text:
John Fraser [also, more commonly then, Frisel or Frisell] (died 1507) was a late medieval Scottish prelate. Born about 1429, or 1430 if later tradition can be believed, with strong connections to the burgh of Linlithgow, Fraser held a variety of high-level ecclesiastical positions in Scotland, including being the first Dean of Restalrig collegiate church (which he helped to found) before becoming Bishop of Ross in 1497, a position he held until his death in 1507.

Early career
Fraser was a university graduate, M. A., and he seems to have been the John Fraser who was Dean of the Faculty of Arts at the University of St Andrews in 1479. He is found as Provost of the collegiate church of Abernethy on 2 February 1476; it is not known when he obtained this position, and the latest documentation of a previous provost occurs all the way back on 13 March 1445. He can be found as the Official of the diocese of Dunblane on 26 August 1476. He was litigating to gain the precentorship of Elgin Cathedral in 1480, although nothing more of this is heard. He is found as rector of the parish church of Douglas on 28 August 1481. After the election of Robert Blackadder as Bishop of Aberdeen on 14 July 1480, Fraser received provision to the now vacant position of Archdeacon of Aberdeen; he did not secure the position because of the lack of royal support, but was still claiming the position in 1488.

Collegiate church of Restalrig
Fraser was the first Dean of the new collegiate church erected on 13 November 1487 at Restalrig in Midlothian. Fraser petitioned the pope for the creation of the collegiate church on 6 May, to be dedicated to the "Holy and Indivisible Trinity" and the Virgin Mary; the church had and was benefiting from the patronage of King James III of Scotland, and the church was called at the time the "King's chapel" or "chapel royal". Fraser founded a chaplaincy in the new collegiate church, to which he donated a tenement he had built in the Canongate.

Bishop of Ross
In the 1490s, Fraser became a royal councillor and Clerk of the Register. Some time before 10 September 1497, Fraser was elected through royal influence to the bishopric of Ross, vacant at least three, possibly five years, since the death of the previous bishop, John Guthrie. He received papal provision on 14 March 1498. On 5 May, the Florentine clerk Ilarion de Portiis acting in Fraser's name paid the papacy 600 gold florins. His name appeared in Scottish sources datable to 3 December as "elect and confirmed of Ross." He was granted the temporalities of the bishopric on 3 January 1499, by which time he had probably received consecration.

On 10 March 1504, Bishop Fraser was present at a meeting of the parliament; on 10 May, he is recorded as granting his cathedral at Fortrose an annual rent of £10 from a tenement he owned in the burgh of Linlithgow. On 15 September 1506, King James IV of Scotland, while at the Chanonry of Ross, granted to the bishop part of the lands of the toun of Arkbol, in the earldom of Ross. The History of the Frazers (Wardlaw MS) claimed that he died on 5 February 1507, aged 78. According to tradition one of the three funeral effigies in Fortrose Cathedral is that of Bishop Fraser. The tradition – attested in the Wardlaw MS History of the Frazers – that he was Abbot of Melrose and Prior of Beauly is now thought to be spurious. Professor Donald Watt omitted him from his list of chancellors of Glasgow Cathedral, a position he was also widely believed to have held.

Notes

References
 Cowan, Ian B. & Easson, David E., Medieval Religious Houses: Scotland With an Appendix on the Houses in the Isle of Man, Second Edition, (London, 1976)
 Dowden, John, The Bishops of Scotland, ed. J. Maitland Thomson, (Glasgow, 1912)
 Keith, Robert, An Historical Catalogue of the Scottish Bishops: Down to the Year 1688, (London, 1824)
 Watt, D. E. R., Fasti Ecclesiae Scotinanae Medii Aevi ad annum 1638, 2nd Draft, (St Andrews, 1969)
 Watt, D. E. R. & Shead, N. F. (eds.), The Heads of Religious Houses in Scotland from the 12th to the 16th Centuries, The Scottish Records Society, New Series, Volume 24, (Edinburgh, 2001)

External links
 Am Baile

15th-century births
1507 deaths
Bishops of Ross (Scotland)
People from Linlithgow
15th-century Scottish Roman Catholic bishops
16th-century Scottish Roman Catholic bishops


text:
Dowd forced to quit as Merseytravel chairman
by Passenger Transport on Jun 13, 2012 • 4:30 pm No Comments
District auditor to investigate claims of financial irregularities
Merseytravel chairman Mark Dowd was last week forced to resign after 20 years in the post, saying that his position had become "untenable" after half of his 16 fellow Labour members on the Integrated Transport Authority called for him to resign.
With opposition Liberal Democrat and Conservative members also calling for him to go, Dowd faced the very real prospect of losing the vote to elect Merseytravel's chairman.
In their letter calling on Dowd to stand down, the eight Labour councillors said that the Merseytravel chair had failed to address a "number of significant concerns about how power has been exercised and public money allocated and spent".
"When we have previously attempted to discuss our concerns with you, you have chosen either to cancel requested meetings or truncate them to such an extent that any in-depth discussion of these serious matters has been prevented," they said.
They added that Merseytravel faces a number of challenges over the next few years, including the procurement of new rolling stock for Merseyrail, constrained public finances and the devolution of funding to the city region.
They continued: "Unfortunately at no time have you articulated a clear, strategic and deliverable vision for transport across the city region."
One of the Labour councillors, Joe Hanson, has written a highly critical report that questions governance arrangements in place at Merseytravel under the leadership of Dowd and Neil Scales, the former chief executive, who left Merseytravel for a new job in Queensland, Australia at the end of last year.
The report has been reviewed by Julian Farmer, the district auditor, who, according to local press reports, is believed to have raised concerns about £2m spent with law firms Bircham Dyson Bell and DLA Piper. Farmer also believes that EU procurement rules could have been broken and that standing orders have not been followed.
This article appears in the latest issue of Passenger Transport. Click here to subscribe.
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text:
\section{Introduction}
Present low energy neutrino oscillation data~\cite{atmos_data,
solar_data,kamland_data} are elegantly explained by the neutrino
oscillation hypothesis with very small masses ($\leq$ 1 eV) of
the light neutrinos. Neutrinos can have either Dirac or Majorana masses.
Small Majorana masses of the light neutrinos, however, can be
generated in a natural way through the seesaw mechanism~\cite{seesaw}
without any fine tuning. This can be achieved by introducing
right handed neutrinos, $N_R$'s, into the electroweak model
which are neutral under the known gauge symmetries. The
Majorana masses of these $N_R$'s are free parameters of the model
and are expected to be either at TeV scale~\cite{sahu&yajnik_prd.05}
or at a higher scale~\cite{type-I-bounds,type-II-bounds}. This
indicates the existence of new physics beyond Standard Model
(SM) at some predictable high energy scale.

The heavy right handed Majorana neutrinos are also an essential ingredient
in currently one of the most favored scenarios of origin of the observed
baryon asymmetry of the Universe (BAU), namely, the ``baryogenesis via
leptogenesis"
scenario~\cite{fukugita.86,luty.92,mohapatra.92,plumacher.96}.
Majorana mass of the
neutrino violates lepton number ($L$) and thus provides a natural
mechanism of generating a lepton asymmetry in the Universe. Specifically,
leptogenesis can occur via the $L$-violating, $CP$-asymmetric,
out-of-equilibrium~\cite{sakharov.67} decay of the $N_R$'s into SM leptons
and Higgs. The resulting $L$-asymmetry is then partially converted to a
baryon ($B$)-asymmetry via the
non perturbative $B+L$ violating (but $B-L$ conserving) electroweak
sphaleron transitions~\cite{krs.85}. The
attractive aspect of the leptogenesis mechanism is the
link it implies between the physics of the heavy right handed neutrino
sector and the experimental data on light neutrino flavor oscillation,
thus making the scenario subject to experimental tests. Indeed,
the magnitude of the $L$ (and thus $B$) asymmetry produced depends on,
among other parameters, the masses of the heavy
neutrinos, which in turn are related to the light neutrino masses via the
seesaw mechanism. The mass-square differences amongst the three light
neutrino species inferred from the results of neutrino experiments,
therefore, place stringent constraints on the leptogenesis hypothesis.

A natural way to implement the leptogenesis scenario is to extend
the SM to a gauge group which includes $B-L$ as a gauge charge.
The heavy neutrino masses are then determined by the scale of spontaneous
breaking of this gauge symmetry. Further, with $B-L$ a conserved gauge
charge and $B+L$ anomalous, we can start with a net $B=L=0$ at a
sufficiently early stage in the Universe. The observed $B$ asymmetry must
then be generated only after the phase transition breaking the
$B-L$ gauge symmetry.

It is well known that phase transitions associated with spontaneous
breaking of gauge symmetries
in the early Universe can, depending on the structure of the symmetry
group and its breaking pattern, lead to formation of cosmic topological
defects~\cite{kibble.76,vilen&shell} of various types. In particular, the
simplest choice for the $B-L$ gauge symmetry group being a
$U(1)_{B-L}$, the phase transition associated with spontaneous
breaking of this $U(1)_{B-L}$ in the early Universe would, under very
general conditions, lead to formation of {\it cosmic
strings}~\cite{kibble.76,vilen&shell} carrying quantized $B-L$
magnetic flux. These ``$B-L$" cosmic strings can be a {\it non-thermal}
source of $N_R$'s whose decay can give an extra contribution
to the $L$ and thereby $B$ asymmetry in addition to that from the decay of
$N_R$'s of purely thermal origin (``thermal'' leptogenesis). This
can happen in the following two ways:

First, since the Higgs field defining the $B-L$ cosmic string is the same
Higgs that also gives mass to the $N_R$ through Yukawa coupling, the
$N_R$'s can be trapped inside the $B-L$ cosmic strings as fermionic zero
modes~\cite{jeannerot.96}. Existence of zero energy solutions of fermions
coupled to a Higgs field that is in a topological vortex string
configuration is well-known~\cite{jackiw.81,weinberg.81}, and has been
studied in a variety of models allowing cosmic
strings~\cite{das.83,witten.85,Stern:1985bg,sdavis.00,vachaspati.01}.
As closed loops of $B-L$ cosmic strings oscillate,
they lose energy due to emission of gravitational radiation and shrink
in size. Eventually, when the size of the loop becomes of the order of
the width of the string, the string loop disappears into massive
particles among which will be the $N_R$'s which were trapped inside the
string as zero modes. Each closed loop
would be expected to release at least one $N_R$ when
it finally disappears, and the decay of these $N_R$'s would
then give a contribution to the BAU through
the leptogenesis route~\cite{jeannerot.96}.

