text:
\section{Introduction}
Dyonic black holes are black holes which carry electric  and magnetic charges of some gauge fields. Some of the dyonic black holes can be realised as the solutions to the supergravity approximation to the critical Heterotic string theory compactified on $T^6$. The proposal for the exact degeneracy of microsates of dyons in the toroidally compactified critical Heterotic string theory
\cite{Dijkgraaf:1996it}-\cite{Shih:2005he}
with a negligible string coupling constat recently has been proved in the ref.\,\cite{David:2006yn}. The logarithm of the degeneracy of dyons defines the statistical entropy.

At the supergravity approximation the Hawking-Bekenstein entropy is in agreement with the large-charge-limit of the statistical entropy. The dominant string corrections to these dyons, the $\alpha'$ corrections, should be in agreement  with the large charge expansion series of the statistical entropy. Ref.\
\cite{Behrndt:1998eq}-\cite{LopesCardoso:2000fp}
 observed that upon the inclusion of the square of the Riemann tensor and a supersymmetric completion of that, the modified Hawking-Bekenstein entropy \cite{wald,wald2} is in agreement with the statistical entropy. Ref.\,\cite{int4} has shown that the inclusion of the Gauss-Bonnet action gives the same corrections in modified Hawking-Bekenstein entropy as those given by the inclusion of the supersymmetric version of the square of the Riemann tensor.

The Gauss-Bonnet Lagrangian or the supersymmetric version of the square of the Riemann tensor are not all the linear $\alpha'$ corrections to the dyonic black holes.  A priori it is not clear that why other linear $\alpha'$ should not contribute to the entropy. Ref.\,\cite{Kraus1,Kraus2} has proved certain non-renormalisation theorems establishing that for a certain family of supesymmetric black holes in the Heterotic string theories the results of the ref.\
\cite{Behrndt:1998eq}-\cite{LopesCardoso:2000fp} are in fact exact.

This work aims to  verify the results of the ref.\,\cite{Kraus1,Kraus2} versus a manifest calculation which takes into account all the four derivative corrections for an extremal supersymmetric dyonic black hole. In the first preprint \cite{Qasem} I left out the coupling of the gravitational Chern-Simons terms to the three form field strength. The authors of the ref.\,\cite{Bindusar} realised this left out and  they further computed the gravitational Chern-Simons corrections to the entropy, based on the frame work which they had developed earlier \cite{Bindusar2}. Here I shall calculate all the four derivative corrections, however excluding the  gravitational Chern-Simons terms, to the entropy. I verify that, as ref.\,\cite{Bindusar} concludes, after the inclusion of the gravitational Chern-Simons terms ``the resulting entropy  agrees perfectly with the results of earlier analysis, in accordance with the non-renormalisation theorems of the ref.\,\cite{Kraus1,Kraus2}''. The note is organised in the following way:

In the second section we consider the Low Energy Effective Action of the Heterotic string theory. We study a KK-compactification of the Heterotic string theory on $T^6$ which is relevant for a BPS static spherical four dimensional dyonic black hole representing a wrapped fundamental string  carrying arbitrary  winding and  momentum charges along one cycle in the presence of the KK-monopole and the H-monopole charges associated to another cycle. This solution is constructed in the ref.\,\cite{Cvetic:1995uj}.

The third section  presents all the linear $\alpha'$ corrections in the critical Heterotic string theory for the Bosonic (NS) backgrounds derived from the string amplitude considerations on a sphere \cite{stringamplitude1,stringamplitude2}.  The compactification process of the second section will be employed to account for all the linear $\alpha'$ corrections in the induced action. The $\alpha'$ corrections will be studied as perturbations outside the horizon. A boundary condition, hereby referred to as the H-boundary conditions, will be imposed on the linear $\alpha'$ corrections to insure that the $\alpha'$ corrections remain bounded on and outside the horizon. It will be noticed that the H-boundary conditions does not necessarily retain the fall off of the fields at the asymptotic infinity. Therefore the charges may receive corrections when the H-boundary conditions are imposed. The charges of the dyonic black hole retain their values  because there exists a scheme in which the dyonic black hole does not receive any $\alpha'$ corrections \cite{Cvetic:1995yq, Horowitz:1994rf}.

In the fourth section, having excluded the gravitational Chern-Simons terms, we shall calculate the induced action near the horizon configuration. We employ the attractor mechanism \cite{Ferrara:1995ih,Strominger:1996kf}  and the entropy formalism \cite{int4,int5} to calculate the modified Hawking-Bekenstein entropy. We will see that when we add the gravitational Chern-Simons corrections \cite{Bindusar} to the results then the linear $\alpha'$ corrections to the thermodynamical entropy is both in perfect agreement with the statistical entropy, and  in accordance  with the non-renormalisation theorems of the ref.\,\cite{Kraus1,Kraus2} .

\section{The compactification of the LEEA}
Let a ten-dimensional Riemannian manifold ${\boldsymbol{M}}_{10}$ homeomorphic to $M_4\times T^{6}$ be considered whose metric has six killing vectors in $T^6$ and $\boldsymbol{M}_{10}$ admits an asymptotically flat region. Let  $\boldsymbol{M}_{10}$ be endowed with a two-form and a scalar fields.  We represent the coordinate patch that covers the asymptotic flat region of $\boldsymbol{M}_{10}$ by $\boldsymbol{x}^{i}$ =$(t$, $x^1$, $x^2$, $x^3$, $y_1$, $y_2$, $z_1$, $\cdots$, $z_4)$ where $x^{\mu}=(t,\cdots,x^3)$ and $(y^m,z^m)=(y_1,y_2,z_1,\cdots,z_4)$ are coordinates respectively on $M_4$ and $T^6$ in such a way that $(dy_1,\cdots,dz_4)$ are the killing vectors. We refer to $x_\mu$ and ($y^m$,$z^m$) respectively as the four dimensions and the compactified space. The string theory can be  studied perturbatively at the vicinity of the asymptotic region of  $\boldsymbol{M}_{10}$ which is covered by $\boldsymbol{x}^i$. We look at this vicinity as a background of the metric, the NS-two form and the dilaton for the propagation of the critical Heterotic string theory,
\begin{eqnarray}
{\boldsymbol{ds^2}}&=&\sum_{\scriptscriptstyle{\mu,\nu=1}}^{4} \boldsymbol{g}_{\mu\nu} (x) dx^{\mu} dx^{\nu} +  \sum_{\scriptscriptstyle{m=1}}^{2}\{2\boldsymbol{g}_{y_m\mu}(x)\,dy_m\, dx^{\mu}+\boldsymbol{g}_{y_my_m}(x) dy_m^2\} +\sum_{\scriptscriptstyle{m=1}}^{4} dz_{m}^2\,,\nonumber\\
{\boldsymbol{B}}&=&\boldsymbol{B}_{\mu\nu}(x)dx^{\mu}\wedge dx^{\nu}+\boldsymbol{B}_{y_1\mu}(x) dx^{\mu}\wedge dy_1+\boldsymbol{B}_{y_2\mu}(x) dx^{\mu}\wedge dy_2\,,\\
{\boldsymbol{\phi}}&=&\boldsymbol{\phi}(x)\,.
\end{eqnarray}
We use the bold symbols to represent the fields in the ten dimensions. We rewrite the metric in the following form
\begin{equation}\label{themetric}
\boldsymbol{d}\boldsymbol{s}^2 = g_{\mu\nu}(x)\, dx^\mu dx^\nu + T_1(x)^2 (dy_1+2  A^1_{\mu}(x)dx^{\mu})^2+ T_2(x)^2(dy_2+2 A_\mu^2(x)dx^\mu)^2+ dz_m^2\,,
\end{equation}
where $g_{\mu\nu}$, $T_1$, $T_2$, $A^1_\mu$ and $A^2_\mu$ are employed to re-express the components of the ten dimensional metric in such a way that we shall see is more convenient. The metric (\ref{themetric}) is invariant under the following transformations
\begin{equation}
\left\{\begin{array}{l}
y_1 \to y_1 - 2 \Lambda^1(x)\\
A^1_\mu(x)\to A^1_\mu(x) + \partial_\mu \Lambda^1(x)
\end{array}
\hspace{1cm},
\right\{\begin{array}{l}
y_2 \to y_2 - 2 \Lambda^2(x)\\
A^2_\mu(x)\to A^2_\mu(x) + \partial_\mu \Lambda^2(x)
\end{array}
\end{equation}
where $\Lambda^1(x)$ and $\Lambda^2(x)$ are arbitrary scalars. These symmetries can be thought as remnants of the ten-dimensional diffeomorphism within the compactification process. We interpret $A^1_\mu(x)$ and $A^2_\mu(x)$ as two distinct $U(1)$ gauge connections in the four dimensions because they are vectors and they have $U(1)$ symmetries associated to them.

We rewrite the NS two-form in the following way
\begin{equation}\label{theB}
\boldsymbol{B} = B_{\mu\nu} dx^\mu\wedge dx^\nu
+ 2 A^3_\mu dx^\mu \wedge (dy_1+ 2 A^1_\nu dx^\nu)
+ 2 A^4_\mu dx^\mu \wedge (dy_2+ 2 A^2_\nu dx^\nu)\,,
\end{equation}
where $B_{\mu\nu}$,  $A^3_\mu$ and $A^4_\mu$ are used to re-express the components of the ten dimensional NS two-form in such a form to guaranty the  convenience in forthcoming computations. Note that the $U(1)$ transformations associated to $A^1_\mu(x)$ and $A^2_\mu(x)$ leave  intact $B_{\mu\nu}(x)$,  $A^3(x)$ and $A^4(x)$ because $dy_i+ 2 A^i_\nu dx^\nu$  is gauge invariant. The sigma model for the background we are considering is invariant under altering $\boldsymbol{B}$ by any exact two-form, i.e.
\begin{equation}
 \boldsymbol{B} \to \boldsymbol{B}+ \boldsymbol{d}\boldsymbol{\Lambda}\,,
\end{equation}
and thus the low energy action is invariant under the symmetry transformation given by $\boldsymbol{B} \to \boldsymbol{B}+ \boldsymbol{d}\boldsymbol{\Lambda}\,$.  A subset of these transformations is given by
\begin{displaymath}
\boldsymbol{\Lambda}=\Lambda_\mu(x) dx^\mu - \Lambda^3(x) dy_1 - \Lambda^4(x) dy_2\,,
\end{displaymath}
and this subset implies that the LEEA is invariant under
\begin{eqnarray}
B  &\to& B+ d \Lambda\,,\\
A^3_\mu(x)&\to& A^3_\mu(x) + \partial_\mu \Lambda^3(x)\,,\\
A^4_\mu(x)&\to& A^4_\mu(x) + \partial_\mu \Lambda^4(x)\,.
\end{eqnarray}
We see that independent $U(1)$ symmetries are associated to $A^3_\mu(x)$ and $A^4_\mu(x)$. These $U(1)$ symmetries are remnants of the gauge symmetries in the ten-dimensions. We interpret $A^3_\mu(x)$ and $A^4_\mu(x)$ as two new distinct gauge connections in the four dimensions.

Because of the symmetries of the metric we can choose a sufficiently large volume for any non-trivial cycle\footnote{A cycle which does not shrink to a point under any given homeomorphism.} in the compactified space within the patch of $\boldsymbol{x}^i$. Therefore we consistently ignore the world-sheet or the target space instantons corrections to the LEEA. The rest of the string corrections to LEEA respects the ten dimensional diffeomorphism symmetry group. Therefore the ten-dimensional low energy effective action can be written by
\begin{equation}\label{10Daction}
\boldsymbol{S}[\boldsymbol{B},\boldsymbol{g},\boldsymbol{\phi}]\, =\,\frac{1}{32\,\pi}\, \int\,d^{10}\boldsymbol{x}\sqrt{-\det \boldsymbol{g}}\, e^{-2\boldsymbol{\phi}}\, \boldsymbol{L}(\boldsymbol{B},\boldsymbol{g},\boldsymbol{\phi})\,,
\end{equation}
where $\boldsymbol{S}[\boldsymbol{B},\boldsymbol{g},\boldsymbol{\phi}]$ includes all the perturbative string corrections and it is invariant under the ten-dimensional diffeomorphism and $\boldsymbol{B} \to \boldsymbol{B}+ \boldsymbol{d}\boldsymbol{\Lambda}$.

