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Martin Maechler

2017-Jul-31 08:52 UTC

[R] Superscript and subscrib R for legend x-axis and y-axis and colour different subjects in longitudinal data with different colours

> Hi Rosa
> something like
> plot(1,1, sub=expression(lambda^"2"))
> So with your example, do you want something like
> plot(c(1:5), CRP7raw[1,], type = "n", xlim=c(1,5), ylim=c(-10,5)
,
>       xlab="Day in ICU",
>       ylab="CRP (mg/dL)",
>       sub = mtext(expression(lambda^2)))
OOps!   Either  plot( ...,  sub = *)
        or	plot( ... ) ; mtext(*)

but not both!
>  CRP7graph <- apply(CRP7, 1, lines, col="gray")
> Cheers
> Petr
> > -----Original Message-----
> > From: R-help [mailto:r-help-bounces at r-project.org] On Behalf Of
Rosa Oliveira
> > Sent: Friday, July 28, 2017 5:07 PM
> > To: r-help mailing list <r-help at r-project.org>; R-help at
r-project.org
> > Subject: [R] Superscript and subscrib R for legend x-axis and y-axis
and colour
> > different subjects in longitudinal data with different colours
> >
> > I am trying to make a x-axis and y-axis titles with both a special
character and a
> > subscript. I am not being able to do this. I think its just a placing
of my
> > parenthesis, but I've tried (seemingly) everything.
> >
> > Even more, when I try the blog users code it works.
> >
> >
> >
> > Is it because I?m using longitudinal data?
> >
> >
> >
> > Even more. Is it possible to colour each one of the 15 lines with a
different
> > colour?
> >
> >
> >
> >
> >
> >
> > library(ggplot2)
> > library(reshape)
> > library(lattice)
> > library(gtable)
> > library(grid)
> >
> > attach(mtcars)
> >
> > beta0 = rnorm (15, 1, .5)
> > beta1 = rnorm (15, -1, .5)
> >
> > tempo = seq(1:5)
> >
> > CRP7raw = matrix(NA, 15, 5)
> > CRP7 = matrix(NA, 15, 5)
> > CRP98raw = matrix(NA, 15, 5)
> > CRP98 = matrix(NA, 15, 5)
> >
> > crp <- for (i in 1:15) {
> >   CRP7raw[i,] = beta0[i] + beta1[i] * tempo
> >   CRP7[i,] =    CRP7raw[i,] + rnorm(5, 0, 2.14)
> >
> >   CRP98raw[i,] = beta0[i] + beta1[i] * tempo
> >   CRP98[i,] =    CRP98raw[i,] + rnorm(5, 0, .1)
> >                         }
> >
> >
> > # plot(c(1:5), CRP7raw[1,], type = "n", xlim=c(1,5),
ylim=c(-10,5) ,
> > #      xlab="Day in ICU",
> > #      ylab="CRP (mg/dL)",
> > #      sub = mtext(expression(paste(lambda)))
> > #
> > # CRP7graph <- apply(CRP7, 1, lines, col="gray")
> >
> >
> >
> >
> >
> >
> > # plot(c(1:5), CRP98raw[1,], type = "n", xlim=c(1,5),
ylim=c(-10,5),
> > #      xlab="Day in ICU",
> > #      ylab="CRP (mg/dL)")
> > # CRP98graph <- apply(CRP98, 1, lines, col="gray")
> >
> > par(mfrow=c(1,2))
> >
> > plot(c(1:5), CRP7raw[1,], type = "n", xlim=c(1,5),
ylim=c(-10,5) ,
> >      xlab="t_i",
> >      ylab="y_ij",
> >      sub = "lambda = 0.7")
> >
> >      CRP7graph <- apply(CRP7, 1, lines, col="gray")
> >
> >
> >      plot(c(1:5), CRP98raw[1,], type = "n", xlim=c(1,5),
ylim=c(-10,5),
> >           xlab="Day in ICU",
> >           ylab="CRP (mg/dL",
> >           sub = "lambda = 0.98")
> >      CRP98graph <- apply(CRP98, 1, lines, col="gray")
> >
> >
> >       [[alternative HTML version deleted]]
> >
> > ______________________________________________
> > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> > and provide commented, minimal, self-contained, reproducible code.
> ________________________________
> Tento e-mail a jak?koliv k n?mu p?ipojen? dokumenty jsou d?v?rn? a jsou
ur?eny pouze jeho adres?t?m.
> Jestli?e jste obdr?el(a) tento e-mail omylem, informujte laskav? neprodlen?
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> Odes?latel e-mailu neodpov?d? za eventu?ln? ?kodu zp?sobenou modifikacemi
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> V p??pad?, ?e je tento e-mail sou??st? obchodn?ho jedn?n?:
> - vyhrazuje si odes?latel pr?vo ukon?it kdykoliv jedn?n? o uzav?en?
smlouvy, a to z jak?hokoliv d?vodu i bez uveden? d?vodu.
> - a obsahuje-li nab?dku, je adres?t opr?vn?n nab?dku bezodkladn? p?ijmout;
Odes?latel tohoto e-mailu (nab?dky) vylu?uje p?ijet? nab?dky ze strany p??jemce
s dodatkem ?i odchylkou.
> - trv? odes?latel na tom, ?e p??slu?n? smlouva je uzav?ena teprve v?slovn?m
dosa?en?m shody na v?ech jej?ch n?le?itostech.
> - odes?latel tohoto emailu informuje, ?e nen? opr?vn?n uzav?rat za
spole?nost ??dn? smlouvy s v?jimkou p??pad?, kdy k tomu byl p?semn? zmocn?n nebo
p?semn? pov??en a takov? pov??en? nebo pln? moc byly adres?tovi tohoto emailu
p??padn? osob?, kterou adres?t zastupuje, p?edlo?eny nebo jejich existence je
adres?tovi ?i osob? j?m zastoupen? zn?m?.
> This e-mail and any documents attached to it may be confidential and are
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> If you received this e-mail by mistake, please immediately inform its
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authorized to use, disseminate, copy or disclose this e-mail in any manner.
> The sender of this e-mail shall not be liable for any possible damage
caused by modifications of the e-mail or by delay with transfer of the email.
> In case that this e-mail forms part of business dealings:
> - the sender reserves the right to end negotiations about entering into a
contract in any time, for any reason, and without stating any reasoning.
> - if the e-mail contains an offer, the recipient is entitled to immediately
accept such offer; The sender of this e-mail (offer) excludes any acceptance of
the offer on the part of the recipient containing any amendment or variation.
> - the sender insists on that the respective contract is concluded only upon
an express mutual agreement on all its aspects.
> - the sender of this e-mail informs that he/she is not authorized to enter
into any contracts on behalf of the company except for cases in which he/she is
expressly authorized to do so in writing, and such authorization or power of
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the person represented by the recipient.
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

