(*^
::[ Information =
"This is a Mathematica Notebook file. It contains ASCII text, and can be
transferred by email, ftp, or other text-file transfer utility. It should
be read or edited using a copy of Mathematica or MathReader. If you
received this as email, use your mail application or copy/paste to save
everything from the line containing (*^ down to the line containing ^*)
into a plain text file. On some systems you may have to give the file a
name ending with ".ma" to allow Mathematica to recognize it as a Notebook.
The line below identifies what version of Mathematica created this file,
but it can be opened using any other version as well.";
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MacintoshStandardFontEncoding;
fontset = title, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e8, 24, "Times";
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fontset = subsubtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, italic, e6, 14, "Times";
fontset = section, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, grayBox, M22, bold, a20, 18, "Times";
fontset = subsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, blackBox, M19, bold, a15, 14, "Times";
fontset = subsubsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, whiteBox, M18, bold, a12, 12, "Times";
fontset = text, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times";
fontset = smalltext, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 10, "Times";
fontset = input, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeInput, M42, N23, bold, L-3, 12, "Courier";
fontset = output, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-3, 12, "Courier";
fontset = message, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, R32768, L-3, 12, "Courier";
fontset = print, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-3, 12, "Courier";
fontset = info, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, B32768, L-3, 12, "Courier";
fontset = postscript, PostScript, formatAsPostScript, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeGraphics, M7, l34, w282, h287, 12, "Courier";
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paletteColors = 128; automaticGrouping; currentKernel;
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:[font = input; preserveAspect]
alpha = {-1/2, -1/3, -1/4, 1/5, 4/7, 3/2};
beta = {-1/6, 3/7, 13/11, -2/3, 2/5, 4/3};
concavity = alpha beta (beta - 1);
origin = {-2,-0.52, -0.52, -0.025, -0.025, -0.25};
vert = {{-2,0},{-0.5,0},{-0.5,0},{0,4},{0,1},{0,4}};
ticks = {{1},{1},{1},{1},{1},{1}};
plot[k_]:= Plot[alpha[[k]]t^beta[[k]],{t,0.001,2},
PlotRange->{{0,2},vert[[k]]},
Ticks->{Table[i-1,{i,5}],Automatic},
AxesOrigin->{-0.1,origin[[k]]},
PlotLabel->N[concavity[[k]]]];
Show[GraphicsArray[Transpose[{Table[plot[i],{i,3}],Table[plot[i],{i,4,6}]}]]]
^*)