Due to the presence of the gravitational Chern-Simons terms the Lagrangian density - $\boldsymbol{L}(\boldsymbol{B},\boldsymbol{g},\boldsymbol{\phi})$-  is not generically invariant under both the ten dimensional diffeomorphism and  gauge symmetry groups. Here we are going to calculate all the linear $\alpha'$ corrections but the gravitational Chern-Simons corrections, therefore we consider the perturbative string corrections which does not include the  gravitational Chern-Simons terms. From this time on we shall consider only this subset of the corrections. Within this subset $\boldsymbol{L}(\boldsymbol{B},\boldsymbol{g},\boldsymbol{\phi})$ can be written in a covariant form in terms of the ten dimensional Riemann tensor, the exterior derivative of $\boldsymbol{B}$, the dilaton and their covariant derivatives respect to the ten dimensional metric,
\begin{eqnarray}
\boldsymbol{L}(\boldsymbol{B},\boldsymbol{g},\boldsymbol{\phi})&=& \boldsymbol{L}(\boldsymbol{R}_{ijkl},\boldsymbol{d}\boldsymbol{B},\boldsymbol{\nabla})\\
\boldsymbol{S}[\boldsymbol{B},\boldsymbol{g},\boldsymbol{\phi}]& =&\frac{1}{32\,\pi}\, \int\,d^{10}\boldsymbol{x}\sqrt{-\det \boldsymbol{g}}\, e^{-2\boldsymbol{\phi}}\, \boldsymbol{L}(\boldsymbol{B},\boldsymbol{g},\boldsymbol{\phi})\,, \label{10Daction1}
\end{eqnarray}
To find the pullback of the action to four dimensions we insert eq.\,(\ref{themetric}) and (\ref{theB}) into the action (\ref{10Daction1}) and we obtain
\begin{equation}\label{4daction}
S\, = \,\frac{1}{32\,\pi}\,\int d^4x  \, \sqrt{-\det g}\, e^{-2\phi}\, L(g_{\mu\nu},B_{\mu\nu}, A^1_\mu,\cdots,A^4_\mu,T_1,T_2,\phi)\,,
\end{equation}
where the integration on the compactified space is understood and we have defined
\begin{equation}\label{thedilaton}
2 \phi = 2 \boldsymbol{\phi} - \ln T_1 - \ln T_2 - \ln V\,,
\end{equation}
and $V$ is the volume of the compactified space. We refer to the eq. (\ref{4daction}) as the induced action. The induced action and the induced lagrangian inherit the remnants symmetries of the ten dimensional action. Thus they are invariant under the four dimensional diffeomorphism group, four $U(1)$ symmetries associated to $A^1_\mu,\cdots,A^4_\mu$ and $B\rightarrow B+d\Lambda$. This means that the induced Lagrangian, for the considered subset of the corrections, is expressible in a covariant form in terms of the Riemann tensor constructed from $g_{\mu\nu}$, the exterior derivatives of the form fields, $T_1$, $T_2$, $\phi$ and their covariant derivatives respect to $g_{\mu\nu}$,
\begin{eqnarray}\label{inducedlagrangian}
{L}&=&{L}(R_{\mu\nu\lambda\eta}, dB, dA^1, \cdots, dA^4, T_1, T_2, \phi, g_{\mu\nu},\nabla_\mu)\,\blacksquare
\end{eqnarray}

\section{Dyonic black holes and the $\alpha'$ corrections}
In the supergravity approximation to the critical Heterotic string theory the action for backgrounds of the metric ($\boldsymbol{g}$), the NS two-form ($\boldsymbol{B}$) and the dilaton ($\boldsymbol{\phi}$ ) reads
\begin{eqnarray}\label{treelevelaction}
\boldsymbol{S}^{(0)}&=&\frac{1}{32 \pi }\int d^{10}\boldsymbol{x}\, \sqrt{-\det\boldsymbol{g}}\,e^{-2\boldsymbol{\phi}}\,({\boldsymbol{R}_{\scriptscriptstyle{\text{Ricci}}}} + 4 |\boldsymbol{\nabla} \boldsymbol{\phi}|^2 - \frac{1}{12} \boldsymbol{H}_{ijk}\boldsymbol{H}^{ijk})\,,
\end{eqnarray}
where
\begin{eqnarray}\label{defineH}
\boldsymbol{H}_{ijk}&=& \boldsymbol{d}\boldsymbol{B}\,=\, {3}\, \boldsymbol{B}_{[ij,k]}\,.
\end{eqnarray}
The linear $\alpha'$ corrections to this action, derived from three \cite{5Gross,5Nishino,5Cai} and four \cite{stringamplitude2,5Green, 5Schwarz} vertex operator insertions \cite{vertex}  in the string amplitude considerations on sphere, are\footnote{Note that ref.\,\cite{stringamplitude2} computed the linear $\alpha'$ corrections for the Heterotic and the Bosonic string theory. Eq. (\ref{LMT}) is  eq.\,(3.24) of the ref.\,\cite{stringamplitude2} for $\lambda_0=\frac{1}{8}$.}
\begin{eqnarray}\label{LMT}\nonumber
\boldsymbol{S}^{(1)}&=&\frac{1}{32 \pi }\int d^{10}\boldsymbol{x} \sqrt{-\det\boldsymbol{g}}~e^{-2\boldsymbol{\phi}}\,\frac{\alpha'}{8}\,\left( {\boldsymbol{R}_{klmn}\boldsymbol{R}^{klmn}}
-\frac{1}{2}\boldsymbol{R}_{klmn}\boldsymbol{H}_{p}^{~kl}\boldsymbol{H}^{pmn} \,\right.\\
&&\left.\hspace{2cm}-\frac{1}{8}\boldsymbol{H}_{k}^{~mn}\boldsymbol{H}_{lmn}\boldsymbol{H}^{kpq}\boldsymbol{H}^{l}_{~pq}
+\frac{1}{24}\boldsymbol{H}_{klm}\boldsymbol{H}^{k}_{~pq}\boldsymbol{H}_{r}^{~lp}\boldsymbol{H}^{rmq}\right)\,,
\end{eqnarray}
plus the Lorentz Chern-Simons term that could be reproduced  by substituting $\boldsymbol{H}$  in the eq.\,(\ref{treelevelaction}) with
\begin{eqnarray}\label{HH}
\boldsymbol{H}^{\star}&=& \boldsymbol{d}\boldsymbol{B}+ \frac{\alpha'}{4}\,\boldsymbol{\omega}_{3L}(\boldsymbol{\Omega})\,,
\end{eqnarray}
where $\boldsymbol{\omega}_{3L}(\boldsymbol{\Omega})$ encodes the gravitational Chern-Simon modification to $\boldsymbol{d}\boldsymbol{B}$. It is the insertion of three vertex functions that produces the Lorentz gravitational Chern-Simons term. Due to  the consistency of the Heterotic string around the flat space-time the eq.\,(\ref{LMT}) being derived from the string amplitude considerations should be in agreement with the related worldsheet-loop calculations of the corresponding sigma model. The corrections given by the eq.\,(\ref{LMT}) are all the four derivative corrections to the action. Thus the eq.\,(\ref{LMT}) should also be compatible with the anomaly cancellation mechanism \cite{DBranes} for the backgrounds of the vanishing $\text{Spin}(32)/Z_2$ or $E8 \times E8$ connection.

The contribution of the gravitation Chern-Simons corrections to the entropy for the dyon we are intersted in has been computed in the ref.\,\cite{Bindusar}. In this note we study all the linear $\alpha'$ corrections but the gravitational Chern-Simons correction to the entropy.   So  we do not include the gravitational Chern-Simons modification to $\boldsymbol{d}\boldsymbol{B}$ in the forthcoming computations and we shall use the eq.\,(\ref{defineH}) rather than the eq.\,(\ref{HH}). At the end we add the gravitation Chern-Simons corrections to the entropy \cite{Bindusar}.

We compactify the ten dimensional background to the four dimensions in the way that we presented in the previous section. This means that we rewrite the ten dimensional background by eq. (\ref{themetric}), (\ref{theB}) and (\ref{thedilaton}) in terms of the four dimensional background fields; the metric $g_{\mu\nu}$, the two-form $B_{\mu\nu}$, the four $U(1)$ gauge connections $A^1 \cdots A^4$ and the three scalars $T_1$, $T_2$ and $\phi$. It is not a hard task to obtain the explicit form of the induced action at the level of supergravity approximation,
\begin{eqnarray}\nonumber
S^{(0)}&=&\frac{1}{32\mathit{\pi}} \int\, d^4x\, \sqrt{-\det g}\,e^{-2\phi}
\left(R- \frac{|dB|^2}{12}+4 |\nabla \phi|^2 -  |\nabla \ln T_{1}|^2 - |{\nabla \ln T_{2}}|^2\right.\\
&&\hspace{3cm}\left.
-|T_{1}\,d A^{1}|^2
-|T_{2}\,d A^{2}|^2
-|\frac{d A^{3}}{T_{1} }|^2
-|\frac{d A^{4}}{T_{2} }|^2\right)\,,
\end{eqnarray}
where $R$ denotes the Ricci scalar of $g_{\mu\nu}$ and integrations by parts are understood. We do not obtain the explicit form of the linear $\alpha'$ corrections to the induced action. We suffice to present the linear $\alpha'$ corrections to the induced action by
\begin{eqnarray}
S^{(1)}&=& \frac{1}{32\, \mathit{\pi} }\int d^4x \, \sqrt{-\det g}\,e^{-2\phi} \,L^{(1)} \,,
\end{eqnarray}
and we know that $L^{(1)}$ is a functional of the four dimensional Riemann tensor, the gauge field strengths and their covariant derivatives,
\begin{eqnarray}
L^{(1)} &=&L^{(1)}(R_{\mu\nu\lambda\eta}, dB, dA^1, \cdots, dA^4, T_1, T_2, \phi, g_{\mu\nu},\nabla_\mu)\,.
\end{eqnarray}
At the level of the four dimensional supergravity approximation we consider a static spherical dyonic black hole which carries electric charges of $A^1$ and $A^3$ and magnetic charges of $A^2$ and $A^4$ in an asymptotically flat space-time. The electric charges of $A^1$ and $A^3$ represent respectively the KK-momentum and winding numbers of a fundamental string wrapped around the cycle of $y_1$. The magnetic charges of $A^2$ and $A^4$ represent respectively the KK-monopole and the H-monopole charges associated to the cycle of $y_2$. The explicit forms of the fields for this dyonic black hole are presented in the ref.\,\cite{Cvetic:1995uj}. When none of the charges is zero then the dyonic black hole has a regular horizon with geometry of $AdS_2\times S^2$ outside which the string loop corrections can be ignored. At the supergravity approximation the $SO(6,22)\times SL(2,Z)$ duality transformations can be applied on the dyonic black hole to obtain a general dyonic black hole \cite{SenOdd}. Reminiscent to T-duality and $\alpha'$ corrections \cite{martin,exir2,T1}, we expect that the duality transformations themselves get modified by the $\alpha'$ corrections. In this note we do not use the duality transformations. We consider a dyonic black hole with large  momentum, winding, KK-monopole and H-monopole charges and we study the $\alpha'$ corrections as perturbations on and outside its horizon.

