text:
\section{Introduction}
The Kitaev model is an exactly solvable \cite{kitaev2006anyons} quantum spin model with fractionalized excitations within the family of spin-liquid models. Candidate materials for its $J_{eff} = 1/2$ ferromagnetic (F) realization are the iridates X$_2$IrO$_{3}$ (X: Li \cite{williams2016incommensurate, majumder2018breakdown}, Na \cite{choi2012spin, ye2012direct, singh2012relevance, gretarsson2013magnetic,yamaji2014first,alpichshev2015confinement}) and $\alpha$-RuCl$_3$ \cite{wulferding2020magnon,kubota2015successive, lampen2018anisotropic, plumb2014alpha, baek2017evidence, wang2017magnetic, zheng2017gapless,lampen2018field, banerjee2018excitations,sandilands2015scattering, sandilands2016spin, majumder2015anisotropic,bachus2020thermodynamic,reschke2019terahertz, zhou2022intermediate}. Recently, there is a growing interest in the search of additional materials \cite{liu2018pseudospin,liu2020kitaev,lin2021field} with perhaps antiferromagnetic (AF) Kitaev type couplings such as Na$_3$Co$_2$SbO$_6$-Na$_2$Co$_2$TeO$_6$ \cite{kim2020antiferromagnetic} and the f-electron based rare-earth oxides \cite{jang2019antiferromagnetic}. The latter quantum magnets have significant spin-orbit coupling magnitude and frustration. Detailed analyses of the underlying physics and the material characteristics have been summarized in numerous reviews \cite{motome2020hunting,winter2017models,balents2010spin,savary2016quantum,zhou2017quantum,broholm2020quantum,knolle2019field}.

The Kitaev model is defined on a honeycomb-lattice with highly anisotropic Ising type exchange couplings at each bond direction.
\begin{eqnarray}\label{KitaevHamiltonian}
H_{K} &=& \sum_{\langle ij \rangle}^{\alpha-bond} K^\alpha S_i^\alpha S_j^\alpha.
\end{eqnarray}
It can host anyonic excitations within the real fermion language. In this approach, each of the Pauli operators is replaced by two composite Majorana fermions $\sigma_j^\alpha = i b^\alpha_j c_j$, $\alpha \in \{ x,y,z\}$ with the local constraint $D_j = b^x_j b^y_j b^z_j c_j = 1$ at site $j$. The basic theoretical work in materializing such an exotic model relies on the Jackeli-Khaliullin mechanism \cite{jackeli2009mott,rau2014generic}. The effective Hamiltonians for transition metals are coupled with additional (extended) edge-sharing \cite{li2017kitaev,motome2020materials} octahedra ligands. In the presence of sufficiently large spin-orbit coupling could eliminate the leading Heisenberg exchange coupling which is typically the dominant term. Thereby the additional Kitaev and other off-diagonal terms become dominant terms. Eventually, most of the recent work has been allocated to the theoretical \cite{janssen2017magnetization,katukuri2014kitaev,laurell2020dynamical, jackeli2009mott,kim2015kitaev} and experimental investigation of the candidate materials. Experimental data suggest that it is highly likely for the candidate materials to have a spin-liquid groundstate (GS) for intermediate magnetic field strengths. This is inferred, in particular, from the continuum of excitations in neutron-scattering experiments \cite{wu2018field}, susceptibility signals for a magnetic instability in the specific-heat data and the magnetic Gr\"uneisen parameter \cite{bachus2020thermodynamic} . A significant amount of work has also focused on alternative mechanisms such as chiral conventional quasiparticles \cite{cookmeyer2018spin,mcclarty2018topological,ye2020phonon,lefranccois2021evidence} or beyond-Kitaev model spin-liquids \cite{gao2019thermal}. In all approaches, the anti/ferromagnetic Kitaev term has to be supplemented by additional interactions for a realistic material specific modeling. Depending on their relative strengths, the direct relation between the thermal Hall coefficient and the Kitaev interaction becomes obscure.

For an established spin-liquid GS, the thermal Hall conductivity (THC) provides a tool to rule in/out a Kitaev spin-liquid state with a half-quantized neutral edge current as its distinct signature. Such a measurement requires a finite applied magnetic field so that the gapless, topologically trivial Kitaev liquid could go into a gapped, topologically non-trivial phase. Recent measurements on $\alpha$-RuCl$_3$ indicate a large \cite{hentrich2019large} and quantized (if not sample dependent) THC \cite{kasahara2018majorana} within a certain window of in-plane magnetic field strength. This region with a suppressed magnetization is located between staggered ferromagnetic chains (known as the ZZ-$\gamma$ phase) and the field polarized (P) phase. Moreover, the anomalous thermal Hall effect even in the absence of out-of-plane magnetic field components \cite{yokoi2020half} may support the topological origin of a transverse heat current. In this respect, a further characterization of the "intermediate phase" for arbitrary magnetic field and directions could provide valuable information for the search of (non-)Abelian anyons.

In spite of numerous studies \cite{nasu2018successive,janssen2019heisenberg,ralko2020novel, liang2018intermediate,ido2020correlation,gordon2019theory, catuneanu2018path,liu2018dirac,ronquillo2019signatures} along special field directions such as [001] and [111], there exists limited knowledge on the complete field-angle dependence of $\kappa_{xy}$ in the Kitaev model. For example, in \cite{yokoi2020half}, the half-quantized THC measurements on $\alpha$-RuCl$_3$ has been attributed to the pure Kitaev spin liquid. Yet, it could be a naive approximation if the additional off-diagonal couplings are significant. The studies on the candidate materials indicate the presence of a relatively large spin-orbit coupling $\Gamma$ term. Ref. \cite{takikawa2019impact} has addressed this issue and also the magnetic field effects perturbatively, yet assuming a KSL GS. In this respect, it is crucial to clarify the effect of large $\Gamma \sim \left| K \right| $ \cite{hwang2020identification,yamada2021quantum} as well as arbitrary magnetic field orientations and strengths to understand the validity of existing results based on the putative F Kitaev GS. Naturally, an unbiased method is needed where the ordered phases and the fractional phases are treated on equal footing.
\begin{figure}
\includegraphics[width=0.47\textwidth]{Fig_1.eps}
\caption{(Color online) The crystal structure of $\alpha$-RuCl$_3$. The Ru atoms (green dots) form a honeycomb-lattice (with black bonds) on the plane perpendicular to the crystallographic [111] direction, referred to as the c-axis. The three bonds are labeled as $x,y$ and $z$. The Cl$^-$ ions form edge-sharing octahedra with two sublattices denoted by blue and orange colors. For the Kitaev only models ($\Gamma=0,\Gamma_p = 0$), the unit cell contains two Ru sites connected by the z-bond. For the Kitaev-$\Gamma$ type models ($\Gamma\ne 0,\Gamma_p \ne 0$), a four-site unit cell is necessary to capture the relevant groundstate. It is indicated by a green dotted rectangle with site labels $1-4$.}
\label{pointGroups}
\end{figure}

In this manuscript, we attempt to answer the following two questions: 1. What is the full phase diagram of the antiferromagnetic Kitaev model in the presence of an external magnetic field pointing in arbitrary directions? 2. What are the effects of the additional $\Gamma$-$\Gamma_p$ off-diagonal terms? Regarding the former, we identify a magnetization process with multiple topological distinct phases depending on the field direction and strength. The phase boundaries are characterized by the first Chern number of the fermionic vacuum. Regarding the latter, we examine the phase diagram of the ($K, \Gamma, \Gamma_p$)-model and identified four different zero-field phases: a zig-zag z (ZZ-z), a polarized (P), an extended KSL, and the Kitaev-$\Gamma$ spin-liquid (K$\Gamma$SL) phases. A focus is given to the experimentally relevant ZZ-z phase, in which the ferromagnetic chains are antiferromagnetically aligned perpendicular to the $z$-bond. Our choice of the unit cell in Fig.\ref{pointGroups} allows only ZZ-$z$ phase . This discussion is elaborated further in Sec.\ref{KGGpHsec}. Then, starting from the ZZ-z GS, we examine the magnetic field response as a function of the off-diagonal coupling strength $\Gamma$ . We identify a region with reduced magnetization and decreased energy gap with finite Chern number, named as the partially polarized (PP) phase. This phase is found to host partial fractionalization.

Throughout this work, we employ a mean-field theory of the Majorana representation with local constraints. The advantage of this approach is that it readily captures the strong correlations inherent within this composite (fractionalized) representation along with the magnetic phases. The detailed derivation of the mean-field equations is provided in the Appendix \ref{MFtheoryDetails}.

The article is divided into three sections. The current introductory section is completed with the additional discussion on the materialization process of the Kitaev model. In section $II$, we identify the thermal Hall coefficients for the pure AF/F Kitaev model for arbitrary magnetic-field orientations and strengths. The critical field strength and the angles for topological phase transitions are determined. In section $III$, the role of the additional off-diagonal terms, $\Gamma,\Gamma_p$ are examined. We complete this section by discussing the implications of our results for the recent thermal Hall experiments on candidate materials.

\subsection{Kitaev materials: $\alpha$-RuCl$_3$}

The experimental side of the search of Kitaev materials has advanced by signatures of massively degenerate, gapless excitations in the iridates XIrO$_3$ and in $\alpha$-RuCl$_3$. The modeling of these specific materials requires additional terms in the spin Hamiltonian. For concernitant materials, the symmetry group is $\mathcal{D}_{3d} = \{\mathcal{I}, 2 \mathcal{C}_3, 3 \mathcal{C}_2, 2 \mathcal{S}_6, 3\mathcal{M} \}$ \cite{jackeli2009mott, rau2014generic, katukuri2014kitaev, janssen2017magnetization}, the symmetry allowed interactions are Kitaev type $K^\alpha S_j^\alpha S_l^\alpha$, Heisenberg type $J \mathbf{S}_j \cdot \mathbf{S}_l$ as well as off-diagonal couplings $\Gamma^\alpha \left( S_j^\beta S_l^\gamma+S_j^\gamma S_l^\beta \right)$, and (when e.g. Ru-Cl environment differs from octahedra) the additional allowed $\Gamma^{\alpha}_p$ terms $\Gamma^{\alpha}_p (S^\beta_j S^\alpha_l+S^\alpha_j S^\beta_l+S^\gamma_j S^\alpha_l+S^\alpha_j S^\gamma_l)$. Therefore, a more general spin coupling term is considered, $\Gamma_{ij}^{\alpha \beta}S_i^\alpha S_j^\beta$ where $\Gamma_{ij}^{\alpha \alpha} \to K,J$ and $\Gamma_{ij}^{\alpha \ne \beta} \to \Gamma, \Gamma_p$. The additional interactions and their role are the subject of current experiments \cite{banerjee2018excitations, lampen2018field, majumder2018breakdown, zheng2017gapless, wang2017magnetic, baek2017evidence, williams2016incommensurate, plumb2014alpha, lampen2018anisotropic,
kubota2015successive}, ab-initio calculations \cite{kim2016revealing}, exact-diagonalization methods \cite{ lee2020magnetic,winter2016challenges,gohlke2018dynamical} and effective low-energy Hubbard Hamiltonians \cite{wang2017theoretical,winter2017models,winter2017breakdown}.

