improve the quality of life of allo-HSCT recipients

Cardioprotection against Heart Failure by Shenfu Injection via TGF- β

Objective. To explore the potential cardioprotective mechanism of Shenfu injection (SFI) against heart failure (HF) by attenuating myocardial fibrosis and cardiac remodeling. Methods and Results. Four weeks after myocardial infarction (MI), adult male Sprague Dawley rats were randomized for 4-week treatment with Valsartan, SFI, or vehicle. Echocardiography and hemodynamics were applied to evaluate cardiac functions. Myocardia of coronary artery ligated (CAD) rats were observed to investigate changes in cardiac structure and function. Our findings suggest that treatment with SFI could inhibit progression of myocardial fibrosis and attenuate cardiac remodeling. In addition, SFI decreased expression of Smad2 and Smad3, while increasing the expression of Smad7 through regulation of TGF-β/Smads signaling pathway. Conclusion. Treatment with SFI in Sprague Dawley rats improves ventricular structure and function and reduces cardiac fibrosis by ameliorating TGF-β/Smads signaling pathway after ventricular remodeling

MoS2 Nanosheets Assembled on Three-Way Nitrogen-Doped Carbon Tubes for Photocatalytic Water Splitting

In this work, a micron-sized three-way nitrogen-doped carbon tube covered with MoS2 nanosheets (TNCT@MoS2) was synthesized and applied in photocatalytic water splitting without any sacrificial agents for the first time. The micron-sized three-way nitrogen-doped carbon tube (TNCT) was facilely synthesized by the calcination of commercial sponge. The MoS2 nanosheets were assembled on the carbon tubes by a hydrothermal method. Compared with MoS2, the TNCT@MoS2 heterostructures showed higher H2 evolution rate, which was ascribed to the improved charge separation efficiency and the increased active sites afforded by the TNCT