Since we do have so many fields in the four dimensions we use a compact notation. Let $\Psi_i$ represent all the fields of the dyonic black hole in a compact fashion\footnote{This collective notation is constructed in analogy with the compact notation used in the ref.\,\cite{Seif}.},
\begin{eqnarray}
 \Psi_i &\in& \left\{ g_{\mu\nu}(x), T_1(x), T_2(x),  A_\mu^{1}(x), \cdots, A_\mu^{4}(x), \phi (x)\right\}\,.
\end{eqnarray}
The action for this compact notation follows
\begin{eqnarray}
S[\Psi] &=& S^{0}[\Psi] + \alpha' S^{1}[\Psi] + O(\alpha'^2)\,,
\end{eqnarray}
the equations of motion of which read
\begin{eqnarray}\label{PsiEq}
0\,=\,\dfrac{\delta S[\Psi]}{\delta \Psi_i} &=& \dfrac{\delta S^0[\Psi]}{\delta \Psi_i} + \alpha' \dfrac{\delta S^1[\Psi]}{\delta \Psi_i} + O(\alpha'^2)\,,
\end{eqnarray}
where $\frac{\delta{~}}{\delta \Psi_i}$ stands for the functional derivative respect to $\Psi_i$. Let us write an $\alpha'$ expansion series for $\Psi_i$ and next solve the eq.\,(\ref{PsiEq}) perturbatively,
\begin{eqnarray}
 \Psi_i & = & \Psi_i^0 + \alpha' \Psi^1_i + O(\alpha'^2) \,.
\end{eqnarray}
Inserting this perturbative expansion in the eq.\,(\ref{PsiEq})  gives
\begin{eqnarray}
\dfrac{\delta S^0[\Psi]}{\delta \Psi_i} \big{|}_{_{\alpha'=0}}+
\alpha' (\dfrac{\delta^2 S^0[\Psi]}{\delta \Psi_i\delta\Psi_j}\big{|}_{_{\alpha'=0}}\Psi^1_j+\dfrac{\delta S^1[\Psi]}{\delta \Psi_i}\big{|}_{_{\alpha'=0}}) + O(\alpha'^2)\,=\,0\,,
\end{eqnarray}
which implies
\begin{eqnarray}\label{SEQ}
\dfrac{\delta S^0[\Psi]}{\delta \Psi_i} \big{|}_{_{\alpha'=0}} &=& 0\,,\\\label{EQAlpha}
\dfrac{\delta^2 S^0[\Psi]}{\delta \Psi_i\delta\Psi_j}\big{|}_{_{\alpha'=0}}\Psi^1_j &=&-\dfrac{\delta S^1[\Psi]}{\delta \Psi_i}\big{|}_{_{\alpha'=0}} \,.
\end{eqnarray}
Note that the eq.\,(\ref{SEQ}) stands for the equations of motion at the supergravity approximation and the eq.\,(\ref{EQAlpha}) gives a set of non-homogeneous linear second order differential equations for $\{\Psi_i^1\}$ for any given solution at the supergravity approximation $\{\Psi_i^0\}$.

Let us first study the solutions to the homogeneous equations corresponding to the eq.\,(\ref{EQAlpha}),
\begin{eqnarray}\label{HomogeneousEquations}
\dfrac{\delta^2 S^0[\Psi]}{\delta \Psi_i\delta\Psi_j}\big{|}_{_{\alpha'=0}}\Psi^1_{j,B} &=&0\,.
\end{eqnarray}
These are the equations describing the fluctuations around $\Psi=\Psi_0$ at the supergravity approximation. For the dyonic black hole, the equation for a static spherical fluctuation of the dilaton in the canonical frame is simplified to
\begin{eqnarray}\label{HODILEQ}
\partial_r ((r-r_{\scriptscriptstyle{H}})^2\partial \phi^{1}_B) &=&0\,,
\end{eqnarray}
where $r_{\scriptscriptstyle{H}}$ is the radius of the horizon and $\phi^{1}_B$ is the fluctuation of the dilaton and we have used the explicit form of the background fields presented in the ref.\,\cite{Cvetic:1995uj}. The general solution of the eq.\,(\ref{HODILEQ}) is diverging on the horizon,
\begin{eqnarray}
\phi^{1}_B (r) &=& \frac{c_1}{r-r_{\scriptscriptstyle{H}}}+c_2\,.
\end{eqnarray}
The diverging mode of the dilaton fluctuations plays the role of the diverging source for the fluctuations of all other fields through their couplings to the dilaton. Thus the fluctuations of all other fields admit modes which  diverge on the horizon. Therefore we conclude that
\begin{quotation}
\hspace{-0.7cm} {\bf Lemma 1:} The general solutions to the homogeneous equations (\ref{HomogeneousEquations})  diverge on the horizon.
\end{quotation}
The  diverging  solutions on the horizon should be excluded by the boundary conditions if we are going to have a smooth solution outside the horizon. Let the following boundary conditions be introduced for the solutions of the eq.\,(\ref{EQAlpha})
\begin{eqnarray}\label{Hboundary}
\left\{
\begin{array}{rcl}
\Psi_i^1(x)\big{|_{_{x=\infty}}}&=&0\,,\\ \\
\Psi_i^1(x)\big{|_{_{x  \text{~on the Horizon}}}}&<&\infty \,,
\end{array}
\right.
\end{eqnarray}
We call the above boundary conditions  as the H-boundary conditions. The first condition of the H-boundary conditions sets the $\alpha'$ corrections to zero at infinity and its second condition excludes the diverging modes on the horizon. Depends on how we decide to represent the metric, some of the components of the metric may diverge on the horizon. For these components of the metric we  substitute the second condition of the H-boundary conditions by
\begin{eqnarray}\label{3.21}
 \lim_{ x\rightarrow\Sigma_h}\,\dfrac{\Psi_i^1(x)}{\Psi_i^0(x)}\,<\,\infty\,,
\end{eqnarray}
where $\Sigma_h$ represents any point on the event horizon. Because the $\alpha'$ corrections reach their largest values on the horizon then having fixed the symmetries the H-boundary conditions guaranty that $\Psi_i^1(x)$ is bounded outside the horizon,
\begin{eqnarray}
\Psi_i^1(x)&<&\infty~,~ \forall  |x|\in [r_H,\infty)\,.
\end{eqnarray}
Second order linear differential equations have two solutions. In general the H-boundary conditions exclude one of them  and identify the other one. There exits no further freedom to impose more constraints on the solutions. Thus we conclude that:
\begin{quotation}
\hspace{-0.7cm} {\bf Lemma 2:} The H-boundary conditions do not necessarily retain the fall off of the fields at asymptotic infinity.
\end{quotation}
Note that these lemmas are not in contradiction with the supersymmetry. If we knew the $\alpha'$  corrections to the onshell supersymmetric constraints then we could have used the supersymmetric constraints rather the equations of motions  to obtain a set of non-homogeneous first order linear differential equations for the $\alpha'$ corrections to the background fields. Requiring the $\alpha'$ corrections to vanish at infinity fixes all the boundary conditions for these first order equations. Thus again we could have concluded that the fall off of the fields at asymptotic infinity might receive $\alpha'$ corrections. In addition we learn that the diverging modes on the horizon are non-supersymmetric fluctuations on the supersymmetric background.

For the Schwarzschild black hole, it is showed  \cite{martin,CallanRCMyers} that imposing the H-boundary conditions   produces corrections to the Newtonian mass of the black hole since the mass is given by the fall off of the time-time component of the canonical metric at asymptotic infinity. The fall off of the fields identifies the charges of the dyonic black hole. Thus the second lemma implies that  the charges of the dyonic black hole might get modified by the $\alpha'$ corrections. Also note that this does not necessarily contradicts the charge quantisation since the quanta of the charge could receive corrections.

In the perturbative studies of the string scattering amplitudes one is allowed to redefine the fields,
\begin{eqnarray}\label{redefinition}
\tilde{\Psi}_i &=& \Psi_i\,+\, \alpha'\, \mathit{R_i}\,+\,O(\alpha'^2)
\end{eqnarray}
where $\mathit{R_i}$ are tensors of appropriate degree and dimension constructed from polynomials of $\Psi_i$ and their derivatives. The field redefinition alters  the induced action and subsequently  the equations of motion. For example a general field redefinition given by the eq.\,(\ref{redefinition}) changes the equations for the linear $\alpha'$ corrections (\ref{EQAlpha}) to,
\begin{eqnarray}\label{alpha-redefined}
\dfrac{\delta^2 S^0[\Psi]}{\delta \Psi_i\delta\Psi_j}\big{|}_{_{\alpha'=0}}\tilde{\Psi}^1_j &=&-\dfrac{\delta S^1[\Psi]}{\delta \Psi_i}\big{|}_{_{\alpha'=0}} - \dfrac{\delta^2 S^0[\Psi]}{\delta \Psi_i\delta\Psi_j}\big{|}_{_{\alpha'=0}}{\mathit{R_i}}\,.
\end{eqnarray}
 The field redefinition ambiguity is related to the freedom in choosing different renormalisation schemes and regularisation methods  in the sigma model. Ref.\,\cite{Cvetic:1995yq} has considered the dyonic black as a generalisation of the null chiral sigma models \cite{Horowitz:1994rf}  and has proven that there exists a scheme in which $\Psi_i^0$ does not receive any $\alpha'$ corrections. This means that there exists $\mathit{R_i}=\mathit{R_i}^\star$ for which the right hand side of the eq.\,(\ref{alpha-redefined}) vanishes and $\tilde{\Psi}^1_j=0$ is the solution to the eq.\,(\ref{alpha-redefined}). Thus the solution in the scheme where the $\alpha'$ corrections are given by the eq.\,(\ref{EQAlpha}) reads
\begin{eqnarray}
{\Psi}_i &=& \Psi_i^0\,-\, \alpha'\, \mathit{R_i}^\star\,+\,O(\alpha'^2)\,.
\end{eqnarray}
Since any field redefinition should contain two derivatives then the fall off of ${\Psi_i}$ at infinity, which is relevant for the charge identification, is the same as the one of $\Psi_i^0$ and we conclude that
\begin{quotation}
\hspace{-0.7cm} {\bf Lemma 3:} There exists no $\alpha'$ correction to the charges of the dyonic black hole.
\end{quotation}

\section{The $\alpha'$ corrections to the entropy of dyons}
The near horizon configuration of the dyonic black hole at the supergravity approximation is $AdS_2\times S^2$. When the horizon is large the $\alpha'$ corrections do not change the geometry of the horizon. Therefore the near horizon configuration of the $\alpha'$ corrected dyonic black hole can be written in the following way
\begin{eqnarray}
ds^2 &=& \mathit{v_1} (-r^2 d\tau^2 + \frac{dr^2}{r^2}) + \mathit{v_2} (d\theta^2 + \sin^2 \theta d\phi^2)\,,\\
T_1 &=& \mathit{T_1} ~,~ T_2\,=\,\mathit{T_2}~,~e^{-2\Phi}\,=\,\mathit{s}\,,\\\label{guagefieldsstrengths}
F^1_{r\tau}&=& \mathit{e_1}~,~F^{3}_{r\tau}\,=\,\mathit{e_3}~,~F^2_{\theta\phi}\,=\,\frac{\mathit{p_2}}{4\,\mathit{\pi}}\sin\theta
~,~F^4_{\theta\phi}\,=\,\frac{\mathit{p_4}}{4\,\mathit{\pi}}\sin\theta\,,
\end{eqnarray}
where the horizon in located at $r=0$ and $\mathit{v_1},\cdots,\mathit{p_4}$ are constant parameters labelling the horizon. Note that $\mathit{v_1}$ and $\mathit{v_2}$ are constant due to the geometry of the horizon and $\mathit{T_1}$, $\mathit{T_2}$, $\mathit{s}$ are constant since they represent the limit of $r\to 0$ of the scalars. $\mathit{e_1}$, $\mathit{e_3}$, $\mathit{p_2}$ and $\mathit{p_4}$ are constant due to the coordinates chosen to represent the background and in accordance with the supergravity approximation.

