text:
\section{Introduction} \indent

The prompt photon production in $ep$ collisions at HERA is a subject of the
intensive studies~[1--4]. The theoretical and experimental investigations of the such processes
have provided a direct probe of the hard subprocess dynamics, since produced photons
are largely insensitive to the effects of final-state hadronization.
Usually photons are called "prompt" if they are coupled to the interacting quarks.
From the theoretical point, these photons in $ep$ collisions can be produced
via direct $\gamma q \to \gamma q$ and resolved production mechanisms. In resolved
events, the photon emitted by the electron fluctuate into a hadronic state
and a gluon and/or a quark of this hadronic fluctuation takes part in the hard
interactions. Also observed final state photon may arise from fragmentation
process~[5], where a quark or gluon decays into $\gamma$.
The cross section of such processes involves relative poorly known
parton-to-photon fragmentation functions~[6].
However, the isolation
criterion which introduced in experimental analyses substantially reduces~[7] the
fragmentation component.
In any case, for the theoretical description of prompt photon production
at modern (HERA, Tevatron) and
future (LHC) colliders the detailed knowledge of parton (quark and gluon) distributions
in a proton and in a photon is necessary.

Usually quark and gluon densities are described by the
Dokshitzer-Gribov-Lipatov-Altarelli-Parizi (DGLAP) evolution equation~[8]
where large logarithmic terms proportional to $\ln \mu^2$ are taken into
account only. The cross sections can be rewritten in terms of process-dependent
hard matrix elements convoluted with quark or gluon density functions.
In this way the dominant contributions come from diagrams where parton emissions
in initial state are strongly ordered in virtuality. This is called collinear
factorization, as the strong ordering means that the virtuality of the parton
entering the hard scattering matrix elements can be neglected compared to the
large scale $\mu$.

However, at high energies (or small $x \sim \mu^2/s \ll 1$) effects of
finite virtualities and transverse
momenta of the incoming partons may become more and
more important. These effects can be systematically accounted for in a
$k_T$-factorization formalism~[9--12]. Just as for DGLAP, in this way it is possible to
factorize an observable into a convolution of process-dependent
hard matrix elements with universal parton distributions.
But as the virtualities and transverse momenta of the emitted partons are no
longer ordered, the matrix elements have to be taken off-shell and the
convolution made also over transverse momentum ${\mathbf k}_T$ with the
unintegrated (i.e.~$k_T$-dependent) parton distributions.
The unintegrated parton distribution $f_a(x,{\mathbf k}_T^2)$
determines the probability to find a type $a$ parton carrying the
longitudinal momentum fraction $x$ and the transverse momentum ${\mathbf k}_T$.
In particular, usage of the unintegrated parton densities have the advantage that it takes
into account true kinematics of the process under consideration even at leading order.

The unintegrated parton distributions $f_a(x,{\mathbf k}_T^2)$ are a subject
of intensive studies~[13, 14]. Various approaches to investigate these quantities
has been proposed. It is believed that at assymptotically large energies (or very small $x$)
the theoretically correct description is given by the Balitsky-Fadin-Kuraev-Lipatov
(BFKL) evolution equation~[15] where large terms proportional to $\ln 1/x$ are
taken into account. Another approach, valid for both small and large
$x$, have been developed by Ciafaloni, Catani, Fiorani and Marchesini,
and is known as the CCFM model~[16]. It introduces angular ordering of emissions
to correctly treat gluon coherence effects. In the limit of
asymptotic energies, it almost equivalent to BFKL~[17--19], but also similar to
the DGLAP evolution for large $x \sim 1$. The resulting unintegrated
gluon distribution depends on two scales, the additional scale ${\bar q}$
is a variable related to the maximum angle allowed in the emission and plays
the role of the evolution scale $\mu$ in the collinear parton densities.

Also it is possible to obtain the two-scale involved unintegrated parton distributions
from the conventional ones using the Kimber-Martin-Ryskin (KMR) prescription~[20].
In this way the $\mu$ dependence in the unintegrated parton distribution
enters only in last step of the evolution, and single scale evolution equations
can be used up to this step. Such procedure can be applied to a proton as well as
photon and is expected to account for the main part of the collinear higher-order QCD corrections.
The KMR-constructed parton densities were used, in particular, to describe the
heavy quark production in $\gamma \gamma$ collisions at CERN LEP2~[21] and
prompt photon hadroproduction at fixed target experiments and at
Fermilab Tevatron~[22] collider (in the double logarithmic approximation).

In the present paper we will apply the KMR method to obtain the unintegrated
quark and gluon distributions in a proton $f_a(x,{\mathbf k}_T^2,\mu^2)$ and in a photon
$f_a^\gamma(x,{\mathbf k}_T^2,\mu^2)$ independently from other authors.
After that, we calculate the inclusive prompt photon
photoproduction at HERA energies. Such calculations in the $k_T$-factorization
approach will be performed for the first time. We will investigate the transverse
energy $E_T^{\gamma}$ and pseudo-rapidity $\eta^{\gamma}$ distributions of the produced
prompt photons and compare our theoretical results with the recent
experimental data taken by the H1~[4] and ZEUS~[3] collaborations.
In order to estimate the theoretical uncertainties of our predictions we will study the
renormalization and factorization scale dependences of the calculated cross sections.
Next we calculate the associated prompt photon and jet production
rates using some physically motivated approximation. In order
to investigate the underlying dynamics more detail, we will study the angular correlations
between the prompt photon and jet in the transverse momentum plane.
It was shown~[23, 24] that theoretical and experimental studying of such quantities
is a direct probe of the non-collinear parton evolution.

The additional motivation of our investigations within the $k_T$-factorization
approach is the fact that the next-to-leading order (NLO)
collinear QCD calculations~[7, 25] are $30 - 40$\% below the data, especially in
rear pseudo-rapidity (electron direction) region. So, one of the main goals
of this paper is to investigate whether the $k_T$-factorization
formalism could give a better description of the HERA data than collinear NLO QCD calculations.

The our paper is organized as follows. In Section 2 the KMR unintegrated parton densities
in a proton and in a photon are obtained and their properties
are discussed. In particular, we compare the KMR gluon distributions with ones taken
from the full CCFM equation.
In Section 3 we present the basic
formulas with a brief review of calculation steps.
In Section 4 we present the numerical results of
our calculations. Finally, in Section 5, we give some conclusions.
The compact analytic expressions for the off-mass shell matrix elements of all the
subprocesses under consideration are given in Appendix. These formulas
may be useful for the subsequent applications.

\section{The KMR unintegrated partons} \indent

The Kimber-Martin-Ryskin approach~[20] is the formalism to construct
parton distributions $f_a(x,{\mathbf k}_T^2,\mu^2)$ unintegrated over the parton
transverse momenta ${\mathbf k}_T^2$ from the known conventional parton
distributions $a(x,\mu^2)$, where $a = xg$ or $a = xq$. This formalism is
valid for a proton as well as photon and can embody
both DGLAP and BFKL contributions. It also accounts for the angular ordering which
comes from coherence effects in gluon emission.

We start from parton distributions in a proton.
The key observation here is that
the $\mu$ dependence of the unintegrated distributions $f_a(x,{\mathbf k}_T^2,\mu^2)$
enters at the last step
of the evolution, and therefore single scale evolution equations (DGLAP
or unified DGLAP-BFKL~[26]) can be used up to this step.
It was shown~[20] that the unintegrated distributions obtained via unified DGLAP-BFKL
evolution are rather similar to those based on the pure DGLAP equations.
It is because the imposion of the angular ordering constraint is more important than
including the BFKL effects. Based on this point,
in our calculations we will use much more simpler DGLAP equation up to the last evolution step.
In this approximation, the unintegrated quark and gluon distributions are given~[20] by
$$
  \displaystyle f_q(x,{\mathbf k}_T^2,\mu^2) = T_q({\mathbf k}_T^2,\mu^2) {\alpha_s({\mathbf k}_T^2)\over 2\pi} \times \atop {
  \displaystyle \times \int\limits_x^1 dz \left[P_{qq}(z) {x\over z} q\left({x\over z},{\mathbf k}_T^2\right) \Theta\left(\Delta - z\right) + P_{qg}(z) {x\over z} g\left({x\over z},{\mathbf k}_T^2\right) \right],} \eqno (1)
$$
$$
  \displaystyle f_g(x,{\mathbf k}_T^2,\mu^2) = T_g({\mathbf k}_T^2,\mu^2) {\alpha_s({\mathbf k}_T^2)\over 2\pi} \times \atop {
  \displaystyle \times \int\limits_x^1 dz \left[\sum_q P_{gq}(z) {x\over z} q\left({x\over z},{\mathbf k}_T^2\right) + P_{gg}(z) {x\over z} g\left({x\over z},{\mathbf k}_T^2\right)\Theta\left(\Delta - z\right) \right],} \eqno (2)
$$

\noindent
where $P_{ab}(z)$ are the usual unregulated leading order DGLAP splitting functions,
and $q(x,\mu^2)$ and $g(x,\mu^2)$ are the conventional quark and gluon densities.
The theta functions which appear in (1) and (2) imply the angular-ordering
constraint $\Delta = \mu/(\mu + |{\mathbf k}_T|)$ specifically to the last
evolution step to regulate the soft gluon
singularities. For other evolution steps, the strong ordering in
transverse momentum within the DGLAP equations automatically
ensures angular ordering. It is important that parton
distributions $f_a(x,{\mathbf k}_T^2,\mu^2)$ extended now into
the ${\mathbf k}_T^2 > \mu^2$ region. This fact is in the clear contrast with the
usual DGLAP evolution\footnote{We would like to note that
cut-off $\Delta$ can be also taken $\Delta = |{\mathbf k}_T|/\mu$~[23]. In this case the unintegrated
parton distributions given by (1) --- (2) vanish for ${\mathbf k}_T^2 > \mu^2$ in accordance with
the DGLAP strong ordering in ${\mathbf k}_T^2$.}.

The virtual (loop) contributions may be resummed
to all orders by the quark and gluon Sudakov form factors
$$
  \ln T_q({\mathbf k}_T^2,\mu^2) = - \int\limits_{{\mathbf k}_T^2}^{\mu^2} {d {\mathbf p}_T^2\over {\mathbf p}_T^2} {\alpha_s({\mathbf p}_T^2)\over 2\pi} \int\limits_0^{z_{\rm max}} dz P_{qq}(z), \eqno (3)
$$
$$
  \ln T_g({\mathbf k}_T^2,\mu^2) = - \int\limits_{{\mathbf k}_T^2}^{\mu^2} {d {\mathbf p}_T^2\over {\mathbf p}_T^2} {\alpha_s({\mathbf p}_T^2)\over 2\pi} \left[ n_f \int\limits_0^1 dz P_{qg}(z) + \int\limits_{z_{\rm min}}^{z_{\rm max}} dz z P_{gg}(z) \right], \eqno (4)
$$

\noindent
where $z_{\rm max} = 1 - z_{\rm min} = {\mu/({\mu + |{\mathbf p}_T|}})$.
The form factors $T_a({\mathbf k}_T^2,\mu^2)$ give the probability of
evolving from a scale ${\mathbf k}_T^2$ to a scale $\mu^2$ without
parton emission. According to (3) and (4) $T_a({\mathbf k}_T^2,\mu^2) = 1$
in the ${\mathbf k}_T^2 > \mu^2$ region.

