Different from the Taylor polynomials, a new formula for function expansion is proposed where the terms are not polynomials. A new infinite series based on the new formula is also proposed, and the new infinite series can keep some important properties of the original functions. Some forms of remainder are also presented for analysis of convergence. In order to show some internal relationships between the new results and Taylor's theorem, some important theorems have been proved in this paper. Finally, Some examples are given and the regions of convergence for the new infinite series are analyzed, the results show that the region of convergence is much larger than that obtained by Taylor's Series.Mathematics Subject Classification: 41A58, 41A20, 41A30, 40A30

Logistics and distribution problem, in essence, is the vehicle routing problem, belonging to NP-hard problem. For drawbacks of basic ant algorithm such as searching for a long time, easy to fall into local optimum, generalized ant colony algorithm has been proposed. Applying the generalized ant colony algorithm to logistics and distribution problem can improve the utilization of the vehicle; reduce transportation costs and achieve the purpose of scientific management of logistics.

This paper aims to analyze passenger flow in subway based on a kind of rational spline weight function neural network, in which the numerator of the spline is a cubic polynomial and the denominator of the spline is a quadratic polynomial, and this kind spline is denoted by 3/2 rational splines. There are many factors affecting the passenger flow. Combined the main influential factors with the self-learning method of neural network, we establish the neural network model of passenger flow in subway. This paper introduces the spline weight function neural network and the passenger flow model based on this neural network. Finally MATLAB simulation verifies that the 3/2 rational spline weight function neural network can be applied to analyze the passenger flow in subway with high accuracy.

A new algorithm of neural networks with B-spline weight jimctions is proposed. The weights obtained after training are B-spline functions defined on the sets of input variables (input patterns). which can be used to extract some important information inherent in the problems. The new algorithm has high approximation accuracy and learning speed. The network's architecture is very simple and the number of B spline weight jimctions to be trained is independent of the number of patterns. Some examples are presented to illustrate good performance of the new algorithm.Index Terms-artificial intelligence, neural networks. weight jimctions. cubic spline functions

How to effectively filter out spam is a topic worthy of further study for the growing proliferation of spam. The main purpose of this paper is to apply a new neural network algorithm to the classification of spam. In this paper, we introduce a second type of spline weight function neural network algorithm, as well as e-mail feature extraction and vectorization, and then introduced the mail sorting process. Experiments show that it can get a relatively high accuracy and recall rate on the spam classification. Therefore, with this new algorithm, we can achieve better classification results.