Second, collapsing, decaying
or repeatedly self-intersecting closed loops of
cosmic strings would in general produce heavy gauge and Higgs bosons of
the underlying spontaneously broken gauge theory. In the context of
cosmic strings in Grand Unified Theories (GUTs), the $CP$ asymmetric
$B$-violating decay of the heavy gauge and Higgs bosons released from
cosmic string loops would produce a net $B$
asymmetry~\cite{pijush.82,brandenberger&co.91,riotto&lewis.94,pijush.98}.
The sphaleron transitions would of course erase the $B$ asymmetry
{\it unless a net $B-L$ was generated}. If the strings under consideration
are the $B-L$ cosmic strings, which can be formed at an intermediate stage
of symmetry breaking in a GUT model based on $SO(10)$, for example, then
the heavy gauge and Higgs bosons released from the decaying or collapsing
$B-L$ cosmic string loops can themselves decay to
$N_R$'s since the $N_R$'s have Yukawa and gauge couplings to the
(string-forming) Higgs and gauge boson, respectively.
The decay of these Higgs and gauge boson generated $N_R$'s can produce a
net $B-L$ and thus contribute to the BAU through the leptogenesis route
irrespective of the existence of zero modes of $N_R$'s on
cosmic strings.

In a previous work~\cite{bha_sahu_yaj.04}, we made a general analytical
estimate of the contribution of the non-thermal $N_R$'s produced by $B-L$
cosmic string loops to BAU. It was shown there that, in order for the
resulting $B$ asymmetry not to exceed the measured BAU inferred from the
WMAP results~\cite{spergel.03}, the mass $M_1$ of lightest right handed
Majorana neutrino had to satisfy the constraint
\begin{equation}
M_1 \mbox{\raisebox{-.6ex}{~$\stackrel{<}{\sim}$~}} 2.4 \times 10^{12}\left(\eta_{B-L}/10^{13}
\gev\right)^{1/2}\gev,
\label{M1-bound}
\end{equation}
where $\eta_{B-L}$ is the $U(1)_{B-L}$ symmetry breaking scale. In
the above mentioned analytical study we had (a) taken the $CP$ asymmetry
parameter $\epsilon_1$ to have its maximum value (see below), (b) not
taken into account the contribution to BAU from the decay of the already
existing thermal $N_R$'s, and (c) neglected all wash-out effects (see
below) on the final $B-L$ asymmetry. Indeed, our aim there was to make a
simple analytical estimate of the possible maximum contribution of
the cosmic string generated non-thermal $N_R$'s to the measured BAU. It
is, of course, clear that a complete analysis of leptogenesis
in presence of cosmic strings can only be done by solving the
full Boltzmann equations~\cite{luty.92,plumacher.96} that include the
non-thermal $N_R$'s of cosmic string origin as well as the already
existing thermal $N_R$'s and take into account all the relevant
interaction processes including the wash out effects. This is the study
taken up in this paper.

The main results obtained in the present paper can be summarized as
follows: First, we confirm the result, obtained earlier in our analytical
study~\cite{bha_sahu_yaj.04}, that $B-L$ cosmic string loops can give
significant contribution to BAU only for $\eta_{B-L}\mbox{\raisebox{-.6ex}{~$\stackrel{>}{\sim}$~}} 10^{11}\gev$.
Second, the numerical solution of the relevant Boltzmann equations in the
present paper has enabled us to track the dynamical evolution of the
contribution of the cosmic string generated non-thermal $N_R$'s to the
final BAU. Specifically, we find that for sufficiently large values of
$\eta_{B-L}$ and for appropriate ranges of values of the other
relevant parameters ${\tilde m_1}$ and $h_1$ as detailed in
sec.~\ref{subsec:solving}, the effect of the cosmic string generated
non-thermal $N_R$'s is to produce a late-time increase of the final
value of BAU as compared to its value in absence of cosmic strings.
This can be understood from the fact that while the thermal abundance of
$N_R$'s decreases exponentially with decreasing temperature, the density
of cosmic string generated $N_R$'s has a power law dependence (on
temperature) inherited from the scaling behavior
of the evolution of cosmic strings, leading to a domination of the
string generated $N_R$'s over the thermal $N_R$'s at late times for
sufficiently large values of $\eta_{B-L}$.
In such situations, we are required to place an {\it upper} bound on the
magnitude of $\sin\delta$, where $\delta$ is the $CP$ violating phase that
determines the $CP$ asymmetry in the heavy neutrino sector, in
order not to overproduce the BAU.

The rest of our paper is organized as follows. In section \ref{sec:brief},
we briefly review the standard thermal baryogenesis via leptogenesis
scenario, and discuss the required lower bounds on the mass of the
lightest right handed neutrino and the $B-L$ symmetry breaking scale.
In section \ref{sec:cosmic} we introduce closed loops of $B-L$ cosmic
strings as non-thermal sources of $N_R$'s and write
down the injection rates of these $N_R$'s due to the two main
processes of disappearance of cosmic string loops. Section
\ref{sec:complete} is devoted to setting up and then solving the relevant
Boltzmann equations for the evolution of the $B-L$ asymmetry, including
the non-thermal $N_R$'s of cosmic string origin in addition to the usual
thermal ones. The effects of the cosmic string generated non-thermal
$N_R$'s on the evolution of the $B-L$ asymmetry are discussed. Finally,
section \ref{sec:conclusion} summarizes our main results.

\section{A brief review of baryogenesis via leptogenesis
\label{sec:brief}}

\subsection{The general framework\label{subsec:general}}
In the model we consider, the lepton asymmetry arises through the
decay of right handed Majorana neutrinos to the SM
leptons ($\ell$) and Higgs ($\phi$) via the Yukawa
coupling
\begin{equation}
\mathcal{L}_{Y}=f_{ij}\bar{\ell}_i\phi N_{R_j}+{\rm h.c.}\,,
\label{yukawa_term}
\end{equation}
where $f_{ij}$ is the Yukawa coupling matrix, and $i,j=1,2,3$
for three flavors.

We use the basis in which the mass matrix of the heavy Majorana
neutrinos, $M$, is diagonal,  where the Majorana neutrinos are defined
by $N_j=\frac{1}{\sqrt{2}}(N_{R_j}+N^c_{R_j})$. However, in
this basis the Dirac mass matrix $m_D$ ($=f v$, $v$ being the
vacuum expectation value of the SM Higgs) of the neutrinos
is not diagonal. The canonical see-saw mechanism then gives the
corresponding light neutrino mass matrix
\begin{equation}
m_\nu=-m_DM^{-1}m_D^T.
\label{neu-mass-matrix}
\end{equation}
In this basis the light neutrino mass matrix $m_{\nu}$ can
be diagonalized by the lepton mixing matrix~\cite{mns-matrix}
$U_L$ to give the three light neutrino masses,
\begin{equation}
{\rm diag}(m_1, m_2, m_3)=U_L^T m_{\nu}U_L.
\label{dia-mass-matrix}
\end{equation}

The best fit values of the mass-square differences
and mixing angles of the light neutrinos from a global three neutrino
flavors oscillation analysis are~\cite{gonzalez-garcia_prd.03}
\begin{equation}
\theta_{\odot}\equiv \theta_{1}\simeq 34^\circ,
~~\theta_{atm}\equiv\theta_{2}=45^\circ, ~~\theta_3 \leq 13^\circ,
\label{bestfit-theta}
\end{equation}
and
\begin{eqnarray}
\Delta m_{\odot}^2\equiv |m_2^2 - m_1^2| &\simeq& 7.1\times 10^{-5}
\,{\rm eV}^2\,, \label{sol-masses}\\
\Delta m_{atm}^2\equiv |m_3^2 - m_1^2| &\simeq & 2.6\times 10^{-3}
\,{\rm eV}^2\,.
\label{atm-masses}
\end{eqnarray}
In the absence of data about the overall scale of neutrino masses, we
shall assume throughout this paper a normal hierarchy,
$m_1\ll m_2\ll m_3$, for the light neutrino masses.
With this assumption equations (\ref{sol-masses}) and (\ref{atm-masses})
give
\begin{eqnarray}
m_2\simeq \sqrt{\Delta m_{\odot}^2}&=& 0.008 \,{\rm eV}\,,\nonumber\\
m_3\simeq \sqrt{\Delta m_{atm}^2}&=&0.05\,{\rm eV}\,.
\label{bestfit-masses}
\end{eqnarray}
We will use the above value of $m_3$ to obtain the upper
bound on $CP$-asymmetry in subsection \ref{subsec:decay}.

\subsection{Decay of heavy Majorana neutrino and $CP$-asymmetry
\label{subsec:decay}}
The $CP$-asymmetry parameter in the decay of $N_i$ is defined as
\begin{equation}
\epsilon_{i}\equiv\frac{\Gamma(N_i\rightarrow \bar{\ell}\phi)-
\Gamma(N_i\rightarrow \ell\phi^\dagger)}{\Gamma(N_{i}
\rightarrow \bar{\ell}\phi)+\Gamma(N_{i}\rightarrow \ell\phi^\dagger)}\,.
\label{epsilon_def}
\end{equation}
We assume a normal mass hierarchy in the heavy Majorana
neutrino sector, $M_{1} < M_{2} < M_{3}$, and further assume that the
final lepton asymmetry is produced mainly by the decays of the lightest
right handed Majorana neutrino, $N_{1}$. The latter is
justified~\cite{luty.92,plumacher.96} because any asymmetry
produced by the decay of $N_{2}$ and $N_{3}$ is erased by the lepton
number violating interactions mediated by $N_{1}$. At an epoch of
temperature $T>M_1$, all the lepton number violating processes
mediated by $N_1$ are in thermal equilibrium. As the Universe
expands and cools to $T\mbox{\raisebox{-.6ex}{~$\stackrel{<}{\sim}$~}} M_1$, the $L$-violating scatterings mediated
by $N_{1}$ freeze out, thus providing the out-of-equilibrium
situation~\cite{sakharov.67} necessary for the survival of any
net $L$-asymmetry generated by the decay of the $N_1$'s. The
final $L$-asymmetry is, therefore, given essentially by the
product of the equilibrium
number density of the $N_1$'s at $T\sim M_1$ and the
$CP$-asymmetry parameter $\epsilon_1$. The latter is
given by~\cite{type-I-bounds,type-II-bounds}
\begin{equation}
|\epsilon_{1}|=\frac{3}{16\pi v^2}M_1 m_3 \sin\delta\,,
\label{epsilon_1}
\end{equation}
where $v\simeq 174\gev$ is the electroweak symmetry breaking
scale and $\delta$ is the $CP$ violating phase. Using the best
fit value of $m_3$ from equation (\ref{bestfit-masses}) the value of
$\epsilon_{1}$ can be written as
\begin{equation}
|\epsilon_{1}|\leq 9.86\times 10^{-8}\left(\frac{M_1}{10^9\gev}
\right)\left(\frac{m_3}{0.05\,{\rm eV}}\right)\,.
\label{epsilon1-max}
\end{equation}