We would like to note that such definition of the $f_a(x,{\mathbf k}_T^2,\mu^2)$ is
correct for ${\mathbf k}_T^2 > \mu_0^2$ only, where
$\mu_0 \sim 1$ GeV is the minimum scale for which DGLAP evolution of the collinear
parton densities is valid. Everywhere in our numerical calculations
we set the starting scale $\mu_0$ to be equal $\mu_0 = 1$ GeV.
Since the starting point of our derivation is the leading order
DGLAP equations, the unintegrated parton distributions must satisfy
the normalisation condition
$$
  a(x,\mu^2) = \int\limits_0^{\mu^2} f_a(x,{\mathbf k}_T^2,\mu^2) d{\mathbf k}_T^2. \eqno(5)
$$

\noindent
This relation will be exactly satisfied if we define~[20]
$$
  f_a(x,{\mathbf k}_T^2,\mu^2)\vert_{{\mathbf k}_T^2 < \mu_0^2} = a(x,\mu_0^2) T_a(\mu_0^2,\mu^2). \eqno(6)
$$

\noindent
Then, we have obtained the unintegrated parton distributions $f_a(x,{\mathbf k}_T^2,\mu^2)$
in a proton. In order to obtain the unintegrated parton distribution $f_a^\gamma(x,{\mathbf k}_T^2,\mu^2)$
in a photon the same formulas (1) --- (4) can be also used~[21]. In the last case the
conventional parton distributions $a(x,\mu^2)$ in a proton should be replaced by
the corresponding parton densities $a^\gamma(x,\mu^2)$ in a photon.

In Figure~1 we show unintegrated parton densities $f_a(x,{\mathbf k}_T^2,\mu^2)$ in a proton at
scale $\mu^2 = 100\,{\rm GeV}^2$ as a function
of $x$ for different values of ${\mathbf k}_T^2$, namely
${\mathbf k}_T^2 = 2\,{\rm GeV}^2$ (a),
${\mathbf k}_T^2 = 5\,{\rm GeV}^2$ (b),
${\mathbf k}_T^2 = 10\,{\rm GeV}^2$ (c) and
${\mathbf k}_T^2 = 20\,{\rm GeV}^2$ (d).
The solid, dashed, short dashed, dotted and dash-dotted lines
correspond to the unintegrated $u + \bar u$, $d + \bar d$, $s$, $c$ and gluon
(divided by factor $10$) distributions, respectively. We have used here the standard
GRV (LO) parametrizations~[27] of the collinear quark and gluon densities $a(x,\mu^2)$.
In order to be sure that normalization condition (5) is correctly
satisfied we have performed the numerical integration of the parton densities
$f_a(x,{\mathbf k}_T^2,\mu^2)$ over transverse momenta ${\mathbf k}_T^2$.
So, in Figure~2 we show our result for effective $u + \bar u$ quark and
gluon (also divided by factor 10) distributions
for different scales
$\mu^2 = 2\,{\rm GeV}^2$ (a),
$\mu^2 = 5\,{\rm GeV}^2$ (b),
$\mu^2 = 10\,{\rm GeV}^2$ (c),
$\mu^2 = 20\,{\rm GeV}^2$ (d).
The solid lines correspond to the effective
densities obtained from the unintegrated
ones using relation (5). The dashed lines correspond to the collinear GRV (LO) parton
distributions. One can see that normalization
condition (5) is exactly satisfied practically for all $x$ and $\mu^2$ values.
There are only rather small (less then few percent)
violations of (5) in the case of the $u + \bar u$ quark distributions
at large $x > 0.2$. We have checked numerically that the expression (5) is true also for
other parton densities in a proton and in a photon.

For comparison we plot in Figure~2 (as dash-dotted lines)
the corresponding LO parton distributions obtained by the CTEQ collaboration~[28]
(CTEQ5L set). It is clear that there are some differences in both
normalization and shape between GRV and CTEQ parametrizations.
In general, the CTEQ curves lie below the GRV ones by about $10$\%.
This difference tends to be small when scale $\mu^2$ is large.
However, the CTEQ collaboration does not provide a set of the
parton distributions in a photon, which are necessary for
calculation of the resolved contributions.
Therefore everywhere in our numerical analysis
we will use only the GRV parametrizations.

It is interesting to compare the KMR-constructed unintegrated parton densities
with the distributions obtained in other approaches. Recently the full
CCFM equation in a proton and in a photon was solved numerically using a Monte Carlo
method, and new fits of the unintegrated gluon
distributions (J2003 set 1 --- 3) have been presented~[29].
The input parameters were fitted to describe the proton structure function $F_2(x,Q^2)$.
These unintegrated gluon densities were used also in description of
the forward jet production
at HERA, charm and bottom production at Tevatron~[29], and charm and $J/\psi$ production at
LEP2 energies~[30]. In Figure 3 we plot KMR (as solid lines) and J2003 set 1 (as dashed lines)
gluon distributions in a proton
at scale $\mu^2 = 100\,{\rm GeV}^2$ as a function
of $x$ for different values of ${\mathbf k}_T^2$, namely
${\mathbf k}_T^2 = 2\,{\rm GeV}^2$ (a),
${\mathbf k}_T^2 = 10\,{\rm GeV}^2$ (b),
${\mathbf k}_T^2 = 20\,{\rm GeV}^2$ (c) and
${\mathbf k}_T^2 = 50\,{\rm GeV}^2$ (d).
One can see that J2003 set 1 gluon density is less steep at small $x$ compared to the
KMR one. The KMR gluon lie below J2003 set 1 at small ${\mathbf k}_T^2$ region
for $x > 3 \cdot 10^{-3}$. Typically the difference between solid and dashed lines
is about 30\% --- 40\% at $x = 0.01$.
This fact results to the some underestimation of the calculated
cross sections in the KMR approach. This
underestimation is about 30\% at HERA and 50\% at Tevatron\footnote{See Ref.~[13] for more details.}.
Therefore we can expect a rather large sensitivity of our predictions to the parton evolution
scheme.

We would like to point out again that behaviour of different unintegrated
parton distributions in a proton
in the small ${\mathbf k}_T^2$ region (which essentially drives
the total cross sections) is very different, as it is clear shown on Figure~3.
However, the CCFM evolution does not include quark-initiated chains and therefore
can not be used in our analysis since prompt photon production at HERA
strongly depends on the quark distributions (see Section~3). Therefore in
our following investigations we will use only the KMR unintegrated parton densities.
But one should remember that dependence of our results on the evolution scheme
may be rather large, and further theoretical attempts (in order to investigate
the unintegrated quark distributions more detail) are necessary to reduce this uncertainty.

\section{Calculation details}

\subsection{The subprocesses under consideration} \indent

In $ep$ collisions at HERA prompt photons can be produced by one
of three mechanisms: a direct production, a single resolved production
and via parton-to-photon fragmentation processes~[5].
The direct contribution to the $\gamma p \to \gamma + X$ process
is the Deep Inelastic Compton (DIC) scattering on the quark (antiquark)
$$
  \gamma (k_1) + q (k_2) \to \gamma (p_{\gamma}) + q (p'), \eqno(7)
$$

\noindent
where the particles four-momenta are given in parentheses. It gives
the ${\cal O}(\alpha^2_{em})$ order contribution to the hadronic
cross section. Here $\alpha_{em}$ is Sommerfeld's fine structure constant.
The single resolved processes are
$$
  q (k_1) + g (k_2) \to \gamma (p_{\gamma}) + q (p'), \eqno(8)
$$
$$
  g (k_1) + q (k_2) \to \gamma (p_{\gamma}) + q (p'), \eqno(9)
$$
$$
  q (k_1) + q (k_2) \to \gamma (p_{\gamma}) + g (p'). \eqno(10)
$$

\noindent
Since the parton distributions in a photon $a_{\gamma}(x,\mu^2)$
have a leading behavior proportional to $\alpha_{em}\ln \mu^2/\Lambda_{\rm QCD}^2 \sim \alpha_{em}/\alpha_s$,
these subprocesses give also
the ${\cal O}(\alpha^2_{em})$ contributions and
therefore should be taken into account in our analysis.

In addition to the direct and resolved production, photons can
be also produced through the fragmentation of a hadronic jet
into a single photon carrying a large fraction $z$ of the jet energy~[5].
These processes are described in terms of quark-to-photon $D_{q\to\gamma}(z,\mu^2)$ and
gluon-to-photon $D_{g\to\gamma}(z,\mu^2)$ fragmentation functions~[7].
The main feature of the fragmentation contribution in leading order is fact that
produced photon balanced by a jet on the opposite side of the event
and accompanied by collinear hadrons on the same side of the event.

It is very important that in order to reduce the huge background
from the secondary photons produced by the decays of $\pi^0$, $\eta$
and $\omega$ mesons the isolation criterion is introduced in the experimental analyses.
This criterion is the following. A photon is isolated if the
amount of hadronic transverse energy $E_T^{\rm had}$, deposited inside
a cone with aperture $R$ centered around the photon direction in the
pseudo-rapidity and azimuthal angle plane, is smaller than
some value $E_T^{\rm max}$:
$$
  \displaystyle E_T^{\rm had} \le E_T^{\rm max},\atop
  \displaystyle (\eta - \eta^{\gamma})^2 + (\phi - \phi^{\gamma})^2 \le R^2. \eqno(11)
$$

\noindent
The both H1 and ZEUS collaborations take $R = 1$, $E_T^{\rm max} = \epsilon E_T^\gamma$ with
$\epsilon = 0.1$ in the experiment~[1--4].
Isolation not only reduces the background
but also significantly reduces the fragmentation components.
It was shown~[7] that after applying the isolation cut (11) the contribution from the
fragmentation subprocesses is about 5 --- 6\% of the total cross section.
Since the dependence of our results on the non-collinear parton evolution scheme may be
rather large (as it was demonstrated in Section~2), in our further analysis we will
neglect the relative small fragmentation contribution and consider only the
direct and resolved production
(7) --- (10). We note that photon produced in these processes is automatically
isolated from the quark or gluon jet by requiring a non-zero transverse momentum
of a photon or jet in the $\gamma p$ center-of-mass frame.

It was claimed~[7, 25] that direct box diagram $\gamma g\to \gamma g$, which is
formally of the next-to-next-to-leading order (NNLO), gives approximately 6\% contribution
to the total NLO cross section. In the present paper we will not take into account
this diagram also.

\subsection{Cross section for prompt photon production} \indent

Let $p_e$ and $p_p$ be the four-momenta of the initial electron and proton.
The direct contribution (7) to the $\gamma p \to \gamma + X$
process in the $k_T$-factorization approach can be written as
$$
  d\sigma^{\rm (dir)} (\gamma p \to \gamma + X) = \sum_{q} \int {dx_2\over x_2} f_q(x_2,{\mathbf k}_{2 T}^2,\mu^2) d{\mathbf k}_{T}^2 {d\phi_2\over 2\pi} d{\hat \sigma} (\gamma q \to \gamma q), \eqno(12)
$$

\noindent
where ${\hat \sigma} (\gamma q \to \gamma q)$ is the hard subprocess cross section
via quark or antiquark having fraction $x_2$ of a initial proton longitudinal
momentum, non-zero transverse momentum ${\mathbf k}_{2 T}$
(${\mathbf k}_{2 T}^2 = - k_{2 T}^2 \neq 0$) and azimuthal angle $\phi_2$.
The expression (12) can be easily rewritten in the form
$$
  \displaystyle \sigma^{\rm (dir)} (\gamma p \to \gamma + X) = \sum_q \int {E_T^\gamma \over 8\pi (x_2 s)^2 (1 - \alpha)} |\bar {\cal M}|^2 (\gamma q \to \gamma q) \times \atop
  \displaystyle \times f_q(x_2,{\mathbf k}_{2 T}^2,\mu^2) dy^\gamma d E_T^\gamma d{\mathbf k}_{2 T}^2 {d\phi_2\over 2\pi} {d\phi^\gamma\over 2\pi}, \eqno(13)
$$

\noindent
where $|\bar {\cal M}|^2 (\gamma q \to \gamma q)$ is the hard
matrix element which depends on the transverse momentum ${\mathbf k}_{2 T}^2$,
$s = (k_1 + p_p)^2$ is the total energy of the subprocess under consideration,
$y^\gamma$, $E_T^\gamma$
and $\phi^\gamma$ are the rapidity, transverse energy and azimuthal angle of the
produced photon in the $\gamma p$ center-of-mass frame, and $\alpha = E_T^\gamma \exp y^\gamma /\sqrt s$.