PIKAL Petr

2017-Jul-31 09:11 UTC

head link

[R] Superscript and subscrib R for legend x-axis and y-axis and colour different subjects in longitudinal data with different colours

Hi Martin

see in line
> -----Original Message-----
> From: Martin Maechler [mailto:maechler at stat.math.ethz.ch]
> Sent: Monday, July 31, 2017 10:52 AM
> To: PIKAL Petr <petr.pikal at precheza.cz>
> Cc: Rosa Oliveira <rosita21 at gmail.com>; r-help mailing list
<r-help at r-
> project.org>
> Subject: Re: [R] Superscript and subscrib R for legend x-axis and y-axis
and
> colour different subjects in longitudinal data with different colours
>
>
> > Hi Rosa
> > something like
>
> > plot(1,1, sub=expression(lambda^"2"))
>
> > So with your example, do you want something like
>
> > plot(c(1:5), CRP7raw[1,], type = "n", xlim=c(1,5),
ylim=c(-10,5) ,
> >       xlab="Day in ICU",
> >       ylab="CRP (mg/dL)",
> >       sub = mtext(expression(lambda^2)))
>
> OOps!   Either  plot( ...,  sub = *)
>         or    plot( ... ) ; mtext(*)
>
> but not both!
You are right, I used a code from OP and did not much think about it. Strangely
enough, the code worked without any complain. Probably mtext is
"stronger" than sub and overrides it.

