Abstract:
Many
forecasting models based on the concepts of Fuzzy time series have been proposed in the past decades.
These models have been widely applied to various problem domains, especially in
dealing with forecasting problems in which historical data are linguistic
values. In this paper, we present a new
fuzzy time series forecasting model, which uses the historical data as the
universe of discourse and uses the K-means clustering algorithm to cluster the
universe of discourse, then adjust the clusters into intervals. The proposed
method is applied for forecasting University enrollment of Alabama. It is shown
that the proposed model achieves a significant improvement in forecasting
accuracy as compared to other fuzzy time series forecasting models.

Abstract:
本文對大陸地區改革開放後出現的盜版成因進行了分析，認為盜版的氾濫與這一時期的制度變更密切相關。文章從出版物成為商品、民營出版經濟成分的出現及市場化的驅動、經濟結構的調整與就業問題的出現、對單位控制的減弱及單位自主權的增加、出版單位體制改革滯後等5個方面分析了制度變更與盜版製品氾濫之間的關係。 This paper discusses the problem of the piracy in Mainland China after 1978, tries to reveal the relationship between the changing of institution and the overflowing of pirate. Chinese government set up the economic reform after 1978, and resulted in the below effect. Firstly, the publication became the merchandise; Secondly, the private sector in publishing field is emerging; Thirdly, the problem of obtaining employment is appearing because of the adjustment of economic structure; Fourthly, the government control of the unit became weaken; and the Fifth, the reform of the publishing house is stagnant.

Abstract:
China’s economic development has maintained a rapid
growth trend since 1978, but the problem of imbalanced income distribution
between urban and rural residents also has been increasingly aggravated. This
paper discusses the relationship between financial development and urban-rural
income disparity and examines the impact of urbanization on the relationship
between financial development and urban-rural income disparity. Then this paper
selects the provincial panel data of 28 provinces in China from 1978 to 2014, using
GMM dynamic model and fixed effect panel model, respectively, to do the
empirical test. The results show that: 1) the imbalance of urban and rural
financial resources is exacerbated by the financial threshold effect, leading
to the fact that the financial development-measured
by scale, efficiency and structure, respectively, expand the urban-rural
income gap. 2) The
developing urbanization will widen the urban-rural income gap. However, as the
urbanization and mainly the urbanization of land is rapid in China, the
expansion effect of the increasing financial development level on the income
gap between urban and rural residents in China will be weakened with the
acceleration of urbanization based on the financial threshold effect. It
provides empirical support for the financial reform and for the assumption that
urbanization development reduces the income gap between urban and rural areas.

Abstract:
Eleman Neural Network (ENN) have been efficient identification tool in many areas (classification and prediction fields) since they have dynamic memories. However, one of the problems often associated with this type of network is the local minima problem which usually occurs in the process of the learning. To solve this problem and speed up the learning process, we propose a method to add a term in error function which related to the neuron saturation of the hidden layer for Elman Neural Network. The activation functions are adapted to prevent neurons in the hidden layer from stucking into saturation area. We apply the new method to the Boolean Series Prediction Questions to demonstrate its validity. Simulation results show that the proposed algorithm has a better ability to find the global minimum than back propagation ENN algorithms within reasonable time.

Abstract:
In this paper, we prove the existence of a family of new non-collision periodic solutions for the classical Newtonian $n$-body problems. In our assumption, the $n=2l\geq4$ particles are invariant under the dihedral rotation group $D_l$ in $\mathbb{R}^3$ such that, at each instant, the $n$ particles form two twisted $l$-regular polygons. Our approach is variational minimizing method and we show that the minimizers are collision-free by level estimates and local deformations.

Abstract:
A classification is obtained for the approximately finite systems associated to cyclic groups with prime orders. Such systems contain natural examples of finite cyclic group actions which do not have the tracial Rokhlin property. Thess examples were constructed by N. C. Phillips.

Abstract:
We introduced and analyzed robust recovery-based a posteriori error estimators for various lower order finite element approximations to interface problems in [9, 10], where the recoveries of the flux and/or gradient are implicit (i.e., requiring solutions of global problems with mass matrices). In this paper, we develop fully explicit recovery-based error estimators for lower order conforming, mixed, and non- conforming finite element approximations to diffusion problems with full coefficient tensor. When the diffusion coefficient is piecewise constant scalar and its distribution is local quasi-monotone, it is shown theoretically that the estimators developed in this paper are robust with respect to the size of jumps. Numerical experiments are also performed to support the theoretical results.

Abstract:
For elliptic interface problems in two- and three-dimensions, this paper establishes a priori error estimates for Crouzeix-Raviart nonconforming, Raviart-Thomas mixed, and discontinuous Galerkin finite element approximations. These estimates are robust with respect to the diffusion coefficient and optimal with respect to local regularity of the solution. Moreover, we obtain these estimates with no assumption on the distribution of the diffusion coefficient.

Abstract:
For non-smooth problems, e.g., interface problems, it is known that adaptive mesh refinement (AMR) algorithms using the Zienkiewicz-Zhu (ZZ) a posteriori error estimator are not efficient to reduce global error. In this paper, we derive and analyze two improved ZZ error estimators for the conforming linear finite element approximation to the diffusion problem with full coefficient tensor. The estimators are based on the piecewise "constant" and linear flux recoveries in the $H(div;\Omega)$ conforming finite element spaces. Both the recoveries are explicit. When the diffusion coefficient is piecewise constant scalar and its distribution is locally quasi-monotone, it is shown theoretically that the estimators developed in this paper are robust with respect to the size of jumps. Numerical experiments are also performed to support the theoretical results.

Abstract:
We call $F:\{0, 1\}^n\times \{0, 1\}^n\to\{0, 1\}$ a symmetric XOR function if for a function $S:\{0, 1, ..., n\}\to\{0, 1\}$, $F(x, y)=S(|x\oplus y|)$, for any $x, y\in\{0, 1\}^n$, where $|x\oplus y|$ is the Hamming weight of the bit-wise XOR of $x$ and $y$. We show that for any such function, (a) the deterministic communication complexity is always $\Theta(n)$ except for four simple functions that have a constant complexity, and (b) up to a polylog factor, the error-bounded randomized and quantum communication complexities are $\Theta(r_0+r_1)$, where $r_0$ and $r_1$ are the minimum integers such that $r_0, r_1\leq n/2$ and $S(k)=S(k+2)$ for all $k\in[r_0, n-r_1)$.