Sobolev inequalities in manifolds with nonnegative intermediate Ricci curvature

We prove Michael-Simon type Sobolev inequalities for $n$-dimensional submanifolds in $(n+m)$-dimensional Riemannian manifolds with nonnegative $(n-1)$-th intermediate Ricci curvature by using the Alexandrov-Bakelman-Pucci method. These inequalities extends Brendle's Michael-Simon type Sobolev inequalities on Riemannian manifolds with nonnegative sectional curvature (arXiv:2009.13717) and Dong-Lin-Lu's Michael-Simon type Sobolev inequalities on Riemannian manifolds with asymptotically nonnegative sectional curvature (arXiv:2203.14624) to the $(n-1)$-Ricci curvature setting. In particular, a simple application of these inequalities gives rise to some isoperimetric inequalities for minimal submanifolds in Riemannian manifolds.Comment: 11 pages. All comments are welcome

5-Methyl-3,3-bis­(morpholin-4-yl)-1-[2-(morpholin-4-yl)eth­yl]-2,3-dihydro-1H-indol-2-one

In the title compound, C23H34N4O4, the morpholine rings adopt chair conformations. The N atom of the indol-2-one group is linked to the N atom of one morpholine ring through a flexible ethyl group with an almost cif conformation. In the crystal, molecules are linked by C—H⋯O interactions into infinite chains along the c direction. The almost parallel infinite chains are further inter­connected via other sets of C—H⋯O inter­actions, forming a three-dimensional framework

Online Updating of Statistical Inference in the Big Data Setting

We present statistical methods for big data arising from online analytical processing, where large amounts of data arrive in streams and require fast analysis without storage/access to the historical data. In particular, we develop iterative estimating algorithms and statistical inferences for linear models and estimating equations that update as new data arrive. These algorithms are computationally efficient, minimally storage-intensive, and allow for possible rank deficiencies in the subset design matrices due to rare-event covariates. Within the linear model setting, the proposed online-updating framework leads to predictive residual tests that can be used to assess the goodness-of-fit of the hypothesized model. We also propose a new online-updating estimator under the estimating equation setting. Theoretical properties of the goodness-of-fit tests and proposed estimators are examined in detail. In simulation studies and real data applications, our estimator compares favorably with competing approaches under the estimating equation setting.Comment: Submitted to Technometric

Rethinking on Challenging “Ricardo Law” and Construct Innovative and Harmonious China

Developed countries, heading by the United States, have been trying to break away from the “Ricardo law” circle, while the US financial crisis has once again declared its failure. As the biggest developing country, China is now challenging the “Ricardo Law”. This paper has a brief rethinking on the western conflictive and harmonious thoughts of World development in order to probe on our ongoing harmonious socialist development. Key words: financial crisis; western economics; "Ricardo Law"; conflictive and harmonious thoughts; harmonious societ

Anti-Corrosive Properties of Alkaloids on Metals

Numerous organic inhibitors have been reported to be used for the corrosion inhibition of various metals, especially, the heterogeneous ring compounds bearing larger electronegativity atoms (i.e., N, O, S, and P), polar functional groups, and conjugated double bonds are the most effective inhibitors. Based on the concept of green chemistry, in recent years, the research of corrosion inhibitor has gradually extracted new environment-friendly corrosion inhibitor from natural animals and plants, because of its advantages in wide source, low cost, low toxicity and subsequent treatment. Alkaloids such as papaverine, strychnine, quinine, nicotine, etc., have been studied as inhibitors for metals corrosion in corrosive media. This chapter aims to review the application of alkaloids for the corrosion inhibition of metals in corrosive media, and the development trend in this field is prospected