One Possible Mechanism for the Principal Mode of Atmospheric Low-Frequency Variabilityin the Northern Hemisphere Winter

With the specified basic flow in the Northern Hemisphere winter, a study is made of the structure characteristics and mechanism of the principal mode of atmospheric low-frequency variability in terms of a linear barotropic model. Statistical and dynamical analyses of the model results indicate that the mode and the related dominant-forcing excitation zone are featured by evident spatial distribution and that the mechanism responsible for the mode bears fetation to the zonal asymmetry of the basic flow and the associated barotropic energy conversion.

A Hybrid Neural Network Model for ENSO Prediction in Combination with Principal Oscillation Pattern Analyses

El Niño-Southern Oscillation(ENSO)can be currently predicted reasonably well six months and longer,but large biases and uncertainties remain in its real-time prediction.Various approaches have been taken to improve understanding of ENSO processes,and different models for ENSO predictions have been developed,including linear statistical models based on principal oscillation pattern(POP)analyses,convolutional neural networks(CNNs),and so on.Here,we develop a novel hybrid model,named as POP-Net,by combining the POP analysis procedure with CNN-long short-term memory(LSTM)algorithm to predict the Niño-3.4 sea surface temperature(SST)index.ENSO predictions are compared with each other from the corresponding three models:POP model,CNN-LSTM model,and POP-Net,respectively.The POP-based pre-processing acts to enhance ENSO-related signals of interest while filtering unrelated noise.Consequently,an improved prediction is achieved in the POP-Net relative to others.The POP-Net shows a high-correlation skill for 17-month lead time prediction(correlation coefficients exceeding 0.5)during the 1994-2020 validation period.The POP-Net also alleviates the spring predictability barrier(SPB).It is concluded that value-added artificial neural networks for improved ENSO predictions are possible by including the process-oriented analyses to enhance signal representations.

An Extension of the Hess-Kato Theorem to Elliptic Systems and Its Applications to Multiple Solution Problems

The Hess-Kato Theorem on the simplicity of the first eigenvalue of a second order elliptic operator is extended to elliptic systems.The theorem is applied to figure out the critical groups of a mountain pass point for functionals which have nonlinear ellipitic systems as Euler Lagrange Equations.A muliple solution result is obtained via the ordered Banach space method and the critical group calculations.

A Kind of Weingarten Surfaces in E^3 with Prescribed Principal Curvatures

In this paper, we construct a kind of Weingarten surfaces in E3 and study its geometric properties. We first derive an explicit diffierential relationship between the principal curvatures of them. Then we prove an existence theorem of this kind of surfaces with prescribed principal curvatures. At last, we present two examples involving the rotation surfaces as the special case, and present several figures to the second example.