Meromorphic functions sharing one value by weight

The uniqueness of meromorphic fuctions sharing one value was studied. Using the concept of weighted sharing, we proved the following theorem. For two meromorphic functions [ and g which are not polynominals of degree less than a positive integer k, if f^nf（k）and g^ng^（k） share （1,2）, where n is another positive integer not less than k＋10, then f^nf^（k） identically equals g^ng ^（k） or f^nf^（k）g^ng^（k） identically equals 1. Particularly for k =1, we improved the results of Yang [Yang CC, Hua XH, Uniqueness and value-sharing of meromorphic functions, Annales Academiae Scientiarum Fennicae Mathematica, 1997, 22： 395-406], and Fang [Fang ML, Hua XH, Entire function that share one value, Journal of Nanjing University, 1996, 13（1）： 44-48. （In Chinese）].

Uniqueness of entire functions concerning weighted sharing

The uniqueness problem of entire functions concerning weighted sharing was discussed, and the following theorem was proved. Let f and 8 be two non-constant entire functions, m, n and k three positive integers, and n〉2k＋4. If Em（1,（f^n）^（k））= Em（1,（g^n）^（k））, then either f（z）=c1c^cz and 8（z）= c2c^cz or f=ts, where c, c1 and c2 are three constants satisfying （-1）^k（c1c2）^n（nc）^2k=], and t is a constant satisfying t^n=1. The theorem generalizes the result of Fang [Fang ML, Uniqueness and value sharing of entire functions, Computer ＆ Mathematics with Applications, 2002, 44： 823-831].

Unicity Theorems of Mesomorphic Functions with Three Weighted Sharing Values

In this paper,with the idea of weighted sharing values,we deal with the problem of uniqueness of mesomorphic functions sharing three weighted values.We obtain some theorems which improve the results of H X Yi and W R L.

Sharing Weights in Shallow Layers via Rotation Group Equivariant Convolutions

The convolution operation possesses the characteristic of translation group equivariance. To achieve more group equivariances, rotation group equivariant convolutions(RGEC) are proposed to acquire both translation and rotation group equivariances.However, previous work paid more attention to the number of parameters and usually ignored other resource costs. In this paper, we construct our networks without introducing extra resource costs. Specifically, a convolution kernel is rotated to different orientations for feature extractions of multiple channels. Meanwhile, much fewer kernels than previous works are used to ensure that the output channel does not increase. To further enhance the orthogonality of kernels in different orientations, we construct the non-maximum-suppression loss on the rotation dimension to suppress the other directions except the most activated one. Considering that the low-level-features benefit more from the rotational symmetry, we only share weights in the shallow layers(SWSL) via RGEC. Extensive experiments on multiple datasets(i.e., Image Net, CIFAR, and MNIST) demonstrate that SWSL can effectively benefit from the higher-degree weight sharing and improve the performances of various networks, including plain and Res Net architectures. Meanwhile, the convolutional kernels and parameters are much fewer(e.g., 75%, 87.5% fewer) in the shallow layers, and no extra computation costs are introduced.

Some Further Results on the Unique Range Sets of Meromorphic Functions

This paper studies the problem of uniqueness of meromorphic functions which share three common sets with weight, and improves a result of M. L. Fang.

Entire Functions Sharing One Value with Finite Weight

This paper deals with some uniqueness problems of entire functions concerning differential polynomials that share one value with finite weight in a different form. We obtain some theorems which generalize some results given by Banerjee, Fang and Hua, Zhang and Lin, Zhang, etc.

Wind speed prediction based on nested shared weight long short-term memory network

With the expansion of wind speed data sets, decreasing model training time is of great significance to the time cost of wind speed prediction. And imperfection of the model evaluation system also affect the wind speed prediction. To address these challenges, a hybrid method based on feature extraction, nested shared weight long short-term memory(NSWLSTM) network and Gaussian process regression(GPR) was proposed. The feature extraction of wind speed promises the best performance of the model. NSWLSTM model reduces the training time of long short-term memory(LSTM) network and improves the prediction accuracy. Besides, it adopted a method combined NSWLSTM with GPR(NSWLSTM-GPR) to provide the probabilistic prediction of wind speed. The probabilistic prediction can provide information that deviates from the predicted value, which is conducive to risk assessment and optimal scheduling. The simulation results show that the proposed method can obtain high-precision point prediction, appropriate prediction interval and reliable probabilistic prediction results with shorter training time on the wind speed prediction.