We have shown  that the part of the induced action which we are intersted in is a functional of the gauge field strengths but not of the gauge fields themselves. Thus the entropy formalism techniques \cite{int4,int5} can be employed to express the parameters of the near horizon configuration in terms of the charges of the dyonic black hole. The entropy formalism utilises the entropy function defined by
\begin{eqnarray}
f(\vec{\mathit{v}},\vec{\mathit{T}},\vec{\mathit{e}},\vec{\mathit{p}},\mathit{s})&=&\frac{1}{32\,\pi}\, \int d\theta d\phi \sqrt{-\det g}\, \mathit{s}\, L(\vec{\mathit{v}},\vec{\mathit{T}},\vec{\mathit{e}},\vec{\mathit{p}})\,,
\end{eqnarray}
where $L(\vec{\mathit{v}},\vec{\mathit{T}},\vec{\mathit{e}},\vec{\mathit{p}})$ is the induced Lagrangian (\ref{inducedlagrangian}) evaluated on the horizon configuration. The equations of motions are equivalent to
\begin{eqnarray}\label{theEQ}
\frac{\partial f(\vec{\mathit{v}},\vec{\mathit{T}},\vec{\mathit{e}},\vec{\mathit{p}},\mathit{s})}{\partial \mathit{v_i}} &=&0\,,\\
\nonumber
\frac{\partial f(\vec{\mathit{v}},\vec{\mathit{T}},\vec{\mathit{e}},\vec{\mathit{p}},\mathit{s})}{\partial \mathit{T_i}} &=&0\,,\\
\nonumber
\frac{\partial f(\vec{\mathit{v}},\vec{\mathit{T}},\vec{\mathit{e}},\vec{\mathit{p}},\mathit{s})}{\partial \mathit{s}} &=&0\,,\\
\nonumber
\frac{\partial f(\vec{v},\vec{\mathit{T}},\vec{e},\vec{p},\mathit{s})}{\partial \mathit{e_i}} &=& \mathit{q_{i}} ~,~i\in\{1,3\}\nonumber
\end{eqnarray}
where $\mathit{q_1}$ and $\mathit{q_3}$ are the electric charges of the dyonic black hole and $\mathit{p_2}$ and $\mathit{p_4}$ are identified as the magnetic charges. In the following we first obtain these equations and next we find their $\alpha'$ perturbative solutions.

To evaluate the induced action on the horizon configuration we use the eq. (\ref{themetric}), (\ref{theB}) and (\ref{thedilaton}) to reconstruct the ten dimensional fields for the near horizon configuration,
\begin{eqnarray}\label{tendg}
d\boldsymbol{s}^2&=& ds^2 + \mathit{T_1} (dy_1\,+\,2\, \mathit{e_1}\, r\, dt)^2 + \mathit{T_2} (dy_2\,-\,\frac{\mathit{p_2}}{2\pi}\,\cos\theta\, d\phi)^2\,+\,dz_m^2\,,\\\label{tendB}
\boldsymbol{B} &=& 2\,\mathit{e_3}\, r\, dt\wedge dy_1\, -\,\frac{\mathit{p_4}}{2\pi}\,\cos\theta\, d\phi\wedge dy_2\,,\\
e^{-2\boldsymbol{\phi}} &=&  {\displaystyle\frac{\mathit{s}} {\mathit{V}\,\mathit{T_1}\, \mathit{T_2}}}\,,
\end{eqnarray}
where $\mathit{V}$ is the volume of the compactified space and the gauges  (\ref{guagefieldsstrengths}) are chosen by
\begin{eqnarray}
A^1_{\mu} &=& [\mathit{e_1}\, r, 0, 0, 0]~,~ A^3_{\mu} \,=\, [\mathit{e_3}\, r, 0,0,0]\,,\\
A^2_{\mu} &=& [0, 0, 0, -\frac{\mathit{p_2}}{4\pi} \cos\theta]~,~ A^4_{\mu} \,=\, [0, 0, 0, -\frac{\mathit{p_4}}{4\pi} \cos\theta]\,.
\end{eqnarray}
In the ten dimensions using the ten dimensional fields - the eq. (\ref{tendg}) and (\ref{tendB})- one finds that
\begin{eqnarray}
\mathit{L_0}&=&{\boldsymbol{R}_{\scriptscriptstyle{\text{Ricci}}}} - \frac{1}{12}\boldsymbol{H}_{ijk}\boldsymbol{H}^{ijk}\,=\,\\ &=&
- {\displaystyle \frac {2}{\mathit{v_1}}}
+ {\displaystyle \frac {2}{\mathit{v_2}}}
+ {\displaystyle \frac {2\mathit{e_1}^{2}\mathit{T_1}^{2}}{\mathit{v_1}^{2}}}
+ {\displaystyle \frac {2\mathit{e_3}^{2}}{\mathit{v_1}^{2}\mathit{T_1}^{2}}}
-{\displaystyle \frac {\mathit{p_2}^{2}\mathit{T_2}^{2}}{8\mathit{v_2}^{2}\pi ^{2}}}
- {\displaystyle \frac {\mathit{p_4}^{2}}{8\mathit{v_2}^{2}\pi ^{2}\mathit{T_2}^{2}}},
\nonumber
\\
\nonumber
\\
\mathit{L_1}&=&
\frac{1}{8}{\boldsymbol{R}_{klmn}\boldsymbol{R}^{klmn}} \,=\,\\
&=&
+ {\displaystyle \frac {1}{2\,\mathit{v_1}^{2}}}
+ {\displaystyle \frac {1}{2\,\mathit{v_2}^{2}}}
- {\displaystyle \frac {3\mathit{e_1}^{2}\mathit{T_1}^{2}}{\mathit{v_1}^{3}}}
- {\displaystyle\frac {3\mathit{p_2}^{2}\mathit{T_2}^{2}}{16\,\mathit{v_2}^{3}\pi ^{2}}}
+ {\displaystyle \frac {11\mathit{T_1}^{4}\mathit{e_1}^{4}}{2\,\mathit{v_1}^{4}}}
+ {\displaystyle \frac {11\mathit{p_2}^{4}\mathit{T_2}^{4}}{512\,\mathit{v_2}^{4}\pi ^{4}}}
\,,
\nonumber\\
\nonumber\\
\mathit{L_2}&=&-\frac{1}{16}
\boldsymbol{R}_{klmn}\boldsymbol{H}_{p}^{~kl}\boldsymbol{H}^{pmn} \,=\,\\ \nonumber
&=&
- {\displaystyle \frac {\mathit{e_3}^{2}}{\mathit{v_1}^{3}\,\mathit{T_1}^{2}}}
- {\displaystyle \frac {\mathit{p_4}^{2}}{16\,\pi ^{2}\,\mathit{v_2}^{3}\,\mathit{T_2}^{2}}}
+ {\displaystyle \frac {\mathit{e_3}^{2}\,\mathit{e_1}^{2}}{\mathit{v_1}^{4}}}
+ {\displaystyle \frac {\mathit{p_4}^{2}\,\mathit{p_2}^{2}}{256\,\pi ^{4}\,\mathit{v_2}^{4}}}\,
,
\\
\mathit{L_3}&=&-\frac{1}{64}
\boldsymbol{H}_{k}^{~mn}\boldsymbol{H}_{lmn}\boldsymbol{H}^{kpq}\boldsymbol{H}^{l}_{~pq}\,=\,
- {\displaystyle \frac {3\,\mathit{e_3}^{4}}{\mathit{v_1}^{4}\,\mathit{T_1}^{4}}}
- {\displaystyle \frac{3\,\mathit{p_4}^{4}}{256\,\pi^{4}\,\mathit{v_2}^{4}\,\mathit{T_2}^{4}}}\,, \\
\mathit{L_4}&=&
\frac{1}{192}\boldsymbol{H}_{klm}\boldsymbol{H}^{k}_{~pq}\boldsymbol{H}_{r}^{~lp}\boldsymbol{H}^{rmq}\,=\,
{\displaystyle \frac {\mathit{e_3}^{4}}{2\,\mathit{v_1}^{4}\,\mathit{T_1}^{4}}}
 + {\displaystyle \frac {\mathit{p_4}^{4}}{512\,\pi ^{4}\,\mathit{v_2}^{4}\,\mathit{T_2}^{4}}} \,.
\end{eqnarray}
Inserting the above expressions in the ten dimensional action at the supergravity approximation (\ref{treelevelaction}) and its linear $\alpha'$ corrections (\ref{LMT}) gives
\begin{eqnarray}
S&=& \boldsymbol{S}\,=\,\frac{1}{32\pi}\int\,dt\,dr\,d\phi\,d\cos\theta~ \mathit{s}\,\mathit{v_1}\,\mathit{v_2}\,(\mathit{L_0}\,+\,\alpha'(\mathit{L_1}+\mathit{L_2}+\mathit{L_3}+\mathit{L_4})) + O(\alpha'^2)\,,\nonumber\\
\end{eqnarray}
where the integration over the compactified space is understood.\footnote{The idea of identifying the induced action near the horizon rather than in the whole of the space was used in the ref.\,\cite{Exirifard:2006wa} to study  the linear $\alpha'$ corrections for singular backgrounds representing a wrapped fundamental string.} Then the entropy function reads
\begin{eqnarray}\label{falpha}
f(\vec{\mathit{v}},\vec{\mathit{T}},\vec{\mathit{e}},\vec{\mathit{p}},\mathit{s}) & = &\frac{1}{8}\mathit{s}\,\mathit{v_1}\,\mathit{v_2}\,(\mathit{L_0}\,+\,\alpha'(\mathit{L_1}+\mathit{L_2}+\mathit{L_3}+\mathit{L_4})) + O(\alpha'^2)\,,
\end{eqnarray}
using which in the eq.\,(\ref{theEQ}) gives the equations of motion near the horizon. These equations should be solved perturbatively. Thus we write $\alpha'$ expansion series for the constant parameters labelling the horizon configuration,
\begin{eqnarray}\label{AH}
\mathit{v_i}&=& \mathit{v_i}^0\, (1\,+\, \alpha'\,\tilde{\mathit{v_i}}\, +\, O(\alpha'^2))\,,\\
\nonumber
\mathit{T_i}&=& \mathit{T_i}^0\, (1\, + \alpha'\,\tilde{\mathit{T_i}}\, +\, O(\alpha'^2))\,,\\
\nonumber
\mathit{e_i}&=& \mathit{e_i}^0\, (1\, + \alpha'\,\tilde{\mathit{e_i}}\, +\, O(\alpha'^2))\,,\\
\nonumber
\mathit{s}&=& \mathit{s}^0\, (1\, + \alpha'\,\tilde{\mathit{s}}\, +\, O(\alpha'^2))\,.
\end{eqnarray}
Not that the electric and magnetic charges are fixed to their values at the supergravity approximation because there exists no $\alpha'$ corrections to the charges of the dyonic black hole.
The equations of motion (\ref{theEQ}) at the supergravity approximation ($\alpha'=0$) are solved by
\begin{eqnarray}\label{HSA}
\mathit{v_1}^0 &=& \mathit{v_2}^0\,=\, \frac{\mathit{p_2}\,\mathit{p_4}}{4\,\pi^2}\,,\\
\nonumber
\mathit{T_1}^0 &=& \sqrt{\frac{\mathit{p_4}}{\mathit{p_2}}}~,~
\nonumber
\mathit{T_2}^0 \,=\,\sqrt{\frac{\mathit{q_1}}{\mathit{q_3}}}\,,\\
\nonumber
\mathit{e_1}^0 &=& \frac{1}{4\pi}\,\sqrt{\frac{{\mathit{q_3}\,\mathit{p_2}\,\mathit{p_4}}}{\mathit{q_1}}}~,~
\nonumber
\mathit{e_3}^0 \,=\, \frac{1}{4\pi}\,\sqrt{\frac{{\mathit{q_1}\,\mathit{p_2}\,\mathit{p_4}}}{\mathit{q_3}}}\,,\\
\nonumber
\mathit{s}^0 &=& 8 \,\pi \, \sqrt{\frac{\mathit{q_1}\,\mathit{q_3}}{\mathit{p_2}\,\mathit{p_4}}}\,.
\end{eqnarray}
These are the horizon configuration parameters at the supergravity approximation. Inserting the eq. (\ref{AH}) and (\ref{HSA}) in the eq.\,(\ref{theEQ}) gives a set of linear algebraic equations for the linear $\alpha'$ corrections (\ref{AH}) to the supergravity approximation (\ref{HSA}). These linear equations are solved by
\begin{eqnarray}
\tilde{\mathit{v}}_{\mathit{1}} &=& 0\,,\\
\frac{1}{2}\tilde{\mathit{v}}_{\mathit{2}}&=&\tilde{\mathit{T}}_{\mathit{2}}\,=\,-\,\tilde{\mathit{T}}_{\mathit{1}}\,=\,-\,\tilde{\mathit{s}}\,=\,
\tilde{\mathit{e}}_{\mathit{1}} \,=\,\tilde{\mathit{e}}_{\mathit{3}}\,=\,\frac{\pi^2}{\mathit{p_2}\,\mathit{p_4}}\,.
\end{eqnarray}
The modified Hawking-Bekenstein (Wald) entropy is expressed by the Legendre transformation of the entropy function
\begin{eqnarray}\label{Waldentropy}
S_{bh} &=& 2\,\pi\,(\mathit{e_1}\,\frac{\partial f(\vec{\mathit{v}},\vec{\mathit{T}},\vec{\mathit{e}},\vec{\mathit{p}},\mathit{s})}{\partial\mathit{e_1}}+\mathit{e_3}\,\frac{\partial f(\vec{\mathit{v}},\vec{\mathit{T}},\vec{\mathit{e}},\vec{\mathit{p}},\mathit{s})}{\partial\mathit{e_3}}-f(\vec{\mathit{v}},\vec{\mathit{T}},\vec{\mathit{e}},\vec{\mathit{p}},\mathit{s}))\,,
\end{eqnarray}
evaluated on the horizon configuration \cite{int4,int5}. Inserting the eq. (\ref{AH})  and  (\ref{HSA})  in the eq.\,(\ref{Waldentropy}) we get
\begin{eqnarray}\label{WaldEntropy1}
S_{bh} &=& \sqrt{\mathit{p_2}\,\mathit{p_4}\,\mathit{q_1}\,\mathit{q_3}}\,(1\,+\,\frac{\pi^2\,\alpha'}{\mathit{p_2}\,\mathit{p_4}})\,+\,O(\alpha'^2)\,.
\end{eqnarray}
We notice that Wald entropy does not depend on the values of $\tilde{\mathit{v}}_{\mathit{1}}$, $\tilde{\mathit{v}}_{\mathit{2}}$, $\tilde{\mathit{T}}_{\mathit{1}}$, $\tilde{\mathit{T}}_{\mathit{2}}$, $\tilde{\mathit{e}}_{\mathit{1}}$, $\tilde{\mathit{e}}_{\mathit{2}}$ and $\tilde{\mathit{s}}$.

