Weighted Estimates for Multilinear Commutators of Marcinkiewicz Integrals with Bounded Kernel

Let $\mu_{\Omega,\vec{b}}$ be the multilinear commutator generalized by $\mu_{\Omega}$, the $n$-dimensional Marcinkiewicz integral with the bounded kernel, and b_{j}\in \Osc_{\exp L^{r_{j}}}(1\le j\le m). In this paper, the following weighted inequalities are proved for $\omega\in A_{\infty}$ and $0<p<\infty$, $$\|\mu_{\Omega}(f)\|_{L^{p}(\omega)}\leq C\|M(f)\|_{L^{p}(\omega)}, \ \ \|\mu_{\Omega,\vec{b}}(f)\|_{L^{p}(\omega)}\leq C\|M_{L(\log L)^{1/r}}(f)\|_{L^{p}(\omega)}.$$ The weighted weak $L(\log L)^{1/r}$ -type estimate is also established when $p=1$ and $\omega\in A_{1}$.Comment: In 2012, it is accepted by Ukrainian Mathematical Journal. And there are 13 page

Weighted estimates for multilinear commutators of Marcinkiewicz integrals with bounded kernel

Let μΩ,b→ be a multilinear commutator generalized by the n-dimensional Marcinkiewicz integral with bounded kernel μ Ώ and let bj ∈OscexpLrj , 1 ≤ j ≤ m. We prove the following weighted inequalities for ω ∈ A ∞ and 0 < p < ∞: The weighted weak L(log L)1/r -type estimate is also established for p =1 and ω ∈ A.Нехай μΩ,b→ — мультилінійний комутатор, що узагальнює μΏ, n-вимірний iнтеграл Марцинкевича з обмеженим ядром, та нехай bj∈OscexpLrj(1≤j≤m). Доведено такі зважені нерівності для ω∈A∞ та 0<p<∞: Зважену слабку оцінку L(log L)1/r -типу також встановлено для p=1 та ω∈A

Reflective Full Subcategories of the Category of L

This paper focuses on the relationship between L-posets and complete L-lattices from the categorical view. By considering a special class of fuzzy closure operators, we prove that the category of complete L-lattices is a reflective full subcategory of the category of L-posets with appropriate morphisms. Moreover, we characterize the Dedekind-MacNeille completions of L-posets and provide an equivalent description for them

Degradation-Aware Self-Attention Based Transformer for Blind Image Super-Resolution

Compared to CNN-based methods, Transformer-based methods achieve impressive image restoration outcomes due to their abilities to model remote dependencies. However, how to apply Transformer-based methods to the field of blind super-resolution (SR) and further make an SR network adaptive to degradation information is still an open problem. In this paper, we propose a new degradation-aware self-attention-based Transformer model, where we incorporate contrastive learning into the Transformer network for learning the degradation representations of input images with unknown noise. In particular, we integrate both CNN and Transformer components into the SR network, where we first use the CNN modulated by the degradation information to extract local features, and then employ the degradation-aware Transformer to extract global semantic features. We apply our proposed model to several popular large-scale benchmark datasets for testing, and achieve the state-of-the-art performance compared to existing methods. In particular, our method yields a PSNR of 32.43 dB on the Urban100 dataset at $\times$2 scale, 0.94 dB higher than DASR, and 26.62 dB on the Urban100 dataset at $\times$4 scale, 0.26 dB improvement over KDSR, setting a new benchmark in this area. Source code is available at: https://github.com/I2-Multimedia-Lab/DSAT/tree/main.Comment: 12 page

Three-way Imbalanced Learning based on Fuzzy Twin SVM

Three-way decision (3WD) is a powerful tool for granular computing to deal with uncertain data, commonly used in information systems, decision-making, and medical care. Three-way decision gets much research in traditional rough set models. However, three-way decision is rarely combined with the currently popular field of machine learning to expand its research. In this paper, three-way decision is connected with SVM, a standard binary classification model in machine learning, for solving imbalanced classification problems that SVM needs to improve. A new three-way fuzzy membership function and a new fuzzy twin support vector machine with three-way membership (TWFTSVM) are proposed. The new three-way fuzzy membership function is defined to increase the certainty of uncertain data in both input space and feature space, which assigns higher fuzzy membership to minority samples compared with majority samples. To evaluate the effectiveness of the proposed model, comparative experiments are designed for forty-seven different datasets with varying imbalance ratios. In addition, datasets with different imbalance ratios are derived from the same dataset to further assess the proposed model's performance. The results show that the proposed model significantly outperforms other traditional SVM-based methods

ENVIRONMENTAL SURROUNDINGS AND PERSONAL WELL-BEING IN URBAN CHINA

We examine the relationship between atmospheric pollution, water pollution, traffic congestion, access to parkland and personal well-being using a survey administered across six Chinese cities in 2007. In contrast to existing studies of the determinants of well-being by economists, which have typically employed single item indicators to measure well-being, we use the Personal Well-Being Index (PWI). We also employ the Job Satisfaction Survey (JSS) to measure job satisfaction, which is one of the variables for which we control when examining the relationship between environmental surroundings and personal well-being. Previous research by psychologists has shown the PWI and JSS to have good psychometric properties in western and Chinese samples. A robust finding is that in cities with higher levels of atmospheric pollution and traffic congestion, respondents report lower levels of personal well-being ceteris paribus. Specifically, we find that a one standard deviation increase in suspended particles or sulphur dioxide emissions is roughly equivalent to a 12-13 per cent reduction in average monthly income in the six cities.China, Environment, Pollution, Personal Well-Being.

ENVIRONMENTAL SURROUNDINGS AND PERSONAL WELL-BEING IN URBAN CHINA

We examine the relationship between atmospheric pollution, water pollution, traffic congestion, access to parkland and personal well-being using a survey administered across six Chinese cities in 2007. In contrast to existing studies of the determinants of well-being by economists, which have typically employed single item indicators to measure well-being, we use the Personal Well-Being Index (PWI). We also employ the Job Satisfaction Survey (JSS) to measure job satisfaction, which is one of the variables for which we control when examining the relationship between environmental surroundings and personal well-being. Previous research by psychologists has shown the PWI and JSS to have good psychometric properties in western and Chinese samples. A robust finding is that in cities with higher levels of atmospheric pollution and traffic congestion, respondents report lower levels of personal well-being ceteris paribus. We find that a one standard deviation increase in suspended particles or sulphur dioxide emissions is roughly equivalent to a 12-13 percent reduction in average monthly income in the six cities. This result suggests that the personal well-being of China's urban population can be enhanced if China were to pursue a more balanced growth path which curtailed atmospheric pollution.China, Environment, Pollution, Personal Well-Being.

catena-Poly[[bis­(1H-benzimidazole-κN 3)palladium(II)]-μ-benzene-1,4-dicarboxyl­ato-κ2 O 1:O 4]

In the title compound, [Pd(C8H4O4)(C7H6N2)2]n, the Pd atom is tetra­coordinated by two carboxyl­ate O atoms from two benzene-1,4-dicarboxyl­ate (bdc) dianions and two N atoms from two benzimidazole ligands, resulting in a slightly distorted tetra­hedral PdO2N2 geometry. The bdc ligand acts as a bridge, linking the Pd atoms into a chain. Inter-chain N—H⋯O hydrogen bonds help to stabilize the crystal structure