On implementing the symbolic preprocessing function over Boolean polynomial rings in Gröbner basis algorithms using linear algebra

Some techniques using linear algebra was introduced by Faugère in F4 to speed up the reduction process during Gr?bner basis computations.These techniques can also be used in fast implementations of F5 and some other signature-based Gr?bner basis algorithms.When these techniques are applied,a very important step is constructing matrices from critical pairs and existing polynomials by the Symbolic Preprocessing function(given in F4).Since multiplications of monomials and polynomials are involved in the Symbolic Preprocessing function,this step can be very costly when the number of involved polynomials/monomials is huge.In this paper,multiplications of monomials and polynomials for a Boolean polynomial ring are investigated and a specific method of implementing the Symbolic Preprocessing function over Boolean polynomial rings is reported.Many examples have been tested by using this method,and the experimental data shows that the new method is very efficient.     

Comments on a Paper on Alleged Misconceptions Regarding the History of Analysis: Who Has Misconceptions?

This comment is analysing the last section of a paper by Piotr Blaszczyk, Mikhail G. Katz, and David Sherry on alleged misconceptions committed by historians of mathematics regarding the history of analysis, published in this journal in the first issue of 2013. Since this section abounds of wrong attributions and denouncing statements regarding my research and a key publication, the comment serves to rectify them and to recall some minimal methodological requirements for historical research.     

An M-Objective Penalty Function Algorithm Under Big Penalty Parameters

Some classical penalty function algorithms may not always be convergent under big penalty parameters in Matlab software, which makes them impossible to find out an optimal solution to constrained optimization problems. In this paper, a novel penalty function (called M-objective penalty function) with one penalty parameter added to both objective and constrained functions of inequality constrained optimization problems is proposed. Based on the M-objective penalty function, an algorithm is developed to solve an optimal solution to the inequality constrained optimization problems, with its convergence proved under some conditions. Furthermore, numerical results show that the proposed algorithm has a much better convergence than the classical penalty function algorithms under big penalty parameters, and is efficient in choosing a penalty parameter in a large range in Matlab software.     

An improved LP model for energy optimization of the integrated iron and steel plant with a cogeneration system in China

In an integrated iron and steel plant with a cogeneration system, recycled energy is continuously transported into the cogeneration system and the electricity is continuously generated, and both of them could not be stored for a long time. Moreover, the generation and consumption of electricity is irregular, which may bring about more unexpected imbalances. Therefore, it is a crucial issue to schedule the entire energy system by optimizing the operation of energy utilization, which includes the raw energy in the production system, the generation electricity in the cogeneration system and the recycled energy in these two systems. In this paper, an improved Linear Programming model for energy optimization in the integrated iron and steel plant with a cogeneration system is established. The improved model focuses on controlling the whole energy flow and scheduling the whole energy consumption in the entire energy system between the production system and cogeneration system through optimizing all kinds of energy distribution and utilization in an integrated iron and steel plant with a cogeneration system. Case study shows that the improved model offers the optimal operation conditions at the higher energy utilization, lower energy cost and lower pollution emissions.     

Theoretical Studies of Thermodynamic Properties of Clusters

正As an extension of our earlier study on the structural properties of the clusters,a recently developed method to calculate the low-temperature vibrational heat capacities of clusters shall be presented.Subsequently,it shall be applied to Aun,Nan,Sin,Gen,and SinGen clusters.Our approach does not attempt to identify phase transitions but focuses on the low temperature behaviour,we find that the vibrational heat capacity of the clusters is strongly     

Advance selling in the presence of product diffusion effect

Product diffusion refers to the phenomenon that the later demand is dependent on the early sales. To investigate how a firm’s advance selling strategy is affected by the effect of product diffusion, we consider a monopolist seller who sells a fashionable product in a market that comprises of myopic and strategic consumers over two periods (i.e., the advance selling season and the regular selling season). For a linear product diffusion effect we find that, when the effect of product diffusion is positive, the seller may set an extremely high advance selling price to induce the strategic consumers to purchase in the regular selling season, which is counter-intuitive. Moreover, the optimal procurement quantity for the seller may increase in the negative effect of product diffusion and decrease in the amount of strategic consumers. When we extend our model to consider a concave quadratic product diffusion effect, however, the optimal procurement quantity is concave in the amount of strategic consumers. Numerical studies are further presented to discuss the managerial insights.     

Some open problems related to creative telescoping

Creative telescoping is the method of choice for obtaining information about definite sums or integrals. It has been intensively studied since the early 1990s, and can now be considered as a classical technique in computer algebra. At the same time, it is still a subject of ongoing research. This paper presents a selection of open problems in this context. The authors would be curious to hear about any substantial progress on any of these problems.     

The distributed representation for societal risk classification toward BBS posts

The risk classification of BBS posts is important to the evaluation of societal risk level within a period. Using the posts collected from Tianya forum as the data source, the authors adopted the societal risk indicators from socio psychology, and conduct document-level multiple societal risk classification of BBS posts. To effectively capture the semantics and word order of documents, a shallow neural network as Paragraph Vector is applied to realize the distributed vector representations of the posts in the vector space. Based on the document vectors, the authors apply one classification method KNN to identify the societal risk category of the posts. The experimental results reveal that paragraph vector in document-level societal risk classification achieves much faster training speed and at least 10% improvements of F-measures than Bag-of-Words. Furthermore, the performance of paragraph vector is also superior to edit distance and Lucene-based search method. The present work is the first attempt of combining document embedding method with socio psychology research results to public opinions area.