\subsection{Thermal leptogenesis and bound on $M_1$
\label{subsec:baryogenesis}}
The $L$-asymmetry, created by the decays of $N_1$, is
partially converted to a $B$-asymmetry by the
nonperturbative sphaleron transitions which violate
$B+L$ but preserve $B-L$. Assuming that sphaleron
transitions are ineffective at temperatures below
the electroweak transition temperature ($T_{\rm EW}$),
the $B$-asymmetry is related to $L$-asymmetry by the
relation~\cite{harvey_turner}
\begin{equation}
B=\frac{p}{p-1}L\simeq -0.55 L\,,
\label{B_L_relation}
\end{equation}
where we have taken $p=28/79$ appropriate for the particle
content in SM. The net baryon asymmetry of the Universe, defined as
$Y_B\equiv (n_B/s)$, can thus be written as
\begin{equation}
Y_B\simeq 0.55\epsilon_1 Y_{N_1}|_{T\simeq M_1}\,d\,,
\label{bau_def}
\end{equation}
where the factor $0.55$ in front comes from equation (\ref{B_L_relation}),
\begin{equation}
Y_{N_1}\equiv\frac{n_{N_1}}{s}\,,
\label{com-neu-den}
\end{equation}
$n_{N_1}$ being the number density of $N_1$,
and $d$ is the dilution factor due to wash-out effects. In the
above equations $s$ stands for the entropy density and is given by
\begin{equation}
s=\frac{2\pi^2}{45}g_{*}T^{3}\simeq 43.86 (g_*/100)T^3\,,
\label{entropy}
\end{equation}
where $g_*$ is the total number of relativistic degrees of freedom
contributing to entropy of the Universe.

The present-day observed value of the baryon-to-photon ratio $\eta\equiv
(n_B-n_{\bar{B}})/n_\gamma$ inferred from the WMAP data
is~\cite{spergel.03}
\begin{eqnarray}
\eta_0^{\rm WMAP} &\simeq& 7.0\, Y_{B,0}\\
&=&\left(6.1^{+0.3}_{-0.2}\right)\times 10^{-10}\,.
\label{eta_0_wmap}
\end{eqnarray}
Using equation (\ref{epsilon1-max}) in equation (\ref{bau_def}) and
comparing with (\ref{eta_0_wmap}) we get
\begin{equation}
M_1\geq 10^9\gev \times\left(\frac{1.6\times
10^{-3}}{Y_{N_1}|_{T\simeq M_1}d }
\right)\left(\frac{0.05 eV}{m_3}\right)\,.
\label{lower-bound-M1}
\end{equation}
Assuming that $N_1$'s are initially (i.e., at $T\gg M_1$) in thermal
equilibrium and they remain so till $T\simeq M_1$, one has
$Y_{N_1}|_{T\simeq M_1}\approx 2.3\times10^{-3}\times (100/g_*)$.
Equation (\ref{lower-bound-M1}) then indicates that the $B-L$ symmetry
breaking scale must satisfy the constraint $\eta_{B-L}\mbox{\raisebox{-.6ex}{~$\stackrel{>}{\sim}$~}}
O(10^9)\gev$ for successful thermal leptogenesis, unless we allow the
Majorana neutrino Yukawa coupling of the lightest right handed neutrino,
$h_1$, to be greater than unity.

\section{$B-L$ cosmic strings as sources of non-thermal heavy
neutrinos\label{sec:cosmic}}
\subsection{$B-L$ cosmic strings and zero modes of $N_R$
\label{subsec:zeromodes}}
The possibility of $B-L$ cosmic strings in various extensions
of the SM were studied in ~\cite{jeannerot&co, yajnik.99}.
For simplicity, we consider in the present paper a model based on the
gauge group
$SU(2)_{\rm L}\otimes U(1)_{\rm Y}\otimes U(1)_{\rm Y'}$, where
$Y'$ is a linear combination of $Y$ and $B-L$~\cite{buc_gre_min.91}.
We then follow the symmetry breaking scheme
\begin{eqnarray}
SU(2)_{L}\otimes U(1)_{Y} \otimes U(1)_{Y'} &\underrightarrow
{\langle \chi \rangle =\eta_{B-L}}& SU(2)_{L}\otimes
U(1)_{Y}\nonumber\\
&\underrightarrow{\langle \phi \rangle =v}&  U(1)_{EM},
\label{symmetry_break}
\end{eqnarray}
where $\chi$ is the Higgs boson required to break the
$U(1)_{Y'}$ gauge symmetry and $\phi^{T}=(\phi^{+}, \phi^{0})$
is the SM Higgs.

As the Universe cools below the critical temperature,
$T_{B-L}$, of the $B-L$ symmetry breaking phase
transition, the Higgs field $\chi$ develops a vacuum
expectation value $\langle \chi \rangle =\eta_{B-L}$. The same
Higgs field also forms strings. The mass per unit length of the string,
$\mu$, is given by~\cite{vilen&shell} $\mu\sim\eta^{2}_{B-L}\sim
T_{B-L}^2$. The exact value of $\mu$ depends on the values of the
parameters of the model, in particular the relevant gauge and Higgs boson
masses, and can differ from $\eta_{B-L}^2$ by up to an order of
magnitude depending on the model~\cite{hill-hodges-turner-prl.87}.
Measurements of CMB anisotropies have been used to place upper bounds on
the fundamental cosmic string parameter $\mu$ in a variety of different
cosmic string models; see, for example, \cite{cmb_limits}.
A recent analysis~\cite{wyman_etal} of data on CMB anisotropies and large
scale structure together puts the bound $G\mu < 3.4 (5)\times 10^{-7}$
at 68 (95)\% c.l. This most likely rules out cosmic string formation at a
typical GUT scale $\sim10^{16}\gev$. However, lighter cosmic strings
arising from symmetry breaking at lower scales, for example, the $B-L$
cosmic strings discussed in this paper, are not ruled out.

The right handed neutrinos acquire Majorana masses from
coupling to the same Higgs field $\chi$,
\begin{equation}
-\mathcal{L}_{\chi-{N_R}}=\frac{1}{2}[ih_{ii}\chi\overline{N_{R_{i}}}
N_{R_{i}}^{c}+{\rm h.c}]\,,
\label{nu-chi-int}
\end{equation}
where $h$ is the Yukawa coupling matrix, and $N_{R}^{c}
=i \sigma^{2}N_{R}^{*}$ defines the Dirac charge conjugation
operation. The equation of motion of $N_R$ in the background of
$\chi$ forming the string admits $|n|$ normalizable zero-modes
in the winding number sector
$n$~\cite{jackiw.81,weinberg.81,jeannerot.96,sdavis.00}. On a straight
string these modes are massless.
However, on a generic string they are expected to acquire effective
masses proportional to the inverse radius of the string
curvature. As soon as this mass becomes comparable to the
mass of the free neutrinos in the bulk medium, these neutrinos
can be emitted from the string. In any
case, when the string loop shrinks and finally decays it emits
various massive particles: the gauge bosons, the heavy Higgs ($\chi$)
and the massive right handed Majorana neutrinos ($N_i$).

\subsection{$N_R$'s from closed loops of $B-L$ cosmic strings
\label{subsec:N_R_from_closed_loops}}
A key physical process that governs the evolution of cosmic string
networks in an expanding Universe is the formation of sub-horizon sized
closed loops which are pinched off from the network whenever a
string segment curves over into a loop and intersects itself. It is this
process that allows the string network to reach a scaling regime, in which
the energy density of the string network scales as a fixed fraction of the
radiation or matter energy density in the Universe; see, e.g.,
Ref.~\cite{vilen&shell} for a text book
discussion of evolution of cosmic strings in the Universe.

After their formation, the closed loops eventually disappear through
either of the following two processes (see
Refs.~\cite{bha_sahu_yaj.04,pijushreport} for the relevant details):

\subsubsection{Slow death\label{subsubsec:slow}}
Closed loops born in non-selfintersecting configurations oscillate freely
with oscillation time period $L/2$ ($L$ being the length of the loop). In
doing so they slowly lose energy due to emission of gravitational
radiation, and thus shrink in size. Eventually, when the radius of the
loop becomes of the order of the width ($\sim\eta_{B-L}^{-1}$) of the
string --- which happens over a time scale large compared to $L$ (hence
``slow'') --- the resulting ``tiny'' loop loses
topological stability and decays into elementary particle quanta including
the gauge- and Higgs bosons associated with the underlying broken symmetry
as well the heavy neutrinos $N_i$'s coupled to the gauge- and Higgs
bosons. While we expect the final number $N_N$ of the heavy
neutrinos released per tiny loop to be of order one, it is difficult
to be more precise, and we keep this number as an undetermined parameter.
Assuming that the energy of a loop going into $N_R$'s is predominantly in
the form of the lightest of the heavy neutrinos, $N_1$'s, the
number of heavy Majorana neutrinos released from the closed loops
disappearing through this ``slow death'' (SD) process per unit time per
unit volume at any time $t$ (in the radiation dominated epoch) can be
written as~\cite{bha_sahu_yaj.04}
\begin{equation}
\left(\frac{dn_{N_1}}{dt}\right)_{\rm SD} =
N_N f_{\rm SD}\frac{1}{x^{2}}\left(\Gamma G \mu\right)^{-1}
\frac{(K+1)^{3/2}}{K}t^{-4}\,,
\label{N_SD_rate}
\end{equation}
where $f_{\rm SD}$ is the fraction of newly born loops which
die through the SD process, $x\sim0.5$ is a numerical factor that
characterizes the scaling configuration of the string network, $\Gamma\sim
100$ is a numerical factor that determines the life time of a
loop due to gravitational radiation emission, and $K\sim O(1)$ is a
numerical factor that determines the average length of the closed loops
at their birth. It is generally argued~\cite{vilen&shell} that $f_{\rm
SD}\simeq 1$.

Using (\ref{com-neu-den}), the above rate then gives the injection rate of
massive Majorana neutrinos from cosmic string closed loops disappearing
through the SD process per comoving volume as
\begin{equation}
\left(\frac{dY^{\rm st}_{N_1}}{dz}\right)_{\rm SD}= \frac{1.57\times
10^{-17}}{z^4}
N_N \left(\frac{M_1}{\eta_{B-L}}\right)^2
\left(\frac{M_1}{\gev}\right),
\label{slowdeath-rate}
\end{equation}
where $z=M_1/T$ is the dimensionless variable with respect to
which the evolution of the various quantities is studied. In the above
we have used the following numerical values for the various constants:
$\Gamma=100$, $x=0.5$, $g_{*}=100$ and $K=1$.

