Well-posedness of a class of perturbed optimization problems in Banach spaces

AbstractLet X be a Banach space and Z a nonempty subset of X. Let J:Z→R be a lower semicontinuous function bounded from below and p⩾1. This paper is concerned with the perturbed optimization problem of finding z0∈Z such that ‖x−z0‖p+J(z0)=infz∈Z{‖x−z‖p+J(z)}, which is denoted by minJ(x,Z). The notions of the J-strictly convex with respect to Z and of the Kadec with respect to Z are introduced and used in the present paper. It is proved that if X is a Kadec Banach space with respect to Z and Z is a closed relatively boundedly weakly compact subset, then the set of all x∈X for which every minimizing sequence of the problem minJ(x,Z) has a converging subsequence is a dense Gδ-subset of X∖Z0, where Z0 is the set of all points z∈Z such that z is a solution of the problem minJ(z,Z). If additionally p>1 and X is J-strictly convex with respect to Z, then the set of all x∈X for which the problem minJ(x,Z) is well-posed is a dense Gδ-subset of X∖Z0

The Analysis of the Properties of Bus Network Topology in Beijing Basing on Complex Networks

The transport network structure plays a crucial role in transport dynamics. To better understand the property of the bus network in big city and reasonably configure the bus lines and transfers, this paper seeks to take the bus network of Beijing as an example and mainly use space L and space P to analyze the network topology properties. The approach is applied to all the bus lines in Beijing which includes 722 lines and 5421 bus station. In the first phase of the approach, space L is used. The results show that the bus network of Beijing is a scale-free network and the degree of more than 99 percent of nodes is lower than 10. The results also show that the network is an assortative network with 46 communities. In a second phase, space P is used to analyze the property of transfer. The results show that the average transfer time of Beijing bus network which is 1.88 and 99.8 percent of arbitrary two pair nodes is reachable within 4 transfers

Interlayer charge transfer in ReS 2 / WS 2 van der Waals heterostructures

We observed ultrafast charge transfer between distorted 1T−ReS2 with anisotropic in-plane electronic and optical properties and 2H−WS2 that is in-plane isotropic. Heterostructures of monolayer ReS2/monolayer WS2 and bilayer ReS2/monolayer WS2 were fabricated by mechanical exfoliation and dry transfer techniques. Significant photoluminescence quenching of WS2 in the heterostructures indicates efficient charge transfer. In femtosecond transient absorption measurements, it was found that holes injected in monolayer or bilayer ReS2 transfer to WS2 on a timescale that is shorter than the time resolution of the measurement. This observation provides evidence that the holes are delocalized in bilayer ReS2, revealing strong van der Waals interlayer couplings. These results also show that ReS2 and WS2 form type-II heterostructures with excellent charge transfer properties

Surface Integral Analogy Approaches to Computing Noise Generated by a 3D High-Lift Wing Configuration

Three surface integral approaches of the acoustic analogies are studied to predict the noise from a three-dimensional, high-lift wing configuration. The approaches refer to the Kirchhoff method, the Ffowcs Williams and Hawkings method of the permeable integral surface and the Curle method. The first two approaches are used to compute the noise generated by the core flow region where the energetic structures exist. The last approach is adopted to predict the noise specifically from the pressure perturbation on the wall. A new way to construct the integral surface that encloses the core region is proposed for the first two methods. Considering the local properties of the flow around the complex objective – the actual wing with high-lift devices – the integral surface based on the vorticity is constructed to follow the flow structures. The noise from the core flow region is based on the dependent integral quantities, which are indicated by the Kirchhoff formulation and by the FWH formulation. The role of each wall component on noise contribution is analyzed using the Curle method. The results of the three methods are then compared

Adhesion evaluation of asphalt-aggregate interface using surface free energy method

The influence of organic additives (Sasobit and RH) and water on the adhesion of the asphalt-aggregate interface was studied according to the surface free energy theory. Two asphalt binders (SK-70 and SK-90), and two aggregate types (limestone and basalt) were used in this study. The sessile drop method was employed to test surface free energy components of asphalt, organic additives and aggregates. The adhesion models of the asphalt-aggregate interface in dry and wet conditions were established, and the adhesion work was calculated subsequently. The energy ratios were built to evaluate the effect of organic additives and water on the adhesiveness of the asphalt-aggregate interface. The results indicate that the addition of organic additives can enhance the adhesion of the asphalt-aggregate interface in dry conditions, because organic additives reduced the surface free energy of asphalt. However, the organic additives have hydrophobic characteristics and are sensitive to water. As a result, the adhesiveness of the asphalt-aggregate interface of the asphalt containing organic additives in wet conditions sharply decreased due to water damage to asphalt and organic additives. Furthermore, the compatibility of asphalt, aggregate with organic additive was noted and discussed

Effect of the Interfacial Energy Landscape on Photoinduced Charge Generation at the ZnPc/MoS2 Interface

This document is the Accepted Manuscript version of a Published Work that appeared in final form in Journal of the American Chemical Society, copyright © American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see https://doi.org/10.1021/jacs.9b05893

DiffusionTalker: Personalization and Acceleration for Speech-Driven 3D Face Diffuser

Speech-driven 3D facial animation has been an attractive task in both academia and industry. Traditional methods mostly focus on learning a deterministic mapping from speech to animation. Recent approaches start to consider the non-deterministic fact of speech-driven 3D face animation and employ the diffusion model for the task. However, personalizing facial animation and accelerating animation generation are still two major limitations of existing diffusion-based methods. To address the above limitations, we propose DiffusionTalker, a diffusion-based method that utilizes contrastive learning to personalize 3D facial animation and knowledge distillation to accelerate 3D animation generation. Specifically, to enable personalization, we introduce a learnable talking identity to aggregate knowledge in audio sequences. The proposed identity embeddings extract customized facial cues across different people in a contrastive learning manner. During inference, users can obtain personalized facial animation based on input audio, reflecting a specific talking style. With a trained diffusion model with hundreds of steps, we distill it into a lightweight model with 8 steps for acceleration. Extensive experiments are conducted to demonstrate that our method outperforms state-of-the-art methods. The code will be released

Multi-energy X-ray linear-array detector enabled by the side-illuminated metal halide scintillator

Conventional scintillator-based X-ray imaging typically captures the full spectral of X-ray photons without distinguishing their energy. However, the absence of X-ray spectral information often results in insufficient image contrast, particularly for substances possessing similar atomic numbers and densities. In this study, we present an innovative multi-energy X-ray linear-array detector that leverages side-illuminated X-ray scintillation using emerging metal halide Cs3Cu2I5. The negligible self-absorption characteristic not only improves the scintillation output but is also beneficial for improving the energy resolution for the side-illuminated scintillation scenarios. By exploiting Beer's law, which governs the absorption of X-ray photons with different energies, the incident X-ray spectral can be reconstructed by analyzing the distribution of scintillation intensity when the scintillator is illuminated from the side. The relative error between the reconstructed and measured X-ray spectral was less than 5.63 %. Our method offers an additional energy-resolving capability for X-ray linear-array detectors commonly used in computed tomography (CT) imaging setups, surpassing the capabilities of conventional energy-integration approaches, all without requiring extra hardware components. A proof-of-concept multi-energy CT imaging system featuring eight energy channels was successfully implemented. This study presents a simple and efficient strategy for achieving multi-energy X-ray detection and CT imaging based on emerging metal halides