The formula for the
resolved contribution to the prompt photon photoproduction in the
$k_T$-factorization approach can be obtained by the similar way. But one should keep in mind that
convolution in (12) should be made also with the unintegrated parton distributions
$f_a^\gamma(x,{\mathbf k}_{T}^2,\mu^2)$ in a photon, i.e.
$$
  \displaystyle d\sigma^{\rm (res)} (\gamma p \to \gamma + X) = \sum_{a,b} \int {dx_1\over x_1} f_a^\gamma(x_1,{\mathbf k}_{1 T}^2,\mu^2) d{\mathbf k}_{1 T}^2 {d\phi_1\over 2\pi} \times \atop
  \displaystyle \times \int {dx_2\over x_2} f_b(x_2,{\mathbf k}_{2 T}^2,\mu^2) d{\mathbf k}_{2 T}^2 {d\phi_2\over 2\pi} d{\hat \sigma} (a b \to \gamma c), \eqno(14)
$$

\noindent
where $a, b, c = q$ and/or $g$, ${\hat \sigma} (a b \to \gamma c)$ is the cross section
of the photon production in the corresponding parton-parton interaction (8) --- (10).
Here parton $a$ has fraction $x_1$ of a initial photon longitudinal
momentum, non-zero transverse momentum ${\mathbf k}_{1 T}$
(${\mathbf k}_{1 T}^2 = - k_{1 T}^2 \neq 0$) and azimuthal angle $\phi_1$.
We can easily obtain the final expression from equation (14). It has the form
$$
  \displaystyle \sigma^{\rm (res)} (\gamma p \to \gamma + X) = \sum_{a,b} \int {E_T^\gamma\over 8\pi (x_1 x_2 s)^2} |\bar {\cal M}|^2(ab \to \gamma c) \times \atop
  \displaystyle \times f_a^\gamma(x_1,{\mathbf k}_{1 T}^2,\mu^2) f_b(x_2,{\mathbf k}_{2 T}^2,\mu^2) d{\mathbf k}_{1 T}^2 d{\mathbf k}_{2 T}^2 dE_T^\gamma dy^\gamma dy^c {d\phi_1\over 2\pi} {d\phi_2\over 2\pi} {d\phi^\gamma\over 2\pi}, \eqno(15)
$$

\noindent
where $y^c$ is the rapidity of the parton $c$ in the $\gamma p$ center-of-mass frame. It is
important that hard matrix elements $|\bar {\cal M}|^2 (ab \to \gamma c)$ depend
on the transverse momenta ${\mathbf k}_{1 T}^2$ and ${\mathbf k}_{2 T}^2$.
We would like to note that if we average the expressions (13) and (15) over
${\mathbf k}_{1 T}$ and ${\mathbf k}_{2 T}$ and take
the limit ${\mathbf k}_{1 T}^2 \to 0$ and ${\mathbf k}_{2 T}^2 \to 0$,
then we obtain well-known expressions for
the prompt photon production in leading-order (LO) perturbative QCD.

The experimental data taken by the H1~[4] and ZEUS~[3] collaborations refer to the prompt
photon production in the $ep$ collisions, where electron
is scattered at small angle and the mediating photon is almost real ($Q^2 \sim 0$).
Therefore $\gamma p$ cross sections (13) and (15)
needs to be weighted with the photon flux in the electron:
$$
  d\sigma(e p\to e' + \gamma + X) = \int f_{\gamma/e}(y) d\sigma(\gamma p \to \gamma + X) dy, \eqno (16)
$$

\noindent
where $y$ is a fraction of the initial electron energy taken by the photon in the laboratory frame,
and we use the Weizacker-Williams approximation for the bremsstrahlung photon
distribution from an electron:
$$
  f_{\gamma/e}(y) = {\alpha_{em} \over 2\pi}\left({1 + (1 - y)^2\over y}\ln{Q^2_{\rm max}\over Q^2_{\rm min}} +
  2m_e^2 y\left({1\over Q^2_{\rm max}} - {1\over Q^2_{\rm min}} \right)\right). \eqno (17)
$$

\noindent
Here $m_e$ is the electron mass,
$Q^2_{\rm min} = m_e^2y^2/(1 - y)^2$ and $Q^2_{\rm max} = 1\,{\rm GeV}^2$,
which is a typical value for the recent photoproduction measurements at the HERA collider.

The multidimensional integration in (13), (15) and (16) has been performed
by means of the Monte Carlo technique, using the routine VEGAS~[31].
The full C$++$ code is available from the authors on
request\footnote{lipatov@theory.sinp.msu.ru}.
For reader's convenience, we collect the analytic expressions for the
off-shell matrix elements which correspond to all partonic subprocesses under consideration
(7) --- (10) in the Appendix. These formulas may be useful for the subsequent applications.

\section{Numerical results} \indent

We now are in a position to present our numerical results. First we describe our
theoretical input and the kinematical conditions. After we fixed the unintegrated
parton distributions in a proton $f_a(x,{\mathbf k}_{T}^2,\mu^2)$ and in a photon
$f_a^\gamma(x,{\mathbf k}_{T}^2,\mu^2)$, the cross sections (13) and (15) depend on
the energy scale $\mu$. As it often done~[7, 25] for prompt photon production,
we choose the renormalization and
factorization scales to be $\mu = \xi E_T^\gamma$.
In order to estimate the theoretical uncertainties of our calculations
we will vary the scale parameter $\xi$ between 1/2 and 2 about the default value $\xi = 1$.
Also we use LO formula
for the strong coupling constant $\alpha_s(\mu^2)$ with $n_f = 3$ active (massless) quark
flavours and $\Lambda_{\rm QCD} = 232$ MeV, such that $\alpha_s(M_Z^2) = 0.1169$.
In our analysis we will not neglect the charm quark mass and set it to be $m_c = 1.4$ GeV.

\subsection{Inclusive prompt photon production} \indent

Experimental data for the inclusive prompt photon production $e p \to e' + \gamma + X$
comes from both ZEUS and H1 collaborations. Two differential cross section are determined: first
as a function of the transverse energy $E_T^\gamma$, and second as
a function of pseudo-rapidity $\eta^\gamma$. The ZEUS data~[3] refer to the
kinematic region\footnote{Here and in the following all kinematic quantities
are given in the laboratory frame where positive OZ axis direction is given by the proton beam.}
defined by $5 < E_T^\gamma < 10$ GeV and $-0.7 < \eta^\gamma < 0.9$ with
electron energy $E_e = 27.5$ GeV and proton energy $E_p = 820$ GeV.
The fraction $y$ of the electron energy trasferred to the photon is restricted
to the range $0.2 < y < 0.9$. Additionally the available ZEUS data for the
prompt photon pseudo-rapidity distributions have been given also for three
subdivisons of the $y$ range, namely $0.2 < y < 0.32$ ($134 < W < 170$ GeV),
$0.32 < y < 0.5$ ($170 < W < 212$ GeV) and $0.5 < y < 0.9$ ($212 < W < 285$ GeV).
The more recent H1 data~[4] refer to the kinematic region
defined by $5 < E_T^\gamma < 10$ GeV, $ - 1 < \eta^\gamma < 0.9$ and $0.2 < y < 0.7$
with electron energy $E_e = 27.6$ GeV and proton energy $E_p = 920$ GeV.

The transverse energy distributions of the inclusive prompt photon for
different kinematical region are shown
in Figures~4 and~5 in comparison to the HERA data.
Instead of presenting our theoretical predictions as continuous lines, we adopt the
binning pattern encoded in the experimental data.
The solid histograms obtained by fixing both the
factorization and normalization scales at the default value $\mu = E_T^\gamma$,
whereas upper and lower dashed histograms correspond to the $\mu = E_T^\gamma/2$ and
$\mu = 2 E_T^\gamma$ scales, respectively. One can see that predicted
cross sections agree well with the experimental data
except the moderate $E_T^\gamma$ region.
We would like to note that overall agreement with data can be improved
when unintegrated quark and gluon distributions in a proton and in a photon
will be studied more detail. It is because the KMR approach tends to
underestimate the calculated cross sections, as it was discussed in Section~2.
The collinear NLO QCD calculations~[7, 25] give the similar description of
the transverse energy distributions measured by the ZEUS collaboration.
At the same time, according to the analysis which was done by the H1
collaboration~[4], in order to obtain a realistic comparison of
their data and theory the corrections for hadronisation
and multiple interactions should be taken into account in the
predictions\footnote{See Ref.~[4] for more details.}.
The correction factors are typically 0.7 --- 0.9 depending on a bin.
The NLO calculations~[7, 25] are approximately 30\% --- 40\% below the H1 data
if the corrections for hadronisation and multiple interactions are
applied. We would like to note that these corrections are not accounted
for in our analysis.
The effect of scale variations in transverse energy distributions
is rather large: the relative difference
between results for $\mu = E_T^\gamma$ and results for $\mu = E_T^\gamma/2$ or
$\mu = 2 E_T^\gamma$ is about 15\%.

The pseudo-rapidity distributions of the inclusive prompt photon production
compared with the HERA data in different kinematical region are
shown in Figures~6 and~7. All histograms here are the same as in Figure~4.
One can see that measured distributions are reasonably
well described in the pseudo-rapidity region
$ - 0.4 \leq \eta^\gamma \leq 0.9$ only. For $ - 1 \leq \eta^\gamma \leq -0.4$
our predictions lie mostly below the experimental
points\footnote{Note that such disagreement between predicted and measured
cross sections is observed for collinear NLO QCD calculations~[7, 25] also.}.
The discrepancy between data and theory at negative $\eta^\gamma$ is
found to be relative strong at low values of the initial photon
fractional momentum $y$. So, in Figures~8,~9 and~10 we show the
inclusive cross sections $d\sigma/d\eta^\gamma$
evaluated for the three $y$ ranges $0.2 < y < 0.32$ ($134 < W < 170$ GeV),
$0.32 < y < 0.5$ ($170 < W < 212$ GeV) and $0.5 < y < 0.9$ ($212 < W < 285$ GeV),
respectively. All histograms here are the same as in Figure~4. In the lowest $y$ range,
both our predictions and experimental data show a peaking at negative $\eta^\gamma$,
but it is stronger in the data. In the high $y$ region, $0.5 < y < 0.9$, a good
agreement is obtained. This fact allows to establish that the above
discussed discrepancy between the data and theory at $- 1 \leq \eta^\gamma \leq - 0.4$ is
coming from the low ($0.2 < y < 0.32$) and medium ($0.32 < y < 0.5$) $y$ region.
The scale variation changes the estimated
cross sections by about 15\%. The collinear NLO QCD calculations~[7, 25] give the
similar description of the pseudo-rapidity distributions
measured by the ZEUS collaboration. At the same time, after
corrections for hadronisation and multiple interactions (not accounted for in our analysis)
the NLO predictions are 30\% --- 40\% below the H1 data.