Here, we focus on $\alpha$-RuCl$_3$ because there are sufficient number of works to compare in the literature to ensure the validity of our approach. The crystal structure of $\alpha-$RuCl$_3$ has a honeycomb structure in Ru-Ru bonds for a cut in the [111] direction (see Fig.\ref{pointGroups}). The Cl atoms are aligned as edge-sharing octahedras. The additional exchange paths through Ru-Cl bonds -in the presence of strong spin-orbit coupling- create a destructive interference for the otherwise leading term $J$, the Heisenberg exchange coupling \cite{jackeli2009mott,rau2014generic}. Therefore, a Kitaev type exchange coupling along with $\Gamma$ and $\Gamma_p$ terms take stage. Experiments in zero magnetic field suggests a long range ZZ-z order for the GS of $\alpha-$RuCl$_3$ \cite{banerjee2018excitations, lampen2018field, majumder2018breakdown, zheng2017gapless, wang2017magnetic, baek2017evidence, williams2016incommensurate, plumb2014alpha, lampen2018anisotropic,
kubota2015successive}. Yet, a finite magnetic field along x-y bonds melts the magnetic order and thereby allows for a transition to a spin-liquid phase \cite{kasahara2018majorana}.

For the calculations described below, we switch to new orthogonal coordinate system ($\hat{e}_1,\hat{e}_2,\hat{e}_3$) with the following transformation,
\begin{equation} \label{xyzVS123}
\begin{pmatrix}\hat{e}_1\\\hat{e}_2 \\ \hat{e}_3\end{pmatrix}=\frac{1}{\sqrt{6}}\begin{pmatrix}1&1&-2\\-\sqrt{3}&\sqrt{3}&0\\\sqrt{2}&\sqrt{2}&\sqrt{2}\end{pmatrix} \begin{pmatrix}\hat{e}_x\\\hat{e}_y\\\hat{e}_z\end{pmatrix}.
\end{equation}
Here, $\hat{e}_3$ points along the [111] direction, while $\hat{e}_1$, $\hat{e}_2$ are in plane unit vectors perpendicular to x-bond and y-bond, respectively.

\begin{figure}
\includegraphics[width=0.47\textwidth]{Fig_2a.eps}
\caption{(Color online) Ferromagnetic Kitaev model: The Chern number map for arbitrary field direction and strength in the $(h_1-h_3)$ plane, where $h_i = \mathbf{h}\cdot \hat{e}_i$ in units of $\left| K \right|$. Topologically distinct GSs with Chern numbers $\nu = \pm 1$ are identified. The trivial phase $\nu = 0$ corresponds to the high-field polarized phase. The red arrows indicates the experimental magnetic field-angles that is used in Ref.\cite{kasahara2018majorana} with $\theta = \pm 60^o$, where $\theta$ is the clockwise angle w.r.t. the $h_3$ axis. $h[001]$ direction is shown for visualization purposes.}
\label{FKitaev_Chern}
\includegraphics[width=0.47\textwidth]{Fig_2b.eps}
\caption{(Color online) Antiferromagnetic Kitaev model: The Chern number map for arbitrary field direction and strength in the $(h_1-h_3)$ plane, where $h_i = \mathbf{h}\cdot \hat{e}_i$ in units of $\left| K \right|$. There are in total five topologically distinct GSs possible with Chern numbers $\nu \in \{0,\pm 1, \pm 2 \}$. $\nu = 0$ phase is the field polarized phase. The red arrows indicates the experimental magnetic field-angles that is used in Ref.\cite{kasahara2018majorana} with $\theta = \pm 60^o$, where $\theta$ is the clockwise angle w.r.t. the $h_3$ axis. $h[001]$ direction is shown for visualization purposes.
}
\label{AFKitaev_Chern}
\end{figure}

\section{Kitaev model in an arbitrary magnetic field}
In materials like $\alpha$-RuCl$_3$ and Na$_2$IrO$_3$, the Kitaev exchange coupling along all bond directions are likely to be equal \cite{jackeli2009mott,rau2014generic}. We therefore consider an isotropic Kitaev coupling, $K^\alpha = K$. The isotropic model supports the trivial gapless B-phase \cite{kitaev2006anyons}. It can host two types of fractionalized excitations, the $\mathbb{Z}_2$ vortices and itinerant fermionic excitations, albeit a topologically trivial groundstate. The system can have a topological phase by an external magnetic field along the [111] direction as it opens an energy gap proportional to $\Delta \sim \frac{h^3}{K^2}$ \cite{kitaev2006anyons} where $h$ is the magnetic field strength. The resulting phase is indexed by a finite integer Chern number. Naturally, the concernitant neutral anyonic excitations do not lead to a quantized electric Hall conductivity, they reveal themselves by a quantized response to a temperature gradient \cite{kitaev2006anyons}. A significant connection between the integer valued Chern number and the "half-integer" conductance arises as the momentum space sum is over the half of the Brillouin zone.

In this section, we consider the Kitaev model in an arbitrarily oriented magnetic field. The Hamiltonian takes the following form ($\mu_B = 1$),
\begin{eqnarray}
H_{K} &=& \sum_{\langle ij \rangle}^{\alpha-bond} K^\alpha S_i^\alpha S_j^\alpha - \sum_{i,\beta} h^\beta S^\beta _i,\\
&=& -\frac{K}{4} \sum_{\langle ij \rangle}^{\alpha-bond} b^\alpha_i c_i b^\alpha_j c_j - \frac{i}{2}\sum_{i,\beta} h^\beta b^\beta _i c_i,
\end{eqnarray}
and $\langle ij \rangle$ indicates the nearest-neighbor sites on the honeycomb-lattice. This model supports topological phase transitions as a function of the magnetic field strengths and orientations (see Appendix \ref{MFtheoryDetails} for the mean-field analysis).

\subsubsection{Ferromagnetic Kitaev model}
We start with the {\bf ferromagnetic Kitaev model} ($K=-1$) which has been extensively studied in the literature before \cite{hickey2019emergence,yokoi2020half}. The Chern number map is shown in Fig.\ref{FKitaev_Chern} for magnetic fields in the a-c plane. The Chern numers are calculated numerically\cite{fukui2005chern}. The radial axe in the selected directions mark the field strengths, $h = \sqrt{h_1^2+h_2^2+h_3^2}$ and $h_i = \mathbf{h}\cdot \hat{e}_i$. The upper half ($h_1-h_3$) plane is sufficient because reversing the field direction simply changes the sign of the Chern number \cite{Comment1}.

In zero field, the KSL groundstate is gapless. At small field strengths $0 < h\ll 1$, the fermionic vacuum becomes topologically non-trivial \cite{kitaev2006anyons} with $\nu = \pm 1$ \cite{Comment2}. The odd valued Chern numbers indicate the presence of non-Abelian anyons \cite{kitaev2006anyons} whereas even valued Chern numbers imply the presence of Abelian anyons. At higher fields beyond $h^F_c \approx 0.18 \left| K \right|$, the system is topologically trivial with a polarized GS. The sequence of states as a function of field strength reproduces the previous result \cite{hickey2019emergence}. In addition, there is an overall sign reversal (e.g. $\nu = 1 \to -1$) upon crossing the $\theta \approx 35^o$ line in the $h_1-h_3$ plane \cite{kitaev2006anyons,yokoi2020half}. Beware that the angle $\theta$ is defined w.r.t. the $h_3$ axis (clock-wise), e.g. positive angle means positive $h_1$ value. The sign change in $\nu$ can be naturally understood by a sign change of any magnetic field components (in this case $h_z$). It is because the Chern number is proportional to the sign of the energy gap created by the product of the magnetic field components, $\nu \sim \text{sgn}(h_x h_y h_z)$. Using the transpose of Eq.\ref{xyzVS123}, the critical line (in the upper $h_1-h_3$ plane) is identified by the angle where $h_z$ changes sign, this is when $-\sqrt{2} h_1 + h_3 = 0$ or $\theta_c = \tan^{-1} (\frac{h_1}{h_3}) \frac{180}{\pi}= \tan^{-1} (\frac{1}{\sqrt{2}})\frac{180}{\pi}$ is satisfied. The same behavior applies for the antiferromagnetic Kitaev model.

Our approach captures all the qualitative properties of the field response for the F Kitaev model. On the quantitative side, the critical field strength for the transition to the polarized phase is six times larger ($h^{MF}_c = 0.18 \left| K \right|$) compared to the exact diagonalization results ($h^{ED}_c = 0.03 \left| K \right|$) \cite{yokoi2020half}.

\subsubsection{Antiferromagnetic Kitaev}
The {\bf antiferromagnetic Kitaev model} is examined in two steps within the upper half of the $h_1-h_3$ plane. We first obtain the Chern number map as shown in Fig.\ref{AFKitaev_Chern}. We supplement this result with three additional plots: The average magnetic moment $\left| \mathbf{M} \right| = \left| \mathbf{M}_A +\mathbf{M}_B \right| /2$ (Fig.\ref{AFKitaev_ThermodyFncs}a), the energy gap $\Delta E_{gap} $ (Fig.\ref{AFKitaev_ThermodyFncs}b) and the mean-field Wilson loop expectation value on a honeycomb plaquette, $\langle \hat{\mathcal{W}} \rangle = 2^6 \langle S_1^xS_2^yS_3^zS_4^xS_5^yS_6^z \rangle$ (Fig.\ref{AFKitaev_ThermodyFncs}c). Note that the Wilson loop $\langle \hat{\mathcal{W}} \rangle$ allows to quantify the existence of an emergent gauge field, which is the direct signature of fractionalization or the emergence of local and itinerant Majorana fermions. $\langle \hat{\mathcal{W}} \rangle$ is calculated by a MF contraction $\langle i b^\alpha_i b_j^\alpha \rangle \langle -i c_i c_j \rangle + ...$ and includes terms such as the magnetic moment pairs, i.e. $m^\alpha_i \sim \langle b^\alpha_i c_i \rangle$. We omit all $\sim \langle b^\alpha_i c_i \rangle$ pairs to capture only the gauge-flux effect.

