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**_formulas
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LaTeX Font Warning: Font shape `U/stmry/b/n' undefined
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Overfull \hbox (54.0614pt too wide) detected at line 556
\OMS/cmsy/m/n/10 R [] [] \OT1/cmr/m/n/10 (\OML/cmm/m/it/10 x[]; [] ; x[]; y[]; 
[] ; y[]\OT1/cmr/m/n/10 )[] \OMS/cmsy/m/n/10 2 \U/msb/m/n/10 R[] [] \OT1/cmr/m/
n/10 (\OML/cmm/m/it/10 x[]; [] ; x[]\OT1/cmr/m/n/10 )[] \OMS/cmsy/m/n/10 2 P\OM
L/cmm/m/it/10 ; \OT1/cmr/m/n/10 (\OML/cmm/m/it/10 y[]; [] ; y[]\OT1/cmr/m/n/10 
)[] \OMS/cmsy/m/n/10 2 Q []\OML/cmm/m/it/10 :
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Overfull \hbox (28.23634pt too wide) detected at line 1016
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2 \U/msb/m/n/10 R[] [] \OT1/cmr/m/n/10 ([]\OML/cmm/m/it/10 ; []\OT1/cmr/m/n/10 
) \OMS/cmsy/m/n/10 2 \OML/cmm/m/it/10 ^^^  \OMS/cmsy/m/n/10 ([])  []h[]\OML/cmm
/m/it/10 ; []\OMS/cmsy/m/n/10 i \OT1/cmr/m/n/10 + \OML/cmm/m/it/10 b \OMS/cmsy/
m/n/10 ^^T \OML/cmm/m/it/10 w[] \OMS/cmsy/m/n/10 ^^T h[]\OML/cmm/m/it/10 ; []\O
MS/cmsy/m/n/10 i \OT1/cmr/m/n/10 + \OML/cmm/m/it/10 d[] \OMS/cmsy/m/n/10 ^ [][]
 \OML/cmm/m/it/10 w[] \OT1/cmr/m/n/10 = \OML/cmm/m/it/10 v[][]:
 []



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Overfull \hbox (9.41321pt too wide) detected at line 1084
\OMS/cmsy/m/n/10 8[] 2 \U/msb/m/n/10 R[]\OML/cmm/m/it/10 ; [] \OMS/cmsy/m/n/10 
2 \U/msb/m/n/10 R[] [] \OT1/cmr/m/n/10 ([]\OML/cmm/m/it/10 ; []\OT1/cmr/m/n/10 
) \OMS/cmsy/m/n/10 2 \OML/cmm/m/it/10 ^^^  \OMS/cmsy/m/n/10 ([])  []h[]\OML/cmm
/m/it/10 ; []\OMS/cmsy/m/n/10 i \OT1/cmr/m/n/10 + \OML/cmm/m/it/10 d [] \OMS/cm
sy/m/n/10 h[]\OML/cmm/m/it/10 ; []\OMS/cmsy/m/n/10 i \OT1/cmr/m/n/10 + \OML/cmm
/m/it/10 b[] \OMS/cmsy/m/n/10 ^ [][] \OML/cmm/m/it/10 w[] \OT1/cmr/m/n/10 = \OM
L/cmm/m/it/10 v[][]:
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Overfull \hbox (14.04169pt too wide) detected at line 1559
\OMS/cmsy/m/n/10 8[] 2 \U/msb/m/n/10 R[]\OML/cmm/m/it/10 ; [] \OMS/cmsy/m/n/10 
2 \U/msb/m/n/10 R[] [] \OT1/cmr/m/n/10 ([]\OML/cmm/m/it/10 ; []\OT1/cmr/m/n/10 
) \OMS/cmsy/m/n/10 2 \OML/cmm/m/it/10 ^^^  \OMS/cmsy/m/n/10 ([])  []h[]\OML/cmm
/m/it/10 ; []\OMS/cmsy/m/n/10 i \OT1/cmr/m/n/10 + \OML/cmm/m/it/10 d \OMS/cmsy/
m/n/10 ^^Q[] h[]\OML/cmm/m/it/10 ; []\OMS/cmsy/m/n/10 i \OT1/cmr/m/n/10 + \OML/
cmm/m/it/10 b[] \OMS/cmsy/m/n/10 ^ [][] \OML/cmm/m/it/10 w[] \OT1/cmr/m/n/10 = 
\OML/cmm/m/it/10 v[][]:
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! Missing $ inserted.
<inserted text> 
                $
l.1909 
       
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Display math should end with $$.
<to be read again> 
                   \tex_par:D 
l.1909 
       
The `$' that I just saw supposedly matches a previous `$$'.
So I shall assume that you typed `$$' both times.