As it was already mentioned above, the dependence of the our results on a
renormalization/factorization scale $\mu$ is rather large, about 10\% --- 15\% in
the wide kinematic range.
There are also additional uncertainties come from the unintegrated parton densities,
as it was discussed in Section~2.
The theoretical uncertainties of the collinear NLO QCD calculations
are about 3\%~[7, 25]. This fact indicates that contribution from
NNLO and high order terms is not significant.
At the same time the strong scale dependence of our results demonstrates the necessarity
of reducing of uncertainties in the non-collinear parton evolution.

The individual contributions from the direct and resolved production
mechanisms to the total cross section in the $k_T$-factorization approach
is about 47\% and 53\%, respectively. In the resolved conribution, the
channels (8), (9) and (10) account for 80\%, 14\% and 6\%.
Additionally, using the Duke-Owens (DO)~[32] parton-to-photon fragmentation functions,
we perform the estimation of the fragmentation component (not shown in Figures).
We find that after applying isolation cut it give only a very small (about few percent)
contribution.

\subsection{Prompt photon production in association with jet} \indent

Now we demonstrate how $k_T$-factorization approach can be
used to calculate the semi-inclusive prompt photon production rates.
The produced photon is
accompanied by a number of partons radiated in the course of the parton evolution.
As it has been noted in Ref.~[33], on the average the parton
transverse momentum decreases from the hard interaction
block towards the proton. As an approximation, we assume that the parton $k'$
emitted in the last evolution step compensates the whole transverse momentum
of the parton participating in the hard subprocess, i.e. ${\mathbf k'}_{T} \simeq - {\mathbf k}_{T}$.
All the other emitted partons are collected together in the proton remnant, which
is assumed to carry only a negligible transverse momentum compared to ${\mathbf k'}_{T}$.
This parton gives rise to a final hadron jet with $E_T^{\rm jet} = |{\mathbf k'}_{T}|$
in addition to the jet produced in the hard subprocess. From these hadron jets
we choose the one carrying the largest transverse energy, and then compute prompt
photon with an associated jet cross sections.

Experimental data for such processes were obtained~[4] very recently by the H1
collaboration. The cross sections measured differentially as a function of
$E_T^\gamma$, $E_T^{\rm jet}$,
and the pseudo-rapidities $\eta^\gamma$ and $\eta^{\rm jet}$ in the
kinematic region defined by $5 < E_T^\gamma < 10$ GeV, $E_T^{\rm jet} > 4.5$ GeV,
$ - 1 < \eta^\gamma < 0.9$, $ - 1 < \eta^{\rm jet} < 2.3$ and $0.2 < y < 0.7$ with
electron energy $E_e = 27.6$ GeV and proton energy $E_p = 920$ GeV.
There are no ZEUS data for the prompt photon plus jet production,
although some data for distribution of events, not corrected for the detector
effects, were presented~[2].

The transverse energy $E_T^\gamma$ and pseudo-rapidity $\eta^\gamma$ distributions
of the prompt photon plus jet production are shown in Figures~11 and~12 in
comparison with H1 data.
All histograms here are the same as in Figure~4. In contrast to the inclusive case, one
can see that our predictions are consistent with the data in most bins, although some
discrepancies are present. The scale variation as it was described above
changes the estimated cross sections by about 10\%. The results of the
collinear NLO calculations~[7, 25]
which include corrections for hadronisation and multiple interactions give the
similar results and consistent with data also.

In Figures~13 and~14 we show our predictions for the transverse energy $E_T^{\rm jet}$ and
pseudo-rapidity $\eta^{\rm jet}$ distributions in comparison with H1 data.
All histograms here are the same as in Figure~4. A rather good agreement between
our results and data is obtained again. It is interesting to note that
shape of the predicted pseudo-rapidity $\eta^{\rm jet}$ distribution coincide
with the one obtained in the collinear NLO calculations~[7, 25].
At the same time the shape of this distribution
is not reproduced by the leading-order QCD calculations~[4].
This fact can demonstrate again that the main part of the collinear
high-order corrections is already included at LO level in
$k_T$-factorization formalism.
The scale dependence of our predictions is about 10\%.

The most important variables for testing the structure of colliding
proton and photon are the longitudinal fractional momenta of partons in these particles.
In order to reconstruct the momentum fractions of the
initial partons from measured quantities the observables $x_\gamma$ and
$x_p$ are introduced~[4]:
$$
  \displaystyle x_\gamma = {E_T^\gamma ( e^{ - \eta^\gamma} + e^{ - \eta^{\rm jet}} )\over 2 y E_e}, \quad
  \displaystyle x_p = {E_T^\gamma ( e^{\eta^\gamma} + e^{\eta^{\rm jet}} )\over 2 E_p}. \eqno(18)
$$

\noindent
These observables make explicit use only of the photon energy, which is better measured
than the jet energy. The $x_\gamma$ distribution is particularly sensitive to the
photon structure function. At large $x_\gamma$ region ($x_\gamma > 0.85$) the cross
section is dominated by the contribution of processes with direct initial photons, whereas
at $x_\gamma < 0.85$ the resolved photon contributions dominate~[4].

So, in Figures~15 and~16 the $x_\gamma$ and $x_p$ distributions are shown in comparison with H1 data.
One can see that our
predictions reasonable agree with experimental data. The NLO calculations~[7, 25] without corrections
for hadronisation and multiple interactions give the similar results. However, NLO calculations
tend to underestimate the H1 data if these corrections are taken into account. The hadronic and
multiple interaction corrections improve the description of the data at $x_\gamma < 0.6$ only~[4].

Further understanding of the process dynamics and in particular of the high-order correction effects
may be obtained from the transverse correlation between the produced prompt photon and the jet.
The H1 collaboration has measured the distribution on the component of the
prompt photon's momentum perpendicular to the jet direction in the transverse plane, i.e.
$$
  p_T = |{\mathbf p}_{T}^\gamma \times {\mathbf p}_{T}^{\rm jet}|/|{\mathbf p}_{T}^{\rm jet}| = E_T^\gamma \sin \Delta \phi, \eqno(19)
$$

\noindent
where $\Delta \phi$ is the difference in azimuth between the photon and the jet. In the
collinear leading order approximation, the distribution over $p_T$ must be simply
a delta function $\delta(p_T)$, since the produced photon and the jet are back-to-back
in the transverse plane. Taking into account the non-vanishing initial parton
transverse momenta ${\mathbf k}_{1 T}$ and ${\mathbf k}_{2 T}$ leads to the violation
of this back-to-back kinematics in the $k_T$-factorization approach.

The normalised $p_T$ distributions are shown in Figures~17 and~18 separately for the
regions $x_\gamma < 0.85$ and $x_\gamma > 0.85$, where direct and resolved photon induced
processes dominate, respectively. All histograms here are the same as in Figure~4.
Our predictions are consistent with the H1 data for all $x_\gamma$ values
except large $p_T$ region. So, at $p_T > 5$ GeV the results of our calculations lie slightly below the
data at $x_\gamma < 0.85$ and above the data at $x_\gamma > 0.85$.
At the same time the NLO QCD prediction~[7] gives a better description of the $p_T$
distributions at $x_\gamma < 0.85$ than another one~[25]. It is because in this region
the cross section is dominated by ${\cal O}(\alpha_s)$ corrections to the processes with
resolved photons, which are not included in the NLO calculations~[25].
In general, we can conclude that our results lie between the predictions~[7] and the predictions~[25]
in the whole $x_\gamma$ range. This fact indicates again that the
main part of the high-order collinear
corrections is effectively included in our calculations.

Finally, we would like to note that there are, of course, still rather
large theoretical uncertainties in our results connected with
unintegrated parton distributions, and it is necessary to work hard until
these uncertainties will be reduced. However, it was shown~[24] that the
properties of different unintegrated parton distributions clear manifest themselves in the
azimuthal correlation between transverse momenta of the final state particles.
Therefore we can expect that further theoretical and experimental studying of
these correlations will give important information about non-collinear parton evolution
dynamics in a proton and in a photon.

\section{Conclusions} \indent

We have investigated the prompt photon photoproduction at the HERA collider in the
$k_T$-factorization approach. In order to obtain the unintegrated quark and gluon distributions
in a proton and in a photon we used the Kimber-Martin-Ryskin prescription. We have investigated
both inclusive and associated with jet prompt photon production rates. Such calculations
in the $k_T$-factorization approach were performed for the first time.

We took into account both the direct and resolved contributions and investigated
the sensitivity of the our results to renormalization and factorization scales. There are,
of course, also theoretical uncertainties due to non-collinear evolution scheme.
However, much more work needs to be done before these uncertainties will be reduced.

We have found that our predictions for the inclusive prompt photon production
are in reasonable agreement with the H1 and ZEUS data except rear (electron direction) pseudo-rapidity
region. In contrast, our results for prompt photon associated with jet are
consistent with data in the whole kinematical range. However, the scale dependence of our results
is rather large compared to the collinear NLO QCD calculations.
At the same time we demonstrate that main part of the standard
high-order corrections is already included in the $k_T$-factorization formalism at
LO level.

Note that in our analysis we neglect the contribution from the fragmentation processes
and from the direct box diagram ($\gamma g \to \gamma g$). Since the relative large
box contribution (about 6\% of the total NLO cross section) is mainly due to large gluonic
content of the proton at small $x$, studying of this subprocess should be also
very interesting in the $k_T$-factorization approach.
We plan to investigate it in detail in the forthcoming publications.

\section{Acknowledgements} \indent

The authors are very grateful also to S.P.~Baranov for encouraging interest
and helpful discussions. This research was supported in part by the FASI of Russian Federation.

\section{Appendix} \indent

Here we present the compact analytic expressions for the
hard matrix elements which appear in (13) and (15). In the
following, $\hat s$, $\hat t$ and $\hat u$ are usual Mandelstam
variables for corresponding $2 \to 2$ subprocesses and
$e_q$ is the fractional electric charge of quark $q$.

We start from the direct subprocess (7). The corresponding
squared matrix element summed over final polarization states and
averaged over initial ones read
$$
  |\bar {\cal M}|^2(\gamma q \to \gamma q) = {\displaystyle 2 (4\pi)^2 \alpha_{em}^2 e_q^4 \over
  \displaystyle (\hat s - m^2)^2 (\hat u - m^2)^2 } F_{\gamma q} ({\mathbf k}_{2 T}^2), \eqno (A.1)
$$

\noindent
where $m$ is the quark mass, and
$$
  F_{\gamma q} ({\mathbf k}_{T}^2) = 6 m^8 - (3 \hat s^2 + 14 \hat s \hat u + 3 \hat u^2) m^4 + (\hat s^3 + 7 \hat s^2 \hat u + \atop 7 \hat u^2 \hat s + \hat u^3) m^2 - (\hat s^2 + \hat u^2) \hat s \hat u. \eqno(A.2)
$$

\noindent
It is important to note that when we calculate the Dirac's traces we set the incoming
quark four-momentum to be equal $k_2 = x_2 p_p$. Therefore these formulas formally are the same as in
the usual leading-order collinear approach and there is no obvious dependence on the
parton transverse momentum ${\mathbf k}_{2 T}$. However, this dependence is present because
we have used true off-shell kinematics in order to
estimate the cross section (13).
It is in the clear contrast with the collinear calculations.