\subsubsection{Quick death\label{subsubsec:quick}}
Some fraction of closed loops may be born in configurations with
waves of high harmonic number. Such string loops have been
shown~\cite{siemens&kibble.95} to have a high probability of
self-intersecting. In this case a loop of length $L$
can break up into a debris of tiny loops of size $\eta_{B-L}
^{-1}$ (at which point they turn into the constituent massive
particles) on a time-scale $\sim L$ (hence ``quick''). Since gravitational
energy loss occurs over a time scale much larger than $L$, these loops do
not radiate any significant amount of energy in gravitational radiation,
and thus almost the entire original energy of these loops would eventually
come out in the form of massive particles.

Assuming again that each tiny loop of size
$\sim \eta_{B-L}^{-1}$ yields a number $N_N$ of heavy neutrinos,
the injection rate of the massive Majorana neutrinos due to this ``quick
death'' (QD) process is given by~\cite{bha_sahu_yaj.04}
\begin{equation}
\left(\frac{dn_{N_1}}{dt}\right)_{\rm QD}=f_{\rm QD} N_N \frac{1}{x^{2}}
\frac{\eta_{B-L}}{t^3}\,,
\label{quick_N_rate}
\end{equation}
where $f_{\rm QD}$ is the fraction of loops that undergo QD.

Note that while each tiny loop yields the same number $N_N$ of the
heavy neutrinos irrespective of the SD or QD nature of the demise of the
loop, the total injection rates of the heavy neutrinos in the two cases
are different because of the different number of tiny loops that result
from an initial big loop and the different time scales involved in the two
cases.

Using (\ref{com-neu-den}) the above rate
(\ref{quick_N_rate}) can be rewritten as
\begin{equation}
\left(\frac{dY^{\rm st}_{N_1}}{dz}\right)_{\rm QD}\simeq \frac{1.36\times
10^{-36}}{z^2} f_{\rm QD} N_N \left(\frac{\eta_{B-L}}{\gev}\right)
\left(\frac{M_1}{\gev}\right).
\label{quickdeath-rate}
\end{equation}

While the value of $f_{\rm QD}$ is not known, there are
constraints~\cite{pijush&rana,pijushreport} on $f_{\rm QD}$ from the
measured flux of the ultrahigh energy cosmic rays above $\sim
5\times10^{19}\,{\rm eV}$ and more stringently from the
cosmic gamma ray background (CGRB) in the 10 MeV -- 100 GeV energy
region measured by the EGRET experiment~\cite{sreekumar}. The latter gives
\begin{equation}
f_{\rm QD}\eta_{16}^{2}\mbox{\raisebox{-.6ex}{~$\stackrel{<}{\sim}$~}} 9.6\times 10^{-6}\,,
\label{f_QD_constraint}
\end{equation}
where $\eta_{16}\equiv(\eta_{B-L}/10^{16}\gev)$. For GUT
scale cosmic strings with $\eta_{16}=1$, for example, the above
constraint implies that $f_{\rm QD}\leq 10^{-5}$, so that
most loops should be in non-selfintersecting configurations,
consistent with our assumption of $f_{\rm SD}\sim 1$.
Note, however, that $f_{\rm QD}$ is not constrained by
(\ref{f_QD_constraint}) for cosmic strings formed at
scales $\eta_{B-L}\mbox{\raisebox{-.6ex}{~$\stackrel{<}{\sim}$~}} 3.1\times 10^{13}\gev$.

\section{Leptogenesis in presence of cosmic strings: towards a complete
analysis\label{sec:complete}}
\subsection{Analytical estimate\label{subsec:analytical}}
In our previous work~\cite{bha_sahu_yaj.04} we made simple analytical
estimates of the maximum possible contributions of cosmic string loops to
leptogenesis. Neglecting the contribution of the thermal $N_R$'s, allowing
the maximal value of the $CP$-violation parameter given by equation
(\ref{epsilon1-max}) and demanding that the resulting value of the
baryon-to-photon ratio not exceed the observed value given by equation
(\ref{eta_0_wmap}), we derived upper bounds on the mass $M_1$ for the SD
and QD processes of decay of cosmic string loops. This is shown
in Figure ~\ref{fig:region} for $N_N=10$ for illustration.

\begin{figure}[ht]
\epsfig{file=constraint_sdqd.ps,angle=-90,width=0.9\textwidth}
\caption{Constraints on $h_1=M_1/\eta_{B-L}$ from consideration of
possible maximal contributions of $B-L$ cosmic string loops to
$B$-asymmetry. Models lying on the thick (thin) solid line can in
principle produce the observed BAU entirely due to the SD (QD) process of
$B-L$ cosmic string loops. Models above the thick solid line are ruled
out from consideration of overproduction of the $B$ asymmetry. The
$h_1=1$ line is also shown for comparison.}
\label{fig:region}
\end{figure}

Figure \ref{fig:region} allows us to identify regions in the
$\eta_{B-L}-M_1$ plane determining models for which cosmic string
processes discussed above can play a significant role in the leptogenesis
mechanism. Clearly, from Figure \ref{fig:region}, cosmic string are
relevant for leptogenesis
only for $\eta_{B-L}\mbox{\raisebox{-.6ex}{~$\stackrel{>}{\sim}$~}} 1.7\times10^{11}\gev$; lower values of
$\eta_{B-L}$ are relevant only if we allow $h_1\geq1$.
Note also that the above lower limit on $\eta_{B-L}$ (for cosmic strings
to be relevant for leptogenesis) is determined by the SD process; the QD
process becomes relevant only at much higher values of $\eta_{B-L}$,
namely, $\eta_{B-L}^{\rm QD}\mbox{\raisebox{-.6ex}{~$\stackrel{>}{\sim}$~}} 1.2\times 10^{14}\gev$.

In this context, it may be mentioned here that, following our previous
work, a recent work~\cite{gu-mao-plb.05} has found that in the case of
degenerate neutrinos (as opposed to hierarchical neutrinos assumed in our
work), the $B-L$ cosmic strings become relevant for
leptogenesis at much higher values of $\eta_{B-L}$ compared to those in
the case of hierarchical neutrinos, e.g., $\eta_{B-L}\mbox{\raisebox{-.6ex}{~$\stackrel{>}{\sim}$~}}
3.3\times10^{15}\gev$ for the SD process and $\eta_{B-L}>10^{16}\gev$ for
the QD process. As already mentioned, we assume hierarchical neutrino
masses in the present paper.

We now proceed towards a complete analysis of leptogenesis in presence
of cosmic strings by first setting up and then solving the relevant
Boltzmann equations that include the non-thermal $N_R$'s
produced from the decaying cosmic string loops as well as the
already existing thermal $N_R$'s and also include all the
relevant wash-out effects.

\subsection{Boltzmann Equations}
The total rate of change of the abundance of $N_1$'s can be written as
\begin{equation}
\frac{dY_{N_1}}{dz}=\left(\frac{dY_{N_1}}{dz}\right)_{D,S}+
\left(\frac{dY_{N_1}}{dz}\right)_{\rm injection}.
\label{eff-rate}
\end{equation}
The first term on the right hand side of equation (\ref{eff-rate})
is given by the usual Boltzmann equation ~\cite{luty.92,plumacher.96}
\begin{equation}
\left(\frac{dY_{N_1}}{dz}\right)_{D,S}=
-(D+S)\left(Y_{N_1}-Y^{\rm eq}_{N_1}\right)\,,
\label{thermal-rate}
\end{equation}
where $D$ and $S$ constitute the decay and $\Delta L=1$
lepton number violating scatterings, respectively, which reduce the number
density of $N_1$, and $Y^{\rm eq}_{N_1}$ is the abundance of $N_1$
in thermal equilibrium.

The second term on the right hand side of equation (\ref{eff-rate}) gives
the rate of injection of $N_1$'s due to disappearance of $B-L$
cosmic string loops:
\begin{equation}
\left(\frac{dY_{N_1}}{dz}\right)_{\rm injection}=\left(
\frac{dY_{N_1}^{\rm st}}{dz}\right)_{\rm SD} + \left(\frac{dY_{N_1}^{\rm
st}}{dz}\right)_{\rm QD},
\label{nonthermal-rate}
\end{equation}
where the two terms on the right hand side are given by
the equations (\ref{slowdeath-rate}) and (\ref{quickdeath-rate}),
respectively.

The two terms in equation (\ref{eff-rate}) compete with
each other. While the first term reduces the density
of $N_1$'s, the second term tries to increase it
through continuous injection of $N_1$'s from
the disappearance of cosmic string loops. The CP-violating decays
of the $N_1$'s produce a net $B-L$ asymmetry. This can be
calculated by solving the Boltzmann equation
\begin{equation}
\frac{dY_{B-L}}{dz} = -\epsilon_{1} D\left(Y_{N_1}-Y^{\rm eq}_
{N_1}\right)-W Y_{B-L}.
\label{asymmetry-rate}
\end{equation}
The first term in equation (\ref{asymmetry-rate})
involving the decay term $D$ produces an asymmetry while a part
of it gets erased by the wash out terms represented by $W$ which includes
the processes of inverse decay as well as the $\Delta L=1$ and
$\Delta L=2$ lepton number violating scatterings. In a recent
work~\cite{strumia.04} it has been claimed that thermal
corrections to the above processes as well as processes
involving gauge bosons are important for the final $B-L$ asymmetry.
However, this is under debate~\cite{buch-bari-plum-ped.04}, and we have
not included these corrections in the present paper.

In equations (\ref{thermal-rate}) and (\ref{asymmetry-rate}),
$D=\Gamma_D/Hz$, where
\begin{equation}
\Gamma_D=\frac{1}{16 \pi v^2}\tilde{m}_1 M_1^2
\label{decay}
\end{equation}
is the decay rate of $N_1$, with
\begin{equation}
\tilde{m}_1 \equiv \frac{(m_D^\dagger m_D)_{11}}{M_1}
\label{eff-neu-mass}
\end{equation}
the {\it effective neutrino mass} parameter~\cite{plumacher.96},
and $H$ is the Hubble expansion parameter. Also,
$S=\Gamma_S/Hz$, where
$\Gamma_S$ is the rate of $\Delta L=1$ lepton number
violating scatterings and $W=\Gamma_W/Hz$, where $\Gamma_W$
is the rate of wash out effects involving the $\Delta L=1$ and
$\Delta L=2$ lepton number violating processes and
inverse decay. The various $\Gamma$s are related to the scattering
densities~\cite{luty.92} $\gamma$'s as
\begin{equation}
\Gamma_i^X(z)=\frac{\gamma_i(z)}{n_X^{\rm eq}}.
\end{equation}
The dependence of the scattering rates involved in $\Delta L=1$
lepton number violating processes on $\tilde{m}_1$ and $M_1$ are
similar to that of the decay rate $\Gamma_{D}$. As the
Universe expands these $\Gamma$'s compete with the Hubble
expansion parameter. In a comoving volume we have (with
same notations as in ~\cite{luty.92})
\begin{equation}
\left(\frac{\gamma_{D}}{sH(M_1)}\right), \left(\frac{
\gamma^{N_1}_{\phi,s}}{sH(M_1)}\right), \left(\frac{
\gamma^{N_1}_{\phi,t}}{sH(M_1)}\right) \propto k_1\tilde{m}_1.
\label{dilution}
\end{equation}
On the other hand the $\gamma$'s for the
$\Delta L=2$ lepton number violating processes depend on
$\tilde{m}_1$ and $M_1$ as
\begin{equation}
\left(\frac{\gamma^l_{N_1}}{sH(M_1)}\right), \left(\frac{
\gamma^l_{N_1,t}}{sH(M_1)}\right) \propto k_2 \tilde{m}_1^2 M_1.
\label{washout}
\end{equation}
In the above equations (\ref{dilution}), (\ref{washout}),
$k_i$, $i=1,2,3$ are dimensionful constants determined from
other parameters; see ~\cite{luty.92} for details.