Considering the overall quantitative response of the AF Kitaev model in Fig.\ref{AFKitaev_ThermodyFncs}, the KSL limit at $h\to 0$ crosses through an intermediate region with increasing field strengths and ultimately reaches a polarized phase. As shown in Fig.\ref{AFKitaev_ThermodyFncs}a, $\left| \mathbf{M} \right|$ gradually increases and saturates at high-fields. Starting with the proximate KSL limit, the magnetic moments gradually increase and saturate to the fully P phase along all directions. In parallel, the Wilson flux $\langle \hat{\mathcal{W}} \rangle$ (see Fig.\ref{AFKitaev_ThermodyFncs}c) decays with increasing field strength indifferent to the field orientation.
\begin{figure*}
\includegraphics[width=1\textwidth]{Fig_3.eps}
\caption{(Color online) Characterizing quantities of the {\bf antiferromagnetic Kitaev model}: {\bf a)}: The average magnetic moment, $\left| \mathbf{M} \right| = \left| \mathbf{M}_A + \mathbf{M}_B \right|/2$ within the upper $h_1-h_3$ plane in units of $\left| K \right|$. The subscripts A and B are sublattice indices. The radial direction is the field strength, $h\in \{0,1\}$. {\bf b)}: The energy gap, $\Delta E_{gap} $ within the upper $h_1-h_3$ plane indicates various sequential gap closures and re-openings. {\bf c)}: The MF contracted Wilson loop expectation value, $\langle \hat{\mathcal{W}} \rangle = 2^6\langle S_1^xS_2^yS_3^zS_4^xS_5^yS_6^z \rangle$ on a honeycomb plaquette.}
\label{AFKitaev_ThermodyFncs}
\end{figure*}

We first consider {\bf the evolution along the $h[111]$ ($\hat{e}_3$) direction}, where $h_1 = h_2 = 0$. The role of the field direction is clearly visible in the topological index of the GS, the Chern number, $\nu$ in Fig.\ref{AFKitaev_Chern}. The fermionic vacuum becomes topologically non-trivial ($\nu = -1$) and open an energy gap proportional to $h_x h_y h_z /\mid K\mid^3$. At larger field strengths (see Fig.\ref{AFKitaev_ThermodyFncs}b), there are two band touchings at $h \approx 0.7 \left| K \right| $ and $0.8 \left| K \right| $. Hence, four topologically distinct phases are encountered as a function of the field strength with the Chern numbers: $\nu = 0 \to -1 \to 2 \to 0$. A noteworthy change in the Chern number is $\nu = -1 \to 2$ by 3 units \cite{Zhang2022}, albeit the change is negative. Such a scenario is possible when three Dirac cones \cite{yilmaz2017hofstadter} are involved in this transition. The even valued Chern number is supposed to have Abelian anyons.

The intermediate phase with $\nu=2$ is extended to the $h_1\ne 0$ region as well as the corresponding finite energy gap in Fig.\ref{AFKitaev_ThermodyFncs}b. The topological GS with a Chern number $\nu = 2$ has also been identified in Refs.\cite{ralko2020novel,jiang2020tuning}. It has been asserted that this phase supports multiple Abelian anyonic species \cite{jiang2020tuning}. Yet, this claim has not been confirmed previously. In the high-field limit, the system goes back to a topologically trivial partially polarized phase with $\nu = 0$.
\begin{figure*}
\includegraphics[width=1\textwidth]{Fig_4.eps}
\caption{(Color online) The GS phase diagram of the K-$\Gamma$-$ \Gamma_p$ model for fixed ferromagnetic Kitaev term, $K= -1$. {\bf a)} Average total magnetization per four-site unit cell, $\left| \mathbf{M} \right| =\left| \sum_{i=1}^4 \mathbf{m}_i \right|/4$. Two distinct regions are readily identified with either vanishing or finite magnetization. The Kitaev spin liquid (KSL), the polarized phase (P), the zig-zag z phase (ZZ-z) and the Kitaev-$\Gamma$ spin liquid phase (K$\Gamma$SL). {\bf b)} The staggered magnetization, $\left| \mathbf{M}_{stag.} \right| =\left| \mathbf{m}_1 + \mathbf{m}_2 -\mathbf{m}_3 -\mathbf{m}_4 \right|/4$ reveals the ZZ-z phase. {\bf c)} The Wilson loop expectation value $\langle \hat{\mathcal{W}} \rangle$ in the mean field factorization as a measure for the total strength of the gauge field. A finite Wilson loop signals the fractionalization of spins as Majorana gauge fields and itinerant Majorana fermions, and thereby distinguishes between KSL and K$\Gamma$SL phases. {\bf d)} The energy gap which distinguishes between the ZZ-z phase and the P-phase. The latter two have vanishing Chern numbers.}
\label{KGGp}
\end{figure*}
The conjectured "multi-species anyon" extends mainly to positive $\theta$ angles as seen in Fig.\ref{AFKitaev_Chern}. Along the negative $\theta$ direction, the $\nu = 2$ region is replaced by a phase with $\nu = 1$. These phases and others are also identified by $\Delta E_{gap} $ map in Fig.\ref{AFKitaev_ThermodyFncs}b.

{\bf Regarding the $h[001]$ field direction}, it has already been studied in the two references \cite{nasu2018successive,hickey2019emergence}. It was suggested that the groundstate is a gapless spin-liquid until it reaches the field-polarized phase. The results of Nasu et. al \cite{nasu2018successive} rely on a mean-field decoupling between their 'chains', while Hickey and Trebst \cite{hickey2019emergence} employed a numerical diagonalization of a small system. Similarly, we observe a small energy gap (see Fig.\ref{AFKitaev_ThermodyFncs}b) until $h \approx 0.7 \left| K \right|$ with the Chern number $\nu = 1$. Interestingly, $\nu$ reverses sign between $0.7 < h / \left| K \right| < 0.8$ $\nu =-1$. Beyond $h \approx 0.8 \left| K \right|$, the system goes into a trivial phase with a vanishing Chern number. In this respect, our MF approach {\bf provides a different} field evolution along the $h[001]$ direction. The analytical treatment and the thermodynamics of $h[001]$ direction will be provided elsewhere \cite{h001Thermodynamics}.

An interesting transition occurs upon sweeping the magnetic field between the $h[001]$ and $h[111]$ directions (see Fig.\ref{AFKitaev_Chern}). At high fields, the two directions are adiabatically connected with $\nu = 0$. Yet, at lower fields, the two regions are topologically distinct. This transition was {\bf unnoted before}. We observe that the states in the vicinity of the $h[001]$ direction are topologically equivalent to the $h[111]$ direction with an energy gap and the Chern number $\nu = -1$. In this respect, the only distinct regions w.r.t. the $h[111]$ direction along this special $h[001]$ direction. At higher fields, the system goes into a topological transition irrespective of the field direction, yet the Chern numbers are field orientation dependent.

Before closing this section, we comment on the field directions $\theta = \pm 60^o$ and $\theta = \pm 90^o$ typically explored in experiments \cite{kasahara2018majorana,yokoi2020half}. The experimentally accessible fields up to $50$ Tesla allows $\alpha$-RuCl$_3$ to cross all the phase boundaries for the materials of interest. We therefore indicate the $\theta = \pm 60^o$ directions with red arrows in Fig.s \ref{FKitaev_Chern} and \ref{AFKitaev_Chern}, whereas the $\theta = \pm 90^o$ indicate the $h_1$ axe. It is clear that the field orientation dependence of $\kappa_{xy}$ could be used to trace a AF type Kitaev term in real materials keeping in mind the material specific additional couplings. The change in $\kappa_{xy}$ is expected to be the integer multiplies of $1/2$ in units of $\frac{\pi }{6} k_B^2 T$. Moreover, the topological transitions are accompanied by the sign change in $\kappa_{xy}$ before the system reaches the high-field polarized phase.

\section{Kitaev - Gamma (K-$\Gamma$-$\Gamma_p$) model}
\subsection{Kitaev - Gamma (K-$\Gamma$-$\Gamma_p$) Model in Zero Field}
In order to bridge the gap between experiments and theory, it is indispensable to include the additional terms readily present in candidate materials. The relevant terms are the off-diagonal exchange terms $\Gamma$, $\Gamma_p$ as well as the Heisenberg coupling $J$. In the following, we consider only $\Gamma$ and $\Gamma_p$ terms \cite{gordon2019theory,saha2019hidden,catuneanu2018path,wang2019one,liu2018dirac,rousochatzakis2017classical,samarakoon2018classical,luo2019gapless}, as they are sufficient to capture the ZZ-$\gamma$ phase. The Hamiltonian for the additional terms is,
\begin{eqnarray}
H_{\Gamma,\Gamma_p} &=& \sum_{\langle ij \rangle,\beta \gamma}^{\alpha-bond} \left| \epsilon^{\alpha\beta\gamma} \right| \Big[ \Gamma S_i^\beta S_j^\gamma + \Gamma_p \left( S_i^\alpha S_j^\beta + S_i^\alpha S_j^\gamma \right) \Big].
\end{eqnarray}

\begin{figure*}
\includegraphics[width=1\textwidth]{Fig_5.eps}
\caption{(Color online) K-$\Gamma$-$\Gamma_p$ model in a tilted magnetic field for $\theta = 60^o$ w.r.t. c-axis for $K = -1$ and $\Gamma_p = -0.17 \left| K \right|$ in $\Gamma$-$h$ space. {\bf a)} The total magnetization per four-site unit cell, $\left| \mathbf{M} \right| = \left| \sum_{i=1}^4 \mathbf{m}_i \right|/4$. {\bf b)}: The staggered magnetization per four-site unit cell, $\left| \mathbf{M}_{stag} \right| = \left( \left|\mathbf{m}_1 + \mathbf{m}_2 -\mathbf{m}_3-\mathbf{m}_4 \right|/4 \right)$. The staggered definition is used to distinguish the ZZ-z phase. Using plots a and b, one can identify four different phases: KSL, ZZ-z, PP (intermediate) and P-phases. Note that, the ZZ-z phase and the P phase regions have trivial topology, $\nu = 0$.{\bf c)}: The Wilson flux expectation per plaquette. The finite region denoted with yellow-orange colors indicates the KSL states, whereas the remaining regions is either highly suppressed with the absence of fractionalization or negative values indicating another polarized phase. {\bf d)}: The energy gap for the groundstate. It reveals a detailed information on how to distinguish each phase. The energy gap vanishes for the KSL while partially suppressed for the intermediate PP phase. {\bf e)}: The magnetic moment vectors for the four-site unit cell. The points with their numbers are indicated on plot a. {\bf f)}: The mean field parameter for the correlation of the x-type Majorana fermions on the x-bond, $X = \langle i b_j^x b_l^x \rangle_x$. It could be treated as the order parameter for the spin fractionalization.}
\label{KGGpUnderH}
\end{figure*}
The typical strengths of $\Gamma$ and $\Gamma_p$ are understood in various materials yet, there is no agreement \cite{winter2017models} on precise values. For $\alpha$-RuCl$_3$ \cite{wang2017theoretical}, the magnitudes are estimated as $\Gamma \sim \left| K \right|$ of AF-type and a small $\Gamma_p \ll \left| K \right|$ of F-type. For convenience, we partially relax the restriction on $\Gamma,\Gamma_p$ to characterize the GS in a larger parameter space.