The squared matrix elements of the resolved photon contributions (8) --- (10)
summed over final polarization states and averaged over initial ones read
$$
  |\bar {\cal M}|^2(q g \to \gamma q) = {\displaystyle (4\pi)^2 \alpha_{em} \alpha_s e_q^2 \over
  \displaystyle 3 (\hat t - m^2)^2 (\hat s - m^2)^2 } F_{q g} ({\mathbf k}_{1 T}^2, {\mathbf k}_{2 T}^2), \eqno (A.3)
$$
$$
  |\bar {\cal M}|^2(g q \to \gamma q) = {\displaystyle (4\pi)^2 \alpha_{em} \alpha_s e_q^2 \over
  \displaystyle 3 (\hat s - m^2)^2 (\hat u - m^2)^2 } F_{g q} ({\mathbf k}_{1 T}^2, {\mathbf k}_{2 T}^2), \eqno (A.4)
$$
$$
  |\bar {\cal M}|^2(q q \to \gamma g) = - {\displaystyle 8 (4\pi)^2 \alpha_{em} \alpha_s e_q^2 \over
  \displaystyle 9 (\hat t - m^2)^2 (\hat u - m^2)^2 } F_{q q} ({\mathbf k}_{1 T}^2, {\mathbf k}_{2 T}^2), \eqno (A.5)
$$

\noindent where functions $F_{qg}({\mathbf k}_{1 T}^2, {\mathbf k}_{2 T}^2)$,
$F_{gq}({\mathbf k}_{1 T}^2, {\mathbf k}_{2 T}^2)$ and $F_{qq}({\mathbf k}_{1 T}^2, {\mathbf k}_{2 T}^2)$ are given by
$$
  F_{q g} ({\mathbf k}_{1 T}^2, {\mathbf k}_{2 T}^2) = 6 m^ 8 - (2 {\mathbf k}_{2 T}^4 + 2 (\hat s + \hat t) {\mathbf k}_{2 T}^2 + 3 \hat s^2 + 3 \hat t^2 + 14 \hat s \hat t)m^4 +
$$
$$
  (2 (\hat s + \hat t) {\mathbf k}_{2 T}^4 + 8 \hat s \hat t {\mathbf k}_{2 T}^2 + \hat s^3 + \hat t^3 + 7 \hat s \hat t^2 + 7 \hat s^2 \hat t) m^2 -
$$
$$
   \hat s \hat t (2 {\mathbf k}_{2 T}^4 + 2 (\hat s + \hat t) {\mathbf k}_{2 T}^2 + \hat s^2 + \hat t^2), \eqno(A.6)
$$
$$
  F_{g q} ({\mathbf k}_{1 T}^2, {\mathbf k}_{2 T}^2) = 6 m^ 8 - (2 {\mathbf k}_{1 T}^4 + 2 (\hat s + \hat u) {\mathbf k}_{1 T}^2 + 3 \hat s^2 + 3 \hat u^2 + 14 \hat s \hat u)m^4 +
$$
$$
  (2 (\hat s + \hat u) {\mathbf k}_{1 T}^4 + 8 \hat s \hat u {\mathbf k}_{1 T}^2 + \hat s^3 + \hat u^3 + 7 \hat s \hat u^2 + 7 \hat s^2 \hat u) m^2 -
$$
$$
   \hat s \hat u (2 {\mathbf k}_{1 T}^4 + 2 (\hat s + \hat u) {\mathbf k}_{1 T}^2 + \hat s^2 + \hat u^2), \eqno(A.7)
$$
$$
  F_{q q} ({\mathbf k}_{1 T}^2, {\mathbf k}_{2 T}^2) = 6 m^8 - (3 \hat t^2 + 3 \hat u^2 + 14 \hat t \hat u) m^4 + (\hat t^3 + \hat u^3 + \atop
  7 \hat t \hat u^2 + 7 \hat t^2 \hat u) m^2 - \hat t \hat u (\hat t^2 + \hat u^2). \eqno(A.8)
$$

\noindent
Since we take into account the ${\mathbf k}_{T}$ depencence of the incoming virtual gluon polarization
tensor, the functions $F_{q g} ({\mathbf k}_{1 T}^2, {\mathbf k}_{2 T}^2)$ and
$F_{g q} ({\mathbf k}_{1 T}^2, {\mathbf k}_{2 T}^2)$ also depend obviously on the
gluon transverse momentum. It is clear that if we take
the limit ${\mathbf k}_{1 T}^2 \to 0$, ${\mathbf k}_{2 T}^2 \to 0$ in (A.1) --- (A.8) we
easily obtain the corresponding collinear formulas.

Finally, we would like to point out again that in numerical computations we use precise
off-shell kinematics and therefore all expressions (A.1) --- (A.8) depends
on the parton transverse momentum. In particular, the incident
parton momentum fractions $x_1$ and $x_2$ in (13) and (15) have some ${\mathbf k}_{T}$ dependence.
In the limit ${\mathbf k}_{1 T} \to 0$, ${\mathbf k}_{2 T} \to 0$ we reproduce
standard leading-order QCD collinear results.

redpajama_set_name: RedPajamaArXiv


text:
Q: How do I set indexes for MySQL queries (JOIN, GROUP BY, ORDER BY, MULTIPLE CONDITIONS) For the below queries I already have a spatial index and indexes on the primary key (ID). Other than that I would like to know how I should set my indexes to make the below queries fast. In some cases the queries are very slow (more than 3 seconds). I'm only using SELECT statements on the tables which need to be fast, so it is not a problem in INSERT is taking longer.
I have two different queries in use.
QUERY 1:
SELECT *

FROM B

LEFT JOIN A AS C
ON B.id = C.id
LEFT JOIN A AS D
ON B.arid = D.id
LEFT JOIN E
ON B.opid = E.id

WHERE C.type='aa' AND D.type='aa'
AND
MBRWithin(C.lat_lng_point, GeomFromText('Polygon((57.5708387771 -6.08774442528, 54.3332809958 -6.08774442528, 54.3332809958 -0.305217949274, 57.5708387771 -0.305217949274, 57.5708387771 -6.08774442528))'))
AND
MBRWithin(destinationsto.lat_lng_point, GeomFromText('Polygon((50.4721888907 -0.111395950546, 47.2346311093 -0.111395950546, 47.2346311093 4.80899595055, 50.4721888907 4.80899595055, 50.4721888907 -0.111395950546))'))
LIMIT 0, 50

QUERY 2:
SELECT *
FROM (
SELECT (GLength(
LineStringFromWKB(
  LineString(
    lat_lng_point,
    GeomFromText('POINT(55.9520598864937 -3.19648118727903)')
  )
 )
))
AS distance

FROM (
SELECT * FROM A
WHERE MBRWithin(lat_lng_point, GeomFromText('Polygon((56.2218563683 -3.67835839361, 55.6822634047 -3.67835839361, 55.6822634047 -2.71460398094, 56.2218563683 -2.71460398094, 56.2218563683 -3.67835839361))'))
AND A.type = 'rr'
) AS A

LEFT JOIN B
ON A.id = B.id
ORDER BY distance ASC, main DESC
) AS t

GROUP BY trid
ORDER BY distance ASC
LIMIT 30

My question is: How do I set my table indexes for the queries above?

redpajama_set_name: RedPajamaStackExchange


The Hutton Mini Bag is a Stone pebbled leather cross body bag with vintage silver metal stud, clasp and hardware details. Sueded interior with a zipped pocket. Twist closure clasp with Aje logo. Leather belt strap with signature Aje buckle. Wear crossbody or as a belt bag.


Plastic Surgeon, Dr. Frank L. Stile offers a variety of injectable wrinkle relaxers at Stile Aesthetics, including BOTOX. Neuromodulators, like BOTOX, Dysport® and XEOMIN® each work by blocking the impulses from the nerve into the facial muscles. The result is that the underlying facial muscles start to relax and the skin begins to smooth out. This leads to younger looking skin that takes off years of aged wrinkles. At Stile Aesthetics, we will create a customized BOTOX treatment plan that will address your unique skin concerns. The effects will last approximately 3 – 4 months after which time you may choose to repeat the treatment. BOTOX can also be combined with other treatment options such as a PRP facial or a liquid facelift.
A BOTOX treatment is usually performed on the same day as your consultation in about 15 – 30 minutes as an outpatient procedure. The plastic surgeon will clean the treatment sites before the BOTOX is injected into the facial muscles with a thin needle. Most patients feel mild to no discomfort during the injection, but a local anesthesia or numbing cream can be used if the patient prefers. Patients will be able to leave immediately after their BOTOX treatment, but they should avoid lying down, touching the injection sites, and exercise for at least 24 hours. There may be temporary bruising, swelling, or redness in the first 1 – 2 days.
While some results will be seen immediately after the treatment, patients will see the results of BOTOX in 3 – 4 days as the dynamic wrinkles begin to soften and smooth. BOTOX treatments usually last 3 – 6 months, so patients are encouraged to schedule their next appointment after their treatment to prevent the results from fading. The plastic surgeon may also suggest a follow-up appointment several weeks after the initial treatment to check the patient's progress and add more BOTOX, if needed.
Make all the facial expressions you want without worrying about creating wrinkles that make you look older and tired by scheduling BOTOX sessions. Injectable wrinkle relaxer treatments with BOTOX Cosmetic will leave you refreshed and rejuvenated.


