1,053 research outputs found
A Note On Obata's Rigidity Theorem I
In this note we present various extensions of Obata's rigidity theorem
concerning the Hessian of a function on a Riemannian manifold. They include
general rigidity theorems for the generalized Obata equation, and hyperbolic
and Euclidean analogs of Obata's theorem. Besides analyzing the full rigidity
case we also characterize the geometry and topology of the underlying manifold
in more general situations.Comment: Some remarks are added. A few typos are removed. The proof of one
lemma is modifie
Rigidity of Schouten Tensor under Conformal Deformation
We obtain some rigidity results for metrics whose Schouten tensor is bounded
from below after conformal transformations. Liang Cheng recently proved that a
complete, nonflat, locally conformally flat manifold with Ricci pinching
condition () must be compact. This answers higher
dimensional Hamilton's pinching conjecture on locally conformally flat
manifolds affirmatively. Since (modified) Schouten tensor being nonnegative is
equivalent to a Ricci pinching condition, our main result yields a simple proof
of Cheng's theorem
Toward Understanding Generative Data Augmentation
Generative data augmentation, which scales datasets by obtaining fake labeled
examples from a trained conditional generative model, boosts classification
performance in various learning tasks including (semi-)supervised learning,
few-shot learning, and adversarially robust learning. However, little work has
theoretically investigated the effect of generative data augmentation. To fill
this gap, we establish a general stability bound in this not independently and
identically distributed (non-i.i.d.) setting, where the learned distribution is
dependent on the original train set and generally not the same as the true
distribution. Our theoretical result includes the divergence between the
learned distribution and the true distribution. It shows that generative data
augmentation can enjoy a faster learning rate when the order of divergence term
is , where is the train
set size and is the corresponding stability constant. We further
specify the learning setup to the Gaussian mixture model and generative
adversarial nets. We prove that in both cases, though generative data
augmentation does not enjoy a faster learning rate, it can improve the learning
guarantees at a constant level when the train set is small, which is
significant when the awful overfitting occurs. Simulation results on the
Gaussian mixture model and empirical results on generative adversarial nets
support our theoretical conclusions. Our code is available at
https://github.com/ML-GSAI/Understanding-GDA.Comment: 39 page
Numerical Simulation of Q345 Steel Pipe Joint Weld
Q345 steel pipe is a commonly used welding material. Whether it is shipbuilding, boiler pressure vessel or construction engineering, the demand for Q345 steel is very large. In this paper, the numerical simulation of Q345 steel pipe is carried out. It is analyzed whether the temperature field and stress field of the welded joint are similar to the reality under the condition of two-layer weld seam, so as to prove that the welding process can be implemented accordingly
An investigation into the role of information and communication technologies on travel behaviour of working adults and youth
This thesis aims to investigate the diverse roles information and communications technologies (ICT) play in shaping individualsā mobility behaviour. In doing so, three strands of interrelated research questions are empirically analysed to better understand the use of ICT and its implications for travel among both working adults and millennials. A cross-sectional analysis is firstly performed to examine the variations in the relationships between Internet use and non-mandatory travel patterns according to household working status. By employing data from the 2005/06 Scottish Household Survey (SHS) and the two-part model, the ICT-travel relationships are found to be characterised by individual employment status and intra-household interactions, which impose different constraints on individualsā non-mandatory mobility patterns. A repeated cross-sectional analysis using the difference-in-differences (DD) estimation and the pooling of cross sections from the 2005/06 SHS data and the 2015 Integrated Multimedia City Data (iMCD) subsequently examines the evolutions in the ICT-travel relationships over time, and how temporal changes differ between the general adult population and the millennial generation. Findings suggest that the changes over time are generally characterised by diminishing complementarity and increasing substitution. Moreover, while the temporal changes for the general population are mostly found among the medium-to-heavy Internet users, for millennials, it is the light or medium-to-light users who see significant temporal changes. Finally, using the longitudinal datasets from the British Household Panel Survey (BHPS) and the Understanding Society Survey, an exploration is undertaken of the direct and indirect effects of prior experience with using ICT (as children) on millennialsā current travel behaviour. The structural equation model is applied to examine the relationships between ICT use, travel choices, and environmental attitude. The longitudinal analysis finds that millennialsā long-term exposure to ICT (since adolescence) may shape their current travel patterns by influencing their environmental attitudes. The findings from these analyses highlight the importance of considering the effects of personal, household, and social characteristics on the ICT-travel interactions. In addition, the research focuses on dynamic interactions and on the indirect or higher-order roles of ICT in affecting travel behaviour as well as on the implications for transport planning practices and policy making
Induction, development and regulation of trimolters: Great progress in the domesticated silkworm (Bombyx mori L.)
As the only truly agricultural and great economic domesticated insect, the silkworm is not only value as a model for genetics and rmolecular biology research, but it also has great value for new silk materials. Induction and regulation of trimolter induced by anti-juvenile hormone have shown vast potential to be significant patterns in silkworm research, especially after the further studies on the regulation mechanism of trimolters. This paper reviews the great progress of the induction technique of trimolter silkworms, particularly focusing on its cocoon quality, cocoon filament and the production of advanced silk materials. This review also presents the control technology of fine filament size and the regulatory mechanism of trimolters during the developmental stages.Key words: Silkworm, trimolter, chemical induction, development, filament control, regulatory mechanism
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