\subsection{Constraint on the effective neutrino mass ($\tilde{m}_1$)
\label{subsec:constraint}}
In order to satisfy the out of equilibrium condition the decay rate of
$N_1$ has to be less than the Hubble expansion parameter. This imposes a
constraint on the effective neutrino mass parameter $\tilde{m}_1$ as
follows. At an epoch $T<M_1$,
\begin{equation}
\frac{\Gamma_D}{H}\equiv \frac
{\tilde{m}_1}{m_*}=K < 1,
\label{decay-con}
\end{equation}
where $m_*$, the {\it cosmological neutrino mass parameter}, is given
by~\cite{fglp}
\begin{equation}
m_*\equiv 4\pi g_*^{1/2}\frac{G_N^{1/2}}{\sqrt{2}G_F}
= 6.4\times 10^{-4}\,{\rm eV},
\label{crit-mass}
\end{equation}
where $g_*$ is the effective number of relativistic degrees of freedom.
We see that a net $B-L$ asymmetry can be generated dynamically
provided $\tilde{m}_1 < m_*$ at an epoch
$T<M_1$. This constraint on $\tilde{m}_1$ can be realized in a model as
follows.

We assume a charge-neutral lepton symmetry for which we take the
texture of the Dirac mass of the neutrino of the
form~\cite{falcone.00}
\begin{equation}
m_D=\begin{pmatrix}
0 & \sqrt{m_e m_{\mu}} & 0\\
\sqrt{m_e m_{\mu}} & m_{\mu} & \sqrt{m_e m_{\tau}}\\
0 & \sqrt{m_e m_{\tau}} & m_{\tau}
\end{pmatrix}\,.
\label{dirac-texture}
\end{equation}
Using (\ref{lower-bound-M1}) and (\ref{dirac-texture}) in
equation (\ref{eff-neu-mass}) we get the constraint to be
\begin{equation}
\tilde{m}_1 \leq 5.25\times 10^{-6}\,{\rm eV},
\end{equation}
which is in consonance with the requirement that
$\tilde{m}_1 < m_*$ at any epoch $T<M_1$.

\subsection{Solving the Boltzmann equations\label{subsec:solving}}
At an epoch $T\gg M_1$ the lepton number violating processes are
sufficiently fast as to set the $B-L$ asymmetry to zero. As the
temperature falls and
becomes comparable to $M_1$, a net $B-L$ asymmetry is generated through
the $CP$-violating decay of $N_1$. The resulting asymmetry can be
obtained by solving the Boltzmann equations. We solve equations
(\ref{eff-rate}) and (\ref{asymmetry-rate}) numerically with the
following initial conditions
\begin{equation}
Y^{\rm in}_{N1}=Y_{N_1}^{\rm eq}~~{\mathrm and}~~ Y^{\rm in}_{B-L}=0.
\label{in_condn}
\end{equation}
Using the first initial condition we solve equation
(\ref{eff-rate}) for $Y_{N_1}$, and the corresponding $B-L$ asymmetry
$Y_{B-L}$ is obtained from equation (\ref{asymmetry-rate}) by using
the second initial condition of equation (\ref{in_condn}).
\begin{figure}[htbp]
\epsfig{file=thasy13-4.eps, width=0.5\textwidth}
\epsfig{file=thstasy13-4.eps, width=0.5\textwidth}
\caption{Evolution of the $B-L$ asymmetry for $\tilde{m}_1=10^{-4}\,{\rm eV}$,
$\eta_{B-L}=10^{13}\gev$ and different values of $M_1$ (a) in absence
of cosmic strings, and (b) in presence of cosmic strings. The $CP$
violation parameter $\epsilon_1$ has been given its maximal value.}
\label{fig:eta=13-4}
\end{figure}

\begin{figure}[htbp]
\epsfig{file=thasy13-5.eps, width=0.5\textwidth}
\epsfig{file=thstasy13-5.eps, width=0.5\textwidth}
\caption{Evolution of the $B-L$ asymmetry for $\tilde{m}_1=10^{-5}\,{\rm eV}$,
$\eta_{B-L}=10^{13}\gev$ and different values of $M_1$ (a) in absence
of cosmic strings, and (b) in presence of cosmic strings. The $CP$
violation parameter $\epsilon_1$ has been given its maximal value.}
\label{fig:eta=13-5}
\end{figure}

In the usual thermal scenario the $B-L$ asymmetry depends on
$\tilde{m}_1$ and $M_1$. In presence of cosmic strings there is in
addition an explicit dependence on $\eta_{B-L}$ since
the injection rate of $N_R$'s from the cosmic string loops explicitly
depends on it. To illustrate the effect of the cosmic string generated
non-thermal $N_R$'s on the evolution of the $B-L$ asymmetry,
we display in Figures \ref{fig:eta=13-4} and \ref{fig:eta=13-5} the
results obtained by numerically solving the Boltzmann
equations described above for some specific values of the various relevant
parameters. It can be seen from Figure~\ref{fig:eta=13-4}(a), for example,
that in the absence of cosmic strings the $B-L$ asymmetry approaches the
final value at $T\simeq 0.1 M_1$ when all the wash out processes fall
out of equilibrium. In contrast, in the presence of cosmic strings, for
sufficiently large values of $M_1$, the $B-L$ asymmetry
continues to build up until the injection rate of $N_R$'s from cosmic
string loops becomes insignificant. For $h_1=1$ this happens around
$T\simeq M_1/600$ (see Figure \ref{fig:eta=13-4}(b)), which is far
lower than in the purely thermal case. As a result of this, in presence
of cosmic strings, for a fixed value of the symmetry breaking scale
$\eta_{B-L}=10^{13}\gev$, for example, the final $B-L$
asymmetry is enhanced by three orders of magnitude for the effective
neutrino mass $\tilde{m}_1=10^{-4}\,{\rm eV}$ (Fig.~\ref{fig:eta=13-4}(b)) and
by two orders of magnitude for $\tilde{m}_1=10^{-5}\,{\rm eV}$
(Fig.~\ref{fig:eta=13-5}(b)). For $\eta_{B-L}=10^{13}\gev$,
the effect of cosmic string essentially disappears for $h_1<0.01$

The above results, in particular the dependence on the value of
$\tilde{m}_1$, can be understood as follows: First let us consider the
purely thermal leptogenesis case, i.e., in absence of cosmic strings.
Below a certain temperature when the wash out processes fall out of
equilibrium the asymmetry produced by the decay of $N_1$'s does not get
wiped out, and the produced $B-L$ asymmetry remains as the final
asymmetry. Since the decay rate of $N_1$'s depends
linearly on $\tilde{m}_1$ (see equation (\ref{dilution})),
a larger value of $\tilde{m}_1$ implies that the condition of
decay in out-of-equilibrium situation is satisfied at a
later time when the abundance of thermal $N_1$'s is smaller,
thus yielding a smaller final value of $Y_{B-L}$. And as expected, this
effect is larger for larger values of $M_1$. Now, in
the presence of cosmic strings, for values
of $\eta_{B-L}$ for which the contribution of the cosmic string
generated $N_1$'s to $Y_{B-L}$ always remains insignificant compared
to that due to the thermal $N_1$'s, the dependence of the final
value of $Y_{B-L}$ on $\tilde{m}_1$ is
essentially the same as in the absence of strings as explained above.
However, for those values of $\eta_{B-L}$ for which the string
contributions to $Y_{B-L}$ are significant compared to the thermal
contribution, the dependence of the final value of $Y_{B-L}$ on
$\tilde{m}_1$ is opposite to that in the absence of cosmic strings, i.e.,
the string contribution increases with increasing values of $\tilde{m}_1$.
This is easy to understand: The string generated $N_R$'s make dominant
contribution to $Y_{B-L}$, if at all, only at late times ($T\ll M_1$) when
the abundance of the thermal $N_R$'s has fallen to insignificant levels.
The decay of the string generated $N_R$'s at such late times
automatically satisfies the out-of-equilibrium condition. In this
situation a larger value of $\tilde{m}_1$ simply implies
a larger rate of decay of the $N_R$'s leading to a quicker development of
the string contribution to $Y_{B-L}$. This, together with the fact that
the injection rate of the $N_R$'s from cosmic string loops is higher at
earlier times, leads to a higher final value of $Y_{B-L}$. Figures
\ref{fig:eta=13-4}(b) and \ref{fig:eta=13-5}(b) plotted for
$\tilde{m}_1=10^{-4}\,{\rm eV}$ and $\tilde{m}_1=10^{-5}\,{\rm eV}$ simultaneously bear
out these expectations.

Note that in Figures \ref{fig:eta=13-4} and \ref{fig:eta=13-5} the CP
asymmetry parameter $\epsilon_1$ has been taken to have its maximum
value, i.e., $\sin\delta=1$ in equation (\ref{epsilon_1}). Clearly, for
this value of $\epsilon_1$ the produced $B$ asymmetry for
$\eta_{B-L}=10^{13}\gev$ and $M_1\mbox{\raisebox{-.6ex}{~$\stackrel{>}{\sim}$~}} 10^{10}\gev$ (i.e.,
$h_1\gsim10^{-3}$) exceeds the observed value given by
$Y_{B-L}^{\rm obs}\sim O(10^{-10})$ even for purely thermal leptogenesis.
Including the effect of cosmic strings only makes the situation worse.
This implies that we must place an upper bound on the CP asymmetry
phase $\delta$ depending on the values of $\eta_{B-L}$, $M_1$ and
$\tilde{m}_1$, in order not to overproduce the $B$ asymmetry.
At the same time, to produce the observed BAU for
$\eta_{B-L}=10^{13}\gev$ and $h_1=1$, for example, we require
$\sin\delta=\sin\delta_{\rm reqd}=O(10^{-7})$ and
$\sin\delta_{\rm reqd}=O(10^{-6})$ for $\tilde{m}_1=10^{-4}\,{\rm eV}$
and $\tilde{m}_1=10^{-5}\,{\rm eV}$, respectively. These values of $\sin\delta$
diminish the purely thermal contributions, $Y_{B-L}^{\rm
th}$, to $O(10^{-13})$ and $O(10^{-12})$, respectively.

