at least on Windows AFAIK no close button is only possible if you disable the complete caption of the window which results in no minimize and maximize buttons too. However no minimize button is possible but you have to stay with the close button. All of this can be done using the Windows API and the SetWindowLong function inside a MEX function.
It migth be easier to implement your own CloseRequestFcn to prevent closing the figure as long the calculation runs. However getting the minimize button to do nothing is not possible from within MATLAB.
Use a small mex (mymex.c):
void mexFunction( int nlhs, mxArray *plhs, int nrhs, const mxArray *prhs)
if (nrhs == 1)
long value = GetWindowLong(*(HWND*)mxGetData(prhs), GWL_STYLE);
plhs = mxCreateLogicalScalar(SetWindowLong(*(HWND*)mxGetData(prhs),GWL_STYLE,(int)(value & ~WS_CAPTION)) > 0);
And call it from MATLAB
jFrame = get(handle(gcf),'JavaFrame');
hWnd = int32(jFrame.fHG1Client.getWindow.getHWnd);