Cheers
Petr
>
> >  CRP7graph <- apply(CRP7, 1, lines, col="gray")
>
> > Cheers
> > Petr
>
>
> > > -----Original Message-----
> > > From: R-help [mailto:r-help-bounces at r-project.org] On Behalf
Of Rosa
> > > Oliveira
> > > Sent: Friday, July 28, 2017 5:07 PM
> > > To: r-help mailing list <r-help at r-project.org>; R-help
at r-project.org
> > > Subject: [R] Superscript and subscrib R for legend x-axis and
y-axis
> > > and colour different subjects in longitudinal data with different
> > > colours
> > >
> > > I am trying to make a x-axis and y-axis titles with both a
special
> > > character and a subscript. I am not being able to do this. I
think
> > > its just a placing of my parenthesis, but I've tried
(seemingly) everything.
> > >
> > > Even more, when I try the blog users code it works.
> > >
> > >
> > >
> > > Is it because I?m using longitudinal data?
> > >
> > >
> > >
> > > Even more. Is it possible to colour each one of the 15 lines with
a
> > > different colour?
> > >
> > >
> > >
> > >
> > >
> > >
> > > library(ggplot2)
> > > library(reshape)
> > > library(lattice)
> > > library(gtable)
> > > library(grid)
> > >
> > > attach(mtcars)
> > >
> > > beta0 = rnorm (15, 1, .5)
> > > beta1 = rnorm (15, -1, .5)
> > >
> > > tempo = seq(1:5)
> > >
> > > CRP7raw = matrix(NA, 15, 5)
> > > CRP7 = matrix(NA, 15, 5)
> > > CRP98raw = matrix(NA, 15, 5)
> > > CRP98 = matrix(NA, 15, 5)
> > >
> > > crp <- for (i in 1:15) {
> > >   CRP7raw[i,] = beta0[i] + beta1[i] * tempo
> > >   CRP7[i,] =    CRP7raw[i,] + rnorm(5, 0, 2.14)
> > >
> > >   CRP98raw[i,] = beta0[i] + beta1[i] * tempo
> > >   CRP98[i,] =    CRP98raw[i,] + rnorm(5, 0, .1)
> > >                         }
> > >
> > >
> > > # plot(c(1:5), CRP7raw[1,], type = "n", xlim=c(1,5),
ylim=c(-10,5) ,
> > > #      xlab="Day in ICU",
> > > #      ylab="CRP (mg/dL)",
> > > #      sub = mtext(expression(paste(lambda)))
> > > #
> > > # CRP7graph <- apply(CRP7, 1, lines, col="gray")
> > >
> > >
> > >
> > >
> > >
> > >
> > > # plot(c(1:5), CRP98raw[1,], type = "n", xlim=c(1,5),
ylim=c(-10,5),
> > > #      xlab="Day in ICU",
> > > #      ylab="CRP (mg/dL)")
> > > # CRP98graph <- apply(CRP98, 1, lines, col="gray")
> > >
> > > par(mfrow=c(1,2))
> > >
> > > plot(c(1:5), CRP7raw[1,], type = "n", xlim=c(1,5),
ylim=c(-10,5) ,
> > >      xlab="t_i",
> > >      ylab="y_ij",
> > >      sub = "lambda = 0.7")
> > >
> > >      CRP7graph <- apply(CRP7, 1, lines, col="gray")
> > >
> > >
> > >      plot(c(1:5), CRP98raw[1,], type = "n",
xlim=c(1,5), ylim=c(-10,5),
> > >           xlab="Day in ICU",
> > >           ylab="CRP (mg/dL",
> > >           sub = "lambda = 0.98")
> > >      CRP98graph <- apply(CRP98, 1, lines,
col="gray")
> > >
> > >
> > >       [[alternative HTML version deleted]]
> > >
> > > ______________________________________________
> > > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more,
see
> > > https://stat.ethz.ch/mailman/listinfo/r-help
> > > PLEASE do read the posting guide
> > > http://www.R-project.org/posting-guide.html
> > > and provide commented, minimal, self-contained, reproducible
code.
>
________________________________
Tento e-mail a jak?koliv k n?mu p?ipojen? dokumenty jsou d?v?rn? a jsou ur?eny
pouze jeho adres?t?m.
Jestli?e jste obdr?el(a) tento e-mail omylem, informujte laskav? neprodlen? jeho
odes?latele. Obsah tohoto emailu i s p??lohami a jeho kopie vyma?te ze sv?ho
syst?mu.
Nejste-li zam??len?m adres?tem tohoto emailu, nejste opr?vn?ni tento email
jakkoliv u??vat, roz?i?ovat, kop?rovat ?i zve?ej?ovat.
Odes?latel e-mailu neodpov?d? za eventu?ln? ?kodu zp?sobenou modifikacemi ?i
zpo?d?n?m p?enosu e-mailu.

