复半正定矩阵的标准形及行列式模的不等式

建立了复半正定矩阵的复相合标准形,由此得到复半正定矩阵行列式模的两个重要不等式,推广了Ｏｓｔｒｏｗｓｋｉｉ－Ｔｕｓｓｋｙ不等式及李俊杰（１９９５）文中的结果。     

用面向对象方法求解图中树的数目的无误差计算

利用面向对象编程方法中的封装，重载等技术，分别生成有理数类和矩阵类来进行图中树的数目无误差计算。并通过链表解决实际计算中所存在的整数溢出问题，使得此方法可以对较大规模的图进行支撑树的计算。     

关于同余方程xs1＋ys2·k（mod n）的最小非零解

本文指出了文献[1]中的一个错误并得到了二元一次同余式xs1 ys2≡k (mod n) 的最小非零解的若干性质.     

关于Pell方程x~2-5(5n±2)y~2=-1(n≡-1(mod4))

讨论了形如x2-5(5n+2)y2=-1(n∈Z+,n≡-1(mod4),5n+2为素数)与x2-5(5n-2)y2=-1(n∈Z+,n≡-1(mod4),5n-2为素数)型Pell方程有正整数解的两个结论.     

Value management and model pluralism in climate science

Non-epistemic values pervade climate modelling, as is now well documented and widely discussed in the philosophy of climate science. Recently, Parker and Winsberg have drawn attention to what can be termed “epistemic inequality”: this is the risk that climate models might more accurately represent the future climates of the geographical regions prioritised by the values of the modellers. In this paper, we promote value management as a way of overcoming epistemic inequality. We argue that value management can be seriously considered as soon as the value-free ideal and inductive risk arguments commonly used to frame the discussions of value influence in climate science are replaced by alternative social accounts of objectivity. We consider objectivity in Longino's sense as well as strong objectivity in Harding's sense to be relevant options here, because they offer concrete proposals that can guide scientific practice in evaluating and designing so-called multi-model ensembles and, in fine, improve their capacity to quantify and express uncertainty in climate projections.     

乘法半群为矩形群的nil扩张的半环

研究了加法半群为半格、乘法半群为矩形群的nil扩张的半环,从半环的子集出发构造乘法半群上的关系,得到H-为半环(Reg(S),+,·)上同余关系的充要条件,给出了矩形群的nil扩张转化为矩形带的nil扩张条件,并将矩形群的nil扩张性质推广到矩形带的nil扩张和矩形群上。     

椭圆曲线y2=x3-17x+114的正整数点

利用唯一分解定理、同余的性质、Legendre符号的性质、奇偶数的性质、Pell方程的解的性质等初等方法证明了椭圆曲线y~2=x~3-17x+114无正整数点.     

非含幺逆半群的半格的同余对

首先通过一族非含幺逆地群Sα的同余对刻画了其半格的同余对,然后由逆半群Sα的半格的同余对刻画了各逆半群Sα的同余对.     

Heyting代数中同余关系的简化

给出了Heyting代数中同余关系的一种简单定义,这种定义并不改变全体滤子和全体同余关系之间的一一对应性,并且借助滤子证明了这种定义是Heyting代数作为泛代数的同余关系的简化。最后证明了全体滤子之集作为完备格同构于全体同余关系之集。