Inspired by $\alpha$-RuCl$_3$, we investigate the GS phase diagram for the $K$-$\Gamma$-$\Gamma_p$ model with a four-site unit cell (see the green dotted rectangle in Fig.\ref{pointGroups}) to capture the relevant phases including the ZZ-z phase. We fix the ferromagnetic Kitaev term ($K = -1$) as the energy unit and examine the phase diagram in $\Gamma$-$\Gamma_p$ space. Fig.\ref{KGGp} a-d show the average magnetic moment ($\left| \mathbf{M} \right| = \left| \sum_{i=1}^4 \mathbf{m}_i \right|/4$ where the index $i$ extends over the four sites unit cell), the staggered magnetic moment ($\left| \mathbf{M}_{stag} \right| =\left|\mathbf{m}_1 + \mathbf{m}_2 -\mathbf{m}_3-\mathbf{m}_4 \right|/4$), the Wilson flux and the energy gap ($\Delta E_{gap}$), respectively. The parameters $\Gamma,\Gamma_p$ cover the range $\Gamma \in [0,0.62] $ and $\Gamma_p \in [-0.3,0] $ in units of $\left| K \right|$. We identify four different phases which are characterized below: KSL, K$\Gamma$SL, P, and the ZZ-z phases. The P \cite{lee2020magnetic} and the ZZ-z phase are distinguished by the directions of the magnetic moments (see Fig.\ref{ZZzpMxyz} in Appendix \ref{KGGpM_is}) as well as by the Wilson flux (Fig.\ref{KGGp}c) and the energy gap (Fig.\ref{KGGp}d). KSL and K$\Gamma$SL phases have suppressed magnetic moments and differ only the average Wilson loop \cite{Comment3}. Yet, the curve separating KSL phase and K$\Gamma$SL phase should not be considered as a sharp boundary. We also identify the characteristic directions of the magnetic moments for each phase in Fig.\ref{KGGpUnderH}d.

Focusing on Fig.\ref{KGGp}a, there is an extended KSL region for relatively small $\left| \Gamma_p \right|$ values. KSL phase is expected to have similar properties as the KSL phase because the Wilson loop of the same magnitude. For larger $\Gamma$ values, there is a crossover to a quantitatively different region named as K$\Gamma$SL \cite{gordon2019theory,wang2019one}. It is also a gapless phase with a suppressed Wilson loop $\mathcal{W}$. For the region where $\Gamma < 0.3 \left| K \right|$ and $\Gamma_p < -0.15 \left| K \right|$, a polarized phase emerges. If the local moments, $m^\alpha \sim \langle i b_i^\alpha c_i \rangle$, were included into the mean-field decomposition of the Wilson loop, a negative $\mathcal{W}$ would be acquired for the P phase \cite{lee2020magnetic}. This phase can be understood by considering the spins as classical vectors for each sublattice, e.g. $\mathbf{S}_A^\alpha= \sin \theta_A \cos \phi_A \hat{x}+ \sin \theta_A \sin \phi_A \hat{y}+ \cos \theta_A \hat{z}$. Exploiting translational invariance, the energy (per unit-cell) then reads
\begin{eqnarray}\label{PolarizedEnergy}
E &=& 3 \left(2\Gamma_p+\Gamma \right) \cos \theta_A \cos \theta_B + \left( K- (2 \Gamma_p +\Gamma) \right) \left( \cos \theta_A \cos \theta_B \sin \theta_A \sin \theta_B \cos (\phi_A-\phi_B)\right).
\end{eqnarray}
The minimization w.r.t. $\{(\theta_A,\phi_A),(\theta_B,\phi_B) \}$ implies all spins to align along the $[111]$ direction.

{\bf Relevant to the candidate materials}, there is a wide region with a ZZ-z phase as shown in Fig.\ref{KGGp} b-d. It is a gapped, topologically trivial and ordered phase \cite{chaloupka2013zigzag}. The average magnetization $\left| \mathbf{M} \right|$ vanishes while the staggered magnetization is saturated $\left| \mathbf{M}_{stag} \right| = 1$. For a four-site unit cell, the ZZ-z region is extended to larger $\Gamma$ and $\Gamma_p$ magnitudes. $\left| \mathbf{M}_{stag} \right|$ has thus the same value as one would find by assuming from the outset that the magnetic moments are purely classical instead of quantum mechanical. Though our method should be capable in capturing quantum mechanical spin fluctuations and hence a ZZ-z phase with $\left| \mathbf{M}_{stag} \right| < 1$ is in principle allowed, such a phase is not realized within our calculations.

\subsection{Kitaev-Gamma (K-$\Gamma$-$\Gamma_p$) Model with Magnetic Field}\label{KGGpHsec}
In this section, we focus on the magnetic field response of the K-$\Gamma$-$\Gamma_p$ model (see Fig.\ref{KGGp}) that is studied in the previous section for fixed $\Gamma_p = -0.17 \left| K \right|$ in $\Gamma-h$ space. Here we remind that at zero field and as an increasing function of $\Gamma$, there are four phases encountered which are the P phase, the KSL phase, the K$\Gamma$SL phase and the ZZ-z phase. We first orient the magnetic field along the experimentally studied direction with $\theta = 60^o$ in the ac plane \cite{kasahara2018majorana}. In Fig.\ref{KGGpUnderH} the encountered phases are identified as KSL, K$\Gamma$SL, ZZ-z, Partially Polarized (PP) and P phase. The field direction is indicated in Fig.\ref{KGGpUnderH} with $\mathbf{h}$ in the ac ($e_1-e_3$) plane. All the identified phases in $\Gamma-h$ space, shown in Fig.\ref{KGGpUnderH}a, are also illustrated with their local moment vectors in Fig.\ref{KGGpUnderH}e.

\begin{itemize}
\item The P phase in which the magnetization points along the $[111]$ ($\theta=0^o$) direction for small $\Gamma$ values was made evident already by the classical spin argument in Eq.\ref{PolarizedEnergy}. It is the phase labeled with (3) in Fig.\ref{KGGpUnderH}e. A finite field with $\theta = 60^o$ tilts the spins out of the $[111]$ direction. A large enough field strength always takes the system into the P phase, though the critical strength depends on the value of $\Gamma$. Also, the direction of the spins lies between $\theta=0^o$ and $\theta = 60^o$.
\item At larger $\Gamma$ values, the KSL is bf stabilized and extended till larger field strengths. Because this region has a finite magnetization at a finite $h$, it can only be identified by a suppressed Wilson flux and the finite energy gap, in Fig.\ref{KGGpUnderH}b-c respectively. Depending on the strength of $\Gamma$, KSL can make a phase transition to either the P phase or the ZZ-z phase. There is small area within ZZ phase region with a suppressed Wilson flux in the vicinity of KSL region where the K$\Gamma$SL phase seems to be the stabilized. It is then replaced by the ZZ-z phase at much smaller field strengths.
\item Focusing on the experimentally relevant region with the ZZ-z phase, this classical phase is stable till a finite magnetic field strength. At this point, it must be underlined that we have limited our investigations to the ZZ phases to be ZZ-z only. It is known that \cite{janssen2017magnetization} different zig-zag phases can be favored under external fields, depending on the field directions. The energetic competition between these states is delicate and we prefer to leave that investigation to the future.
\item Moreover, we indeed observe an intermediate phase before the polarized phase. Because it has a relatively suppressed magnetic moment (see Fig.\ref{KGGpUnderH}a) -indicating the presence of quantum fluctuations- we call it the partially polarized phase. It is a region of finite energy gap (see Fig.\ref{KGGpUnderH}c). The PP phase is present for a wide range of $\Gamma$ values. Even if it seems to be disconnected from the extended KSL region with a vanishing Wilson flux, the existence of finite fractionalization is observed. In Fig.\ref{KGGpUnderH}f, we show one such indicator as the correlation of the x-type Majorana fermions on the x-bond, $X = \langle i b_j^x b_l^x \rangle_x$ (see Fig.\ref{KGGpHThet1a} for other indicators).
\item The anti-symmetric thermal Hall conductivity tensor is proportional to the total Chern number of the fermionic vacuum $\kappa_{xy}^A = (\kappa_{xy}-\kappa_{yx})/2 \sim \nu$. It is the component that is routinely measured in the THC experiments (E.g. see \cite{kasahara2018majorana,yokoi2020half,czajka2021oscillations}). We now relate $\nu$ to the $K$-$\Gamma$-$\Gamma_p$ model in a magnetic field and discuss its implications. Firstly, at h=0 in Fig.\ref{KGGp}, the ZZ-z phase is a collinear phase which can be mapped back to itself by a time-reversal operator and a translation of spins by one unit along the $z$-bond. Naturally, it indicates a trivial Chern number with a vanishing anti-symmetric thermal Hall coefficient, $\kappa_{xy} - \kappa_{yx} \sim \nu = 0$ (We also numerically verify $\nu = 0$ for the ZZ-z phase and the P phase, see Fig.\ref{KGGpUnderH}b). Within the PP phase, the system has a smaller energy gap compared to the ZZ-z phase and the P phase as seen in Fig.\ref{KGGpUnderH}d. We observe a highly non-trivial Chern number distribution within the PP phase depending on $\Gamma$ and $h$. Our conclusion is that the GS wavefunction highly unlikely to have a unit Chern number originated from the pure Kitaev model.
\item There can be two sources of finite Chern number: The fractionalized modes of the extended K$\Gamma$SL or the spin edge states. We plot the fractionalization order parameter $X = \langle i b^x_j b^x_l \rangle_x$ in Fig.\ref{KGGpUnderH}f and $X$ is indeed finite within the PP phase. Thereby it suggests an {affirmative} scenario for the existence of the fractionalized excitations within the intermediate phase in realistic Kitaev models.
\end{itemize}

\begin{figure*}
\includegraphics[width=0.7\textwidth]{Fig_6.eps}
\caption{(Color online) The density plot the for the absolute magnetization per site ($M_{abs}$) in $h_1-h_3$ space. $M_{abs} =\frac{1}{4 }\sum_{i=1}^4 \left| \mathbf{m}_i \right|$. The model parameters are chosen to host a ZZ-z GS as $K= -1, \Gamma = 0.5 \left| K \right|$ and $\Gamma_p = -0.17 \left| K \right|$. One can identify four different phases: the ZZ-z (1) phase at small field strengths, the canted ZZ-z (2) phase at larger field strength with a wider window along $h_1 = 0$ line, the PP phase (3,4) at intermediate field strengths and finally the P-phase (5) at high-field strengths. The corresponding magnetic moment vectors of each site in a four-site unit cell are labeled from $1$ to $5$.}
\label{ZZzpFieldSweepACMtot1}
\end{figure*}

We now extend our studies to arbitrary field directions. We calculate the absolute magnetization under arbitrary magnetic field (in a-c plane) in Fig.\ref{ZZzpFieldSweepACMtot1}, where $M_{abs} =\frac{1}{4 }\sum_{i=1}^4 \left| \mathbf{m}_i \right|$. We set the couplings as $K=-1,\Gamma=0.5 \left| K \right|, \Gamma_p = -0.17 \left| K \right|$ such that the GS is in ZZ-z phase. The radial direction is the field strength where $\theta$ is the polar angle w.r.t. the c-axis. The ZZ-z phase is stable for small field strengths for all directions. The extended ZZ-z phase can be seen in other studies \cite{janssen2017magnetization,lee2020magnetic} if $\Gamma$ is comparable to the Kitaev term.
It is also known \cite{janssen2017magnetization} that ZZ-z phase is more stable to a perpendicular magnetic field since the spins can tilt towards the field direction more easily. For $\Gamma <\left| K \right| $, $\mathbf{M}_{stag}$ tend to lie closer to the $x-y$ plane ($\theta = 35^o$), with a small out of plane $z$-component (see Appendix \ref{KGGpM_is} and the figures therein). Similarly, within this context, the perpendicular field mainly points around $\theta = - 55^o$ to $- 60^o$. Consequently, the directions $\theta \in [-60^o, 0]$ stabilizes the ZZ-z phase. In this regard, the THC experiment on $\alpha$-RuCl$_3$ has revealed that the magnetic field responses for $\theta=\pm 60^o$ directions are not symmetrical but the system has a wider intermediate region \cite{yokoi2020half} for $\theta = +60^o$. We indeed verify a wider intermediate region (less stable ZZ-z phase) for $\theta= 60^o$ compared to $- 60^o$. On the contrary, for the field directions closer to the $x-y$ plane ($\theta$ is around $35^o$ or $-150^o$), the ZZ-z phase is highly unstable and paves the way for the PP phase as an intermediate phase. Because the magnetic field is not along $[111]$, the rotational symmetry is already broken and we cannot talk about the nematic phases in literature \cite{lee2020magnetic}.
\section{CONCLUSION}
We sum up this work by referring back to the initially posed questions. Regarding the phase diagram of the AF Kitaev model in a magnetic field: We identified an additional topologically non-trivial groundstate with Abelian anyons (even Chern number $\nu = \pm 2$) in addition to the $\nu = \pm1$ vacuum mainly referred to in the literature as the source of the half-quantized THC. The magnetic field response is sensitive to the magnetic field orientation and strength upon which several topological transitions are encountered for fields in the a-c plane. We emphasize that the gapless phases are hard to trace and demand for special numerical care (e.g. for fields in the $h[001]$ direction).

