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For a visual, animated, description of basic behavior of such functions, I recommend: http://reference.wolfram.com/legacy/flash/ (You may want to turn on your computer's sound.)


These three functions are similar (speaking commonly), and in some applications any of them could be used, yet they have very different special applications. Rudimentarily: Map wraps (sub)expressions in a given Head, and returns the modified input Apply replaces Heads in (sub)expressions, and returns the modified input Scan "visits" (sub)expressions, ...


Specifying EdgeForm resolves the country borders. Latitude and longitude...well here is a clumsy way. Depending on your desired grid you may have to clean up conversion. myc[name_] := If[name == "UnitedStates", Red, Lighter[Gray]] lat = Quiet[ Line /@ Table[ Table[GeoGridPosition[GeoPosition[{j, k, 0}], "WinkelTripel"][[1, {1, 2}]], {j, ...


Padding additional brackets is not the right way to do it. You should use the right function for the task, which is Map: matrices = {{{3, 2}, {2, 3}}, {{3, 2}, {2, 3}}}; Eigenvalues /@ matrices If you're insistent on using Apply (why?), then the following ways work: Eigenvalues[{##}] & @@@ matrices Eigenvalues @@@ List /@ matrices


I got it: one has to put additional brackets around the first pure function: {({{foo[#1, #2], foo[#1, #1]}, {foo[#1, #1], foo[#1, #2]}})} & @@@ {{1, 2}, {1, 2}}


I was thinking about a more readable way because your question under rm's answer Any take on Q2 above? slightly indicates that you couldn't take it further although the idea to solve Q2 was similar. I guess my solution is in no way as easy as I had hoped it to be, but I give it anyway. What it does is that it separates the tasks a bit. The distributor ...


Here's a way to write out the map concisely: Q1: {1 - #, ##2} Through[Join[{1 &}, f]@#] & @@@ A (* {{1 - a1, b1 f1[a1], c1 f2[a1], d1 f3[a1], e1 f4[a1]}, {1 - a2, b2 f1[a2], c2 f2[a2], d2 f3[a2], e2 f4[a2]}, {1 - a3, b3 f1[a3], c3 f2[a3], d3 f3[a3], e3 f4[a3]}} *) Q2: Join[{1 - #[[1]]}, MapThread[#3 #@#2 &, {f, Most@#, Rest@#}]] ...

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