V p??pad?, ?e je tento e-mail sou??st? obchodn?ho jedn?n?:
- vyhrazuje si odes?latel pr?vo ukon?it kdykoliv jedn?n? o uzav?en? smlouvy, a
to z jak?hokoliv d?vodu i bez uveden? d?vodu.
- a obsahuje-li nab?dku, je adres?t opr?vn?n nab?dku bezodkladn? p?ijmout;
Odes?latel tohoto e-mailu (nab?dky) vylu?uje p?ijet? nab?dky ze strany p??jemce
s dodatkem ?i odchylkou.
- trv? odes?latel na tom, ?e p??slu?n? smlouva je uzav?ena teprve v?slovn?m
dosa?en?m shody na v?ech jej?ch n?le?itostech.
- odes?latel tohoto emailu informuje, ?e nen? opr?vn?n uzav?rat za spole?nost
??dn? smlouvy s v?jimkou p??pad?, kdy k tomu byl p?semn? zmocn?n nebo p?semn?
pov??en a takov? pov??en? nebo pln? moc byly adres?tovi tohoto emailu p??padn?
osob?, kterou adres?t zastupuje, p?edlo?eny nebo jejich existence je adres?tovi
?i osob? j?m zastoupen? zn?m?.

This e-mail and any documents attached to it may be confidential and are
intended only for its intended recipients.
If you received this e-mail by mistake, please immediately inform its sender.
Delete the contents of this e-mail with all attachments and its copies from your
system.
If you are not the intended recipient of this e-mail, you are not authorized to
use, disseminate, copy or disclose this e-mail in any manner.
The sender of this e-mail shall not be liable for any possible damage caused by
modifications of the e-mail or by delay with transfer of the email.

In case that this e-mail forms part of business dealings:
- the sender reserves the right to end negotiations about entering into a
contract in any time, for any reason, and without stating any reasoning.
- if the e-mail contains an offer, the recipient is entitled to immediately
accept such offer; The sender of this e-mail (offer) excludes any acceptance of
the offer on the part of the recipient containing any amendment or variation.
- the sender insists on that the respective contract is concluded only upon an
express mutual agreement on all its aspects.
- the sender of this e-mail informs that he/she is not authorized to enter into
any contracts on behalf of the company except for cases in which he/she is
expressly authorized to do so in writing, and such authorization or power of
attorney is submitted to the recipient or the person represented by the
recipient, or the existence of such authorization is known to the recipient of
the person represented by the recipient.

Martin Maechler

2017-Jul-31 09:28 UTC

head link

[R] Superscript and subscrib R for legend x-axis and y-axis and colour different subjects in longitudinal data with different colours

>>>>> PIKAL Petr <petr.pikal at precheza.cz>
>>>>>     on Mon, 31 Jul 2017 09:11:18 +0000 writes:
    > Hi Martin see in line

    >> -----Original Message----- From: Martin Maechler
    >> [mailto:maechler at stat.math.ethz.ch] Sent: Monday, July
    >> 31, 2017 10:52 AM To: PIKAL Petr <petr.pikal at precheza.cz>
    >> Cc: Rosa Oliveira <rosita21 at gmail.com>; r-help mailing
    >> list <r-help at r-
    project.org> 
    >> Subject: Re: [R] Superscript and subscrib R for legend
    >> x-axis and y-axis and colour different subjects in
    >> longitudinal data with different colours
    >> 
    >> 
    >> > Hi Rosa > something like
    >> 
    >> > plot(1,1, sub=expression(lambda^"2"))
    >> 
    >> > So with your example, do you want something like
    >> 
    >> > plot(c(1:5), CRP7raw[1,], type = "n", xlim=c(1,5),
    >> ylim=c(-10,5) , > xlab="Day in ICU", >
ylab="CRP
    >> (mg/dL)", > sub = mtext(expression(lambda^2)))
    >> 
    >> OOps!  Either plot( ..., sub = *) or plot( ... ) ;
    >> mtext(*)
    >> 
    >> but not both!