Regarding the role of the additional off-diagonal $\Gamma$-$\Gamma_p$ terms in the modelling of real materials, we have shown that the pure Kitaev picture changes dramatically for comparable strength of $\Gamma \sim \left| K \right|$ in favor of a K$\Gamma$SL as the gauge-flux expectation value per plaquette vanishes, $\mathcal{W} = 0$. The magnetic field, in this respect, seems to drive $\alpha$-RuCl$_3$ into an intermediate K$\Gamma$SL with coexisting order. Partial fractionalization is still observed in a magnetic field which is clearly different from the Kitaev spin liquid phase, again due to the absence of gauge flux. However, the chosen Chern number calculation method in the intermediate phase does not work efficiently for our purposes. Even though the GS Chern number was understood to be highly different from the pure Kitaev model, we could not draw a final conclusion due to its rapidly changing character in $\Gamma$-h space. In this respect a more precise calculation method is in order.

Comparing our results with the experimental and theoretical results readily available in the literature, we found a qualitatively satisfying agreement for all limits of $K,\Gamma,\Gamma_p$ and $\mathbf{h}$. Our findings also capture the asymmetry in the thermal Hall response in Ref.\cite{yokoi2020half} for $\theta = \pm 60^o$ magnetic field orientations in a straightforward way.

This work raises several questions to be addressed in particular about the detailed character of the intermediate phase and its (anyonic) excitations. Unsettled remains the underlying physical mechanism that breaks $\pm K$ symmetry of the pure Kitaev when a magnetic field is present. And it has to be explored how our conceptually simple and comprehensive formalism can be applied to comply with the recently observed oscillations \cite{czajka2021oscillations} in the longitudinal thermal conductivity as a function of inverse magnetic field.
\begin{acknowledgments}
A.P.K. was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through project number 107745057 TRR 80. Part of this work was performed while FSY was in Taiwan, supported by the Ministry of Science and Technology, Taiwan, under grant numbers MOST 107-2112-M-001-035-MY3 and MOST 108-2811-M-001-618.
\end{acknowledgments}


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text:
Powered By Modified Charkha, Women Spin Success Stories In Kashmir
A delicate pashmina yarn holds promise for hundreds of women in Kashmir valley. Powered by a modified charkha, over 200 women spinners have ended the year 2022 with doubling their output and income.
The modification in the age-old charkha has changed the life of Shaesta Bilal. Since the income is based on output of spinning, the foot pedal charkha has come to her aid.
In Srinagar's downtown area, women like Shaesta are spinning the finest yarn in the world and modified charkha has given them confidence and self-reliance.
"This (modified charka) has given us the means to make a living so that we are self-reliant. Thank God we are earning more and we are not dependent on anybody. Now I'm not financially dependent on my husband," said Shaesta Bilal.
Ms Shaesta was given a new charkha and training by a pashmina shawl trader in Srinagar a year ago. Since then she has graduated to a resource person for other women.
Over the last one year, more than 200 women have been trained and given modified charkhas. The initiative is part of an effort to protect and preserve the genuine age-old craft of pashmina shawls, which is facing a massive invasion of fake and machine-made shawls.
The government has also started GI (geographical indicator) tagging of Kashmiri shawls to preserve its unique character and value in the market.
Over the years, the number of women spinning pashmina has come down drastically in Kashmir valley, mainly due to low wages and less output on the traditional charkha.
According to Mujtaba Qadri, who owns the training centre for women spinners and equip them with the new charkha, the modifications in the tool were made by Shere-e-Kashmir Agricultural University a few years ago.
"I started training with a few women initially. Once we saw the results that we were able to double the produce, which in turns doubles the income of women, I decided to run this programme," said Mujaba, who runs a family shawl business.
Besides providing modified charkha for free, Mujtaba also give a-15 day training course to women spinners. "From our centre, over 200 women have been trained in the last one year and we have provided them modified charkha as well," he said.
At the centre, Nusrat Begum says life has become a bit easier for her after she was trained to use the new charkha. From squatting on the floor to sitting on a chair, her spinning production has doubled.
"It has helped me a great deal. I used to spin three gram of yarn on the old charkha. Now I can spin six grams," said Ms Begum.
For centuries, the secret behind Kashmir's elegant pashmina shawls is fine spinning by women. It further goes to master artisans for weaving. For making some shawls with intricate work, it takes months and even a year to weave.
While the new charkha helps women spin more and earn more, the wages are still less. For a knot, which is 10 threads of yarn, they are being paid Re 1.5. They want more.
"The charkha is very useful to us. We are thankful to Qadri sahib as he gave us this charkha for free and we are doing very well on it. We work at home and also train others. We requested him if could increase our wages," said Yasmeena.

redpajama_set_name: RedPajamaCommonCrawl


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Americans all across the country are celebrating Thanksgiving and spending time with friends and family counting their blessings. Melania Trump has a lot to be grateful for and she took the opportunity to let the world know that with a Thanksgiving message posted on Thursday.
Melania Trump said the holiday season has officially begun and wished everyone a "wonderful Thanksgiving" with a post on Instagram Wednesday.
"We started the holiday season with the turkey pardon at @whitehouse yesterday. Have a wonderful Thanksgiving!" the first lady captioned her post, along with a few pictures from Tuesday's annual White House Turkey Pardon Ceremony where she joined President Donald Trump.
We started the holiday season with the turkey pardon at @whitehouse yesterday. Have a wonderful Thanksgiving!
Melania has been doing a phenomenal job as First Lady, hasn't she?
Happy Thanksgiving to everyone out there.


text:
Politics (football season only)
Buffalo Stampede
The Rick Serafin Buffalo Sports & Political Forum
Eric Trump Threatens Republicans That Vote Against His Father
By Professor Pigworth, January 6 in Politics (football season only)
Professor Pigworth 336
Wouldn't it be really funny if it turned out that Donald and his criminal family were in reality incredibly innocent, decent, upstanding, unselfish, misunderstood, kind-hearted souls who only wanted what was best for their fellow citizens and were victims of a cruel, harsh, unforgiving establishment that conspires every day to destroy well-intentioned "outsiders"?
Eric Trump, the president's second son, has threatened to unseat Republicans that do not attempt to block the certification of Joe Biden as the 2020 presidential winner later today in the US Congress.
"I will personally work to defeat every single Republican Senator/Congressman who doesn't stand up against this fraud -- they will be primaried in their next election and they will lose," he tweeted on Tuesday night.
It came after he warned any lawmaker that did not attempt to thwart the vote that "their political career is over" because his father's political movement was "going nowhere".
Around 140 Republicans in the House of Representatives and at least 12 Republican senators say they will vote against Biden's certification. It's seen as a last-ditch effort that has no chance of succeeding because a majority in both chambers is required and Democrats control the House.
Many in Washington believe that Eric's older brother, Donald Jr, has presidential ambitions of his own.
In fact, before President Trump himself began mulling the idea of running for president again in 2024, Republicans had actively been talking about Don Jr taking the reins.
https://www.bbc.co.uk/news/live/election-us-2020-55558355
Thebowflexbody 2,340
VIP Club Member
FanBack 900
Range Member
41 minutes ago, Thebowflexbody said:
If you keep owning Pig's mind, we may have to go to court, produce our deeds and get a ruling.
3 minutes ago, FanBack said:
Indeed. He's in England so I imagine his ass is still LOCKED DOWN.
SackMan518 5,319
Trusted News Source
@Professor Pigworth, oh hey, how's Boris?
Sack "The Buffalo Range's TRUSTED News Source!"
"When a well-packaged web of lies has been sold gradually to the masses over generations, the truth will seem utterly preposterous and its speaker a raving lunatic." ~ Dresden James
Parler @NYexile
1 hour ago, SackMan518 said:
Boris Yeltsin? He snuffed it some years ago. Couldn't hold his vodka apparently.
Or did you mean Boris Johnson? I'm not, as it happens, a supporter of his, but I can report that he's alarmed by events in Washington and embarrassed for your Donald. Here's what he just had to say:
Prime Minister Boris Johnson has condemned "disgraceful scenes" as protesters stormed the US Capitol, adding: "The United States stands for democracy around the world and it is now vital that there should be a peaceful and orderly transfer of power."
In fact, all party leaders in the UK are appalled by events there:
Labour leader Sir Keir Starmer condemned the 'protestors' on social media.
He tweeted: "Horrendous scenes from the US.
"These are not 'protestors' -- this a direct attack on democracy and legislators carrying out the will of the American people."
Scotland's First Minister Nicola Sturgeon tweeted that the scenes from the Capitol were "utterly horrifying".
She added: "Solidarity with those in (the United States) on the side of democracy and the peaceful and constitutional transfer of power. Shame on those who have incited this attack on democracy."
Shadow Secretary of State for International Trade Emily Thornberry described the scenes in Washington as "profoundly shocking".
She tweeted: "Profoundly shocking scenes in the Capitol tonight.
"Listening to Republican Congressman Kinzinger saying 'if this was Belarus we'd be calling it a coup attempt'. 'The guard rails will hold'. 'The President is guilty of cowardice – he should accept that he's lost'."
Lisa Nandy, Labour's shadow foreign secretary, commented: "Terrible scenes from the USA.
"This is the legacy of a politics of hate that pits people against each other and threatens the foundations of democracy.
"We must stand firm with legislators under attack and the American people who have the right to choose their own destiny."
Layla Moran, foreign affairs spokeswoman for the Liberal Democrats, said the Prime Minister should condemn the Trump supporters.
She said: "The scenes coming out of Washington tonight are an attack on democracy.
"Liberal Democrats call on Boris Johnson to condemn the violent actions of President Trump's supporters breaking into the Capitol.
"An attack on democracy anywhere is an attack on democracy everywhere."
Labour MP David Lammy described Donald Trump as "an enemy of democracy".
He tweeted: "Donald Trump is an enemy of democracy. Every British politician who failed to condemn his actions after the presidential election should issue an apology tonight."
Meanwhile, the mayor of Greater Manchester Andy Burnham tweeted: "Any UK politician who gave Trump the time of day should be ashamed right now."
2 minutes ago, Professor Pigworth said:
I care as much about what fake Conservative Boris says as I do of your own opinion. About 0.
1 minute ago, SackMan518 said:
And yet you asked about him. That's why I replied.
Just now, Professor Pigworth said:
I asked with the intention of hearing your opinion about how he's running England and his stellar COVID-19 numbers yet you tried to pivot and threw up a quote about what he says about our situation in the US. He needs to handle his own shit first. Maybe you should help him since you're a self declared genius?
Just now, SackMan518 said:
LOL. Yep.
25 minutes ago, SackMan518 said:
Oh. You didn't specify. As I said, I'm not a supporter of his. I'm not actually a fan of any politician of any party.
Anyway, since you ask, I don't think he's done a very good job of handling the Chinese virus. He's generally been too slow and late when it comes to enacting tougher measures.
So you think that he should not comment on developments in other countries until he first deals successfully with the virus in the UK? I see. All right. I would have thought he could have more than one kind of food on his plate. Isn't that usually how it works with heads of government?
You think I'm a self-declared genius? Why, no, I've never said anything remotely like that about myself. It's interesting, though, that you would bring that up and speak about me in such flattering terms.
Thank you for that, Sack. You're a really good egg. Your mind is full of Trump mush, but you're a good egg.
3 hours ago, Professor Pigworth said:
If this statement is true you would be ambivalent about Trump instead of having TDS. Not buying it.
An olive branch??????? LOL


