On properties not inherited by monoids from their Schützenberger groups

We give an example of a monoid with finitely many left and right ideals, all of whose Schützenberger groups are presentable by finite complete rewriting systems, and so each have finite derivation type, but such that the monoid itself does not have finite derivation type, and therefore does not admit a presentation by a finite complete rewriting system. The example also serves as a counterexample to several other natural questions regarding complete rewriting systems and finite derivation type. Specifically it allows us to construct two finitely generated monoids M and N with isometric Cayley graphs, where N has finite derivation type (respectively, admits a presentation by a finite complete rewriting system) but M does not. This contrasts with the case of finitely generated groups for which finite derivation type is known to be a quasi-isometry invariant. The same example is also used to show that neither of these two properties is preserved under finite Green index extensions.     

Some algebraic methods for solving multiobjective polynomial integer programs

Multiobjective discrete programming is a well-known family of optimization problems with a large spectrum of applications. The linear case has been tackled by many authors during the past few years. However, the polynomial case has not been studied in detail due to its theoretical and computational difficulties. This paper presents an algebraic approach for solving these problems. We propose a methodology based on transforming the polynomial optimization problem to the problem of solving one or more systems of polynomial equations and we use certain Gröbner bases to solve these systems. Different transformations give different methodologies that are theoretically stated and compared by some computational tests via the algorithms that they induce.     

On the decoding of binary cyclic codes with the Newton identities

We revisit in this paper the concept of decoding binary cyclic codes with Gröbner bases. These ideas were first introduced by Cooper, then Chen, Reed, Helleseth and Truong, and eventually by Orsini and Sala. We discuss here another way of putting the decoding problem into equations: the Newton identities. Although these identities have been extensively used for decoding, the work was done manually, to provide formulas for the coefficients of the locator polynomial. This was achieved by Reed, Chen, Truong and others in a long series of papers, for decoding quadratic residue codes, on a case-by-case basis. It is tempting to automate these computations, using elimination theory and Gröbner bases.Thus, we study in this paper the properties of the system defined by the Newton identities, for decoding binary cyclic codes. This is done in two steps, first we prove some facts about the variety associated with this system, then we prove that the ideal itself contains relevant equations for decoding, which lead to formulas.Then we consider the so-called online Gröbner basis decoding, where the work of computing a Gröbner basis is done for each received word. It is much more efficient for practical purposes than preprocessing and substituting into the formulas. Finally, we conclude with some computational results, for codes of interesting length (about one hundred).     

Analysing singularities of a benchmark problem

The purpose of this paper is to analyze the singularities of a well known benchmark problem “Andrews’ squeezing mechanism.” We show that for physically relevant parameter values this system admits singularities, and describe explicit conditions for the parameters. The method is based on Gröbner bases computations and ideal decomposition. It is algorithmic and can thus be applied to study constraint singularities which arise in more general situations as well.     

Fuzzy functions with LSE

“Fuzzy Functions” are proposed to be determined by the least squares estimation (LSE) technique for the development of fuzzy system models. These functions, “Fuzzy Functions with LSE” are proposed as alternate representation and reasoning schemas to the fuzzy rule base approaches. These “Fuzzy Functions” can be more easily obtained and implemented by those who are not familiar with an in-depth knowledge of fuzzy theory. Working knowledge of a fuzzy clustering algorithm such as FCM or its variations would be sufficient to obtain membership values of input vectors. The membership values together with scalar input variables are then used by the LSE technique to determine “Fuzzy Functions” for each cluster identified by FCM. These functions are different from “Fuzzy Rule Base” approaches as well as “Fuzzy Regression” approaches. Various transformations of the membership values are included as new variables in addition to original selected scalar input variables; and at times, a logistic transformation of non-scalar original selected input variables may also be included as a new variable. A comparison of “Fuzzy Functions-LSE” with Ordinary Least Squares Estimation (OLSE)” approach show that “Fuzzy Function-LSE” provide better results in the order of 10% or better with respect to RMSE measure for both training and test cases of data sets.     

Balancing Misclassification Rates in Classification-Tree Models of Software Quality

Software product and process metrics can be useful predictorsof which modules are likely to have faults during operations.Developers and managers can use such predictions by softwarequality models to focus enhancement efforts before release.However, in practice, software quality modeling methods in theliterature may not produce a useful balance between the two kindsof misclassification rates, especially when there are few faultymodules.This paper presents a practical classificationrule in the context of classification tree models that allowsappropriate emphasis on each type of misclassification accordingto the needs of the project. This is especially important whenthe faulty modules are rare.An industrial case study using classification trees, illustrates the tradeoffs.The trees were built using the TREEDISC algorithm whichis a refinement of the CHAID algorithm. We examinedtwo releases of a very large telecommunications system, and builtmodels suited to two points in the development life cycle: theend of coding and the end of beta testing. Both trees had onlyfive significant predictors, out of 28 and 42 candidates, respectively.We interpreted the structure of the classification trees, andwe found the models had useful accuracy.     

Reaction chemistry of gossypol and its derivatives

Gossypol, a complex polyphenolic compound, is a naturally occurring highly colored yellow pigment found in the small intercellular pigment glands in the leaves, stems, roots, and seed of cotton plants. In cottonseed, gossypol contributes to its toxicity and therefore it is regarded as an unwanted processing component. It was not until its antitumor and male infertility activities were discovered that gossypol was considered as a valueadded natural product from cottonseed with useful physiological and chemical properties. These serendipitous discoveries created much excitement, and an enormous amount of research on gossypol has ensued. Since then, much research has focused on the preparation of suitable gossypol derivatives for medicinal applications. This review summarizes current knowledge about gossypol, its stereochemistry, tautomerism, and the many varied reactions the gossypol molecule can undergo.     

论高职院校教育科学研究基地在管理中的作用

高职学院教育科学研究基地除了在人才培养模式改革中发挥重要作用之外,它在学院的管理中也发挥重要作用,具体表现为对学院管理工作的推动作用、引导作用和评价作用。     

Syntheses of Ferrocenyl Schiff Bases Using Molecular Sieves and AlCl3 as Catalysts

In order to study the donor ability of ferrocenylimines as directing ortho metalation group（DMG） to lithium alkylide to prepare planar chiral ferrocene, a series of ferrocenyl schiff bases were synthesized by new methods using molecular sieves（0.4nm） and AlCl3 as catalysts. The reaction periods were reduced using these two catalysts in contrast with Al2O3, which was a traditional method used in the literature. In addition, as an important feature of these schiff bases, we found that they were unstable as oils in air or when filtrated through silica gel, but were stable as solids. The structures of the new compounds were confirmed by IR, ^1H NMR and HRMS.     

卡尔曼滤波同时pH滴定法研究

将卡尔曼滤波(KF)递推算法，用于多组分同时pH滴定中，讨论了方法原理，pH通道的选挥，同时对二、三、四元系统混合酸(碱)试祥，进行了多次测定，获得满意结果。