We have calculated the value of $Y_{B-L}$ for a range of
values of $\eta_{B-L}$, $h_1$ and $\tilde{m}_1$, both in the purely
thermal case, $Y_{B-L}^{\rm th}$, and with the effect of cosmic strings
included, $Y_{B-L}^{\rm th+st}$. The results for
$\eta_{B-L}=10^{12}\gev$ and $\eta_{B-L}=10^{11}\gev$ are
summarized in Tables \ref{table-1} and \ref{table-2}, respectively, where
we also indicate the order of magnitude of $\sin\delta_{\rm reqd}$, the
value
of $\sin\delta$ required to produce the observed $B$ asymmetry, for
each set of the chosen parameters.

From these Tables as well as from Figures \ref{fig:eta=13-4} and
\ref{fig:eta=13-5} we see that there exist ranges of values of the
parameters $\eta_{B-L}$, $h_1$, $\tilde{m}_1$ and $\delta$ for which the
cosmic string generated $N_R$'s make the dominant contribution to and
indeed produce the observed BAU while the purely thermal leptogenesis
mechanism is not sufficient.

\begin{table}[htbp]
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
$h_1$ & \multicolumn{3}{|c|} {$\tilde{m}_1=10^{-4}\,{\rm eV}$} &
\multicolumn{3}{|c|} {$\tilde{m}_1=10^{-5}\,{\rm eV}$} \\ \cline{2-7}
 & $Y^{\rm th}_{B-L}$ & $Y^{\rm th+st}_{B-L}$ & $\log(\sin\delta_{\rm
reqd})$
& $Y^{\rm th}_{B-L}$ & $Y^{\rm th+st}_{B-L}$ & $\log(\sin\delta_{\rm
reqd})$\\
[2mm]\hline
1 & $2.72\times 10^{-7}$ & $1.23\times 10^{-5}$ & $-5$ &
$3.90\times 10^{-7}$ & $1.59\times 10^{-6}$ & $-4$\\ [2mm]\hline
0.1 & $3.10\times 10^{-8}$ & $3.22\times 10^{-8}$ & $-2$
& $3.97\times 10^{-8}$ & $3.98\times 10^{-8}$ & $-2$\\
[2mm]\hline
0.01 & $3.25\times 10^{-9}$ & $3.25\times 10^{-9}$  & $-1$
& $4.04\times 10^{-9}$ & $4.04\times 10^{-9}$ & $-1$\\ [2mm]\hline
0.001 & $3.39\times 10^{-10}$ & $3.39\times 10^{-10}$ & 0 &
$4.11\times 10^{-10}$ & $4.11\times 10^{-10}$ & 0\\[2mm]\hline
\end{tabular}
\end{center}
\caption{The $B-L$ asymmetry in the purely thermal leptogenesis
case ($Y^{\rm th}_{B-L}$) and in presence of $B-L$ cosmic strings
($Y^{\rm th+st}_{B-L}$) for $\eta_{B-L}=10^{12}\gev$ and different values
of the Yukawa coupling $h_1$ and the effective neutrino mass
$\tilde{m}_1$. The order of magnitude of the value of $\sin\delta$
required to
produce the observed BAU, $\sin\delta_{\rm reqd}$, for each set of
values of the parameters $\tilde{m}_1$ and $h_1$, is also given.}
\label{table-1}
\end{table}

\begin{table}[htbp]
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
$h_1$ & \multicolumn{3}{|c|} {$\tilde{m}_1=10^{-4}\,{\rm eV}$} &
\multicolumn{3} {|c|} {$\tilde{m}_1=10^{-5}\,{\rm eV}$}\\ \cline{2-7}
 & $Y^{\rm th}_{B-L}$ & $Y^{\rm th+st}_{B-L}$ & $\log(\sin\delta_{\rm
reqd})$
& $Y^{\rm th}_{B-L}$ & $Y^{\rm th+st}_{B-L}$ & $\log(\sin\delta_{\rm
reqd})$\\
[2mm]\hline
1 & $3.10\times 10^{-8}$ & $1.51 \times 10^{-7}$ & $-3$ & $3.97\times
10^{-8}$ & $5.17\times 10^{-8}$ & $-2$ \\ [2mm]\hline
0.1 & $3.25\times 10^{-9}$ & $3.27\times 10^{-9}$ & $-1$
& $4.04\times 10^{-8}$ & $4.04\times 10^{-9}$ & $-1$\\
[2mm]\hline
0.01 & $3.39\times 10^{-10}$ & $3.39\times 10^{-10}$ & 0 & $ 4.11\times
10^{-10}$ & $4.11\times 10^{-10}$ &  0\\ [2mm]\hline
\end{tabular}
\end{center}
\caption{Same as Table \ref{table-1} but for $\eta_{B-L}=10^{11}\gev$.}
\label{table-2}
\end{table}
\section{Conclusion\label{sec:conclusion}}
We have studied the effect of $B-L$ cosmic strings arising from the
breaking of a $U(1)_{B-L}$ gauge symmetry, on the baryon asymmetry of the
Universe. The disappearance of closed loops of $B-L$ cosmic strings can
produce heavy right handed neutrinos, $N_R$'s, whose $CP$-asymmetric decay
in out-of-thermal equilibrium condition can give rise to a net lepton
($L$) asymmetry which is then converted, due to sphaleron transitions, to
a Baryon ($B$) asymmetry. We have solved the relevant Boltzmann
equations that include the effects of both thermal and string generated
non-thermal $N_R$'s. By exploring the parameter region spanned by the
effective light neutrino mass parameter $\tilde{m}_1$, the mass $M_1$ of
the lightest of the heavy right-handed neutrinos (or equivalently the
Yukawa coupling $h_1$) and the scale of the $B-L$ symmetry breaking,
$\eta_{B-L}$, we found that there exist ranges of values of
these parameters, in particular with $\eta_{B-L} > 10^{11}\gev$
and $h_1\mbox{\raisebox{-.6ex}{~$\stackrel{>}{\sim}$~}} 0.01$, for which the cosmic string generated non-thermal
$N_R$'s can give the dominant contribution to, and indeed produce, the
observed Baryon Asymmetry of the Universe when the purely thermal
leptogenesis mechanism is not sufficient. We have also discussed how,
depending on the values of $\eta_{B-L}$, $\tilde{m}_1$ and $h_1$, our
results lead to upper bounds on the $CP$ violating phase $\delta$ that
determines the relevant $CP$ asymmetry in the decay of the heavy right
handed neutrino responsible for generating the $L$-asymmetry.

\section*{Acknowledgment}
The work of UAY and NS is supported in part by a grant from
Department of Science and Technology. UAY wishes to thank the
hospitality  of PRL Ahmedabad where part of this paper was completed.

redpajama_set_name: RedPajamaArXiv


text:
Italy prepares passenger ship to treat Covid-19 patients
Italy is transforming a passenger ship into a floating hospital that will treat coronavirus (Covid-19) patients.
Port of Genoa, where the ship is currently located. Credit: Eustace Bagge.
The vessel will be equipped to treat hundreds of patients. Currently, the ship is docked in the Port of Genoa in Liguria.
Liguria region president Giovanni Toti said: "If our medical specialists confirm that technical conditions are met, patients will be able to find hospitality on this naval unit where a few hundreds of beds will be put at the disposal of the most fragile categories of people."
The move comes at a time when Italy, one of the worst affected countries, has already tightened a country-wide lockdown to control the spread of the virus.
On 13 March, 15,113 Covid-19 cases and 1,016 deaths were reported in Italy.
Once arrangements are completed, the ship will host intensive care and resuscitation units and will provide all essential services.
The authorities may also use it as a quarantine location for Covid-19 patients or as a support unit to isolate people who came in contact with coronavirus patients.
The move to equip the ship as a floating health centre is part of the government's efforts to reduce hospital pressure. Additional ships may be transformed into floating hospitals if required.
Currently, intensive care departments across the country are already treating more than a thousand patients, which represents approximately one-fifth of the national capacity.
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State-of-the-art Maritime Transponders and Automatic Identification System (AIS) Solutions
TSI Turbo Service International
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Insulation for Marine Engines and Exhaust
Malaysia reports four Covid-19 cases on ship
Singapore's MPA adopts measures for safe port operations
ICS issues new protocol to tackle Covid-19 cases on ships
COVID-19: Poll finds business sentiment is improving
Concerns over the spread of COVID-19 declining since June: Poll


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All modernising economic sectors need functional financing systems to stand a chance to reach their full potentials. Lending to agriculture however, traditionally suffers from the perception of banking institutions that risks associated with farming are hard to calculate due to the great uncertainties of weather and recently increasingly that of climate change — especially obviously in countries that are strongly affected by it.
In the eyes of lenders, default risks of agriculture are even higher when it comes to loans for smallholder farmers because most of them lack collateral.
For a substantial agricultural transformation in Africa the fundamental inclusion of smallholder farmers is absolutely critical. They produce up to 80 percent of the food supply in sub-Saharan Africa. Therefore it is the main concern of the continental policy framework called the Comprehensive Africa Agricultural Development Programme (CAADP).
The Malabo Declaration reemphasized the need for heightened public investment into agriculture and still there is an urgent call to find ways to increase funding for agriculture from the private sector. Private sector funding will not only leverage existing public investments, it will also fill the critical financing gap to boost agribusinesses.
Delivering on the Malabo Declaration goes beyond planning and investment. It's also about reforming economic policies and institutional capabilities through creating an enabling environment for overall innovation and economic transformation. To support an increasingly strong private sector in Africa, all economic policy actions should put greater emphasis on farmers and entrepreneurs along agricultural value chains who are at the centre of all these reforms.
A continent-wide approach to agriculture issues in Africa has led to proposals around intra-African trade and regional and continental value chain issues. A continental approach may also enhance policy coherence at the country level, facilitate peer learning, and promote national reform processes.
As an integral part of the National Agricultural Investment Plans (NAIP), CAP-F is a tool which facilitates private sector investments into agriculture.
In the context of CAP-F, policy change and the creation of the creation of the right conducive environment are achieved through identification of policy actions/reforms, gathering and development of policy reform commitments. Identification of priority value chains as per Malabo Declaration and development of strong business cases as part of the CAP-F process should boost investment mobilization at the country level. Coordination mechanisms at country and regional levels, as well as well as stakeholder dialogue and mutual accountability mechanisms are key ingredients for a successful private sector involvement which leverages public sector's interventions in agriculture.
With its Policy Advice, Climate Change, ATVET (Agricultural Technical and Vocational Education Training) modules GIZ supports mainstreaming of key themes into the NAIP process, supports CAADP country missions, implementation of the CAP-F to ensure inclusive agricultural transformation.
By the means of the CAADP Support Programme, GIZ provides support to Uganda towards developing an agricultural finance policy, which is currently making its way through the legislative approval process. Even though agriculture issues are mainly discussed at the Ministry of Agriculture, agricultural finance has found a home and a champion at the Ministry of Finance, as a result of better public sector coordination and harmonization of agricultural finance issues. Moreover, increased coordination in the agricultural sector through GIZ support has heightened private sector interest in agricultural investments in Uganda.
To ensure an inclusive agriculture sector, Africa's Heads of State adopted a continental policy framework deemed as the Comprehensive Africa Agricultural Development Programme (CAADP) in Maputo in 2003, hence called the Maputo declaration. In terms of agriculture development, the Heads of State committed to public investment of at least 10% of their respective national budgets to agriculture or at least a minimum of 6% of their GDP — at the country level.
In 2013 in Malabo, the Heads of State reconfirmed their commitments to the CAADP principles.