    > You are right, I used a code from OP and did not much
    > think about it. Strangely enough, the code worked without
    > any complain. Probably mtext is "stronger" than sub and
    > overrides it.

Well, well, "the magic of R"  .....
Not quite:  mtext(..) is a valid function call that is evaluated
before plot() finishes; then it returns NULL invisibly, and
'plot(*, sub=NULL)' does nothing "coincidentally" (but for
good
reasons)

Martin

    > Cheers Petr

    >> 
    >> > CRP7graph <- apply(CRP7, 1, lines, col="gray")
    >> 
    >> > Cheers > Petr
    >> 
    >> 
    >> > > -----Original Message----- > > From: R-help
    >> [mailto:r-help-bounces at r-project.org] On Behalf Of Rosa >
    >> > Oliveira > > Sent: Friday, July 28, 2017 5:07 PM >
>
    >> To: r-help mailing list <r-help at r-project.org>;
    >> R-help at r-project.org > > Subject: [R] Superscript and
    >> subscrib R for legend x-axis and y-axis > > and colour
    >> different subjects in longitudinal data with different >
    >> > colours
    >> > >
    >> > > I am trying to make a x-axis and y-axis titles with
    >> both a special > > character and a subscript. I am not
    >> being able to do this. I think > > its just a placing of
    >> my parenthesis, but I've tried (seemingly) everything.
    >> > >
    >> > > Even more, when I try the blog users code it works.
    >> > >
    >> > >
    >> > >
    >> > > Is it because I?m using longitudinal data?
    >> > >
    >> > >
    >> > >
    >> > > Even more. Is it possible to colour each one of the
    >> 15 lines with a > > different colour?
    >> > >
    >> > >
    >> > >
    >> > >
    >> > >
    >> > >
    >> > > library(ggplot2) > > library(reshape) > >
    >> library(lattice) > > library(gtable) > > library(grid)
    >> > >
    >> > > attach(mtcars)
    >> > >
    >> > > beta0 = rnorm (15, 1, .5) > > beta1 = rnorm (15,
-1,
    >> .5)
    >> > >
    >> > > tempo = seq(1:5)
    >> > >
    >> > > CRP7raw = matrix(NA, 15, 5) > > CRP7 = matrix(NA,
15,
    >> 5) > > CRP98raw = matrix(NA, 15, 5) > > CRP98    
>> matrix(NA, 15, 5)
    >> > >
    >> > > crp <- for (i in 1:15) { > > CRP7raw[i,] =
beta0[i] +
    >> beta1[i] * tempo > > CRP7[i,] = CRP7raw[i,] + rnorm(5, 0,
    >> 2.14)
    >> > >
    >> > > CRP98raw[i,] = beta0[i] + beta1[i] * tempo > >
    >> CRP98[i,] = CRP98raw[i,] + rnorm(5, 0, .1) > > }
    >> > >
    >> > >
    >> > > # plot(c(1:5), CRP7raw[1,], type = "n",
xlim=c(1,5),
    >> ylim=c(-10,5) , > > # xlab="Day in ICU", > >
# ylab="CRP
    >> (mg/dL)", > > # sub = mtext(expression(paste(lambda)))
    >> > > #
    >> > > # CRP7graph <- apply(CRP7, 1, lines,
col="gray")
    >> > >
    >> > >
    >> > >
    >> > >
    >> > >
    >> > >
    >> > > # plot(c(1:5), CRP98raw[1,], type = "n",
xlim=c(1,5),
    >> ylim=c(-10,5), > > # xlab="Day in ICU", > > #
ylab="CRP
    >> (mg/dL)") > > # CRP98graph <- apply(CRP98, 1, lines,
    >> col="gray")
    >> > >
    >> > > par(mfrow=c(1,2))
    >> > >
    >> > > plot(c(1:5), CRP7raw[1,], type = "n",
xlim=c(1,5),
    >> ylim=c(-10,5) , > > xlab="t_i", > >
ylab="y_ij", > > sub
    >> = "lambda = 0.7")
    >> > >
    >> > > CRP7graph <- apply(CRP7, 1, lines,
col="gray")
    >> > >
    >> > >
    >> > > plot(c(1:5), CRP98raw[1,], type = "n",
xlim=c(1,5),
    >> ylim=c(-10,5), > > xlab="Day in ICU", > >
ylab="CRP
    >> (mg/dL", > > sub = "lambda = 0.98") > >
CRP98graph <-
    >> apply(CRP98, 1, lines, col="gray")
    >> > >
    >> > >
    >> > > [[alternative HTML version deleted]]
    >> > >
    >> > > ______________________________________________ > >
    >> R-help at r-project.org mailing list -- To UNSUBSCRIBE and
    >> more, see > >
    >> https://stat.ethz.ch/mailman/listinfo/r-help > > PLEASE
    >> do read the posting guide > >
    >> http://www.R-project.org/posting-guide.html > > and
    >> provide commented, minimal, self-contained, reproducible
    >> code.
    >> 

