Weighted composition operators preserving various Lipschitz constants

Let $\mathrm{Lip}(X)$, $\mathrm{Lip}^b(X)$, $\mathrm{Lip}^{\mathrm{loc}}(X)$ and $\mathrm{Lip}^\mathrm{pt}(X)$ be the vector spaces of Lipschitz, bounded Lipschitz, locally Lipschitz and pointwise Lipschitz (real-valued) functions defined on a metric space $(X, d_X)$, respectively. We show that if a weighted composition operator $Tf=h\cdot f\circ \varphi$ defines a bijection between such vector spaces preserving Lipschitz constants, local Lipschitz constants or pointwise Lipschitz constants, then $h= \pm1/\alpha$ is a constant function for some scalar $\alpha>0$ and $\varphi$ is an $\alpha$-dilation. Let $U$ be open connected and $V$ be open, or both $U,V$ are convex bodies, in normed linear spaces $E, F$, respectively. Let $Tf=h\cdot f\circ\varphi$ be a bijective weighed composition operator between the vector spaces $\mathrm{Lip}(U)$ and $\mathrm{Lip}(V)$, $\mathrm{Lip}^b(U)$ and $\mathrm{Lip}^b(V)$, $\mathrm{Lip}^\mathrm{loc}(U)$ and $\mathrm{Lip}^\mathrm{loc}(V)$, or $\mathrm{Lip}^\mathrm{pt}(U)$ and $\mathrm{Lip}^\mathrm{pt}(V)$, preserving the Lipschitz, locally Lipschitz, or pointwise Lipschitz constants, respectively. We show that there is a linear isometry $A: F\to E$, an $\alpha>0$ and a vector $b\in E$ such that $\varphi(x)=\alpha Ax + b$, and $h$ is a constant function assuming value $\pm 1/\alpha$. More concrete results are obtained for the special cases when $E=F=\mathbb{R}^n$, or when $U,V$ are $n$-dimensional flat manifolds.Comment: to appear in "Annals of Mathematical Sciences and Applications

Various generative adversarial networks model for synthetic prohibitory sign image generation

A synthetic image is a critical issue for computer vision. Traffic sign images synthesized from standard models are commonly used to build computer recognition algorithms for acquiring more knowledge on various and low-cost research issues. Convolutional Neural Network (CNN) achieves excellent detection and recognition of traffic signs with sufficient annotated training data. The consistency of the entire vision system is dependent on neural networks. However, locating traffic sign datasets from most countries in the world is complicated. This work uses various generative adversarial networks (GAN) models to construct intricate images, such as Least Squares Generative Adversarial Networks (LSGAN), Deep Convolutional Generative Adversarial Networks (DCGAN), and Wasserstein Generative Adversarial Networks (WGAN). This paper also discusses, in particular, the quality of the images produced by various GANs with different parameters. For processing, we use a picture with a specific number and scale. The Structural Similarity Index (SSIM) and Mean Squared Error (MSE) will be used to measure image consistency. Between the generated image and the corresponding real image, the SSIM values will be compared. As a result, the images display a strong similarity to the real image when using more training images. LSGAN outperformed other GAN models in the experiment with maximum SSIM values achieved using 200 images as inputs, 2000 epochs, and size 32 × 32

IMPLEMENT AN EXTENSION CORD POWER SOCKET WITH EMERGENCY LIGHTING AND VOICE CONTROL LIGHTING FUNCTIONS

Conventional power sockets are equipped with an extension cord. Even with anti-overload devices, incidents of accidental discharge or damage to electrical appliances may still incur due to external factors. To address this problem, this study integrated the voice control and lighting functions to the design of the power socket with an extension cord. The proposed design is space-efficient and versatile, and can be used in living rooms, bedrooms, and other places having electrical appliances. The proposed design also integrated emergency lighting and flashlight functions, so as to expand the practicality and safety of the power socket

Long-term Characteristics of Healthcare-associated Infections in a Neonatal Intensive Care Unit

Background/PurposeHealthcare-associated infections in neonatal intensive care units (NICUs) are associated with a significant risk of morbidity and mortality. Knowledge regarding pathogens, primary sources of infection and antibiotic resistance in the NICU is essential for developing management strategies. This study aimed to analyze the long-term characteristics of healthcare-associated infections in a tertiary referral center in southern Taiwan.MethodsInfants < 30 days old, with positive blood, cerebrospinal fluid, urine or tissue fluid cultures during hospitalization in the NICU of National Cheng Kung University Hospital from July 1989 to June 2008 were included in the study.ResultsIn total, 1,417 organisms and episodes were identified during the study period. Gram-positive organisms, Gram-negative organisms and fungi constituted 923 (65.1%), 358 (25.3%) and 136 (9.6%) of the pathogens, respectively. Of the Gram-positive organisms, coagulase-negative staphylococci (51.5%), Staphylococcus aureus (34.8%) and Enterococcus spp. (6.1%) were the major pathogens; and 27% of Staphylococcus aureus isolates were oxacillin-resistant. For the Gram-negative organisms, Klebsiella pneumoniae (22%), Pseudomonas aeruginosa (21.8%), Escherichia coli (16.7%) and Enterobacter cloacae (16.7%) were dominant. Also, Candida albicans accounted for 50% of fungal infections. The most common source of infection was bloodstream infection (59.0%), and 5.6% of these were catheter-related. Skin and soft tissue infections were also frequent (26.3%).ConclusionBloodstream and skin/soft tissue infections caused by commensal species play an important role in healthcare-associated infections in the NICU. New measures should be developed in response to the changing patterns in the NICU

3D rGO aerogel with superior electrochemical performance for K – Ion battery

As one possible alternative metal to lithium in ion batteries, potassium has recently attracted considerable attention as a result of its geochemical abundance and low cost. In this work, a detailed study of the electrochemical properties of potassium ion storage was performed using reduced graphene oxide (rGO) aerogel as a negative electrode material. The influence of the nature of the electrolyte and the drying methods used were investigated in order to optimize the electrochemical performance of freeze-dried rGO in potassium-ion batteries (PIBs). Electrochemical impedance spectroscopy (EIS) were used to assess the performance of our rGO material in PIBs. Used as the negative electrode, freeze-dried rGO can deliver a high capacity of 267 mA h/g at C/3 rate together with 78% capacity retention during 100 cycles, combined with high rate capability (92 mA h/g at 6.7C). This set of results makes rGO aerogel a promising electrode material for PIBs

The relationship between compensation committee quality and the voluntary adoption of clawback provisions

This paper examines how compensation committee quality is related to the voluntary adoption of clawback provisions. Because fair value information has some reliability issues, this paper further examines whether the amount of Level 3 fair values affect the relationship between compensation committee quality and the voluntary adoption of clawback provisions. Using a sample drawn from the U.S. firms from 2008 to 2015, the results show that the compensation committee quality is positively related to the voluntary adoption of clawback provisions. Additionally, the positive relationship between compensation committee quality and the voluntary adoption of clawback provisions is more pronounced for firms with higher Level 3 fair values