Increasing stability in the linearized inverse Schr\"{o}dinger potential problem with power type nonlinearities

We consider increasing stability in the inverse Schr\"{o}dinger potential problem with power type nonlinearities at a large wavenumber. Two linearization approaches, with respect to small boundary data and small potential function, are proposed and their performance on the inverse Schr\"{o}dinger potential problem is investigated. It can be observed that higher order linearization for small boundary data can provide an increasing stability for an arbitrary power type nonlinearity term if the wavenumber is chosen large. Meanwhile, linearization with respect to the potential function leads to increasing stability for a quadratic nonlinearity term, which highlights the advantage of nonlinearity in solving the inverse Schr\"{o}dinger potential problem. Noticing that both linearization approaches can be numerically approximated, we provide several reconstruction algorithms for the quadratic and general power type nonlinearity terms, where one of these algorithms is designed based on boundary measurements of multiple wavenumbers. Several numerical examples shed light on the efficiency of our proposed algorithms.Comment: 29 pages, 7 figure

Increasing stability of the first order linearized inverse Schr\"{o}dinger potential problem with integer power type nonlinearities

We investigate the increasing stability of the inverse Schr\"{o}dinger potential problem with integer power type nonlinearities at a large wavenumber. By considering the first order linearized system with respect to the unknown potential function, a combination formula of the first order linearization is proposed, which provides a Lipschitz type stability for the recovery of the Fourier coefficients of the unknown potential function in low frequency mode. These stability results highlight the advantage of nonlinearity in solving this inverse potential problem by explicitly quantifying the dependence to the wavenumber and the nonlinearities index. A reconstruction algorithm for general power type nonlinearities is also provided. Several numerical examples illuminate the efficiency of our proposed algorithm.Comment: 37 pages, 8 figure

COVID-19 in Japan: What could happen in the future? (Recent developments on inverse problems for partial differential equations and their applications)

This paper was finished in February, 2020 and posted in MedRxiv on Feb. 28th, 2020.COVID-19 has been impacting on the whole world critically and constantly Since December 2019. We have independently developed a novel statistical time delay dynamic model on the basis of the distribution models from CCDC. Based only on the numbers of confirmed cases in different regions in China, the model can clearly reveal that the containment of the epidemic highly depends on early and effective isolation. We apply the model on the epidemic in Japan and conclude that there could be a rapid outbreak in Japan if no effective quarantine measures are carried out immediately

Multi-echelon inventory modeling and supply redesign

Thesis: M. Eng. in Supply Chain Management, Massachusetts Institute of Technology, Supply Chain Management Program, 2017.Cataloged from PDF version of thesis.Includes bibliographical references (pages 46-49).Many businesses struggle to optimize the flow of inventory and finished goods through existing plants and facilities. The integration of inventory costs, organizational processes, and changing business dynamics make it difficult to determine the optimal flow. This thesis examines the flow of raw materials and finished goods through the supply chain of a multi-national oilfield services company. We study a centralized inventory approach, assessed through heuristics, against the existing decentralized approach. Sensitivity analysis with regard to service level, and mode of transport strengthened the analysis. We show that demand aggregation and lead time are important factors in determining the upper echelon for a company's internal distribution model. Potential safety stock reduction is 2%, which is mainly due to the improved coordination for materials flowing to the final echelon in the supply chain. However, pipeline inventory increases by 12% as a result of longer lead times.by Patrick Scott and Boxi Xu.M. Eng. in Supply Chain Managemen

On permutation symmetries of hopfield model neural network

Discrete Hopfield neural network (DHNN) is studied by performing permutation operations on the synaptic weight matrix. The storable patterns set stored with Hebbian learning algorithm in a network without losing memories is studied, and a condition which makes sure all the patterns of the storable patterns set have a same basin size of attraction is proposed. Then, the permutation symmetries of the network are studied associating with the stored patterns set. A construction of the storable patterns set satisfying that condition is achieved by consideration of their invariance under a point group

Graphene oxide architectures prepared by molecular combing on hydrophilic-hydrophobic micropatterns

A novel graphene oxide (GO) architecture is fabricated on hydrophilic-hydrophobic patterned alkanethiol self-assembled monolayers on Au by molecular combing of GO sheets. With hydrazine reduction, the reduced GO architecture-based device is demonstrated to detect NO2 gas. This simple method shows the potential to control the shape, orientation and position of GO sheets over large areas

Bi(Zn2/3Nb1/3)O3-(K0.5Na0.5)NbO3 high-temperature lead-freeferroelectric ceramics with low capacitance variation in a broad temperature usage range

The xBi(Zn2/3Nb1/3)O3–(1−x)(K0.5Na0.5)NbO3 (abbreviated as xBZN–(1−x)KNN) ceramics have been synthesized using the conventional solid-state sintering method. The phase structure, dielectric properties and “relaxorlike” behavior of the ceramics were investigated. The 0.03BZN–0.97KNN ceramics show a broad and stable permittivity maximum near 2000 and lower dielectric loss (≤5%) at a broad temperature usage range (100°C–400°C) and the capacitance variation (ΔC/C150°C) is maintained smaller than ±15%. The 0.03BZN–0.97KNN ceramics only possess the diffuse phase transition and no frequency dispersion of dielectric permittivity, which indicates that 0.03BZN–0.97KNN ceramics is a high temperature “relaxorlike” ferroelectric ceramics. These results indicate that 0.03BZN–0.97KNN ceramics are excellent promising candidates for preparing high-temperature multilayer ceramics capacitors