text:
The 8 Best Black Leggings
By Rachel Cavanaugh
There are too many awesome things about black leggings to count — they're comfortable, they go with everything, they hide stains ... and the list goes on. When it comes to finding the best black leggings, you'll usually want a combination of the following:
Softness: This one is kind of a no-brainer — you obviously want them to feel soft and cozy. Cotton tends to be the softest material, but it's also warm, so unless you're shopping for cold weather leggings, stick with polyester or other breathable blends.
Stretchiness and Recovery: Being comfortable is the whole point of leggings, so stretch is a key factor. However, you'll also want the fabric to have good recovery so they don't get baggy. Fabrics likes spandex, elastane, and LYCRA (which are all basically the same) will give you the most flexibility.
Moisture Management: If you plan to wear your legging to the gym or in hot weather, you'll want material that's breathable, moisture-wicking, and quick-drying. This will best be achieved via fabrics like polyester, rayon, and nylon.
With these considerations in mind, I've put together a list of the best black leggings on Amazon. I've included different categories for various occasions. Take a scroll to find the best fit for your closet.
1. The Best Casual Leggings
Conceited High-Waisted Women's Leggings
What's great about them: With more than 3,600 reviews, these hugely popular leggings — which can easily be worn as pants — have a virtual cult following. They're fully opaque, making them a great around-town option, and super comfortable, too. The combination means you can lounge on the couch comfortably but then run to the store without looking like you're wearing jammies. They have a high waist with quality stitching and a stretchy, cozy feel.
What fans say: "So very soft, I want to wear them for every occasion, and I DO!!! I wear these with dresses, skirts, long shirts as if they are regular pants because they are in no way see through- so who cares right!!! I love them, I bought a pair in black and teal, and am going back for more."
Available sizes: 0 to 10, 12 to 22
2. The Best Leggings To Wear To Work
Bamans Women's Stretch Yoga Dress Pants
What's great about them: If you're searching for the best leggings to wear to work, look no further than these sleek, black yoga tights from Bamans. They offer the perfect combination of comfort and professionalism. The material is made from a polyester-spandex blend that's soft, stretchy, and breathable (no pools of sweat during PowerPoint presentations). On top of all of that, they have pockets in the front and back for storage. Basically, wearing these leggings is like going to the office in sweatpants but looking like you're wearing freshly-pressed slacks.
Available sizes: Small - XX-Large
3. The Best Leggings To Wear Under Dresses
Daily Ritual Women's Ponte Knit Legging
What's great about them: Made from breathable rayon and nylon with a hint of spandex for stretch, these leggings not only look great as pants, but they're the best leggings for under dresses. They're thin and lightweight, so they don't feel bulky, and the ventilated fabric prevents you from getting hot. These high-waisted leggings are also smooth, so they move well with your dress rather than catching or bunching up. Best of all, each size comes in four different lengths to accommodate a wide range of heights.
What fans say: "These were perfect under a dress and with boots. The tummy support is great and they are very comfortable. Would recommend and plan to buy more colors."
Available sizes: X-Small - XX-Large (Short, Regular, Long, and Extra Long)
4. The Most Comfortable
LMB Women's Extra-Soft High-Waist Leggings
What's great about them: These soft and cozy tights are some of the most comfortable leggings on Amazon, according to reviewers. The fabric is constructed with mostly polyester (aka they're super soft) and a little spandex (aka they're flexible, too). They have a high waist to help them stay put and a contoured design that feels comfy and looks cute. They're super affordable and come in more than 40 other colors should you tire of black. A few reviewers wrote that they do wear out easily around the waist, so these might not be the most durable leggings. However, if you're looking for a cheap option that's extra comfortable, these are a great choice.
What fans say: "I am in love with these leggings!!! The yoga waist band and buttery soft fabric make these the most comfortable pair of pants I have ever worn. Nice high waistband, too, so I feel covered but not bulky in any way ... My only wish is that they would make these in patterns, too, instead of just the solids, but I am still over the moon to have found these leggings!"
Available sizes: One Size, X-Large/XXX-Large, Plus Size
5. The Best For Working Out
Under Armour Women's HeatGear Armour Legging
What's great about them: When it comes to the best leggings for working out, these stretchy tights from Under Armour fit the bill. The polyester-elastane mix makes them stretchy and breathable. And as a bonus, the material is antimicrobial, so they won't get stinky in the hamper. I personally have these leggings, and I can attest to how comfy they are — and moisture-wicking, too. My favorite part is that they stay up better than most of the other workout leggings I own. I can run, bike, hike, or participate in other high-movement exercises without spending the whole time yanking my tights up.
What fans say: "Absolutely love these leggings, and would highly consider buying more. They arrived promptly and fit like a glove.
Available sizes: X-Small - X-Large
6. The Best Compression Leggings
Reebok Women's Legging Full Length Performance Compression Pants
What's great about them: Whether you get sore after working out or just want to improve your circulation during exercise, these mild compression tights are an excellent option. Like several other pants on this list, they feature a blend of polyester and spandex (aka "polyspan") that offers moisture-wicking properties in addition to breathability. They are lightweight, bulk-free, and quick-drying. The mild compression is light enough that they don't feel too tight, yet they are still effective at reducing muscle fatigue and minimizing post-workout aches.
What fans say: "Love these leggings!! I have issues with leggings and usually have to buy them with a drawstring or have one put in but these stayed in place the whole time. So comfortable, long and with some compression. Definitely going to get another pair."
7. The Warmest Leggings For Winter
Yogipace Women's Fleece Lined Leggings Yoga Pants
What's great about them: Boasting hundreds of glowing reviews, these warm, fleece-lined leggings are some of the most-loved leggings on Amazon. Beyond just being warm, they're also water-resistant, come in a range of sizes and inseam lengths, and two pockets.
What fans say: "LOVE these leggings. Just wore them multiple days in a row on a trip to Iceland, was wishing I had brought 3 more pairs! Could not believe how warm yet breathable they were. Kept up great with movement, fluctuating temps, and iffy weather. Was also worried about water resistance, but never felt wet even though it rained the whole trip and we went behind waterfalls. "
Available sizes: XS-XXL, Tall, Regular, and Petite Inseam
8. The Best Capris Leggings
Free Country Women's Panel Capri
What's great about them: Whether you're searching for something to wear in the spring and summer, or you just like to have extra style options, these black capri leggings are a wonderful choice. The polyester-spandex blend is soft and moisture-wicking, so they're suitable for lounging around, as well as for working out. Plus, the trim is cute and trendy, so you can wear them with regular outfits, too. Not only that, but it also has reflective piping, so if you run or work out at night, you'll be extra visible.
What fans say: "These are high quality. Feel awesome."
Available sizes: Small, Large, X-Large
Elite Daily may receive a portion of sales from products purchased from this article, which was created independently from Elite Daily's editorial and sales departments.

redpajama_set_name: RedPajamaCommonCrawl


The primary goal of De Jure, the online platform of the UMKC Law Review, is to provide an online source for attorneys, judges, professors and current Law Review members, to access up-to-date responses, reflections and analysis of topics that change and evolve faster than the speed of print. We welcome submissions that adhere to our online parameters for publication and which are of the highest quality.
We hope that you enjoy reading the original thoughts, responses and ruminations of your friends and colleagues as they contemplate the evolving law under which we live and how we might contribute to its path.
*Please see De Jure submission information.


The Tickling Media Forum > STORIES > Tickling Stories > The Feather Game!
View Full Version : The Feather Game!
My older sister, Jodie, who believed that spanking was beyond her powers, would remove the shoes and socks of my younger sister (Laura) and I and would mercilessly tickle our soft bare soles with either a feather or her nails for a period of three minutes, when she babysat for us and we gave her any trouble. She continued to use the punishment until I was about 11 or 12, but either my parents had no objection to her using this on us, or never found out. I began to enjoy the punishment and tried to find ways to get her to use it, and also longed to tickle Jodie's feet, which remain luscious to this day (I succeeded in both goals,) though Laura had her objections and incredibly sensitive feet.
When I was 14, around the summer of '85, perhaps the most memorable tickling experience happened to me. Laura had about four of her friends over at our house for some kind of meeting. We were all barefoot because of the heat, which was typical summer shoe wear in our town without any hassle from those "No Shirt, No Shoes, No Service" signs. Towards the afternoon we all came inside, and you can only imagine how I felt at the time when they all came in wiggling their dusty barefeet and toes in my face, and several of them were complaining of how they ached. Many wanted foot massages.
- His/her big toes are tied together and honey, gravy or tuna is spread on their bare feet, and a cat or dog or other animal is invited to lick it off.
- S/he has his/her bare feet tickled until s/he reveals his/her most ticklish spot (if it's on the feet s/he has to say where on the feet. Anything said here can be used against him/her in extended tickling sessions. (After the punishment s/he remains a victim and is tickled at intervals longer than what were originally 3-4 minutes long.
You can also create a number of other punishments (please post if you do) or omit this part completely.
Reluctantly, she rolled onto a bed in the guest bedroom, propped up her feet that Lacey devotedly bound together, and slid on Jodie's night mask, which we usd as a blindfold. Lacey, probably also a foot fetishist, then sat on top of her legs to secure her. I didn't think her feet were as ticklish as they were, so I began the tickle torture by first massaging the balls of her feet, allowing anticipation, and then suddenly swept my feather up and down her bound soles. She was forcing back laughter as I did, and tried to cover up one foot with the other, which proved impossible because her big toes were tied together. She curled her toes in fear, which I bent back, and began to scribble against her bare feet with the feather's quille. She screamed out laughter. However, the foot tickling only lasted for about two minutes. She suddenly screamed out "Stop it! Jason!" but while using language slightly coarser than that.
In a way, I was glad to have been caught and unselfishly placed the night mask over my eyes and stretched out my dusty bare feet for the tickling. In silence, my tormentor was chosen. I soon felt the nylon being wrapped around my ankles and my toes being strung together. Someone held down my legs and the tickling began.
In addition to foot tickling, I am also a fan of barefooting and at the time would walk barefoot in order to build up my feet for track running throughout high school. My feet were like leather by July of that year, but were still no match for the tickling.
A stiff feather pricked at various parts of my feet, which jumped and quivered against their restraints. Finally it slithered up and down my feet and tried to cover the most ticklish part of my feet; the tops, over with my toes. Strange hands, however, held them back, and the skin on my feet tightened. Then the feather made a full attack. It moved like some kind of hyperactive spider on my bare soles, crawling over the arches, heels, insteps. Laughs and half thought reactions fluttered, escaping from my throat like frightened birds. The hand then parted my toes and the feather was at work again, sawing between them. I couldn't help but lower the blindfold with my free hands to see who this skilled tickler was. I slowly pushed it back, only to catch a sudden glimpse of Lacey who continued to administer the torture I was beginning to become less conscious of.


text:
Filly Face-off
It is not every day that the horse racing community finds themselves looking at two spectacular fillies at the same time. Generally, the colts are the biggest sensations and racing enthusiasts often try to convince owners to race the biggest names in racing against each other, for a breathtaking showdown. But this time around they are asking for a filly face-off. With the spectacular performances delivered by both Zenyatta and Rachel Alexandra, no-one can argue that theses two fillies have brought a renewed excitement to the horse racing industry.
Zenyatta made headlines last year with her perfect performances. Many had compared her to racing sensation Curlin, and others predicted that she might be able to surpass his achievements. This wonderful five year old has now won all ten her career starts, with her latest victory being at Hollywood Park, in the Milady Handicap. All though she has an unbeaten career behind her, she is yet to be raced against her male counterparts, but is still viewed as one of the best older horses on the track, across the board.
Rachel Alexandra catapulted herself and her racing career into the limelight with an amazing win in the Preakness Stakes. As a late entry, Rachel Alexandra delivered a spectacular victory over race favorite Mine That Bird, proving that she is capable of providing the colts with worthy competition. It is anticipated that she will be in the starting gates at the Belmont Stakes, and this three year old has most certainly taken horse racing by storm.
Although both these fillies have shown tremendous talent and skill on their own career paths, horse racing enthusiasts are now wondering what would happen, should these two racing ladies meet. Zenyatta, with her relaxed style, prefers to remain behind and then deliver a devastating blow to her competitors near the end of a race, while Rachel Alexandra goes full tilt from start to finish and usually has everyone else in the field trying to catch up. Pitting these greatly different styles of racing against each other, would create a historical showdown and an unforgettable race. It is hoped that the paths of these two racing greats will meet, and provide horse racing with an event to remember.


