Covering matroid

In this paper, we propose a new type of matroids, namely covering matroids, and investigate the connections with the second type of covering-based rough sets and some existing special matroids. Firstly, as an extension of partitions, coverings are more natural combinatorial objects and can sometimes be more efficient to deal with problems in the real world. Through extending partitions to coverings, we propose a new type of matroids called covering matroids and prove them to be an extension of partition matroids. Secondly, since some researchers have successfully applied partition matroids to classical rough sets, we study the relationships between covering matroids and covering-based rough sets which are an extension of classical rough sets. Thirdly, in matroid theory, there are many special matroids, such as transversal matroids, partition matroids, 2-circuit matroid and partition-circuit matroids. The relationships among several special matroids and covering matroids are studied.Comment: 15 page

Parametric matroid of rough set

Rough set is mainly concerned with the approximations of objects through an equivalence relation on a universe. Matroid is a combinatorial generalization of linear independence in vector spaces. In this paper, we define a parametric set family, with any subset of a universe as its parameter, to connect rough sets and matroids. On the one hand, for a universe and an equivalence relation on the universe, a parametric set family is defined through the lower approximation operator. This parametric set family is proved to satisfy the independent set axiom of matroids, therefore it can generate a matroid, called a parametric matroid of the rough set. Three equivalent representations of the parametric set family are obtained. Moreover, the parametric matroid of the rough set is proved to be the direct sum of a partition-circuit matroid and a free matroid. On the other hand, since partition-circuit matroids were well studied through the lower approximation number, we use it to investigate the parametric matroid of the rough set. Several characteristics of the parametric matroid of the rough set, such as independent sets, bases, circuits, the rank function and the closure operator, are expressed by the lower approximation number.Comment: 15 page

Characteristic of partition-circuit matroid through approximation number

Rough set theory is a useful tool to deal with uncertain, granular and incomplete knowledge in information systems. And it is based on equivalence relations or partitions. Matroid theory is a structure that generalizes linear independence in vector spaces, and has a variety of applications in many fields. In this paper, we propose a new type of matroids, namely, partition-circuit matroids, which are induced by partitions. Firstly, a partition satisfies circuit axioms in matroid theory, then it can induce a matroid which is called a partition-circuit matroid. A partition and an equivalence relation on the same universe are one-to-one corresponding, then some characteristics of partition-circuit matroids are studied through rough sets. Secondly, similar to the upper approximation number which is proposed by Wang and Zhu, we define the lower approximation number. Some characteristics of partition-circuit matroids and the dual matroids of them are investigated through the lower approximation number and the upper approximation number.Comment: 12 page

Research on the Practical Teaching System of Business English Based on “Experimental Learning”

Practical teaching, as an indispensable part of college teaching system, is an important way to cultivate innovative and entrepreneurial talents. There is still certain gap between the quality of talent training in colleges and the talent demand of social and economic development. This research discusses the reform and practice of practical teaching system with a case study, aiming to explore a new path of the practical teaching system of Business Englis

An Improved Foam Modeling Technique and Its Application to Petroleum Drilling and Production Practice

Foam is one of the most common used multiphase fluid in Underbalanced Drilling (UBD) and Managed Pressure Drilling (MPD). Because of its low density, high capacity of lifting and carrying cuttings, low cost and compatibility with formations, foam has become more superior than the conventional drilling mud when depleted reservoir pressure, severe lost circulation, or unstable borehole are encountered. In general, the success of foam applications rely on the understanding of the fundamentals of foam rheology in downhole conditions. Foam rheology has been studied for decades. Conventional foam rheological models such as Power Law, Bingham Plastic, Herschel-Bulkley to explain foam behavior usually fail to interpret the monitored circulating pressure changes in operation, not to mention foam behaviors in downhole. Understanding bubble size and foam texture impacts at different foam quality ranges in the foam model development become very significant. A new foam rheological model based on Low-Quality Regime (LQR) and High-Quality Regime (HQR) behaviors is developed. This new model, which originally came from comprehensive foam flow experiments, together with the visualization of foam texture and bubble distribution, is proved to be easily and conveniently implemented for industry use in this study. The model requires nine model parameters – three (uwRef, ugRef,DPRef) to define the transition region, four to capture Power-Law rheology in both HQR and LQR (KH, nH, KL, nL), and two to describe the sensitivity of steady-state pressure drops as a function of gas and liquid velocities in both regimes (mH, mL). With the newly developed foam model, we apply it in the following two foam applications in petroleum industry, in which the foam rheology and foam handling are the main concerns for successes. First of all, a foam drilling and wellbore clean-up application with foam is investigated. These scenarios consider foam circulation into 10000 ft long wells at different inclination angles with a long vertical, inclined, or horizontal trajectory. The results are compared with two existing foam modeling techniques, so-called Chen et al.’s model (based on the correlations for wet foams only) and Edrisi and Kam’s model (based on wet- and dry-foam rheological properties with five model parameters). The conclusions show that, with or without formation fluid influx, the new foam model demonstrates the robustness of the new modeling technique in all scenarios capturing foam flow characteristics better, whenever the situation forms stable fine-textured foams or unstable coarse-textured foams. Second, foam-assisted mud cap drilling for gas migration situation, which simulatesthe process with accurate foam characteristics when foams are used to suppress gas kicks under certain well and fluid conditions, is presented. The new foam model with Two Flow Regimes is used throughout the simulation process. The results show how mud-cap drilling parameters (such as pressure, foam density (or equivalent mud weight), foam velocity, and foam quality) change at different operating conditions and scenarios. Moreover, a set of field data from a wellbore clean-up with foam operation is demonstrated and the circulating pressure changes provide the evidence of Two Flow Regimes

Biochemical changes in low-salt solid-state fermented soy sauce

Low-salt solid-state fermentation soy sauce was prepared with defatted soy bean and wheat bran. Biochemical changes during the aging of the soy sauce mash were investigated. Results showed that after a 15-day aging period, the contents of total nitrogen, formol titration nitrogen, free amino acids, reducing sugar, total sugar and the brown color were increased. However, pH was decreased during the fermentation period. Furthermore, contents of total free amino acids in low-salt solid-state fermentation soy sauce fluctuated during the fermentation period, and in most periods, it was increased. The analysis of free amino acid composition shows that the contents of glutamic acid, aspartic acid, alanine and leucine were higher than other amino acids. Therefore, it means that these amino acids may contribute to the taste and flavor of low-salt solid-state fermentation soy sauce. The biochemical changes characters were due to enzyme activities, solution balance and reaction balance, and biochemical changes contributed to the improvement of the flavor of low-salt solid-state fermented soy sauce. Analyzing the biochemical change in the fermented process of soy sauce is helpful in finding out the shortcoming of low-salt solid-state fermented soy sauce.Key words: Low-salt solid-state fermented soy sauce, biochemical changes, fermentation period, chemicalcomposition