To find all the linear $\alpha'$ corrections to the entropy we should add the contribution of the gravitational Chern-Simons term to the eq.\,(\ref{WaldEntropy1}). For the supersymmetric dyon the gravitational Chern-Simons corrections to the entropy reads \cite{Bindusar}
\begin{eqnarray}
S^{(1)}_{CS} &=& \sqrt{\mathit{p_2}\,\mathit{p_4}\,\mathit{q_1}\,\mathit{q_3}}\,(\frac{\pi^2\,\alpha'}{\mathit{p_2}\,\mathit{p_4}})\,+\,O(\alpha'^2)\,.
\end{eqnarray}
Adding this to the eq.\,(\ref{WaldEntropy1}) we find
\begin{eqnarray}\label{WaldEntropy}
S_{BH} &=& \sqrt{\mathit{p_2}\,\mathit{p_4}\,\mathit{q_1}\,\mathit{q_3}}\,(1\,+\,2\,\frac{\pi^2\,\alpha'}{\mathit{p_2}\,\mathit{p_4}})\,+\,O(\alpha'^2)\,,
\end{eqnarray}
as all the linear $\alpha'$ corrections to the entropy.

In the following we would like to compare all the linear  $\alpha'$ corrections to the entropy (\ref{WaldEntropy}) with the corrections given by only the inclusion of the Gauss-Bonnet Lagrangian in the induced action \cite{int4}. The square of the Riemann tensor of the four dimensional metric is
\begin{eqnarray}\label{R2}
\frac{1}{8}\,R_{ijkl}\,R^{ijkl} & = & \frac{1}{2\,\mathit{v_1}^2} \,+\, \frac{1}{2\,\mathit{v_2}^2}\,.
\end{eqnarray}
We see that the eq.\,(\ref{R2}) coincides with the first two terms in $\mathit{L_1}$. In total ten terms in $\mathit{L_1}+\mathit{L_2}+\mathit{L_3}+\mathit{L_4}$ are not given by the square of the Riemann tensor. The Gauss-Bonnet  Lagrangian in the four dimensions is
\begin{eqnarray}
L_{GB} &=& R_{ijkl}\,R^{ijkl} \,-\,4\,R_{ij}\,R^{ij}\,+\,R^2\,=\,-\,\frac{8}{\mathit{v_1}\,\mathit{v_2}}\,.
\end{eqnarray}
Including the Gauss-Bonnet action to the induced action at the supergravity approximation is equal to including the eq.\,(\ref{R2}) and performing a field redefinition. Thus ten terms in the linear $\alpha'$ corrections to the induced action are not produced by the inclusion of the Gauss-Bonnet action. The inclusion of the Gauss-Bonnet action in the induced action at supergravity approximation gives the following entropy function
\begin{eqnarray}\label{fGB}
f^\star &=& \frac{1}{8}\, \mathit{s}^\star\,\mathit{v_1}^\star\,\mathit{v_2}^\star\,(\mathit{L_0}\,+\,\frac{\alpha'}{8}\,L_{GB})
\,=\,\frac{1}{8}\,  \mathit{s}^\star\,\mathit{v_1}^\star\,\mathit{v_2}^\star\,\mathit{L_0}\,-\,\frac{\alpha'}{8}\,\mathit{s}^\star \,+\,O(\alpha')\,,
\end{eqnarray}
where we used the superscript $^\star$ to distinguish the near horizon parameters identified by the eq.\,(\ref{fGB}) with those identified by the eq.\,(\ref{falpha}).  This entropy function (\ref{fGB}) identifies the horizon configuration parameters to
\begin{eqnarray}
 \frac{\mathit{v_i}^\star}{\mathit{v_i}^0}\,=\,\frac{\mathit{e_i}^\star}{\mathit{e_i}^0}\,=\,1\,+\frac{2\,\pi^2 \,\alpha'}{\mathit{p_2}\,\mathit{p_4}}\,,~\frac{\mathit{T_i}^\star}{\mathit{T_i}^0}=1\,,~\frac{\mathit{s}^\star}{\mathit{s}^0}\,=\,1\,-\frac{2\pi^2 \,\alpha'}{\mathit{p_2}\,\mathit{p_4}}
\end{eqnarray}
where $v_1^0$, $\cdots$, $s^0$ are given by eq.\,(\ref{HSA}) and for which the entropy reads
\begin{eqnarray}\label{StatEntropy}
{S}_{GB} &=& \sqrt{\mathit{p_2}\,\mathit{p_4}\,\mathit{q_1}\,\mathit{q_3}}\,(1\,+\,\frac{2\,\pi^2\,\alpha'}{\mathit{p_2}\,\mathit{p_4}})\,+\,O(\alpha')\,,
\end{eqnarray}
Ref.\,\cite{int4} has included the Gauss-Bonnet action in the induced action at the supergravity approximation and has solved the corresponding truncated $\alpha'$-corrected  equations of motion exactly. We note that the eq.\,(\ref{StatEntropy}) is in agreement with the large charge expansion of eq.\,(3.13) of the ref.\,\cite{int4} after setting $n=2\,\mathit{q_1}$, $w=2\,\mathit{q_3}$, $\tilde{N}=\frac{\mathit{p_2}}{4\,\pi}$, $\tilde{W}=\frac{\mathit{p_4}}{4\,\pi}$ and using the unit of $\alpha'=16$.

 We notice that the eq.\,(\ref{StatEntropy}) is  in agreement with the eq.\,(\ref{WaldEntropy}) therefore we verify that all the linear $\alpha'$ corrections to the entropy of a supersymetric dyon with a large horizon can be reproduced by  the inclusion of only the Gauss-Bonnet Lagrangian to its Lagrangian density at the supergravity approximation. This is in accordance with the non-renormalisable theorems of the ref.\,\cite{Kraus1,Kraus2} and the conclusion of the ref.\,\cite{Bindusar}.

Also note that the inclusion of only the Gauss-Bonnet Lagrangian to the supergravity approximation is in agreement \cite{int4}  with  the inclusion of the supersymmetric version of the square of the Riemann tensor \cite{Behrndt:1998eq}-\cite{LopesCardoso:2000fp} which  in turn is in agreement with the large charge expansion series of the statistical entropy \cite{Dijkgraaf:1996it}-\cite{David:2006yn}, and thus all the linear $\alpha'$ corrections to the entropy are in agreement with the statistical entropy.

\section*{Acknowledgements}
I would like to thank Loriano Bonora and Martin O'loughlin for discussions throughout the work and careful reading of the draft. I would like to thank Justin David for discussions. I thank Marco Serone for discussions on the second section.