text:
La maduixera, fraulera o fraguera (Fragaria vesca) és una planta herbàcia perenne, vivaç, estolonífera, de fulles trifoliades, de flors blanques i de fruits en núcula, disposats sobre receptacles carnosos i vermells, anomenats en conjunt maduixes. Poden tenir fins a cinc flors per planta, amb cinc pètals que es toquen, de color crema. És de port baix i es multiplica vegetativament per estolons o sexualment a través de llavors. La temperatura òptima de creixement és 10-13 °C a la nit i 18-22 °C durant el dia. A l'hivern alenteix el seu metabolisme i quan va arribant l'estiu dona la màxima esplendor de fruit. Arriba a assolir una altura entre 5 i 30 centímetres.

Les espècies de maduixa són originàries de les regions holàrtica i neotropical. Es fa en boscos o llocs ombrívols. En estat silvestre, es pot trobar en totes les zones temperades de l'hemisferi Nord. És conreada pels seus fruits anomenats 'fragues', 'fraules' o 'maduixes', però ha estat quasi totalment substituïda per la fraga, fraula o maduixot, un híbrid o encreuament en part d'origen americà.

Hàbitat
Es pot trobar en boscos temperats, en les vores dels camins, matolls... En estat silvestre es troba en totes les zones temperades de l'hemisferi nord, tot i que es pot cultivar en tot el món.
Creix en les orles dels boscos, clars, en zones humides, en general. Des del nivell del mar als 1900 m d'altitud. Es caracteritza de comunitats de la classe Epilobietea angustifolii de plantes vivaces, que estan denominades per hemicriptòfits de port elevat i aspecte megafòrbic. Es desenvolupen sobre sòls que han patit una ràpida mineralització de la matèria orgànica que ha estat ocasionada per tallades, cremades, obertura de camins o pistes forestals. El pH òptim del sòl per tal que pugui créixer la Fragaria vesca és entre 4.5 i 7.5.
Als Països Catalans manca a les Balears i només es troba al nord del País Valencià de 1.000 a 1.600 metres d'altitud. Al Principat de Catalunya la podem trobar a les quatre províncies.

La forma vital segons Raunkjaer és l'hemicriptòfit, ja que els meristemes es troben just arran de terra en l'estació desfavorable.

Morfologia
És una planta perenne i herbàcia amb pilositat de tipus pubescent perquè presenta pèls curts i suaus.

La tija és de tipus epigea (es desenvolupa a l'aire), de mida reduïda (per la qual cosa s'anomena corona) i prima amb escames foliars. En diversos punts li sorgeixen els estolons que donaran lloc a noves plantes.

La rel és fasciculada i se'n distingeixen rels primàries (més grosses i de color cafè fosc) i rels secundàries (més primes i de color marfil). La seva forma és cònica, i poden arribar a una profunditat que oscil·la entre els 40 i els 80 centímetres.

La fulla és simple, trilobulada, peciolada i amb una divisió de marge dentada. La textura és herbàcia per la part superior i de naturalesa sedosa pel revers. La seva nervadura és pennada.

Poden haver-hi flors perfectes (hermafrodites) que tenen òrgans masculins i femenins (estams i pistils respectivament) o imperfectes (unisexuals), amb un sol òrgan femení o masculí. Les flors blanques s'organitzen en inflorescències cimoses, de tiges no modificades, en les que una bràctea substitueix en cada nus a una fulla mentre que la gemma axil·lar d'aquesta es desenvolupa en una branca secundària o eix de la inflorescència.

La flor és de simetria actinomorfa. El periant està compost per un calze de cinc sèpals i la corol·la està formada generalment per cinc pètals de color crema. Aquests pètals són de forma variable (el·líptics, arrodonits...)

A l'androceu hi ha nombrosos òrgans masculins, anomenats estams, compostos cadascun per un filament de longitud variable que sosté les anteres (contenen el pol·len). Les anteres estan disposades en tres verticils, fonamentalment en múltiples de cinc i poden arribar fins a quaranta, inserits en la perifèria del receptacle, un òrgan que té forma de copa invertida.
Tenen un calze de cinc peces esberlades, cinc pètals arrodonits, nombrosos estams i pistils.

El gineceu està compost per nombrosos carpels lliures localitzats en la zona axial del receptacle floral. De cadascun sorgeix un estil lateral que fineix en un estigma engruixit.

L'ovari és súper i la concrescència és pluricarpel·lar de tipus apocàrpic.

Quan fructifica el receptacle floral, augmenta de mida fins a arribar als 10 o 17 mm adquirint forma ovoide i color vermell intens. Sobre el receptacle es disposen nombrosos aquenis d'uns 0,8 mm, que són en realitat els autèntics fruits, formant-se un eteri d'olor vermell, dolç i aromàtic.

El fruit, anomenat maduixa o fraula, és el resultat de l'agregació de molts carpels secs diminuts sobre un receptacle hipertrofiat de color vermell escarlata.

La planta pol·linitza tant per insectes com pel vent.

Les maduixes contenen una gran quantitat d'àcids orgànics i vitamina C, substàncies minerals i sucres per la qual raó és molt apreciat pel seu gust i les seves aplicacions en medicina. Altres components actius són: pigments, olis essencials, tanins i flavonoides. Tenen un gust dolç i àcid.

Conreu
Les maduixeres que es conreen habitualment són plantes no híbrides de les espècies Fragaria vesca (maduixera europea) o Fragaria virginiana (maduixera nord-americana). El maduixot o fraga és, en canvi un híbrid.

La maduixera és un cultiu que s'adapta molt bé a tota mena de climes, tot i així la seva temperatura mínima biològica és de 6 °C. A temperatures inferiors a 12 °C apareixen fruits deformats a causa del fred.
La part vegetativa de la maduixera és altament resistent a gelades, arribant a suportar temperatures fins a – 20 °C, encara que els òrgans florals són malferits quan els valors són inferiors a 0 °C.
Els valors adequats per a una fructificació adequada se situen rodejant els 15-20 °C de mitjana anual.
Per tal que la maduixera tingui un desenvolupament favorable, necessiten un sòl sorrenc. Rics en humus, però poden créixer en qualsevol mena de terreny mentre estiguin ben drenades.

A les zones fredes, les maduixes solen plantar-se al principi de la primavera, i a mitjan estiu, o més tard als llocs més càlids. Les plantes formen el fruit a la primavera de l'any següent, entre març i agost, i la resta de mesos de l'any s'alenteix el seu creixement. Hi ha varietats que produeixen a la tardor una segona collita de fruits més petits. Gairebé tots els maduixers es multipliquen mitjançant estolons els quals es formen en uns dos mesos després de l'estació de l'any de plantació.

La maduixera té una vida mitjana de 4-5 anys, però quan és cultivada per a treure'n rendiment econòmic només és útil durant dos anys, ja que després es torna feble i vulnerable davant plagues i insectes, i per això s'han de treure del camp de recol·lecció i substituir-les per noves. La collita es fa evitant les hores més caloroses del dia perquè es conservin millor i mai no s'emmagatzemen o transporten en grans recipients per a evitar-ne l'esclafament.

Són paràsits del maduixer insectes com el borinot de la rosa, que forada les fulles i pon ous a les flors; el piral de la vinya i els minadors de les fulles.

Contingut químic i aplicacions terapèutiques

El rizoma, l'arrel i les fulles componen la droga (part utilitzada).

Els components actius del fruit de la maduixera són els pigments, olis essencials, vitamina C, tanins i flavonoides.

A les fulles, els principis actius que trobem són tanins condensats, flavones, flavonoides, leucoantocianòsids, traces d'oli essencial, petites quantitats d'àcid ascòrbic, alcohol tripèrnic: fraganol, sals potàssiques.
L'arrel presenta tanins catèquics (12%) i pirogàl·lics; alcohol tripèrnic: fraganol, sals potàssiques.
Als fruits trobem abundants derivats antociànics, oli essencial, pectina, heteròsid (fragaròsid).

Les fulles i les arrels s'utilitzen en infusions i són diürètiques i astringents (pel seu alt contingut en tanins). Els tanins donen una acció astringent (antidiarreica i hemostàtica local) i les sals de potassi una acció diürètica. A causa de la composició present en fulles, pot utilitzar-se contra diarrees, enterocolitis i en estats en els quals es requereix una augmentació de la diüresi, com és el cas d'afeccions genitourinàries (cistitis, uretritis, pielonefritis, oligúria i urolitiasi), hiperazotèmia, gota, hipertensió arterial, edemes i sobrepès acompanyat de retenció de líquids.

En ús tòpic s'utilitzen els components de les fulles per a ferides i ulceracions dèrmiques, bucals o corneals, blefaritis, conjuntivitis, parodontopaties, faringitis, èczemes, eritemes, prurits i vulvovaginitis.

La ingesta del fruit combat la fragilitat capil·lar, les varius i les hemorroides. També s'empra per a alleujar la reuma i l'artritis. Gràcies als seus derivats antociànics, ajuda l'absorció de la vitamina C (efecte vitamínic P).