! Missing $ inserted.
<inserted text> 
                $
l.1910   \left
              (i + \sum_{v \in V}i_{v}v\right)
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Missing $ inserted.
<inserted text> 
                $
l.1916 
       
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.


! LaTeX Error: Bad math environment delimiter.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1917 \]
         
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

! Missing $ inserted.
<inserted text> 
                $
l.1917 \]
         
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Display math should end with $$.
<to be read again> 
                   \endgroup 
l.1917 \]
         
The `$' that I just saw supposedly matches a previous `$$'.
So I shall assume that you typed `$$' both times.



[513]
! Missing $ inserted.
<inserted text> 
                $
l.1921 
       
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Display math should end with $$.
<to be read again> 
                   \tex_par:D 
l.1921 
       
The `$' that I just saw supposedly matches a previous `$$'.
So I shall assume that you typed `$$' both times.

! Missing $ inserted.
<inserted text> 
                $
l.1922   \left
              (i + \sum_{v \in V}i_{v}v\right)
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Missing $ inserted.
<inserted text> 
                $
l.1928 
       
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.


! LaTeX Error: Bad math environment delimiter.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1929 \]
         
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

! Missing $ inserted.
<inserted text> 
                $
l.1929 \]
         
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Display math should end with $$.
<to be read again> 
                   \endgroup 
l.1929 \]
         
The `$' that I just saw supposedly matches a previous `$$'.
So I shall assume that you typed `$$' both times.



[514]
! Missing $ inserted.
<inserted text> 
                $
l.1933 
       
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Display math should end with $$.
<to be read again> 
                   \tex_par:D 
l.1933 
       
The `$' that I just saw supposedly matches a previous `$$'.
So I shall assume that you typed `$$' both times.

! Missing $ inserted.
<inserted text> 
                $
l.1935   \amlf
              
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Missing $ inserted.
<inserted text> 
                $
l.1940 
       
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.


! LaTeX Error: Bad math environment delimiter.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1941 \]
         
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

! Missing $ inserted.
<inserted text> 
                $
l.1941 \]
         
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Display math should end with $$.
<to be read again> 
                   \endgroup 
l.1941 \]
         
The `$' that I just saw supposedly matches a previous `$$'.
So I shall assume that you typed `$$' both times.



[515]
! Missing $ inserted.
<inserted text> 
                $
l.1945 
       
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Display math should end with $$.
<to be read again> 
                   \tex_par:D 
l.1945 
       
The `$' that I just saw supposedly matches a previous `$$'.
So I shall assume that you typed `$$' both times.

! Missing $ inserted.
<inserted text> 
                $
l.1946   \left
              (i + \sum_{v \in V}i_{v}v\right)
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Missing $ inserted.
<inserted text> 
                $
l.1952 
       
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.


! LaTeX Error: Bad math environment delimiter.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.1953 \]
         
Your command was ignored.
Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

! Missing $ inserted.
<inserted text> 
                $
l.1953 \]
         
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Display math should end with $$.
<to be read again> 
                   \endgroup 
l.1953 \]
         
The `$' that I just saw supposedly matches a previous `$$'.
So I shall assume that you typed `$$' both times.