    > ________________________________ Tento e-mail a jak?koliv
    > k n?mu p?ipojen? dokumenty jsou d?v?rn? a jsou ur?eny
    > pouze jeho adres?t?m.  Jestli?e jste obdr?el(a) tento
    > e-mail omylem, informujte laskav? neprodlen? jeho
    > odes?latele. Obsah tohoto emailu i s p??lohami a jeho
    > kopie vyma?te ze sv?ho syst?mu.  Nejste-li zam??len?m
    > adres?tem tohoto emailu, nejste opr?vn?ni tento email
    > jakkoliv u??vat, roz?i?ovat, kop?rovat ?i zve?ej?ovat.
    > Odes?latel e-mailu neodpov?d? za eventu?ln? ?kodu
    > zp?sobenou modifikacemi ?i zpo?d?n?m p?enosu e-mailu.

    > V p??pad?, ?e je tento e-mail sou??st? obchodn?ho jedn?n?:
    > - vyhrazuje si odes?latel pr?vo ukon?it kdykoliv jedn?n? o
    > uzav?en? smlouvy, a to z jak?hokoliv d?vodu i bez uveden?
    > d?vodu.  - a obsahuje-li nab?dku, je adres?t opr?vn?n
    > nab?dku bezodkladn? p?ijmout; Odes?latel tohoto e-mailu
    > (nab?dky) vylu?uje p?ijet? nab?dky ze strany p??jemce s
    > dodatkem ?i odchylkou.  - trv? odes?latel na tom, ?e
    > p??slu?n? smlouva je uzav?ena teprve v?slovn?m dosa?en?m
    > shody na v?ech jej?ch n?le?itostech.  - odes?latel tohoto
    > emailu informuje, ?e nen? opr?vn?n uzav?rat za spole?nost
    > ??dn? smlouvy s v?jimkou p??pad?, kdy k tomu byl p?semn?
    > zmocn?n nebo p?semn? pov??en a takov? pov??en? nebo pln?
    > moc byly adres?tovi tohoto emailu p??padn? osob?, kterou
    > adres?t zastupuje, p?edlo?eny nebo jejich existence je
    > adres?tovi ?i osob? j?m zastoupen? zn?m?.

    > This e-mail and any documents attached to it may be
    > confidential and are intended only for its intended
    > recipients.  If you received this e-mail by mistake,
    > please immediately inform its sender. Delete the contents
    > of this e-mail with all attachments and its copies from
    > your system.  If you are not the intended recipient of
    > this e-mail, you are not authorized to use, disseminate,
    > copy or disclose this e-mail in any manner.  The sender of
    > this e-mail shall not be liable for any possible damage
    > caused by modifications of the e-mail or by delay with
    > transfer of the email.

    > In case that this e-mail forms part of business dealings:
    > - the sender reserves the right to end negotiations about
    > entering into a contract in any time, for any reason, and
    > without stating any reasoning.  - if the e-mail contains
    > an offer, the recipient is entitled to immediately accept
    > such offer; The sender of this e-mail (offer) excludes any
    > acceptance of the offer on the part of the recipient
    > containing any amendment or variation.  - the sender
    > insists on that the respective contract is concluded only
    > upon an express mutual agreement on all its aspects.  -
    > the sender of this e-mail informs that he/she is not
    > authorized to enter into any contracts on behalf of the
    > company except for cases in which he/she is expressly
    > authorized to do so in writing, and such authorization or
    > power of attorney is submitted to the recipient or the
    > person represented by the recipient, or the existence of
    > such authorization is known to the recipient of the person
    > represented by the recipient.

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