秩函数

This paper gives definitions of the closure operator, interior operator and complement operator in poset matroids, of which the underlying posets have an order-reversing involution, and then studies some properties of these operators.

本文将主要研究偏序集拟阵和模糊拟阵中的这些生成运算，要点及主要内容如下：一、给出了限制和收缩作用相等的一个充要条件，显示了秩函数在研究偏序集拟阵中的重要作用。

The study includes the fuzzy independent set, fuzzy bases, fuzzy circuits, fuzzy rank, fuzzy hyperplanes, fuzzy closure operator, fuzzy submatroid, quasi-fuzzy graph matroids, fuzzy graphic matroids, fuzzy dual matroid and so on.

研究的内容包括模糊拟阵的独立集，模糊基，模糊圈，模糊秩函数，模糊超平面，模糊闭包算子，模糊子拟阵，准模糊图拟阵，模糊图拟阵，模糊拟阵的对偶和模糊拟阵的运算等等。

The study includes fuzzy bases, fuzzy circuits, fuzzy rank function, fuzzy hyperplanes, fuzzy closure operator, fuzzy submatrods, quasi-fuzzy graph matroid, fuzzy graphic matroids, fuzzy dual matroid and so on.

研究的内容包括模糊拟阵的模糊基，模糊圈，模糊秩函数，模糊超平面，模糊闭包算子，模糊子拟阵，准模糊图拟阵，模糊图拟阵，模糊拟阵的对偶等等。

It is shown that for an exchange ring R, the lattice of directed convex subgroups of K〓 is isomorphic to the lattice of all stably co-finite and semiprimitive ideals of R.

作为特殊情形立得Goodearl的结果[41，定理15.20]，作为直接应用，给出了exchange环秩函数存性的一个新刻画。

In Section 5, we use the corank function of poset matroids to investigate the relationship between a poset matroid and its dual.

在第5节，我们用偏序集拟阵的余秩函数来研究偏序集拟阵与其对偶之间的关系。

In the last section, we characterize the combinatorial schemes in terms of rank, nullity and derivative functions.

第7节根据秩函数、零度函数和导出函数刻画了组合概型。

Since a partially ordered set has longitudinal and lateral structures, the characterization of poset matroids by rank function is much more complicated than that of the classical matoid.

因为一个偏序集有横向与纵向的结构，因此我们用秩函数来刻画偏序集拟阵要比刻画经典拟阵要复杂得多，但还是有章可寻。

We first prove that a directly finite exchange ring satisfying the comparability axiom has a unique rank function.

5.3证明了满足比较公理的直有限exchange存在唯一的秩函数。

Basing on the existing theory of crisp matroids and fuzzy matroids, the paper studies mainly fuzzy rank function and fuzzy submodularity function, The main contributions of the pap...

本文在现有拟阵和模糊拟阵理论的基础上主要研究了模糊秩函数以及模糊子模函数等内容，现分述如下：(1)从传统的子模函数出发，定义了模糊子模函数。

About the theory of the model errors, there are many theoretical problems to be solved, and many disscusional fields to be expanded and perfected.

但是测量平差中的模型误差的理论还有许多问题有待完善、扩展、深入，如函数模型可扩展到附有条件模型、概括函数模型、非线性模型；随机模型可扩展到相关、秩亏等情况；误差理论可扩展到线性近似误差。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。