text:
The TRADE > News > Regions > Americas > Brazil abolishes tax for foreign equity trades
Americas December 1, 2011 5:36 PM GMT
Brazil abolishes tax for foreign equity trades
The Brazilian government has repealed a tax placed on foreign investors trading equities, in a move which domestic exchange BM&F Bovespa believes is sure to stimulate trading activity in the country.
The IOF tax, which stood at 2% for equities since its launch in October 2009, has now been eliminated. The tax was also removed for debt instruments that have a tenor of four years or longer.
The levy was introduced by the Brazilian government in order to help it control the rapid appreciation of the Brazilian real. It was initially set at 2% for all initial investments made by foreigners in fixed income and derivatives transactions. The tax was increased to 6% for fixed income transactions in October 2010.
"We are not easing our currency policy. If there is any risk of the currency appreciating, we will increase the IOF on derivatives," Brazilian finance minister Guido Mantega is reported to have said at a press conference today.
The announcement by the Brazilian government had an instant positive impact on equities prices in the country, with shares in BM&F Bovespa surging by almost 7% today.
"By reducing the IOF to 0% on foreign investments for equities, the government has sent a clear message about the importance of the capital markets as a way to support local companies," Sergio Gullo, chief representative for BM&F Bovespa in EMEA, told theTRADEnews.com. "The removal of the tax will encourage more foreign investment to our market."
The removal of the IOF tax may also help to bring more high-frequency trading (HFT) to Brazil, the increase of which BM&F Bovespa has identified as a key aspect of its growth strategy. Gullo says that the exchange believes HFT will reach 20% of overall equity trading volumes in the next few years.
As part of its plans to attract HFT, BM&F Bovespa has partnered with US exchange operator CME Group to develop Puma, a new US$200 million multi-asst class trading platform. The new platform will be able to process 200 million messages per day and offer an average round-trip latency of 1.1 milliseconds.
"The removal of the tax has very little downside and it appears that the Brazilian government is not concerned about the effect of equity trading on currency appreciation," said Danielle Tierney, analyst at consultancy Aite Group. "It will be more of a positive for HFT firms than traditional market participants. The exchange should have no trouble in reaching its 20% HFT target."
Tagged: regulation
« IPC opens link to Eurex


Hi. I was in the mood for something cute today–here it is!
The fight's going to be in the Senate. Be prepared for battle. "Just two months ago, Democratic National Committee chair Rep. Debbie Wasserman Schultz insisted — repeatedly — that House Democrats would run on ObamaCare and win back control of the chamber. Just a day after Barack Obama himself defended ObamaCare in the State of the Union speech, they're singing a different tune. Donors and strategists will move resources away from House races and instead focus on trying to salvage control of the Senate." Democrats donors and strategists to concede defeat in the House?
Sound advice. "Last week, if you tuned into the Grammys, you were treated to a gaudy spectacle of pretentious elitists, wealthy drug addicts and godless Satanists patting each other on the back and congratulating themselves for another year spent dumping toxic waste directly into America's soul. If you watched the State of the Union address tonight, you saw the exact same sort of thing all over again. Except with less dancing. And more clothing (thank God)." For the love of God, can we just abolish the State of the Union Address already?
Hunger Games in real life. "At a time of great economic insecurity, it's not great politics to make government workers the "haves" of the labor market: paid above-market wages and shielded from the chronic risk of job loss that most of the rest of America faces. Oh, sure, this is true for everyone — professionals often have to take a pay cut to work for the government. But to the average person sweating it out through rounds of layoffs at a job they don't like very much, government workers seem to have it very good by comparison." MEGAN MCARDLE: Not All Democrats Want A Higher Minimum Wage.


This page lists the active job posts at B-Open where you can join a rapidly expanding business working on massive datasets with cutting-edge open source technology. Does that sound like an interesting challenge?
As a "DevOps / Linux Engineer" at B-Open you will deploy and manage systems and data processing pipelines for European agencies monitoring the environment from space. You will join a team that combines a strong research-oriented attitude with a solid industrial background and humor. We build software that works and have fun doing it!
As a "Scientific Software Engineer" at B-Open you will develop software and in particular design algorithms and data processing pipelines for European agencies monitoring the environment. You will join a team that combines a strong research-oriented attitude with a solid industrial background and humor. We build software that works and have fun doing it!
You didn't find a good match, but you still think it would be great to work together? Don't worry, we are always on the look for talent, just send an open application via the form below.