Tanmateix, també presenta certes contraindicacions pel que fa a les fulles davant la gastritis i l'úlcera gastroduodenal. Això es deu al fet que els tanins poden irritar la mucosa gàstrica. Els efectes secundaris que se li atribueixen per via interna són una coloració vermellosa de l'orina i les femtes (per l'eliminació de pigments) encara que no té una patologia rellevant. Per altra banda els fruits contenen glicoproteïnes que poden provocar al·lèrgies en persones hipersensibles. Sempre que s'empri aquesta planta cal assegurar-se que fulles i fruits provenen de cultiu biològic (la producció agrícola intensiva requereix l'aplicació freqüent d'insecticides i herbicides). En definitiva es pot dir que la toxicitat no és de gaire importància en aquesta planta, per bé que les fulles pansides sí que presenten una certa toxicitat.

Aplicacions culinàries
Quant a les aplicacions culinàries, les maduixes s'utilitzen per preparar melmelades i postres. Tradicionalment, s'han utilitzat per a donar color a merengues, nates i batudes amb llet per a l'elaboració de gelats. És habitual menjar-se-les amb nata, sucre o regades amb moscatell.

Són apreciades molt pel seu contingut en vitamines i minerals i les seves propietats reconstituents i depuratives.

Les seves fulles s'utilitzen per a aromatitzar guisats de carn. També per a preparar un té depuratiu i calmant que, malgrat que tenyeix l'orina d'un color vermellós, no té contraindicacions.

Altres aplicacions
Com passa amb altres rosàcies, aquesta planta s'associa a l'amor. Però pel color roig del fruit, les maduixes madures són símbol de sensualitat i passió. Es diu que si una dona embarassada porta damunt seu una bosseta amb fulles de la maduixera, aquestes alleugen les molèsties de l'embaràs.

Notes

Bibliografia
 VV.AA., Botànica, Ed. McGrawHill-Interamericana, Madrid 2003
 P. Font Quer, Diccionario de botánica, Ed. Labor, Barcelona 1982
 Murray W. Nabors, Introducción a la botánica, Ed. Pearson, Madrid 2006

Fragaria
Plantes medicinals rosàcies

redpajama_set_name: RedPajamaWikipedia


I also had a question about the 3dLME output. When you specify GLTs and then generate a report, the report lists the size of the significant clusters and coordinates of the peak voxels, but is it possible to also list the t-statistics and p-values? Or is that not recommended?
Thank you, and sorry for the multiple questions!


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The number of pilgrims travelling to Iraq from Iran to perform religious rituals on Arbaeen has surpassed 1.4 million, an Iranian official announced.
Speaking to reporters at Chazzabeh border crossing in the southwestern province of Khuzestan on Monday, Head of Iran's Hajj and Pilgrimage Organization Saeed Ohadi said more than 1.4 million pilgrims have travelled to Iraq via Iran's western border crossings for the Arbaeen procession.
He also expected the number to rise to 2 million by the day of Arbaeen, which falls on November 20 this year.
Ohadi further warned the pilgrims not to head to the Iraqi border without a valid passport and a visa, rejecting the possibility of getting a visa at the border.
His comments came after Iranian Deputy Foreign Minister Hassan Qashqavi cautioned that illegal entry into Iraq, namely without a valid visa, will carry a prison sentence of up to six years.
Last year, more than 20 million pilgrims from all over the world gathered in Karbala on Arbaeen.


It's July - and swelteringly hot - so in my world at least it means the Holidays have started. Last week the fireplace was lit and the house was filled with lots of sparkly decorations, a white tree, two models, a photographer (hi John Cullen!), two assistants, an art director (hey Jason Kang!), a wardrobe stylist, a hair and makeup person, plus a couple of extra folks who were roped in to lend a hand. And, we were lucky enough to have smartypants food stylist Ashley Denton on set too, who took a couple of secs in between shots to snap a few pics of the goings-on with the Instagram app on his iPhone. They turned out super-cool, so I thought it'd be fun to share them (there's more on Ash's Instagram stream here).
Yep, it's all very Christmas-y, but in that last shot you'll see something far more practical, the Eames Hang-It-All that's now installed in the front hall to handle a slew of jackets, trucker hats, dog leashes, and towels (for our occasionally mucky Whippet, Spot). It was a splurge for sure - after shopping around I found the best price for a new one on eBay - and, funnily enough, it's the only Eames piece in the house. Happy Holidays!


text:
Vovše so naselje v Občini Litija.

Sklici in opombe

Glej tudi
 seznam naselij v Sloveniji

Naselja Občine Litija


text:
Why Use South Dakota? The Benefits of South Dakota Trust Law
#1 trust law and a top-ranked state by Trusts & Estates magazine.
South Dakota Trust Law Dominance
Over the last decade, South Dakota has been recognized as a leader in trust law and a top-ranked state by Trusts & Estates magazine.
Advisor friendly trust companies find South Dakota trust statutes important for wealth migration. The South Dakota legislature is in session every year, allowing for more progressive and current action and oversight of trust legislation compared to other states.
South Dakota, in 1983, was one of the first states to permit trusts to exist in perpetuity. South Dakota was the first state with a discretionary trust statute for asset protection.
South Dakota does not require trust documents to be filed publicly. Updates or changes to a trust do not need to be filed with a South Dakota court. Privacy is a priority in South Dakota. Delaware provides a considerable less favorable privacy rules with only a 3-year seal.
Dynastic Features
At Wealth Advisors Trust Company, family members, and their professional advisors are involved in traditional roles fulfilled by the trustee through directed or delegated trusts.
South Dakota has no state income or state capital gains tax for those assets held in trust.
Directed Trust/Delegated Trusts
South Dakota legal trust statutes allow the creators of a trust to direct or to delegate the trust company to follow the investment choices and asset allocation decisions of an outside advisor. In these directed or delegated trust arrangements, control over the assets (and the investment fees they generate) remains with the legacy advisor, while the corporate trustee administers the trust itself.
In these directed or delegated trust arrangements, control over the assets (and the investment fees they generate) remains with the legacy advisor, while the corporate trustee administers the trust itself.
Self-settled Trusts
Also known as Asset Protection Trust, South Dakota has enacted legislation which prohibits judicial foreclosure and creditor attachment on beneficial interests in trusts, powers of appointment held by beneficiaries, and reserved powers by a beneficiary. Additionally, a power of appointment in a trust is specifically excluded as a property interest. South Dakota was the first state with a discretionary trust statue for asset protection.
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The dark fic JangoObi AU where the Mandalorian empire didn't fall (Revan wasn't a thing and their momentum kept going, essentially) and now we are in the prequel age, which literally no one asked for but you're all getting anyways.
Obi-Wan is on a basic evacuation mission when he has to ward off the Mandalorian forces himself, resulting in his capture. He wakes up to find himself an unwilling participant in one of the more intense integration programs.
Now, he must try to escape out of a seemingly inescapable system and hold on to his own identity in the mean time, while going through the program designed to break those like him into Mandalorians.
To top it all off, he seems to have caught the attention of the Mand'alor himself, Jango Fett.
There were many things that Obi-Wan learned that first year as a Padawan, but few were ever so more useful than one. It was a skill that he would use throughout the rest of his life, and applicable in many ways for many things.
Obi-Wan watched over Anakin's son from afar, because, of course he did. Luke is family.
But Anakin upon discovering Obi-Wan's son, in rage and grief did something different.
Luke/Rey Tudor AU with him as Mary I and her as Philip II, I promise they end up much happier than their historical counterparts.
Part 8 of There is no such thing as "too much Luke/Rey"!
Anakin Skywalker hated politicians, at least the major part of them. There were only a few that he actually liked, Padme for an instance, Bail Organa seemed nice too and of course his Master's 'girlfriend'.
"Now, what do you think, Anakin?" the older male's slimy voice brought the young Skywalker out of his amusing thoughts and he scolded himself for not having paid attention to the Chancellor of all people.
It's heaven and hell to see her again.
"We get back what shouldn't be gone! The recovery service with an (almost) 100% success rate!" This is the motto of Stardust Retrieval, a special repossession service that helps people get back the things that were taken from them. Stardust Retrieval is composed of Jyn Erso and Cassian Andor.
In this mission: they recruit a bunch of allies, and nearly lose their minds.
Oh, and Jyn needs to face some of the ghosts of her past again.
A typical day in the life of Stardust Retrieval!
A little LoTR and Star Wars fusion because Think Better of Me, Father, by I_Gave_You_Fair_Warning bit into my brain and I had to write a little, in case you weren't already suffering enough.
All it took was five minutes for everything to be ripped away from you.
Padmé Naberrie muss gezwungenermaßen heiraten. Da trifft es sich gut das der begehrte Jungeselle Captain Obi-Wan Kenobi eine Gattin sucht.
Padmés Lieblingstag ist seit neustem der Freitag.
Padmé und Obi-Wan stranden aufgrund eines Schadens ihres Raumschiffes auf einem Planeten. Dies hat nicht geahnte Folgen für ihrer beider Leben.
Anakin finding Obi-Wan after the events in 'The Lawless' and the conversation that ensues.
It has been thirteen years since the destruction of the Jedi Order. The Sith Lord, Sidious, rules the galaxy in the guise of Emperor Palpatine, and with Vader at his side, no one dares oppose him. Fortunately, a small band of dissenters has come together on Tatooine. Led by Jedi Master Obi-Wan Kenobi and former senator, Padmé Amidala, the small group of rebels begins preparations for their first large-scale attack against the Empire. Meanwhile, Lord Vader tirelessly searches for force-sensitives to aide him in his quest to overthrow Palpatine and rule the galaxy with an iron first.


text:
John Davies (John Davies of Nercwys; 26 May 1799 – 5 March 1879) was a Welsh Calvinistic Methodist minister, preacher and writer.

He was born at Llanerch, in the parish of Llanarmon-yn-Iâl. His parents were Joseph and Eleanor Davies; a photograph of Eleanor (née Parry) is held by the National Library of Wales. He was baptised in the parish church on 31 May 1799, but the family moved to Rhos Ithel, Nercwys, in about 1800, and later to Mold; he grew up in the Mold area. At the age of 16, in 1815, he is known to have become a member of Mold Methodist Society. A few years later he began preaching, and in 1834 he was ordained. Though he was an itinerant preacher, his home remained in the Nercwys area of Flintshire; hence the place name was used as an additional epithet to differentiate him from others named John Davies.

His writings include a commentary on the Book of Proverbs (1869). In 1875, he received a testimonial from the chapel where he officiated, "in acknowledgement of his personal worth and abilities". At the age of 76, he had been preaching for 53 years and was the oldest-but-one minister still officiating in North Wales. It was calculated that he had preached 18,779 times in the course of his career. The total sum collected was £100.

Davies died in March 1879. His portrait hangs in Flintshire Record Office together with that of the novelist Daniel Owen, who was christened by him.

References

1799 births
1879 deaths
19th-century Welsh writers
19th-century Welsh Methodist ministers
Welsh Calvinist and Reformed Christians


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