\providecommand{\href}[2]{#2}\begingroup\raggedright

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Nation to face drought conditions in next two months, weathermen warn
Laos is likely to face an acute water shortage over the next two months as rivers continue to fall to lower-than-normal levels.
In a long-term forecast issued on February 10, the Department of Meteorology and Hydrology under the Ministry of Natural Resources and Environment warned of the possibility of extreme conditions during the annual dry season.
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Home » Digital Humanities » Puerto Rican Labor » Puerto Ricans and Labor Organizing during the 1930s
Puerto Ricans and Labor Organizing during the 1930s
The Depression unleashed a torrent of working class organizing and protest in New York City. Both the Communist and Socialist Parties responded to the new desperate conditions, but the Communist Party connected most firmly with New York's Puerto Rican and other Spanish speaking communities. During the early 1930s the Communist Party organized its own militant industrial unions in competition with the unions affiliated with the American Federation of Labor or those associated with the Socialist Party. The Communist Party's Trade Union Unity League (TUUL) brought together these new unions as part of its class confrontational line. The Communist Party also organized hundreds of unemployed councils, leagues and workers committees which could mobilize mass protests quickly. The Party dissolved the TUUL in 1935 when it changed to a policy of alliances with a less revolutionary rhetoric even as its activists expanded their role in the growth of industrial unions and working-class movements during the late 1930s.
The TUUL had a Spanish-speaking local "bureau" in the Communist Party's Casa Obrera de Habla Espanola in East Harlem and a national Spanish-speaking desk in downtown Manhattan.[1] In 1931, the Party's Puerto Rican leader Alberto Sanchez followed the radicalized line of attacking "los lideres traidores del IWW," accusing them of being agents of capitalism.[2] Nearly all the industries in which Puerto Ricans concentrated experienced the surge of labor and Left organizing. This included docks, ships, garment shops, metal work plants, cafeterias, hotels, cigar shops, food processing plants, and so forth. In factory after factory, Puerto Rican workers (and a growing number of Spanish-speaking organizers) mobilized in defense of workers' ability to earn a living. At the Eagle pencil factory on East 14th St., a Communist Party-led organizing effort included Spanish speakers. At this plant, half the workers were fired, reducing the force by hundreds. By December, all 1100 workers were on strike. Vida Obrera, newspaper of the Hispanic Section of the Communist Party, reported hearing Juan Pacheco, a Puerto Rican Communist Party sympathizer and member of the strike committee spoke to workers at their meetings at the nearby Labor Temple on the "franco optimismo de la huelga…ahora mismo salimos todos para el 'picket line'". Pacheco reported that the police "ha castigado a una companera que hacia el 'picketing'…la companera se defendio valientemente, a pesar de que fue atacada de manera cobarde por dos policias." At one point 150 Spanish-speaking workers were formed in two files holding out signs and singing political songs.[3]
Puerto Rican laundry workers, most of them women, also came into contact with Communist Party-led organizing for their own unions (the WTUL) during the early 1930s. TUUL organizers demanded $20 a week and seven hour days, inviting the Spanish-speaking workers to join the "Cleaners and Laundry Workers League."[4] A WTUL led strike in 1934 received significant solidarity, including from Eleanor Roosevelt and her secret service agents.[5]
In 1930, Vida Obrera noted how many Spanish speakers had joined leftist unions as the TUUL expanded its drive to organize food, garment and other sectors. The Communist Party was astute about creating collectivities designed specifically to appeal to Latinos and Puerto Ricans. These relatively short lived efforts included the Asociacion Obrera Puertorriqueña, the Santiago Brooks (named after a Cuban Labor Leader), the Hispanic sections of the FWIU and the Needle Trades Workers Industrial union, the Hispanic section of the Anti-imperialist League of the Americas, The Liga Obrera Mexicana, the Centro Obrero de Habla Española de Brooklyn and Manhattan.[6]
The first years of the Depression led to severe reversals for garment workers and their unions. Massive layoffs meant unions lost most of their members, and wage cuts impoverished the workers. Sweatshop conditions returned to the city's factories. Puerto Rican women (and some men) had entered the garment industry in the 1920s, but numbers grew in the partial recovery after 1932. The largest garment union was the International Ladies Garment Workers Union (ILGWU), formed in 1900 and led by Jewish socialist immigrants, to unite many unions in the industry. ILGWU Local 22 became the largest local that agglomerated the core of the industry: the dressmakers.[7]
During the early 1930s, Local 22 was in a process of recovery. The Depression reduced employment in garment dramatically, and in 1929 Local 22 had been reduced to 8000 members.[8] By 1933 The NRA and the slow recovery created conditions for a new wave of organizing.[9] The leaders of Local 22 made their first explicit appeal to Spanish speaking workers in July 1931, inviting workers to a meeting with presentations in Spanish.[10] Local 22 was led by former Communist Party leader Charles (Sasha) Zimmerman and it quickly developed a positive reputation for being a critical part of the lives of thousands of Puerto Rican and Latina garment workers. Local 22 was very successful after the 1933 general strike and organizing drive and it recruited 2000 new Puerto Rican members, increasing dramatically its Hispanic membership.[11] The strike was a success and provided improvements: a 35-hour week, a 90/cent minimum and the prohibition of overtime (to force employers to spread out the available work to the largest number of workers). Puerto Rican women joined a growing membership within ILGWU which expanded to 200,000 including 3,000 Hispanics, 2,000 of which were in Local 22 and 700 in Local 91 (8%).[12] Local 22 had the largest concentration of Puerto Rican women in the industry. Spanish speaking members were 6.5% of Local 22 membership in the mid-1930s.[13] At Hudson Dress in East Harlem about 100 Spanish-speaking women with extremely low wages went on strike in October 1937, spurred by the organizers of Local 22. The workers sought to join the union and improve their wages.[14]
Continue to Puerto Ricans and Labor
Organizing during the 1930s Page 2
1] "Que debemos hacer por la Trade Union Unity League," Voz Obrera, September 1930.
[2]"Los lideres traidores…," Vida Obrera, 8 June 1931.
[3] Vida Obrera, 8 December 1930; Vida Obrera, 1 December 1930.
[4] Vida Obrera, 27 October 1930.
[5] Carson, Jennifer Lynn. ""It Takes Revolution and Evolution": New York City's Women Laundry Workers in the First Half of the Twentieth Century." Ph.D. Dissertation. University of Toronto, 2007, 158.
[6] Vida Obrera, 1 December 1930.
[7] Leeder, Elaine J. The Gentle General: Rose Pesotta, Anarchist and Labor Organizer. Albany, N.Y: State University of New York Press, 1993, 34; Nadel, Stanley. "Reds Versus Pinks: A Civil War in the International Ladies Garment Workers Union." New York History 66, no. 1 (1985): 48-72; Prickett, James Robert. "Communists and the Communist Issue in the American Labor Movement, 1920-1950." Ph.D., University of California, Los Angeles, 1975, Chap. 2; Katz, Daniel. "Race, Gender, and Labor Education: ILGWU Locals 22 and 91, 1933-1937." Labor's Heritage 11, no. 1 (2000): 4-19; Katz, Daniel. All Together Different : Yiddish Socialists, Garment Workers, and the Labor Roots of Multiculturalism. New York: New York University Press, 2011, 99.
[8] Katz, Daniel. All Together Different: Yiddish Socialists, Garment Workers, and the Labor Roots of Multiculturalism. New York: New York University Press, 2011, 112
[9] Estimate of unemployment, Local 22 membership, Zimmerman Papers, ILGWU Collection, Kheel Center, Cornell University.
[10]Katz, Daniel. All Together Different : Yiddish Socialists, Garment Workers, and the Labor Roots of Multiculturalism. New York: New York University Press, 2011, 114.
[11] Asher, Robert Stephenson Charles. Labor Divided: Race and Ethnicity in United States Labor Struggles, 1835-1960. Albany: State University of New York Press, 1990. Ortiz, Altagracia. "'En La Aguja y El Pedal Eche La Hiel': Puerto Rican Women in the Garment Industry of New York City, 1920-1980." In Puerto Rican Women and Work: Bridges in Transnational Labor, edited by Ortiz Altagracia. Philadelphia: Temple University Press, 1996; Laurentz, Robert. "Racial/Ethnic Conflict in the New York City Garment Industry, 1933-1980." Ph.D. Dissertation, State University of New York at Binghamton, 1980.
[12] Katz, Daniel. All Together Different: Yiddish Socialists, Garment Workers, and the Labor Roots of Multiculturalism. New York: New York University Press, 2011, 120-4, 135.
[13] Herberg, Will. "The Old-Timers and the Newcomers." Journal of Social Issues 9, no. 1 (1953): 12-19.
[14] La Voz, 20 October 1937.


