2018年3月8日 · Let $H$ and $K$ be subgroups of $G$. Prove that $HK$ is a subgroup of $G$ if and only if $HK=KH$. In particular, the condition holds if $hk=kh$ for all $h$ in $H$ and $k$ in $K$.

Let $H$ and $K$ be subgroups of a group $G$. We know that $HK$ is a subgroup of $G$ if and only if $HK=KH$. Is it true that $HK$ is a subgroup of $G$ if and only if either $H$ or $K$ is a normal subgroup of $G$? Clearly if $H$ or $K$ is a normal subgroup of $G$, then $HK=KH$ which implies $HK$ is a subgroup of $G$.

2019年12月23日 · Hint the First: for arbitrary subgroups H and K, HK is a subgroup if and only if HK = KH as sets. Hint the Second: if K is normal, then for each h ∈ H, hK = Kh. As to your work: note that kh is not obviously in HK: it is a product of something in K by something in H, not of something in H by something in K.

水解常数(Hydrolysis equilibrium constant)即水解平衡常数。水解常数是表示水解的程度的量，常用符号Kh表示。盐类在溶液中，与水作用而改变溶液的酸碱性的反应叫作盐类的水解。

黄铁矿氧化产生的Fe^3+水解生成Fe (OH)3沉淀时，其水解常数kh=kw/ka (Fe^3+)=1×10^-14/6.3×10^-3≈1.6×10^-12，由此计算理论pH值可预测矿物表面反应进程，为生态修复方案提供数据支撑。 历史维度上，该关系式的建立与酸碱质子理论的发展密不可分。 1923年布朗斯特和劳莱提出质子理论后，科学家们逐步认识到水解反应本质是质子转移过程，由此将传统的水解常数与解离常数统一在质子理论框架下，这一理论突破使原先分散的化学现象获得了统一解释。 现代 …

2022年5月28日 · At 400 K, the root mean square (rms) speed of a gas × (mol. mass = 40 ) is equal to most probable speed of gas y at 60 K. Find the molecular mass of gas Y. Calculate the decrease in the vapour pressure when 1.81 g×10−2 kg of a solute (molecular mass = 57 ) is dissolved in 0.1 kg of water. Vapour pressure of water is 1.223x.

This means that KH helps neutralize acids and prevents your pH from changing too rapidly, which is useful because sudden pH crashes can cause health issues in your fish. Low KH means your water has less buffering capacity and the pH swings easily. High KH means your water has more buffering capacity and the pH level is hard to change.

2024年9月10日 · Learn how to maintain proper KH levels in your aquarium. Read our guide for tips on how to raise & lower KH in aquarium and ensuring a healthy tank environment!

2021年11月15日 · KH is probably the most important water quality parameter after salinity and temperature. More important maybe, than Phosphate. Corals can survive a wide range of Phosphate levels but if the KH is too low for a prolonged period, all aquarium corals will die.

2016年11月9日 · Let $H$ and $K$ be normal subgroups of $G$, if $H \cap K = \{e\}$ prove that $hk = kh$ for all $h \in H, k \in K$ [duplicate]