Global weak solution of 3-D focusing energy-critical nonlinear Schr\"odinger equation

In this article, we prove the existence of global weak solutions to the three-dimensional focusing energy-critical nonlinear Schr\"odinger (NLS) equation in the non-radial case. Furthermore, we prove the weak-strong uniqueness for some class of initial data. The main ingredient of our new approach is to use solutions of an energy-critical Ginzburg-Landau equation as approximations for the corresponding nonlinear Sch\"ordinger equation. In our proofs, we first show the dichotomy of global well-posedness versus finite time blow-up of energy-critical Ginzburg-Landau equation in $\dot{H}^1( \mathbb{R}^d)$ for $d = 3,4$ when the energy is less than the energy of the stationary solution $W$. We follow the strategy of C. E. Kenig and F. Merle [25,26], using a concentration-compactness/rigidity argument to reduce the global well-posedness to the exclusion of a critical element. The critical element is ruled out by dissipation of the Ginzburg-Landau equation, including local smoothness, backwards uniqueness and unique continuation. The existence of global weak solution of the three dimensional focusing energy-critical nonlinear Schr\"odinger equation in the non-radial case then follows from the global well-posedness of the energy-critical Ginzburg-Landau equation via a limitation argument. We also adapt the arguments of M. Struwe [37,38] to prove the weak-strong uniqueness when the $\dot{H}^1$-norm of the initial data is bounded by a constant depending on the stationary solution $W$.Comment: 35 page

Vibration and noise analysis of heavy-duty trucks based on powertrain lightweighting

Vehicle lightweighting has been considered as one of the most important solutions to improve fuel economy and reduce harmful emissions. Considering the PowerTrain System (PTS) lightweighting of a heavy-duty truck tractor, cast iron of which the transmission shell was made is replaced with aluminum. Such weight reduction caused the irrationality of the natural frequency matching and the vehicle NVH performance become worse. In order to evaluate the influence of PTS lightweighting on the vibration and noise, the theoretical analysis and experimental tests have been done. The Genetic Algorithm (GA) method was adopted for the Powertrain Mounting System (PMS) optimization. Considering the installation position of PMS, the limitations of package space, cost and available time, the mounting stiffness was chosen as the design variables. One combination of the main vibration energy distribution of PMS was selected as the objective function of optimization design. After optimization, the vehicle experimental study was carried out to investigate the vibration and noise performance of the PMS at idle and Whole Open Throttle (WOT). The test results show that the optimization of PMS had a significant improvement on the vehicle vibration and noise performance

Targeting Integrin-β1 Impedes Cytokine-Induced Osteoclast Differentiation: A Potential Pharmacological Intervention in Pathological Osteolysis

Purpose: To examine whether integrin-β1 is essential for osteoclast differentiation and function and if it can be targeted for pharmacological intervention in pathological osteolysis.Methods: Control and Integrin-β1 knockdown RAW 264.7 cells were treated with receptor activator of nuclear factor kappa-B (RANKL) or TNF-α and evaluated for osteoclast differentiation. Osteoclast differentiation and function were evaluated by marker protein analysis, tartrate-resistant acid phosphatase (TRAP) and resorption assays. Furthermore, downstream molecular signaling analysis was probed using small molecule inhibitors and blocking antibodies, and evaluated by immunoblotting.Results: Integrin-β1 knockdown cells showed reduced osteoclast differentiation following TNF-α treatment while no change was seen after RANKL treatment (p < 0.05). Immunoblot-based molecular signaling analysis showed involvement of MAPK kinase signaling in mediating TNF-α/integrin-β1- induced osteoclastogenesis. Finally, when MAPK kinase inhibitor (2.5 and 5 μM; p < 0.05) and integrin- β1 blocking antibody (2.5 and 5 μg/mL; p < 0.05) was used to specifically attenuate TNF-α induced osteoclastogenesis, no change was observed in RANKL-induced osteoclast formation.Conclusion: The data obtained highlight the role of integrin-β1 in TNF-α-induced osteoclastogenesis, but not in RANKL pathway. Given that, inflammatory cytokine secretions such as TNF-α are progressively implicated in pathological osteolysis, targeting this pathway may attenuate osteolysis in pathological bone tissues.Keywords: Osteoclast differentiation, Integrin-β1, Receptor activator of nuclear factor kappa-B, TNFalpha, Mitogen activated protein kinase, Cytokines, Skeletal diseas