text:
Twelve Centuries of English Poetry and Prose
Escrito por Alphonso Gerald Newcomer
a ship at a league's distance, beckoning with | his hand, straining his lungs, anil tearing his I throat; but all in vain:
'' Nec vox nee verba sequuntur.
"Nor voice, nor words ensued.
"We continued here three weeks in this dismal plight. At length, upon a turn of wind, the air about us began to thaw. Our cabin was immediately filled with a dry clattering sound, which I afterwards found to be the crackling of consonants that broke above our heads, and were often mixed with a gentle hissing, which I imputed to the letter s, that occurs so frequently in the English tongue. I soon after felt a breeze of whispers rushing by my ear; for those, being of a soft and gentle substance, immediately liquefied in the warm wind that blew across our cabin. These were soon followed by syllables and short words, and at length by entire sentences, that melted sooner or later, as they were more or less congealed; so that we now heard every thing that had been spoken during the whole three weeks that we had been silent, if I may use that expression. It was now very early in the morning, and yet, to my surprise, I heard somebody say, 'Sir John, it is midnight, and time for the ship's crew to go to-bed.' This I knew to be the pilot's voice; and, upon recollecting myself, I concluded that he had spoken these words to me some days before, though I could not hear them until the present thaw. My reader will easily imagine how the whole crew was amazed to hear every man talking, and see no man opening his mouth. In the midst of this great surprise we were all in, we heard a volley of oaths and curses, lasting for a long while, and uttered in a very hoarse voice, which I knew belonged to the boatswain, who was a very choleric fellow, and had taken his opportunity of cursing and swearing at me, when he thought I could not hear him; for I had several times given him the strappado'1 on that account, as I did not fail to repeat it for these his pious soliloquies, when I got him on shipboard.
'' I must not omit the names of several beauties in Wapping,« which were heard every now and then, in the midst of a long sigh that accompanied them; as, 'Dear Kate!' 'Pretty Mrs. Peggy!' 'When shall I see my Sue
s A severe form of mill- o A quarter of London t a r y punishment alone the Thames which usually din- frequented by sealocated the arms. men.
| again!' This betrayed several amours which had been concealed until that time, and furnished us with a great deal of mirth in our return to England.
"When this confusion of voices was pretty well over, though I was afraid to offer at speaking, as fearing I should not be heard, I proposed a visit to the Dutch cabin, which lay about a mile farther up in the country. My crew were extremely rejoiced to find they had again recovered their hearing; though every man uttered his voice with the same apprehensions that I had done,
"Et timide verba intermissa retentat.
'' And try'd his tongue, his silence softly broke.
"At about half-a-mile's distance from our cabin we heard the groanings of a bear, which at first startled us; but, upon enquiry, we were informed by some of our company, that he was dead, and now lay in salt, having been killed upon that very spot about a fortnight before, in the time of the frost. Not far from the same place, we were likewise entertained with some posthumous snarls, and barkings of a fox.
"We at length arrived at the little Dutch settlement; and, upon entering the room, found it filled with sighs that smelt of brandy, and several other unsavoury sounds, that were altogether inarticulate. My valet, who was an Irishman, fell into so great a rage at what he heard, that he drew his sword; but not knowing where to lay the blame, he put it up again. We were stunned with these confused noises, but did not hear a single word until about half-an-hour after; which I ascribed to the harsh and obdurate sounds of that language, which wanted more time than ours to melt, and become audible.
"After having here met with a very hearty welcome, we went to the cabin of the French, who, to make amends for their three weeks' silence, were talking and disputing with greater rapidity and confusion than I ever heard in an assembly, even of that nation. Their language, as I found, upon the first giving of the weather, fell asunder and dissolved. I was here convinced of an error, into which I had before fallen; for I fancied, that for the freezing of the sound, it was necessary for it to be wrapped up, and, as it were, preserved in breath: but I found my mistake when I heard the sound of a kit7 playing a minuet over our heads. I
7 A small fiddle.
asked the occasion of it; upon which one of the | company told me that it would play there I above a week longer; 'for,' says he, 'finding ourselves bereft of speech, we prevailed upon one of the company, who had his musical instrument about him, to play to us from morning to night; all which time was employed in dancing in order to dissipate our chagrin, ami titer Xe temps."*
Here Sir John gives very good philosophical reason, why the kit could not be heard during the frost; but, as they are something prolix, 1 pass them over in silence, and shall only observe, that the honourable author seems, by his quotations, to have been well versed in the ancient poets, which perhaps raised his fancy above the ordinary pitch of historians, and very much contributed to the embellishment of his writings.
A COQUETTE'S HEART.
The Spectator, No. 281. Tuesday, January 22, 1712.
Pectoribus inhians spirantia consulit exta.
Virg. ^En. iv. 64. Anxious the reeking entrails he consults.
Having already given an account of the dissection of a beau's head, with the several dis- | eoveries made on that occasion; I shall here, according to my promise, enter upon the dissection of a coquette's heart, and communicate to the public such particularities as we observed in that curious piece of anatomy.
I should perhaps^ have waived this undertaking, had not I been put in mind of my promise by several of my unknown correspondents, who are very importunate with me to make an example of the coquette, us I have already done of the beau. It is therefore, in compliance with the request of friends, that I have looked over the minutes of my former dream, in order to give the public an exact relation of it, which I fihall enter upon without farther preface.
Our operator, before he engaged in this visionary dissection, told us that there was nothing in his art more difficult than to lay open the heart of a coquette, by reason of the many labyrinths and recesses which are to be found in it, and which do not appear in the heart of any other animal.
He desired us first of all to observe the pericardium, or outward case of the heart,
K kill time
which we did very attentively; and by the help of our glasses discerned in it millions of little scars, which seemed to have been occasioned by the points of innumerable darts and arrows, that from time to time had glanced upou the outward coat; though we could not discover the smallest orifice by which any of them had entered and pierced the inward substance.
Every smatterer in anatomy knows that this pericardium, or case of the heart, contains in it a thin reddish liquor, supposed to be bred from the vapours which exhale out of the heart, and being stopped here, are condensed into this watery substance. Upon examining this liquor, we found that it had in it all the qualities of that spirit which is made use of in the thermometer to show the change of weather.
Nor must I here omit an experiment one of the company assured us he himself had made with this liquor, which he found in great quantity about the heart of a coquette whom he had formerly dissected. He affirmed to us, that he had actually inelosed it in a small tube made after the manner of a weather-glass; but that, instead of acquainting him with the variations of the atmosphere, it showed him the qualities of those persons who entered the room where it stood. He affirmed also, that it rose at the approach of a plume of feathers, an embroidered coat, or a pair of fringed gloves; ami that it fell as soon as an ill-shaped periwig, a clumsy pair of shoes, or an unfashionable coat came into his house. Nay, he proceeded so far as to assure us, that upon his laughing aloud when he stood by it, the liquor mounted very sensibly, and immediately sunk again upon his looking serious. In short, he told us that he knew very well by this invention, whenever he had a man of sense or :i coxcomb in his room.
Having cleared away the pericardium, or the case, and liquor above-mentioned, we came to the heart itself. The outward surface of it was extremely slippery, and the mucro, or point, so very cold withal, that upon endeavouring to take hold of it, it glided through the fingers like a smooth piece of ice.
The fibres were turned and twisted in a more intricate and perplexed manner than they are usually found in other hearts; insomuch that the whole heart was wound up together like a tiordian knot, and must have had very irregular and unequal motions, while it was employed in its vital function.
One thing we thought very observable, namely, that upon examining all the vessels which came into it, or issued nut of it, we could not discover any communication th:it it liail witU the tongue.
We could not but take notire likewise that M-veral of those little nerves in the heart which are affected by the sentiments of love, hatred, and other passions, did not descend to this before us from the brain, but from the muscles which lie about the eye.
lTpon weighing the heart in my hand, I found it to be extremely light, and consequently ipry hollow, which I did not wonder at, when, u|wn looking into the inside of it, 1 saw multitudes of cells and cavities running one within another, as our historians describe the apartments of Kosamond's bower.* Several of these little hollows were stuffed with innumerable sorts of trifles, which I shall forbear giving any particular account of, and shall, therefore, only take notice of what lay first and uppermost, which, upon our unfolding it, and applying our microscopes to it, nppeared to be a flame-coloured hood.
We are informed that the lady of this heart, when living, received the addresses of several who made love to her, and did not only give each of them encouragement, but made everyone she conversed with believe that she regarded him with an eye of kindness; for which reason we expected to have seen the impression of multitudes of faces among the several plaits and foldings of the heart; but to our great surprise not a single print of this nature discovered itself till wo came into the very core and rent re of it. We there observed a little figure, which, upon applying our glasses to it, appeared dressed in a very fantastic manner. The more 1 looked upon it, the more I thought I had seen the face before, but could not possibly recollect either the place or time; when at length one of the company, who had examined this figure more nicely than the rest, showed us plainly by the make of its fare, and the several turns of its features, that the little idol which was thus lodged in the very middle of the heart was the deceased beau, whose head 1 gave some account of in my last Tuesday's paper.
As soon as we had finished our dissection, we resolved to make an experiment of the heart, not being able to determine among ourselves the nature of its substance, which differed in so many particulars from that in the heart of other females. Accordingly, we laid it into a
• Henry IT., it was said. Imtlt a labyrinth to conceal the abode of "Fair Rosamond."
pan of bnniing coals, when we observed in it a certain salamandrine quality, that made it capable of living in the midst of tire and tlame, without being consumed or so much as singed.
As we were admiring this strange phenomenon, and standing round the heart in a circle, it gave a most prodigious sigh, or rather crack, and dispersed all at once in smoke and vapour. This imaginary noise, which methought was louder than the burst of a cannon, produced such a violent shake in my brain, that it dissipated the fumes of sleep, and left me in an instant broad awake.
THE VISION OF MIRZA.
The Spectator, Sn. 159. Saturday, September 1, 1711.
—Omneni, qua1 nunc obducta tuenti Mortales hebetat visus tihi. et humida circum Caligat. imbem eripiam—
Virg. ^En. ii. 604.
The cloud, which, intercepting the clear light, Hangs o 'cr thy eyes, and blunts thy mortal
sight, I will remove—
When I was at Grand Cairo, I picked up several Oriental manuscripts, which I have still by me. Among others I met with one entitled The Visions of Mirzn, which I have read over with great pleasure. I intend to give it to the public when 1 have no other entertainment for them; and shall begin with the first vision, which I have translated word for word as follows:—
"On the fifth day of the moon, which according to the custom of my forefathers I always keep holy, after having washed myself, and offered up my morning devotions, I ascended the high hills of Bagdad, in order to pass the rest of the day in meditation and prayer. As 1 was here airing myself on the tops of the mountains, 1 fell into a profound ! contemplation on the vanity of human life; and passing from one thought to another, 'Surely,' said I, 'man is but a shadow, and life a dream.' Whilst I was thus musing, I cast my eyes towards the summit of a rock that was not far from me, where I discovered one in the habit of a shepherd, with a musical instrument in his hand. As I looked upon him he applied it to his lips, and began to play upon it. The sound of it was exceedingly sweet, and wrought into a variety of tunes that were inexpressibly melodious, and altogether different from anything I had ever heard. They put me in mind of those heavenly airs that are played to the departed souls of good men upon their first arrival in Paradise, to wear out the impressions of their last agonies, and qualify them for the pleasures of that happy place. My heart melted away in secret raptures.
'' I had been often told that the rock before me was the haunt of a Genius ;> and that several had been entertained with music who had passed by it, but never heard that the musician had before made himself visible. When he had raised my thoughts by those transporting airs which he played to taste the pleasures of his conversation, as I looked upon him like one astonished, he beckoned to me, and by the waving of his hand directed me to approach the place where he sat. I drew near with that reverence which is due to a superior nature; and as my heart was entirely subdued by the captivating strains I had heard, I fell down at his feet and wept. The Genius smiled upon me with a look of compassion and affability that familiarized him to my imagination, and at once dispelled all the fears and apprehensions with which I approached him. He lifted me from the ground, and taking me by the hand, 'Mir/.a,' said he, 'I have heard thee in thy soliloquies; follow me.'
"He then led me to the highest pinnacle of ithe rock, and placing me on the top of it, 'Cast thy eyes eastward,' said he, 'and tell me what thou seest.' 'I see,' said I, 'a huge valley, :and a prodigious tide of water rolling through it.' 'The valley that thou seest,' said he, 'is the Vale of Misery, and the tide of water that thou seest is part of the great Tide of Eternity.' 'What is the reason,' said I, 'that the tide I see rises out of a thick mist at one end, and again loses itself in a thick mist at the other?' 'What thou seest,' said he, 'is that portion of eternity which is called time, measured out by the sun, and reaching from the beginning of the world to its consummation. Examine now,' said he, 'this sea that is bounded with darkness at both ends, and tell me what thou discoverest in it.' 'I see a bridge,' said I, 'standing in the midst of the tide.' 'The bridge thou seest,' said he, 'is Human Life: consider it attentively.' Upon a more leisurely survey of it, I found that it consisted of threescore and ten entire arches, with several broken arches, which added to those that were entire,
1 spirit
made up the number about a hundred. As I was counting the arches, the Genius told mo that this bridge consisted at first of a thousand arches; but that a great flood swept away the rest, and left the bridge in the ruinous condition I now beheld it. 'But tell me farther,' said he, 'what thou discoverest on it.' 'I sec multitudes of people passing over it,' said I, 'and a black cloud hanging on each end of it.' As 1 looked more attentively, I saw several of the passengers dropping through the bridge into the great tide that flowed underneath it; and upon farther examination, perceived there were innumerable trap-doors that lay concealed in the bridge, which the passengers no sooner trod upon, but they fell through them into the tide, and immediately disappeared. These hidden pit-falls were set very thick at the entrance of the bridge, so that throngs of people no sooner broke through the cloud, but many of them fell into them. They grew thinner towards the middle, but multiplied and lay closer together towards the end of the arches that were entire.
"There were indeed some persons, but their number was very small, that continued a kind of hobbling march on the broken arches, but fell through one after another, being quite tired and spent with so long a walk.
"I passed some time in the contemplation of this wonderful structure, and the great variety of objects which it presented. My heart was filled with a deep melancholy to see several dropping unexpectedly in the midst of mirth and jollity, and catching at everything that stood by them to save themselves. Some were looking up towards the heavens in a thoughtful posture, and in the midst of a speculation stumbled and fell out of sight. Multitudes were very busy in the pursuit of bubbles that glittered in their eyes and danced before them; but often when they thought themselves within the reach of them, their footing failed and down they sunk. In this confusion of objects, I observed some who ran to and fro upon the bridge, thrusting several persons on trap-doors which did not seem to lie in their way, and which they might have escaped had they not been thus forced upon them.
"The Genius seeing me indulge myself on this melancholy prospect, told me I had dwelt long enough upon it. 'Take thine eyes off the bridge,' said he, 'and tell me if thou yet seest anything thou dost not comprehend.' Upon looking up, 'What mean,' said I, 'those great flights of birds that are perpetually hovering
about the bridge, and settling upon it from time to time? 1 see vultures, harpies, ravens, cormorants, and among ninny other feathered creatures several little winged boys, that perch in great numbers upon the middle arches. 'These,' said the Genius, 'are Envy, Avarice, Superstition, Despair, Love, with the like cares and passions that infest human life.'
'' I here fetched a deep sigh. 'Alas,' said I, 'Man was made in vain! how is he given away to misery and mortality! tortured in life, and swallowed up in death!' The Genius being moved with compassion towards me, bid me quit so uncomfortable a prospect. 'Look no more,' said he, 'on man in the first stage of bis existence, in his setting out for eternity; but east thine eye on that thick mist into which the tide bears the several generations of mortals that fall into it. I directed my sight as 1 was ordered, and (whether or no the good Genius strengthened it with any supernatural foree, or dissipated part of the mist that was before too thick for the eye to penetrate) I saw the valley opening at the farther end, and spreading forth into an immense ocean, that had a huge Tock of adamant running through the midst of it, and dividing it into two equal parts. The clouds still rested on one half of it, insomuch that I could discover nothing in it; but the other appeared to me a vast ocean planted with innumerable islands, that were I covered with fruits and flowers, and interwoven with a thousand little shining seas that ran among them. I could see persons dressed in glorious habits with garlands upon their heads, passing among the trees, lying down by the sides of fountains, or resting on beds of flowers; and could hear a confused harmony of singing birds, falling waters, human voices, and musical instruments. Gladness grew in me upon the discovery of so delightful a scene. I wished for the wings of an eagle, that I might fly away to those happy seats; but the Genius told me there was no passage to them, except through the gates of death that I saw opening every moment upon the bridge. 'The islands,' said he, 'that lie so fresh and green before thee, and with which the whole face of the ocean appears spotted as far as thou canst see, are more in number than the sands on the sea-shore: there are myriads of islands behind those which thou here discoverest, reaching farther than thine eye, or even thine Imagination can extend itself. These are the mansions of good men after death, who, according to the degree and kinds of virtue in which they
excelled, are distributed among these several islands, which abound with pleasures of different kinds and degrees, suitable to the relishes and perfections of those who are settled in them: every island is a paradise accommodated to its respective inhabitants. Are not these, O Mirza, habitations worth contending for! Does life appear miserable that gives thee opportunities of earning such a reward? Is death to be feared that will convey thee to so happy an existence? Think not man was made in vain, who has such an eternity reserved for him.' I gazed with inexpressible pleasure on these happy islands. At length, said I, 'Show me now, I beseech thee, the secrets that lie hid under those dark clouds which cover the ocean on the other side of the rock of adamant.' The Genius making me no answer, I turned me about to address myself to him a second time, but I found that he had left me; I then turned again to the vision which I had been so long contemplating; but instead of the rolling tide, the arched bridge, and the happy islands, I saw nothing but the long hollow valley of Bagdad, with oxen, sheep, and camels grazing upon the sides of it."
MATTHEW PRIOR (1664-1721)
TO A CHILD OF QUALITY FIVE YEABS
Lords, knights, and 'squires, the numerous
That wear the fair Miss Mary's fetters, Were summoned by her high command, To show their passions by their letters.
My pen among the rest I took,
Lest those bright eyes that cannot read
Should dart their kindling fires, and look
The power they have to be obeyed. *
Nor quality, nor reputation,
Forbid me yet my flame to tell,
Dear Five-years-old befriends my passion,
And I may write till she can spell.
For, while she makes her silk-worms beds
With all the tender things I swear;
Whilst all the house my passion reads
In papers round her baby's hair; 16
She may receive and own my flame,
For, though the strictest prudes should know
She'll pass for a most virtuous dame
And I for an unhappy poet.