text:
Sparrow was an email client for OS X and iOS. After a 4-month beta period, Sparrow went on sale in the Mac App Store on February 9, 2011 and became the top paid and
Sparrow Mail Client For Iphone
Google Buys Mac and iPhone Mail Client Sparrow
The 25 Best Email Apps For iOS (iPhone & iPad)
Email client alternatives to Sparrow for the Mac | Engadget
Make Sparrow Default Mail Client in iOS - UltraLinx
Sparrow is a Worthy Replacement for the iPhone's Mail App ...
Sparrow mail app review for iPhone - Every Interaction
Sparrow (email client) - Wikipedia
Goodbye Sparrow: 8 Alternatives to Sparrow for Email
The Best Email Client for iPhone - Lifehacker
Sparrow - The Best Mail Client for iPhone, Gorgeous Too ...
Sparrow For iPhone Is Everything You Could Possibly Want ...
E-Mail-Client Sparrow für iOS erhältlich | heise online
Mail vs Sparrow: The Two Best iOS Email Clients Face to Face
The best email client for iPhone, iPad, Mac and Android ...
Sparrow for iPhone Is a Killer Email App for iPhone (with ...
Alternative email clients for Sparrow on the iPhone | Engadget
Sparrow for iPhone Review - MacStories
The Best Email Apps for iPhone 2020 - lifewire.com
Sparrow Is The Best Email App For Your iPhone Since Apple ...
Sparrow For iPhone Email App Now Available In The App Store
Google continues its shopping spree and buys Sparrow, a mail client for Mac and the iPhone. The Sparrow team will work on Gmail. E-Mail-Client: Sparrow ist für das iPhone erhältlich. Sparrow kann nun auch auf dem iPhone und iPod touch zum Empfangen und Versenden von E-Mails genutzt werden. Bisher gab es den ...
Mail+ (iPhone, iPod touch & iPad — $9.99) — Mail+ is a mail client to read and manage your emails and send emails with attachments to single contacts, to groups, to handpicked set of contacts or to distribution lists. If you like your email app to be similar to Facebook/Twitter apps, the Sparrow for iPhone (and iPod touch) client is now available. It has not hit the United States, but it will be $2.99 when it ...
Sparrow announced late last week that the company had been acquired by Google; that means that the Sparrow email clients have been put into maintenance mode, with no new features expected going ... Sparrow mail client for iPhone. App Icon Design Process Application Icon Engineering Design Process. More information
Sparrow is easily the best mail client for iOS. It does everything you can think of and it does it beautifully. The one problem with iOS though is that you Inbox by Gmail, which Google appears to view as a replacement for the popular email client Sparrow, has been very quietly updated, notes TechCrunch, to include a native build for iPad.
Sparrow is a Worthy Replacement for the iPhone's Mail App john paul titlow / 15 Mar 2012 / Mobile As far as iOS apps go, the native email client for iPhone is pretty bare bones and not ... Sparrow for iPhone. The Sparrow can be said as the best email client and it has been specially made to provide the pleasant and the efficient mailing facility. The latest threading system and the nice navigation pane it has been laced up with nice features. It also has got the POP support and the IMAP facility and the people can use the Hotmail ...
Sparrow initially produced a desktop email client that closely resembled the mac twitter desktop app in appearance and stripped-back simplicity. We probably do 80% of our emailing through desktop clients during office hours and so found the Sparrow desktop app to be too simple for our needs. The demand to manage many projects and organize mails ... The much-loved email client Sparrow has today been updated with support for the iPhone 5′s larger screen and Apple's Passbook. The update, noticed by reader Matt Gibstein, should be available ...
Sparrow was an email client for OS X and iOS. After a 4-month beta period, Sparrow went on sale in the Mac App Store on February 9, 2011 and became the top paid and top grossing app in less than one day. The much-loved email client Sparrow will be getting another compatibility update, adding support for the iPhone 5's larger screen. The news came from a tweet by Sparrow founder Dom Leca today.
Postbox has been around for a number of years now and the creators consider it to be the best desktop Gmail client for Mac and Windows. Now with Sparrow "gone", I'd probably have to agree. Postbox is a full featured email client that supports IMAP and POP accounts as well as Exchange (for all of us corporate types out there). Another added nicety is that Postbox supports OmniFocus and Evernote integration. Good stuff. Ever since seeing so many gushing reviews about this iPhone mail client, I had to take a look at it myself. I was curious what all the hoopla was about, and wether this would live up to the hype. When I saw screenshots of the application, I was immediately reminded of the Gmail mail client (in terms of interface) and liked how Sparrow seemed to use the limited real estate of the iPhone. Since ... On Rue Reaumur in Paris, France, 27 year old Dominique Leca leads a small team of engineers and one designer on a quest to build a better mail app for iPhone. A few mail clients exist (like...
You have an insane amount of choices for email clients on the iPhone and each does something a little differently than the rest. Shockingly, our pick for the best of these options goes to ... Alternative Mail Client Sparrow Arrives on iPhone Thursday March 15, 2012 11:49 AM PDT by Jordan Golson Sparrow , a popular alternative mail client on OS X, has arrived on the iPhone .
If you have multiple email accounts which you use on a regular basis, like me, managing those accounts can be a right pain. The built-in mail client on the As I explained in the past here on MacStories, my iOS email workflow was perfectly fine until Sparrow showed interesting new ways to interact with messages on the iPhone. Sparrow got acquired by Google, which, a few months later, came out with a completely revamped Gmail app that is now my primary client for searching and composing longer ... We previously mentioned some email clients for Android i.e. Boomerang, SolMail and so on but we didn't cover any article with email client for Mac or iOS. Today, I am going to fulfil your demand by introducing Sparrow, the best ever email client which has been acquired by Google itself. Previously Sparrow was a independent email app for Mac ...
There are a number of half-baked third-party email clients for the iPhone, but until now, there hasn't been a real replacement for the iPhone's built-in Mail app. Sparrow for iPhone finally ... Seit heute morgen ist Sparrow for iPhone im App Store zu finden. Sparrow for Mac ist schon seit einiger Zeit der E-Mail-Client meiner Wahl. Das Interface ist wunderschön und bringt (fast) alle Vorteile und Features von Gmail in eine native OS X App. Sparrow for iPhone soll das Erlebnis aufs iPhone bringen. Sparrow Google. Next Up Sparrow Google . Topics. Share Tweet ... Name * Email * Website. Save my name, email, and website in this browser for the next time I comment. Popular. Apple TV. Apple TV Screensavers and their Locations Identified. Apple. iPhone XS and XS Max Wallpapers in High Quality for Download. iOS. iPhone X Wallpapers for Download. How To. How to Eject a Stuck CD or DVD From Your ...
Wer nach einer Alternative für Apples E-Mail-Client unter iOS sucht, kann nun auch zu einer mobilen Version des populären Desktop-Mailers Sparrow greifen. Die App steht seit Donnerstag für 2,39 ... It's easy to choose and set up a mailbox in Windows OS, but when it comes to Mac, we have ample of options to choose from. Out of all the existing email clients, Sparrow Mail (Email Client for Mac) stands on the top of the list with its updated version to provide more features to the users. We may earn a commission for purchases using our links. Learn more.. Command your email Best email apps for your iPhone and iPad in 2020 Apple's Mail app can get the job done, but there are many better alternatives out there.
An in-depth comparison of Sparrow for iOS and Apple's native Mail app, the two best iOS (iPhone, iPad, iPod touch) email clients. If you are a Mac user, chances are you've at least heard of the Sparrow email client. The app is minimal compared to the bulky default Mail software, and features a simple user interface and quick load times. Word on the street has been that the Sparrow team might be looking to bring Sparrow to the iPhone. Apple Mail is a free client that comes preinstalled on every new Mac sold—that in itself makes it a solid default choice for Mac users. The application's trademark postage stamp icon hasn't changed a lot over the years, and despite steady development from Apple, the client still retains its old-school feel.
Discuss email privately. Invite teammates to discuss specific email and threads. Ask questions, get answers, and keep everyone in the loop. The new Spark feels like the first product that may finally solve email communication and assignments for the MacStories team. As a solution to this many third party developers have come up with interesting mail apps that offer more than one demands. Sparrow is one amazing mail client that has been serving Mac OS for quite some time now. Recently the developer released the Sparrow iPhone mail client which we will be reviewing in this post. The best email apps for iPhone and iPad, 2016 edition Now that Mailbox is gone, what's an iOS power user to do?
iOS: The popular email client for Macs, Sparrow, released its iPhone version today. On top of sporting a similar look to the desktop client, the app comes packed with a few handy features ... Sparrow is an attempt to get away from supercomplex, feature-packed e-mail clients in favor of a simpler e-mail experience. The interface is elegant while remaining very straightforward: the left ...
This means that iPhone owners can continue to use the current version of Sparrow, but at some point, iOS is going to outpace the app and you're going to need to switch to a different email client ... I recently reviewed Sparrow Mail app for iPhone. If you haven't read the review, please do. Sparrow is an incredible desktop email client for Macs that has finally made its way to the iOS AppStore. I raved about it in my review and now I'd like to share a few tips that I've picked up […] Google Pulls Sparrow Email App From iOS and Mac App Stores. Apps. Sparrow for iOS to Get iPhone 5 Update, Despite Being Acquired by Google . Apps. Google Acquires Sparrow Mail Client for Mac and iOS. Apps. Sparrow for Mac Updated With Retina Display Support and Mountain Lion Compatibility. Apps. Sparrow for iPhone Finally Updated With POP Support. Apps. Sparrow for iPad: Coming Soon to the App ...
For the first time, Apple is letting a third-party developer sell a full-featured, custom email client that uses its proprietary email engine to iPhone users. Sparrow, already popular on the Mac and available on the Mac App Store, comes to the iPhone's App Store today, and it promises to offer a newer, fresh take on email to lure back ... Sparrow is a new email app for the iPhone from the makers of the Sparrow app for the Mac OS X desktop (a favorite among TechSpot staffers using Macs). It aims to offer a better email experience ...
Mail lets you star mail to highlight it, file it in folders, search fast and get your inbox filtered by a handful of useful categories (including people, social updates, and those important travel emails). For sending email, Yahoo! Mail shines with impressive image sending and attachment support as well as its unique and colorful email stationery. Sparrow, a popular email client for Mac, and more recently iOS, has been one of my favorite mail clients for both platforms over the past few months. However, some may not want to drop $9.99 for the Mac version and $2.99 for the iPhone version only to be dissapointed if it doesn't meet their needs. This isn't a huge deal for the Mac client ...
Sparrow ($2.99) by Sparrow is the much-anticipated email app for your iPhone. Is it everything you dreamed of in an iPhone email client? I've been using Sparrow on my Mac since the first beta. It ... An email client is—like the Mail app already installed on your iPhone—an app that you can use to access your email account, regardless of what service you actually use. With one or two exceptions, we only considered apps that supported all the major email providers, such as Gmail, Yahoo Mail, iCloud Mail, and IMAP and POP accounts. We also ... Sparrow, the much-beloved email client for Mac and iPhone, was essentially discontinued after it was purchased by Google last summer — but its influence is still being felt. Just take a look at ...
The highly-anticipated iPhone email client called Sparrow is now available in the App Store. The app costs $2.99 and promises an enhanced emailing Even without POP or push notifications, though, Sparrow is easily the best email client available for the iPhone. It is much easier to use than iOS Mail, and it kicks the crap out of the Gmail app — which I am still happy exists, but would like to see a little lovin' happening. Google Acquires Sparrow – a Popular Email Client for iOS and Mac by iPhoneHeat on Jul 21, 2012 Google has acquired Sparrow, a star 3rd party email application for iOS and Mac OS.
Wer nach einer Alternative für Apples E-Mail-Client unter iOS sucht, kann nun auch zu einer mobilen Version des populären Desktop-Mailers Sparrow greifen. Die App steht seit Donnerstag für 2,39 . This means that iPhone owners can continue to use the current version of Sparrow, but at some point, iOS is going to outpace the app and you're going to need to switch to a different email client . Wireshark filters ipad. Discuss email privately. Invite teammates to discuss specific email and threads. Ask questions, get answers, and keep everyone in the loop. The new Spark feels like the first product that may finally solve email communication and assignments for the MacStories team. An in-depth comparison of Sparrow for iOS and Apple's native Mail app, the two best iOS (iPhone, iPad, iPod touch) email clients. If you have multiple email accounts which you use on a regular basis, like me, managing those accounts can be a right pain. The built-in mail client on the Postbox has been around for a number of years now and the creators consider it to be the best desktop Gmail client for Mac and Windows. Now with Sparrow "gone", I'd probably have to agree. Postbox is a full featured email client that supports IMAP and POP accounts as well as Exchange (for all of us corporate types out there). Another added nicety is that Postbox supports OmniFocus and Evernote integration. Good stuff. The highly-anticipated iPhone email client called Sparrow is now available in the App Store. The app costs $2.99 and promises an enhanced emailing Sparrow ($2.99) by Sparrow is the much-anticipated email app for your iPhone. Is it everything you dreamed of in an iPhone email client? I've been using Sparrow on my Mac since the first beta. It . Yaramar hotel fuengirola tripadvisor mexico. There are a number of half-baked third-party email clients for the iPhone, but until now, there hasn't been a real replacement for the iPhone's built-in Mail app. Sparrow for iPhone finally . Sparrow is a Worthy Replacement for the iPhone's Mail App john paul titlow / 15 Mar 2012 / Mobile As far as iOS apps go, the native email client for iPhone is pretty bare bones and not . Sparrow was an email client for OS X and iOS. After a 4-month beta period, Sparrow went on sale in the Mac App Store on February 9, 2011 and became the top paid and top grossing app in less than one day.


text:
VOIR TOUS LES INVESTISSEMENTS
Paragon Print & Packaging
Paragon Print & Packaging is a leading manufacturer of responsible packaging for the retail food and non-food industry.
The company provides a range of packaging solutions including printed labels, sleeves, cartons, film solutions and lined boards to a number of the UK's major food retailers. Paragon operates ten manufacturing facilities in the UK and employs more than 1,200 staff.
Equistone has a long-standing relationship with Paragon and has remained invested in the business since 2001. In 2005, Equistone partially realised its investment in Paragon and re-invested funds in 2007 to support the continued development of the company.
Since investment, Paragon has continued its impressive growth, with turnover increasing from £113m in 2007 to a forecasted £178m in 2012, despite the economic downturn.
Equistone has worked alongside the management team to develop the business with a number of initiatives including:
Strengthening revenue growth and geographic footprint through acquisitions, new partnerships and organic growth.
Building scale in core product areas through significant investment in a second film production site and a dedicated "sleeve and board" facility.
Diversifying Paragon's product offering and strengthening its customer proposition through strategic acquisitions, including Skanem and Sessions of York.
Expanding its customer base from 560 to over 1,800 in 2012.
Transitioning leadership from the founder of the business, Tony Lennon, to current Group Managing Director Mark Lapping in 2010. Mark was a highly respected internal candidate who joined the group in 2007, and Tony continues to provide consultancy services to the management team.
Equistone announced the successful sale of its investment in Paragon to Sun Capital Partners for an undisclosed sum.
Durée d'investissement
oct. 2007 - déc. 2012
SECTEUR D'ACTIVITE:
Evolution du chiffre d'affaires
£113m / £178m
Nombre d'employés à l'acquisition
TYPE D'INVESTISSEMENT
Secondary MBO
Equistone has provided a tremendous amount of support during its investment period and we are delighted with the Company's performance to date, as well as our prime positioning in the market place.
Mark Lapping, CEO, Paragon Print & Packaging
L'équipe Equistone
Communiqués de presse associés
Equistone sells Paragon Print & Packaging to Sun European Partners
Opérations de croissance externe
Sessions of York (UK)


text:
Q: c3 failed to parse when using .toString() There is a similar question mentioned here, however, it doesn't solve my problem. A trivial c3 script fails to load data when using .toString() method on var dates = ["2015-03-07", "2015-03-09"]
data: {
    x: 'x',
    xFormat: '%Y-%m-%d', // 'xFormat' can be used as custom format of 'x'
    columns: [
        ['x', dates.toString()],
        ['data1', 30, 200, 100, 400, 150, 250],
        ['data2', 130, 340, 200, 500, 250, 350]
    ]
},
axis: {
    x: {
        type: 'timeseries',
        tick: {
            format: '%Y-%m-%d'
        }
    }
}

