Java might be redundant for Jupyter support
The installation instructions for the Jupyter Kernel say to install OpenJDK before installing Conda. However, running conda install jupyter-sysml-kernel will install the Conda package openjdk which seems to have the effect of reinstalling OpenJDK but only for that specific Conda environment.
Activating the Conda environment sets the JAVA_HOME environment variable to its own Java installation. If I understand Jupyter correctly, the kernel will always run in the environment it was installed with, so the manually installed OpenJDK won't ever be ran in Jupyter. If what I said is correct in all cases, the Java should be removed from the installation instructions.
I do agree on the fact that it is unnecessary to have an installation of java.
I tried to follow instructions with a Windows environment with miniconda and not setting any java env variable. First jupyter was not loading the kernel due to not finding the kernel file. At the end I had to change the kernel.json associatted to the jupyter-sysml-kernel to point to the path where there was the installed miniconda openjdk installation (if the env is activated I guess, as @NCGThompson points, the java openjdk should be directly recognized without having to change this line) and review that the -jar argument was pointing to the right path where the jupyter-sysml-kernel was actually installed (in my case by default it was pointing to a non existing pseudo linux distro dirpath)
It seems to load the kernel fine now, but the install.bat should be reviewed to automate the configuration.