Olivier is the partner leading the global Indirect Tax Recovery offering. Leveraging Deloitte proprietary Revatic Smart technology, a standardized global approach and a worldwide network of indirect tax specialists, Deloitte assists businesses through the VAT recovery lifecycle. Olivier combines the role of Global Indirect Tax Recovery lead with the role of responsible partner for the Romandie indirect tax team and co-leader for Deloitte's Global Tax Center Europe in Brussels.


text:
package org.apache.qpid.jms.provider.amqp;

import java.io.IOException;
import java.util.ArrayList;
import java.util.LinkedHashSet;
import java.util.LinkedList;
import java.util.List;
import java.util.Set;

import javax.jms.JMSException;

import org.apache.qpid.jms.message.JmsOutboundMessageDispatch;
import org.apache.qpid.jms.message.facade.JmsMessageFacade;
import org.apache.qpid.jms.meta.JmsProducerInfo;
import org.apache.qpid.jms.provider.AsyncResult;
import org.apache.qpid.jms.provider.amqp.message.AmqpJmsMessageFacade;
import org.apache.qpid.jms.util.IOExceptionSupport;
import org.apache.qpid.proton.amqp.Binary;
import org.apache.qpid.proton.amqp.messaging.Accepted;
import org.apache.qpid.proton.amqp.messaging.Modified;
import org.apache.qpid.proton.amqp.messaging.Outcome;
import org.apache.qpid.proton.amqp.messaging.Rejected;
import org.apache.qpid.proton.amqp.messaging.Released;
import org.apache.qpid.proton.amqp.transaction.TransactionalState;
import org.apache.qpid.proton.amqp.transport.DeliveryState;
import org.apache.qpid.proton.amqp.transport.ErrorCondition;
import org.apache.qpid.proton.engine.Delivery;
import org.apache.qpid.proton.engine.Sender;
import org.apache.qpid.proton.message.Message;
import org.slf4j.Logger;
import org.slf4j.LoggerFactory;

/**
 * AMQP Producer object that is used to manage JMS MessageProducer semantics.
 *
 * This Producer is fixed to a given JmsDestination and can only produce messages to it.
 */
public class AmqpFixedProducer extends AmqpProducer {

    private static final Logger LOG = LoggerFactory.getLogger(AmqpFixedProducer.class);
    private static final byte[] EMPTY_BYTE_ARRAY = new byte[] {};

    private final AmqpTransferTagGenerator tagGenerator = new AmqpTransferTagGenerator(true);
    private final Set<Delivery> pending = new LinkedHashSet<Delivery>();
    private final LinkedList<PendingSend> pendingSends = new LinkedList<PendingSend>();
    private byte[] encodeBuffer = new byte[1024 * 8];
    private boolean presettle = false;

    public AmqpFixedProducer(AmqpSession session, JmsProducerInfo info) {
        super(session, info);
    }

    public AmqpFixedProducer(AmqpSession session, JmsProducerInfo info, Sender sender) {
        super(session, info, sender);
    }

    @Override
    public void close(AsyncResult request) {
        // If any sends are held we need to wait for them to complete.
        if (!pendingSends.isEmpty()) {
            this.closeRequest = request;
            return;
        }

        super.close(request);
    }

    @Override
    public boolean send(JmsOutboundMessageDispatch envelope, AsyncResult request) throws IOException, JMSException {
        // TODO - Handle the case where remote has no credit which means we can't send to it.
        //        We need to hold the send until remote credit becomes available but we should
        //        also have a send timeout option and filter timed out sends.
        if (getEndpoint().getCredit() <= 0) {
            LOG.trace("Holding Message send until credit is available.");
            // Once a message goes into a held mode we no longer can send it async, so
            // we clear the async flag if set to avoid the sender never getting notified.
            envelope.setSendAsync(false);
            this.pendingSends.addLast(new PendingSend(envelope, request));
            return false;
        } else {
            doSend(envelope, request);
            return true;
        }
    }

    private void doSend(JmsOutboundMessageDispatch envelope, AsyncResult request) throws IOException, JMSException {
        JmsMessageFacade facade = envelope.getMessage().getFacade();

        LOG.trace("Producer sending message: {}", envelope);

        byte[] tag = tagGenerator.getNextTag();
        Delivery delivery = null;

        if (presettle) {
            delivery = getEndpoint().delivery(EMPTY_BYTE_ARRAY, 0, 0);
        } else {
            delivery = getEndpoint().delivery(tag, 0, tag.length);
        }

        delivery.setContext(request);

        if (session.isTransacted()) {
            Binary amqpTxId = session.getTransactionContext().getAmqpTransactionId();
            TransactionalState state = new TransactionalState();
            state.setTxnId(amqpTxId);
            delivery.disposition(state);
        }

        AmqpJmsMessageFacade amqpMessageFacade = (AmqpJmsMessageFacade) facade;
        encodeAndSend(amqpMessageFacade.getAmqpMessage(), delivery);

        if (presettle) {
            delivery.settle();
        } else {
            pending.add(delivery);
            getEndpoint().advance();
        }

        if (envelope.isSendAsync() || presettle) {
            request.onSuccess();
        }
    }

    private void encodeAndSend(Message message, Delivery delivery) throws IOException {

        int encodedSize;
        while (true) {
            try {
                encodedSize = message.encode(encodeBuffer, 0, encodeBuffer.length);
                break;
            } catch (java.nio.BufferOverflowException e) {
                encodeBuffer = new byte[encodeBuffer.length * 2];
            }
        }

        int sentSoFar = 0;

        while (true) {
            int sent = getEndpoint().send(encodeBuffer, sentSoFar, encodedSize - sentSoFar);
            if (sent > 0) {
                sentSoFar += sent;
                if ((encodedSize - sentSoFar) == 0) {
                    break;
                }
            } else {
                LOG.warn("{} failed to send any data from current Message.", this);
            }
        }
    }

    @Override
    public void processFlowUpdates(AmqpProvider provider) throws IOException {
        if (!pendingSends.isEmpty() && getEndpoint().getCredit() > 0) {
            while (getEndpoint().getCredit() > 0 && !pendingSends.isEmpty()) {
                LOG.trace("Dispatching previously held send");
                PendingSend held = pendingSends.pop();
                try {
                    doSend(held.envelope, held.request);
                } catch (JMSException e) {
                    throw IOExceptionSupport.create(e);
                }
            }
        }

        // Once the pending sends queue is drained we can propagate the close request.
        if (pendingSends.isEmpty() && isAwaitingClose()) {
            super.close(closeRequest);
        }

        super.processFlowUpdates(provider);
    }

    @Override
    public void processDeliveryUpdates(AmqpProvider provider) throws IOException {
        List<Delivery> toRemove = new ArrayList<Delivery>();

        for (Delivery delivery : pending) {
            DeliveryState state = delivery.getRemoteState();
            if (state == null) {
                continue;
            }

            Outcome outcome = null;
            if (state instanceof TransactionalState) {
                LOG.trace("State of delivery is Transactional, retrieving outcome: {}", state);
                outcome = ((TransactionalState) state).getOutcome();
            } else if (state instanceof Outcome) {
                outcome = (Outcome) state;
            } else {
                LOG.warn("Message send updated with unsupported state: {}", state);
                outcome = null;
            }

            AsyncResult request = (AsyncResult) delivery.getContext();
            Exception deliveryError = null;

            if (outcome instanceof Accepted) {
                LOG.trace("Outcome of delivery was accepted: {}", delivery);
                if (request != null && !request.isComplete()) {
                    request.onSuccess();
                }
            } else if (outcome instanceof Rejected) {
                LOG.trace("Outcome of delivery was rejected: {}", delivery);
                ErrorCondition remoteError = ((Rejected) outcome).getError();
                if (remoteError == null) {
                    remoteError = getEndpoint().getRemoteCondition();
                }

                deliveryError = AmqpSupport.convertToException(remoteError);
            } else if (outcome instanceof Released) {
                LOG.trace("Outcome of delivery was released: {}", delivery);
                deliveryError = new JMSException("Delivery failed: released by receiver");
            } else if (outcome instanceof Modified) {
                LOG.trace("Outcome of delivery was modified: {}", delivery);
                deliveryError = new JMSException("Delivery failed: failure at remote");
            }

            if (deliveryError != null) {
                if (request != null && !request.isComplete()) {
                    request.onFailure(deliveryError);
                } else {
                    connection.getProvider().fireNonFatalProviderException(deliveryError);
                }
            }

            tagGenerator.returnTag(delivery.getTag());
            toRemove.add(delivery);
            delivery.settle();
        }

        pending.removeAll(toRemove);

        super.processDeliveryUpdates(provider);
    }

    public AmqpSession getSession() {
        return session;
    }

    @Override
    public boolean isAnonymous() {
        return getResourceInfo().getDestination() == null;
    }

    @Override
    public void setPresettle(boolean presettle) {
        this.presettle = presettle;
    }

    @Override
    public boolean isPresettle() {
        return presettle;
    }

    @Override
    public String toString() {
        return "AmqpFixedProducer { " + getProducerId() + " }";
    }

    private static class PendingSend {

        public JmsOutboundMessageDispatch envelope;
        public AsyncResult request;

        public PendingSend(JmsOutboundMessageDispatch envelope, AsyncResult request) {
            this.envelope = envelope;
            this.request = request;
        }
    }

    @Override
    public void remotelyClosed(AmqpProvider provider) {
        super.remotelyClosed(provider);

        Exception ex = AmqpSupport.convertToException(getEndpoint().getRemoteCondition());
        if (ex == null) {
            // TODO: create/use a more specific/appropriate exception type?
            ex = new JMSException("Producer closed remotely before message transfer result was notified");
        }

        for (Delivery delivery : pending) {
            try {
                AsyncResult request = (AsyncResult) delivery.getContext();

                if (request != null && !request.isComplete()) {
                    request.onFailure(ex);
                }

                delivery.settle();
                tagGenerator.returnTag(delivery.getTag());
            } catch (Exception e) {
                LOG.debug("Caught exception when failing pending send during remote producer closure: {}", delivery, e);
            }
        }

        pending.clear();
    }
}

redpajama_set_name: RedPajamaGithub


text:
Q: Scraping with multiple IP, in java Well basically I have a scraping application.
It scrapes around n items per minute.
currently i have only one IP.
The site i'm scraping allows me 3 connections per IP.
I'm thinking about getting another IP.
so i'll be able to get 6 connections.
in theory i should be able to get n items in 40 seconds, more or less.
currently i'm using java (commons-httpcore) to get the job done.
I'm not sure if this is java question or an OS question.
my machine has IP 1 and IP 2
how do i connect to, say, www.microsoft.com,
using IP 1 and using IP2?
how can i specify, which ip i want to use to do a connection?

A: // requires HttpComponents Client 4.*
DefaultHttpClient httpclient = new DefaultHttpClient();
httpclient.getParams().setParameter(
  ConnRoutePNames.LOCAL_ADDRESS,
  InetAddress.getByName("10.10.10.10")
);

See: http://hc.apache.org/httpcomponents-client/httpclient/apidocs/index.html


Mega-Lite introduces the Nova-Lite series of lighting fixtures designed for both stage and house lighting needs. There are six new fixtures in the series with extra-wide coverage offering color changing, white and ultra violet output options.
The Nova-Lite Q200 (RGBW), Nova-Lite T200 (RGB) and Nova-Lite UV200 (ultra violet) fixtures are all equipped with a 200-watt single source LED. The Nova-Lite VW150 (variable white), Nova-Lite WW150 (warm white) and Nova-Lite CW150 (cool white) house a 150-watt LED. The units have a 55-degree reflector beam angle and also ship with 30-degree and 15-degree lenses for longer throw applications.
A 60-degree diffuser accessory is available for softening the edge of the output. A barn door is also an available accessory. These units are designed for house light applications and come with a hanging adapter designed to fit a ½ inch all-thread or steal cable. Additionally, the series is ETL listed.


This chapter considers strategies that can be applied by various entities to improve the collection of these data and facilitate subsequent reporting of stratified quality measures.
It begins by examining current practices and issues related to collecting and sharing data across the health care system.
To identify the next steps toward improving data collection, it is helpful to understand these opportunities and challenges in the context of current practices.
While a range of health and health care entities collect data, the data do not flow among these entities in a cohesive or standardized way.
Entities within the health care system face challenges when collecting race, ethnicity, and language data from patients, enrollees, members, and respondents.
Explicitly expressing the rationale for the data collection and training staff, organizational leadership, and the public to appreciate the need to use valid collection mechanisms may improve the situation.
Nevertheless, some entities face health information technology (Health IT) constraints and internal resistance.
Indirect estimation techniques, when used with an understanding of the probabilistic nature of the data, can supplement direct data collection efforts Addressing health and health care disparities requires the full involvement of organizations that have an existing infrastructure for quality measurement and improvement.Although hospitals, community health centers (CHCs), physician practices, health plans, and local, state, and federal agencies can all play key roles by incorporating race, ethnicity, and language data into existing data collection and quality reporting efforts, each faces opportunities and challenges in attempting to achieve this objective.