Am I missing something here? The error is as follows
Failed to parse x '2015-03-07,2015-03-09' to Date object

A: .toString turns the array into one string, use this  in the columns property instead
['x'].concat(dates),

redpajama_set_name: RedPajamaStackExchange


Jesus Foretold: Just a Coincidence?
How Did the Life of Jesus Impact the World?
Is Digital Addiction Stunting Your Spiritual Growth?
If you've said "Yes" to Jesus, you've just started the greatest adventure of your life. And this isn't a one-time decision — following Him and growing in your faith is a lifelong process. In this series, you'll read about what it means to have a relationship with Jesus, the importance of confession, the miracle of God's grace, the power of the Holy Spirit in your life, and how to get to know God better, every single day.
The abundant life Jesus offers you is a journey of faith. It won't happen by accident. Daily surrender is required, but it's not about letting go and letting God. It's about running to Jesus, holding on to Him, and saying "Yes" to what He asks you to do. It's admitting that you can't do it without Him — that you need the Holy Spirit to empower you.
To be a Christian apologetic doesn't mean you go around saying, "Sorry, I'm a Christian." In this series, you'll find a variety of articles that provide philosophical as well as practical responses for some of the toughest questions out there.
Church. It's whole purpose is to bring glory to the Creator, to worship Him, and proclaim His message of hope and healing in this world. It's a community of people who do life together, who take care of one another, and who are family.
The book of Acts has a lot to teach us about what a life fully committed to God looks like. Are you ready to see what the abundant life is all about? In this four part series you'll work through several sections in the book of Acts and you'll have the chance to talk to a mentor as you learn.
Many of us obsess about God's calling on our lives. We may wonder what kind of career God is leading us to; we dream about making a difference, about falling into the exact and concrete will of God. And when things don't fall into place like we think they should, we may wonder whether or not we even have a calling.
You know you should trust God. You desperately want Him to rescue you and guide you through the maze of life. Yet the phrase "trust God" can seem so trite; your mind swims with the "what if" possibilities that threaten to overtake you.


Sometimes it is hard to think of a memorable person in your life. Then again, it may be easy to think of a memorable person that had a negative influence on your life.
Hello everyone. This book, "A Memorable Person" from the :Through the Storm: series is my book. This is my first book so I hope everyone check it out. If you want me to make more books, then just comment. Thank you!
My other published page name is jwriter.


text:
/* -*- Mode: C; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
#include <stdio.h>
#include <stdlib.h>
#include <unistd.h>
#include <time.h>
#include <monkey/mk_core/mk_list.h>

#include <fluent-bit/flb_mem.h>
#include <fluent-bit/aws/flb_aws_error_reporter.h>

#include "flb_tests_internal.h"

const char* file_path = "/tmp/error.log";
const char* error_message_1 = "[engine] scheduler could not start";
const char* error_message_2 = "[engine] scheduler could not stop";

void test_flb_aws_error_reporter_create() {

    setenv(STATUS_MESSAGE_FILE_PATH_ENV, file_path, 1);
    struct flb_aws_error_reporter *error_reporter = flb_aws_error_reporter_create();
    TEST_CHECK((void*) error_reporter != NULL);
    TEST_CHECK((void*)error_reporter->file_path != NULL);
    TEST_CHECK(flb_sds_cmp(error_reporter->file_path, file_path, strlen(file_path)) == 0);
    TEST_CHECK(error_reporter->ttl == STATUS_MESSAGE_TTL_DEFAULT);
    TEST_CHECK(error_reporter->max_size == STATUS_MESSAGE_MAX_BYTE_LENGTH_DEFAULT);
    flb_aws_error_reporter_destroy(error_reporter);
}

void test_flb_aws_error_reporter_write() {

    int size;
    char error_message_3[1041];
    for (int i = 0; i < 1040; i++) {
        error_message_3[i] = 'a';
    }
    error_message_3[1040] = '\0';

    setenv(STATUS_MESSAGE_FILE_PATH_ENV, file_path, 1);

    struct flb_aws_error_reporter *error_reporter = flb_aws_error_reporter_create();
    flb_aws_error_reporter_write(error_reporter, error_message_1);
    size = mk_list_size(&error_reporter->messages);
    TEST_CHECK(size == 1);
    /* message same with the latest one will be combined*/
    flb_aws_error_reporter_write(error_reporter, error_message_1);
    size = mk_list_size(&error_reporter->messages);
    TEST_CHECK(size == 1);

    /* message different of the latest one will be combined*/
    flb_aws_error_reporter_write(error_reporter, error_message_2);
    size = mk_list_size(&error_reporter->messages);
    TEST_CHECK(size == 2);

    /* message larger than max size limit*/
    flb_aws_error_reporter_write(error_reporter, error_message_3);
    size = mk_list_size(&error_reporter->messages);
    TEST_CHECK(size == 1);

    flb_aws_error_reporter_destroy(error_reporter);
}

void test_flb_aws_error_reporter_clean() {

    setenv(STATUS_MESSAGE_FILE_PATH_ENV, file_path, 1);
    struct flb_aws_error_reporter *error_reporter = flb_aws_error_reporter_create();
    flb_aws_error_reporter_write(error_reporter, error_message_1);
    time_t start = time(NULL);
    while (time(NULL) - start <= error_reporter->ttl) {
        flb_aws_error_reporter_clean(error_reporter);
    }
    TEST_CHECK(mk_list_size(&error_reporter->messages) == 0);

    flb_aws_error_reporter_destroy(error_reporter);
}

TEST_LIST = {
    { "test_flb_aws_error_reporter_create", test_flb_aws_error_reporter_create},
    {"test_flb_aws_error_reporter_write", test_flb_aws_error_reporter_write},
    {"test_flb_aws_error_reporter_clean", test_flb_aws_error_reporter_clean},
    { 0 }
};

redpajama_set_name: RedPajamaGithub


text:
Intraday effects of ambient PM1 on emergency department visits in Guangzhou, China: A case-crossover study
Liu, Linjiong, Song, Fujian, Fang, Jiaying, Wei, Jing, Ho, Hung Chak, Song, Yimeng, Zhang, Yuanyuan, Wang, Lu, Yang, Zhiming, Hu, Chengyang and Zhang, Yunquan (2021) Intraday effects of ambient PM1 on emergency department visits in Guangzhou, China: A case-crossover study. Science of the Total Environment, 750. ISSN 0048-9697
PDF (Accepted_Manuscript) - Submitted Version
Restricted to Repository staff only until 15 September 2021.
Background Short-term exposure to PM2.5 has been widely associated with human morbidity and mortality. However, most up-to-date research was conducted at a daily timescale, neglecting the intra-day variations in both exposure and outcome. As an important fraction in PM2.5, PM1 has not been investigated about the very acute effects within a few hours. Methods Hourly data for size-specific PMs (i.e., PM1, PM2.5, and PM10), all-cause emergency department (ED) visits and meteorological factors were collected from Guangzhou, China, 2015–2016. A time-stratified case-crossover design with conditional logistic regression analysis was performed to evaluate the hourly association between size-specific PMs and ED visits, adjusting for hourly mean temperature and relative humidity. Subgroup analyses stratified by age, sex and season were conducted to identify potential effect modifiers. Results A total of 292,743 cases of ED visits were included. The effects of size-specific PMs exhibited highly similar lag patterns, wherein estimated odds ratio (OR) experienced a slight rise from lag 0–3 to 4–6 h and subsequently attenuated to null along with the extension of lag periods. In comparison with PM2.5 and PM10, PM1 induced slightly larger effects on ED visits. At lag 0–3 h, for instance, ED visits increased by 1.49% (95% confidence interval: 1.18–1.79%), 1.39% (1.12–1.66%) and 1.18% (0.97–1.40%) associated with a 10-μg/m3 rise, respectively, in PM1, PM2.5 and PM10. We have detected a significant effect modification by season, with larger PM1-associated OR during the cold months (1.017, 1.013 to 1.021) compared with the warm months (1.010, 1.005 to 1.015). Conclusions Our study provided brand-new evidence regarding the adverse impact of PM1 exposure on human health within several hours. PM-associated effects were significantly more potent during the cold months. These findings may aid health policy-makers in establishing hourly air quality standards and optimizing the allocation of emergency medical resources.
Faculty of Medicine and Health Sciences > Norwich Medical School
10.1016/j.scitotenv.2020.142347


text:
'Be Fit, But Not Fat': New Mantra Policemen Need To Follow For Service Awards
The recent MHA order dated September 13 states that all those officers whose names will now be recommended, will belong to a "Shape 1" fitness category.
All India | Written by Neeta Sharma | Updated: September 14, 2017 22:45 IST
A new Home Ministry order singles out unfit police officers for different service awards (File)
New Delhi: "Be fit, but not fat" is a new mantra the Ministry of Home Affairs (MHA) is chiming for all Indian Police Service (IPS) officers who aspire to get a meritorious or distinguished service award.
The "Shape 1" fitness category mentions the highest levels of fitness in terms of physical capacity, psychological health, hearing, appendages and eyesight.
The order states that from now on an officer can be recommended only three times for any award. It also says state police needs to do background checks on the integrity and character of the officers before recommending an officer for the awards.
The IPS fraternity is not enthusiastic about these new guidelines. "You give these awards after years of service for fairness for professionalism and how well an officer has been able to establish the rule of law in the area he or she is working. So how is fitness a parameter for all this?" asked a DG ranking officer.
According to the officer, it is not a good idea to judge officers on the basis of physical fitness for these awards. "If this is the criteria then mostly officers who run marathons or officers who regularly visit the gym would be the only front runners," he added.
Another senior IPS officer questioned the weight criteria of the awards, saying that the awards are only given because one has been an effective officer for almost two decades.
Meritorious awards are given after 18 years of service in the police and the Distinguished Service award is given only after 25 years of service.
The government had also recently linked the promotion of IPS officers to physical fitness. The promotions system is already in force among the central para-military forces, where senior officers must be certified in the "Shape 1" category.
Many police officers also ridiculed the Ministry order for only singling out IPS officers. They questioned why IAS officers are also not judged by the same criteria.
According to a Home Ministry official, all IPS officers will from now be asked to take a mandatory physical fitness test at an approved government hospital or before a certified medical board, ahead of promotion to the next level of seniority.
The reasoning behind the criteria making proper fitness mandatory for IPS officers is that they, particularly at the DIG, IG, ADG and DG levels, need to lead from the front and set an example for those under their command to take physical fitness seriously.
According to the Home Ministry official, an IPS officer, "unlike an IAS officer needs to be physically fit and active to handle field assignments in times of unrest and other law & order emergencies".
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Indian Police ServiceShape 1 CategoryMinistry of Home Affairs


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