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Overfull \hbox (70.22289pt too wide) detected at line 2440
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10 a\OMS/cmsy/m/n/10 j\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 j\OML/cmm/m/it/10 b\O
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[] \OT1/cmr/m/n/10 [\OMS/cmsy/m/n/10 ^^@\OML/cmm/m/it/10 ^^L[]; ^^L[]\OT1/cmr/m
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/n/10 ) \OMS/cmsy/m/n/10 
[] \OT1/cmr/m/n/10 [\OMS/cmsy/m/n/10 ^^@\OML/cmm/m/it/10 ^^L[]; ^^L[]\OT1/cmr/m
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 []



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Overfull \hbox (130.9454pt too wide) detected at line 3101
\U/stmry/b/n/10 L\OML/cmm/m/it/10 e[] \OMS/cmsy/m/n/10 ^^H \OML/cmm/m/it/10 e[]
\U/stmry/b/n/10 M [] \OT1/cmr/m/n/10 = \U/stmry/b/n/10 L\OML/cmm/m/it/10 e[]\U/
stmry/b/n/10 M [] \U/msa/m/n/10 ^^A[] \U/stmry/b/n/10 L\OML/cmm/m/it/10 e[]\U/s
tmry/b/n/10 M [] \U/msa/m/n/10 ^^A[] \OML/cmm/m/it/10 "[] [] \U/msa/m/n/10 ^^A[
] \OML/cmm/m/it/10 "[] [] \U/msa/m/n/10 ^^A[] \OML/cmm/m/it/10 mf[]\OT1/cmr/m/n
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 []



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Overfull \hbox (130.9454pt too wide) detected at line 3153
\U/stmry/b/n/10 L\OML/cmm/m/it/10 e[] \OMS/cmsy/m/n/10 	 \OML/cmm/m/it/10 e[]\U
/stmry/b/n/10 M [] \OT1/cmr/m/n/10 = \U/stmry/b/n/10 L\OML/cmm/m/it/10 e[]\U/st
mry/b/n/10 M [] \U/msa/m/n/10 ^^L[] \U/stmry/b/n/10 L\OML/cmm/m/it/10 e[]\U/stm
ry/b/n/10 M [] \U/msa/m/n/10 ^^A[] \OML/cmm/m/it/10 "[] [] \U/msa/m/n/10 ^^A[] 
\OML/cmm/m/it/10 "[] [] \U/msa/m/n/10 ^^A[] \OML/cmm/m/it/10 mf[]\OT1/cmr/m/n/1
0 [\OMS/cmsy/m/n/10 ^^@\OT1/cmr/m/n/10 1\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 1]
 []



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Overfull \hbox (75.32413pt too wide) detected at line 3188
\U/stmry/b/n/10 L\OT1/cmr/m/n/10 [\OML/cmm/m/it/10 a; b\OT1/cmr/m/n/10 ] \OMS/c
msy/m/n/10 
 \OML/cmm/m/it/10 e[]\U/stmry/b/n/10 M [] \OT1/cmr/m/n/10 = [] \U/msa/m/n/10 ^^
A[] [] ^^A[] \OML/cmm/m/it/10 mf[]\OT1/cmr/m/n/10 [\OMS/cmsy/m/n/10 ^^@\OT1/cmr
/m/n/10 1\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 1]\OML/cmm/m/it/10 :
 []



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Overfull \hbox (75.32413pt too wide) detected at line 3257
\U/stmry/b/n/10 L\OML/cmm/m/it/10 e[] \OMS/cmsy/m/n/10  \OT1/cmr/m/n/10 [\OML/
cmm/m/it/10 a; b\OT1/cmr/m/n/10 ]\U/stmry/b/n/10 M [] \OT1/cmr/m/n/10 = [] \U/m
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 ^^@\OT1/cmr/m/n/10 1\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 1]\OML/cmm/m/it/10 ;
 []



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[894] (./_formulas.aux)
 ***********
LaTeX2e <2024-11-01> patch level 2
L3 programming layer <2025-01-18>
 ***********

LaTeX Font Warning: Some font shapes were not available, defaults substituted.

 ) 
Here is how much of TeX's memory you used:
 3173 strings out of 475103
 44414 string characters out of 5764903
 436540 words of memory out of 5000000
 26155 multiletter control sequences out of 15000+600000
 565453 words of font info for 62 fonts, out of 8000000 for 9000
 59 hyphenation exceptions out of 8191
 72i,13n,79p,226b,164s stack positions out of 10000i,1000n,20000p,200000b,10000s

Output written on _formulas.dvi (894 pages, 197732 bytes).
