4,561 research outputs found
Sobolev inequalities in manifolds with nonnegative intermediate Ricci curvature
We prove Michael-Simon type Sobolev inequalities for -dimensional
submanifolds in -dimensional Riemannian manifolds with nonnegative
-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 -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
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