Target Field staff played a delayed feed of the national anthem on the Jumbotron while Brian Dozier homered to open the game and Eddie Rosario followed it with a two-run dinger, but despite missing nearly all the action, and the game becoming predictably uncompetitive, I still think the world needs more one-game playoffs.
The Minnesota Twins were the David to the Goliaths of the Major League Baseball Playoffs. ESPN's Sports Nation staff ranked Minnesota's roster last amongst the MLB playoff teams in all three areas -- lineup, starting pitching and relief pitching.
The Twins were huge underdogs not just to win the American League pennant, but the Wild Card Game. A $100 bet on the Twins to beat the Yankees would have paid $225. Those are the worst odds in the short history of MLB one-game playoffs. In the first American League Wild Card Game, a $100 bet on the Baltimore Orioles to beat the Texas Rangers paid $195.
Better yet, a $100 bet on that guy who had never boxed before against that guy who had never lost before would have paid just $40 more than a bet on the Twins to beat the Yankees. Apparently 50 million Americans watched that fight, which would be 15 percent of the U.S. population. The overnight rating for the American League Wild Card Game was 5.2, meaning Nielsen estimates 5.2 percent of households watched the game -- up 58 percent from last year.
So people watched because anything can happen in one game -- and did it ever. We saw baseball like never before because of the one-game playoff format. For better or worse, we saw how managers can affect a game -- something that isn't the case over the course of a 162-game season -- or even a seven-game series.
Paul Molitor might win the American League Manager of the Year Award, but Joe Girardi was the better manager Tuesday. He made all the right moves. Girardi lifted starter Luis Severino after a third of an inning before his postseason ERA ballooned over 100 (it's 81.00). When the Yankees badly needed to strand two runners in scoring position with just one out down three runs in the first inning, Girardi called on Chad Green, who struck out Byron Buxton and Jason Castro -- who didn't touch a ball and probably should have been lifted for a pinch hitter at some point with three catchers on the Twins' roster.
Molitor could have lifted Ervin Santana after a third of an inning, too. Santana was visibly struggling with his command, but instead of going to Trevor Hildenberger with two runners on, Molitor left Santana to allow the home run that tied it and sucked whatever mojo the Twins had stolen in the first half of the inning.
Girardi used his best bullpen pitcher (by the numbers at least) in the most dire situation while Molitor used his best bullpen pitcher, Trevor Hildenberger, to start the sixth inning down three runs -- with nobody on base! And instead of lifting Santana for Hildenberger, Molitor went to Jose Berrios, who like Santana, struggles to find his command early in games. Berrios predictably allowed a home run that put the Twins in a seemingly insurmountable three-run hole with the best of the Yankee bullpen yet to come.
Whatever mojo Molitor might have had in negotiating an extension with the Twins, he's lost it in my opinion. When one game is your season, that game must be managed flawlessly. But that's part of the beauty of one-game playoffs. Managers are faced with situations that don't exist outside of a one-game playoff -- like removing your starting pitcher with one out in the first inning.
Anything could have happened on Tuesday in New York, but the better team won, as is mostly the case in MLB one-game playoffs. The favorite is 7-3 in MLB Wild Card Games, with those previously mentioned 2012 Orioles being the biggest underdog to advance. The 2014 Kansas City Royals were barely underdogs against the Oakland Athletics at +101, and the 2015 Houston Astros and Yankees were basically drawing even, but the Astros were playing in New York.
So if the better team wins the one-game playoff 70 percent of the time, the world needs more one-game playoffs. I'm not advocating the expansion of the MLB Wild Card format, but in a world where so much is wrong, one-game playoffs like that of the MLB and NFL Playoffs and NCAA March Madness provide wildly entertaining relief. I hope there's a tie for a division championship or a three-way tie for a Wild Card spot next season.


It looks like a wonderful place for a stroll.
Very pretty photo. The autumn has been mild all over the U.S. and Europe, I think. However, that has changed here and neither of you get any sympathy from me. It is 20 F (-6 C) on the thermometer outside my kitchen window at 5:00 p.m. I certainly do have the heat on. In fact, I need to plan my dinner: a ribeye steak on the grill. Yes, I positioned my grill so that I can easily clear the snow away from it. And the bottle of Bordeaux awaits. Hmmm, I think it's cocktail time. Winter won't stop me from eating well!
If we are all mentioning the weather, I was approaching a rain shower on I95 expressway in Miami and within 3 minutes, I drove out of it and into beautiful humid weather. Nothing I saw in my drive, tho, was as romantic looking as this.
So, after that message, I had to call PHXCDG. She is doing well. It's nice to have friends around the world, n'est-ce pas?
Gorgeous—I'd like to be strolling there right now. We had lovely weather here in NYC this weekend too, but are looking forward to rain. Hope your good weather lasts!
Beautiful! As I look outside onto the leaf-covered ground with the 28 degree weather, I'm thinking..."At least the sun is shining!" :) Hope you all have a fabulous Monday!
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Stack and glue flower pots together- Use for keys, etc to put in entry or for jewelry in the bedroom. Such a good idea!!
Find 22 Pumpkin Decorating ideas all in one place. Simple DIY craft tutorial ideas that are perfect for Halloween and Fall decor.


This is our first summer with Bear and he is definitely a water dog, he loves jumping and swimming in the lake at the dog park. So this summer we have been giving our dogs baths almost weekly. Bear being the lab he is, doesn't really mind bath time so much, but Ginger is not a fan at all.
So when my daughter called me from the store saying she found this gadget called the Woof Washer 360, I thought it was worth a try. Maybe it would make bath time easier and quicker?
Well, unfortunately, this product doesn't live up to its expectations. As you can see in the video I struggled with the Woof Washer 360. It works okay to get the dogs wet, but the soap feature fails big time.
As you can see by the reviews on Amazon, I'm not alone in my frustration with this product.
When I bathe my dogs, I like to lather the soap, scrub their coat so I know they're clean. The Woof Washer 360 simply sprays mildly soapy water on the dog, but not enough soap to really clean anything.
I struggled to get the arms of the sprayer to stay open. The first time out of the box it seemed to stay open, but the second time trying it, the arms kept collapsing on the dog.
For a dog, like our Ginger, that doesn't like baths, to begin with, it makes bath time even scarier. Trying to hold Ginger from running away in one hand and holding the washer in the other was difficult.
The water pressure is low, so I didn't feel it was enough to really clean the dog deep down.
Water filters through the container that holds the soap, which then disburses it through the arms of the washer. But this waters down the soap very quickly and in the few minutes I attempted to use this product, the soap was so watered down, it was useless.
So I suppose if you want to rinse your dog, this would be okay. But the Woof Washer 360 does not really give your dog a good clean bath.
The Woof Washer 360 is not worth spending any amount of money on unless you are looking to simply rinse your dog. Using the hose with a standard garden sprayer attachment like this one is much more efficient and easier to use than the Woof Washer 360.


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Lexmark MS811 have a drivers for each operating system. asfadriver.com provide download link for Lexmark MS811 Driver. you can download directly from link at the end of post, this driver is supported for Lexmark MS811n and Lexmark MS811dn/MS811DTN drivers.


The resource provides a piece of networked storage in the cluster provisioned by an administrator. It is a resource in the cluster just like a node is a cluster resource. Persistent Volumes have a lifecycle independent of any individual pod that uses the PV.
spec - (Required) Spec of the persistent volume owned by the cluster. See below.
node_affinity - (Optional) NodeAffinity defines constraints that limit what nodes this volume can be accessed from. This field influences the scheduling of pods that use this volume.
persistent_volume_source - (Required) The specification of a persistent volume.
required - (Optional) Required specifies hard node constraints that must be met.
node_selector_terms - (Required) A list of node selector terms. The terms are ORed.
match_expressions - (Optional) A list of node selector requirements by node's labels.
match_fields - (Optional) A list of node selector requirements by node's fields.
key - (Required) The label key that the selector applies to.
operator - (Required) Represents a key's relationship to a set of values. Valid operators are In, NotIn, Exists, DoesNotExist. Gt, and Lt.
values - (Optional) An array of string values. If the operator is In or NotIn, the values array must be non-empty. If the operator is Exists or DoesNotExist, the values array must be empty. If the operator is Gt or Lt, the values array must have a single element, which will be interpreted as an integer. This array is replaced during a strategic merge patch.
azure_disk - (Optional) Represents an Azure Data Disk mount on the host and bind mount to the pod.
azure_file - (Optional) Represents an Azure File Service mount on the host and bind mount to the pod.
fc - (Optional) Represents a Fibre Channel resource that is attached to a kubelet's host machine and then exposed to the pod.
flex_volume - (Optional) Represents a generic volume resource that is provisioned/attached using an exec based plugin. This is an alpha feature and may change in future.
iscsi - (Optional) Represents an ISCSI Disk resource that is attached to a kubelet's host machine and then exposed to the pod. Provisioned by an admin.
partition - (Optional) The partition in the volume that you want to mount. If omitted, the default is to mount by volume name. Examples: For volume /dev/sda1, you specify the partition as "1". Similarly, the volume partition for /dev/sda is "0" (or you can leave the property empty).
caching_mode - (Required) Host Caching mode: None, Read Only, Read Write.
fs_type - (Optional) Filesystem type to mount. Must be a filesystem type supported by the host operating system. Ex. "ext4", "xfs", "ntfs". Implicitly inferred to be "ext4" if unspecified.
read_only - (Optional) Whether to force the read-only setting in VolumeMounts. Defaults to false (read/write).
driver - (Required) Driver is the name of the driver to use for this volume.
fs_type - (Optional) Filesystem type to mount. Must be a filesystem type supported by the host operating system. Ex. "ext4", "xfs", "ntfs". The default filesystem depends on FlexVolume script.
options - (Optional) Extra command options if any.
read_only - (Optional) Whether to force the ReadOnly setting in VolumeMounts. Defaults to false (read/write).
secret_ref - (Optional) Reference to the secret object containing sensitive information to pass to the plugin scripts. This may be empty if no secret object is specified. If the secret object contains more than one secret, all secrets are passed to the plugin scripts.
iqn - (Required) Target iSCSI Qualified Name.
iscsi_interface - (Optional) iSCSI interface name that uses an iSCSI transport. Defaults to 'default' (tcp).
lun - (Optional) iSCSI target lun number.
read_only - (Optional) Whether to force the read-only setting in VolumeMounts. Defaults to false.
target_portal - (Required) iSCSI target portal. The portal is either an IP or ip_addr:port if the port is other than default (typically TCP ports 860 and 3260).
self_link - A URL representing this persistent volume.
read_only - (Optional) Whether to force the Quobyte volume to be mounted with read-only permissions. Defaults to false.
volume - (Required) Volume is a string that references an already created Quobyte volume by name.
rbd_pool - (Optional) The rados pool name. Default is rbd. For more info see http://releases.k8s.io/HEAD/examples/volumes/rbd/README.md#how-to-use-it.
Persistent Volume can be imported using its name, e.g.