in a way that is not legally or officially acceptable

Many of the certified signatures were invalidly collected. 许多经认证的签名不是通过合法手段收集的。

They claimed that the election had been held, but invalidly. 他们声称选举已经举行，但并未得到官方的承认。

in a way that is not correct, usually because of not being logical or not based on correct information

These calculations invalidly compare a large country with many small ones. 这些计算方法无效地将一个大国与许多小国进行了比较。

They decided that the plea was invalidly entered. 他们认定抗辩无效。