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<HTML
><HEAD
><TITLE
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BGCOLOR="#FFFFFF"
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><DIV
CLASS="ARTICLE"
><DIV
CLASS="SECT1"
><H1
CLASS="SECT1"
><A
NAME="JOELIB.DESCRIPTOR"
></A
>Descriptor</H1
><DIV
CLASS="SECT2"
><H2
CLASS="SECT2"
><A
NAME="JOELIB.DESCRIPTORS.KIERSHAPE1"
></A
>Kier Shape 1</H2
><P
>The Kier shape
<IMG
SRC="formulas/kier1.gif"> descriptor [<A
HREF="bibliography.html#TC00"
>tc00</A
>]
can be defined as :</P
><DIV
CLASS="EQUATION"
><A
NAME="AEN10"
></A
><P
><B
>Equation 1. Kier shape 1</B
></P
><DIV
CLASS="MEDIAOBJECT"
><P
><IMG
SRC="formulas/kier1_1.gif"
ALIGN="CENTER"></P
></DIV
></DIV
><P
><SPAN
CLASS="bold"
><B
CLASS="EMPHASIS"
>P<SUB
>max</SUB
></B
></SPAN
> is the maximum number of paths of length 1.
<SPAN
CLASS="bold"
><B
CLASS="EMPHASIS"
>P<SUB
>min</SUB
></B
></SPAN
> is the minimum number of paths of length 1 in a molecule graph of same
atom number.
<SPAN
CLASS="bold"
><B
CLASS="EMPHASIS"
>P1</B
></SPAN
> is the number of paths in the given molecule of length 1.
or:</P
><DIV
CLASS="EQUATION"
><A
NAME="AEN21"
></A
><P
><B
>Equation 2. Kier shape 1 (alternative formulation)</B
></P
><DIV
CLASS="MEDIAOBJECT"
><P
><IMG
SRC="formulas/kier1_2.gif"
ALIGN="CENTER"></P
></DIV
></DIV
><P
><SPAN
CLASS="bold"
><B
CLASS="EMPHASIS"
>A</B
></SPAN
> means the number of nodes in the molecules graph.
<SPAN
CLASS="bold"
><B
CLASS="EMPHASIS"
>P1</B
></SPAN
> is the number of paths of length 1 in the given molecule.</P
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