ABSTRACT

The current research investigates the core partial order for its further properties. We introduce a new property for matrices of index at most 1, namely $(B-A{)}^{◯\mathrm{\#}}=B^{◯\mathrm{\#}}-A^{◯\mathrm{\#}}$ and is called as ‘the core-subtractivity’. This property then is used to explore relations between the powers and subtractivity properties of the core partial order. In particular, we prove that $A\stackrel{◯\mathrm{\#}}{\le }B$ is equivalent to $(B-A)\stackrel{◯\mathrm{\#}}{\le }B$ under the core-subtractivity property. We also examine some new conditions under which the core partial order is equivalent to the minus and diamond partial orders.

中文翻译：

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核心偏序的一些新结果

摘要

目前的研究调查了核心偏序的进一步属性。我们为索引至多为 1 的矩阵引入一个新的性质，即$(乙-\mathrm{一个}{)}^{◯\mathrm{\#}}={乙}^{◯\mathrm{\#}}-{\mathrm{一个}}^{◯\mathrm{\#}}$并被称为“核心减法”。然后，此属性用于探索核心偏序的幂和减法属性之间的关系。特别地，我们证明$\mathrm{一个}\stackrel{◯\mathrm{\#}}{\le }乙$相当于$(乙-\mathrm{一个})\stackrel{◯\mathrm{\#}}{\le }乙$在 core-subtractivity 属性下。我们还研究了一些新的条件，在这些条件下，核心偏序等价于减号和菱形偏序。