DALLAS, Sept. 20, 2018 /PRNewswire/ — Generational Group, a leading mergers and acquisitions advisor for privately held businesses, is pleased to announce today that David Fergusson has joined the firm as Senior Managing Director and Group Leader – M&A. Mr. Fergusson will open and lead an M&A office in Manhattan. His responsibilities will include leading the firm's expansion across the Northeast region and Canada, and establishing a cross border international M&A practice.
DALLAS, Sept. 19, 2018 /PRNewswire/ — Generational Group, a leading mergers and acquisitions advisor for privately held businesses, is pleased to announce that it recently surpassed a major M&A milestone, having now transferred over $4 billion in wealth to its clients.
DALLAS, Aug. 27, 2018 /PRNewswire/ — Generational Group (Generational) a leading mergers and acquisitions advisor for privately-held, middle-market businesses, is pleased to announce that it has signed a national sponsorship agreement with Vistage Worldwide (Vistage). The agreement solidifies Generational's commitment to providing M&A educational conferences and related services to the Vistage network.
DALLAS, Aug. 22, 2018 /PRNewswire/ — Generational Equity, a leading mergers and acquisitions advisor for privately held, middle-market businesses, is pleased to announce continued expansion of the firm with the opening of a new office in Columbus, Ohio. The Columbus office will be led by Jerry Yocum, Managing Director, Mergers & Acquisitions.
DALLAS, Aug. 1, 2018 /PRNewswire/ — Generational Equity, a leading mergers and acquisitions advisor for privately held businesses, is pleased to announce the sale of its client, Polymer Solutions Inc., to SGS North America Inc. The acquisition closed May 31, 2018.


text:
Lifesaving Gear Arrives in the Hurunui
Monday, 17 June 2019, 2:53 pm
Press Release: Hurunui District Council
The Hurunui is getting brand new, outdoor defibrillators to assist some of our most remote communities.
The New Zealand Red Cross have provided four automated external defibrillators (AEDs) to our district and, in doing so, brought an additional safety net to some of our most isolated areas.
These AEDs came about after our Emergency Management Officer put in a request to the New Zealand Red Cross for an outdoor AED in Mount Lyford. The NZ Red Cross assessed the request in reference to their November 2016 Earthquake Recovery Programme. They then offered four new AEDs to the Hurunui, as part of the recovery programme, adding to our future resilience and preparedness.
Two of the four AEDs have already been installed, one in Mt Lyford, on the outside of the Mt Lyford Lodge, and the other in Scargill/Motunau Reserve, on the side of the squash courts. The remaining two are to be installed on the Conway Hall and at the Boylel River Department of Conservation Camping Ground.
Dean Eades, our Emergency Management Officer, explained perfectly how we are all feeling in light of the news AEDs. "We are over the moon that Red Cross have provided our more isolated communities with this lifesaving equipment" he said. "The new defibs [defibrillators] add to the resilience of our communities"
Karyn Jans, Part Owner/Operator of Mt Lyford Lodge, explained how the new outdoor unit [accessible at all hours] is great for the community. "For us it's a lifesaving piece of equipment that is needed and is now accessible to the whole area."
Michael Donoghue, Recovery Manager with New Zealand Red Cross, said: "The evidence is clear – these devices can save lives in an emergency when each minute is critical. We would like to remind anyone who is living, working or travelling in rural communities to take a moment to find out where the nearest AED is located.
"We are delighted to provide these four additional units into the Hurunui district. This has only been possible with the help of our amazing donors, who support New Zealand Red Cross. Each device has an expected lifespan of about 8 years, which will also include refreshing batteries and pads when needed. If you are keen to sponsor a new AED for your community please get in touch."
Dean Eades
Emergency Management Officer
Hurunui District Council
dean.eades@hurunui.govt.nz
To talk to the Red Cross about AED Sponsorship:
Mary Baines
Senior Communications Advisor
New Zealand Red Cross
Mary.Baines@redcross.org.nz
Find more from Hurunui District Council on InfoPages.


text:
The Return of Martin Guerre
Preface and Introduction Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Epilogue
All Themes Identity and Property Narrative and Authority Women, Honor, and Power The Nature of Evidence
All Characters Martin Guerre Bertrande de Rols Arnaud du Tilh Sanxi the Elder Pierre Sanxi the Younger Bernarde du Tilh Jean d'Escornebeuf Jean de Coras Guillaume Le Sueur Michel de Montaigne
All Symbols Martin's Wooden Leg The Carnival Mask
Instant downloads of all 1393 LitChart PDFs (including The Return of Martin Guerre).
Natalie Zemon Davis
Teachers and parents! Struggling with distance learning? Our Teacher Edition on The Return of Martin Guerre can help.
Preface and Introduction
Identity and Property
Narrative and Authority
Women, Honor, and Power
The Nature of Evidence
Martin Guerre
Bertrande de Rols
Arnaud du Tilh
Sanxi the Elder
Sanxi the Younger
Bernarde du Tilh
Jean d'Escornebeuf
Jean de Coras
Guillaume Le Sueur
Martin's Wooden Leg
The Carnival Mask
The Return of Martin Guerre: Chapter 11 Summary & Analysis
Themes and Colors Key
LitCharts assigns a color and icon to each theme in The Return of Martin Guerre, which you can use to track the themes throughout the work.
Le Sueur's book about the case, Admiranda historia (published in 1561) is a straightforward news pamphlet that simply summarizes the case and draws an appropriate moral at the end. The book sold well, suggesting that there was significant appetite for news about the case. By contrast, Davis describes Coras's Arrest Memorable, published in the same year, as an "innovative" book. Although the book resembles a traditional legal commentary, Coras in fact devotes relatively little attention to legal matters, choosing instead to focus on the story and characters. The book was in French rather than Latin, the language of the courts. He described the case of Martin Guerre as "prodigious," implying it was unlike anything that France had ever seen before. Davis points out that Coras was probably the first legal figure in France to write a book about the law for popular publication.
Davis draws a contrast between a more traditional legal narrative, the Admiranda historia, and Coras's Arrest Memorable. Coras's book represents a new way of writing about the law—perhaps much as Davis's book frames itself as a new way of writing about the past. For one, Coras's book was far more accessible: it was written in a language people could read, and it was intended for popular publication rather than an audience of fellow lawyers and legal scholars. It focused not on dry legal facts but on the more colorful details of the case. In this sense, the Arrest Memorable is a book that encompasses multiple genres: part legal narrative, part social critique, part fiction.
Active Themes
This "new use of a traditional form" allowed Coras to play with the relationship between "text" and "annotation." Unlike a conventional legal commentary, which presents cases with marginal explanations by the author, Coras's annotations often had little to do with the law and focused instead on social and philosophical issues.
Coras's book shows the way that a traditional narrative form—the legal commentary—can be subverted and used in a new way. Where the reader might expect notes on the details of the law, Coras instead presents annotations on the law's broader social implications.
Davis suggests that Coras used the case to comment on ideas and issues that mattered to him, such as evidence, the nature of proof, and social problems like child marriage and spousal abandonment. Both Coras and Le Sueur may have found that the story contained a Protestant message. They dedicated their books to Protestant patrons, and they suggested that this case might not have happened under a Protestant church, since a Protestant church would have allowed Bertrande to dissolve her marriage after her abandonment.
A case like Martin Guerre's mattered not just because it was sensational and unusual, but because it became a way of commenting on larger social concerns. For example, Coras could use the complexities of church law to suggest that Protestantism might offer a better alternative to the strict rules of Catholicism.
Coras's Arrest Memorable mounts arguments for and against the accused. For example, he calls Arnaud the "defendant" in the text and "this prodigious offender" in the annotation. He also makes some changes, exaggerating Arnaud's powers of memory and accusing him of greater crimes (including dealings with the devil). He writes that Bertrande was easily deceived by "the weakness of her sex," but is unsympathetic to Martin for abandoning his wife, and he leaves out the details of Arnaud's confession.
By omitting the details of Arnaud's confession, Coras leaves the reader with doubts that the court really did convict the right man. Although on the one hand he seems to condemn Arnaud, he is also more sympathetic to him in some places—lending the book a narrative complexity that one doesn't often find in legal commentaries.
Get the entire The Return of Martin Guerre LitChart as a printable PDF.
In the 1565 edition, Coras adds a description of Arnaud's confession at Artigat. His annotation describes the story as "a tragedy for this fine peasant" that "makes it hard to tell the difference between tragedy and comedy." Davis points out that Coras is being very innovative here, since French tragedies and tragicomedies—like, for example, the popular translations of the Histoires tragiques of Bandello— typically feature only aristocratic personages. It also suggests that he may have been sympathetic to Arnaud as a tragic hero. In this reading, the tragedy is in Arnaud's punishment, not in the crime.
Davis suggests that Coras's book is so memorable in part because it leaves the reader with a fundamental ambiguity: is Arnaud a villain or a hero? The outcome of the case, which ended with Arnaud's conviction and execution, would suggest the former. But by describing the case as a "tragedy," Coras leaves room for a different interpretation.
Related Quotes with Explanations


text:
Features Harvesting Sustainability
California secures 45 MW of green energy.
Apr. 13, 2012 - The Imperial Irrigation District Board of Directors has approved a 10-year power purchase agreement with a local energy producer to secure 45 megawatts of green energy.
April 13, 2012 By Imperial Irrigation District Board of Directors
Apr. 13, 2012 – Aiming to meet California's renewable energy requirements, the
Imperial Irrigation District Board of Directors today unanimously
approved a 10-year power purchase agreement with a local energy producer
to secure 45 megawatts of green energy.
At an annual average cost of $35 million, IID will begin delivering
electricity generated by the Greenleaf Power biomass facility, located
in the district's Riverside County community of Mecca, starting May 1.
The acquisition of this new source of energy enhances and
diversifies IID's renewable energy portfolio from 12 to 18 percent,
moving the utility closer to reaching its renewable energy goals.
California law requires utilities deliver 20 percent green energy by 2013, 25 percent by 2016 and 33 percent by 2020.
"Our contract with Desert View Power represents our due diligence in
not only working to meet California's aggressive green energy goals,
but doing so in a way that is cost competitive and supports a proven
renewable energy leader in our own backyard," said John Pierre
Menvielle, board President.
Located 40 miles south of Palm Springs, Desert View Power is the
largest biomass energy producer in California. The facility incorporates
state-of-the art technology to generate electricity from clean urban
wood waste, forest and agricultural residue.
The facility uses a circulating fluid-bed technology, making it one
of the more advanced biomass power facilities in North America.
In 2010, under operator Colmac Energy, the facility was recognized
as one of the top six best renewable energy power plants in the nation
due to its impressive environmental accomplishments. Built in 1992, the
plant produces up to 47 megawatts of green energy and employs 39 people.
In early 2012, IID affirmed its commitment to California's Renewable
Portfolio Enforcement Program by resolving to meet the state's
compliance targets. In doing so, it also drafted a renewable portfolio
standards policy that includes a detailed enforcement program and
procurement plan.
Pellet prices increase as oil soars
Denmark invests in wood pellets