Trace theorems for functions of bounded variation in metric spaces

In this paper we show existence of traces of functions of bounded variation on the boundary of a certain class of domains in metric measure spaces equipped with a doubling measure supporting a 1-Poincaré inequality, and obtain $L^1$ estimates of the trace functions. In contrast with the treatment of traces given in other papers on this subject, the traces we consider do not require knowledge of the function in the exterior of the domain. We also establish a Maz'ya-type inequality for functions of bounded variation that vanish on a set of positive capacity.     

Stability of steady multi-wave configurations for the full Euler equations of compressible fluid flow

We are concerned with the stability of steady multi-wave configurations for the full Euler equations of compressible fluid flow. In this paper, we focus on the stability of steady four-wave configurations that are the solutions of the Riemann problem in the flow direction, consisting of two shocks, one vortex sheet, and one entropy wave, which is one of the core multi-wave configurations for the two-dimensional Euler equations. It is proved that such steady four-wave configurations in supersonic flow are stable in structure globally, even under the BV perturbation of the incoming flow in the flow direction. In order to achieve this, we first formulate the problem as the Cauchy problem (initial value problem) in the flow direction, and then develop a modified Glimm difference scheme and identify a Glimm-type functional to obtain the required BV estimates by tracing the interactions not only between the strong shocks and weak waves, but also between the strong vortex sheet/entropy wave and weak waves. The key feature of the Euler equations is that the reflection coefficient is always less than $1$, when a weak wave of different family interacts with the strong vortex sheet/entropy wave or the shock wave, which is crucial to guarantee that the Glimm functional is decreasing. Then these estimates are employed to establish the convergence of the approximate solutions to a global entropy solution, close to the background solution of steady four-wave configuration.     

Postharvest Drying Techniques Regulate Secondary Metabolites and Anti-Neuroinflammatory Activities of Ganoderma lucidum

Ganoderma lucidum extract is a potent traditional remedy for curing various ailments. Drying is the most important postharvest step during the processing of Ganoderma lucidum. The drying process mainly involves heat (36 h at 60 °C) and freeze-drying (36 h at −80 °C). We investigated the effects of different postharvest drying protocols on the metabolites profiling of Ganoderma lucidum using GC-MS, followed by an investigation of the anti-neuroinflammatory potential in LPS-treated BV2 microglial cells. A total of 109 primary metabolites were detected from heat and freeze-dried samples. Primary metabolite profiling showed higher levels of amino acids (17.4%) and monosaccharides (8.8%) in the heat-dried extracts, whereas high levels of organic acids (64.1%) were present in the freeze-dried samples. The enzymatic activity, such as ATP-citrate synthase, pyruvate kinase, glyceraldehyde-3-phosphatase dehydrogenase, glutamine synthase, fructose-bisphosphate aldolase, and D-3-phosphoglycerate dehydrogenase, related to the reverse tricarboxylic acid cycle were significantly high in the heat-dried samples. We also observed a decreased phosphorylation level of the MAP kinase (Erk1/2, p38, and JNK) and NF-κB subunit p65 in the heat-dried samples of the BV2 microglia cells. The current study suggests that heat drying improves the production of ganoderic acids by the upregulation of TCA-related pathways, which, in turn, gives a significant reduction in the inflammatory response of LPS-induced BV2 cells. This may be attributed to the inhibition of NF-κB and MAP kinase signaling pathways in cells treated with heat-dried extracts.     

An Image Denoising-Deblurring Adaptive Variational Problem in BV Space

In this paper, we establish the existence and uniqueness of a BV solution to an initial boundary value problem for a nonlinear integro-differential equation, which is related to a denoising and deblurring variational model in image restoration. Several experiments relevant to the restoration model are performed and numerical results are discussed.     

Convergence of a misanthrope process to the entropy solution of 1D problems

We prove the convergence, in some strong sense, of a Markov process called “a misanthrope process” to the entropy weak solution of a one-dimensional scalar nonlinear hyperbolic equation. Such a process may be used for the simulation of traffic flows. The convergence proof relies on the uniqueness of entropy Young measure solutions to the nonlinear hyperbolic equation, which holds for both the bounded and the unbounded cases. In the unbounded case, we also prove an error estimate. Finally, numerical results show how this convergence result may be understood in practical cases.     

A Poincaré lemma for sigma models of AKSZ type

For a sigma model of AKSZ type, we show that the local BRST cohomology is isomorphic to the cohomology of the target space differential when restricted to coordinate neighborhoods both in the base and in the target. An analogous result is shown to hold for the cohomology in the space of functional multivectors. Applications of these latter cohomology classes in the context of the inverse problem of the calculus of variation for general gauge systems are also discussed.     

Low on-resistance high-voltage lateral double-diffused metal oxide semiconductor with a buried improved super-junction layer

A novel low specific on-resistance （Ron,sp） lateral double-diffused metal oxide semiconductor （LDMOS） with a buried improved super-junction （BISJ） layer is proposed. A super-junction layer is buried in the drift region and the P pillar is split into two parts with different doping concentrations. Firstly, the buried super-junction layer causes the multiple-direction assisted depletion effect. The drift region doping concentration of the BISJ LDMOS is therefore much higher than that of the conventional LDMOS. Secondly, the buried super-junction layer provides a bulk low on-resistance path. Both of them reduce Ron,sp greatly. Thirdly, the electric field modulation effect of the new electric field peak introduced by the step doped P pillar improves the breakdown voltage （BV）. The BISJ LDMOS exhibits a BV of 300 V and Ron,sp of 8.08 mΩ·cm2 which increases BV by 35% and reduces Ron,sp by 60% compared with those of a conventional LDMOS with a drift length of 15 μm, respectively.