text:
\section{Introduction}
\label{sec:intro}
The magnetic field is a crucial ingredient in the star formation process.
Both observational and theoretical studies indicate that the magnetic field is closely related to various phenomena such as protostellar jets, outflows, and circumstellar disks.
Magnetized prestellar clouds can be classified into two types: supercritical and subcritical \citep{mestel56,spitzer68,shu83}.
In the former, gravity dominates the magnetic field, which cannot support the prestellar cloud, and a prompt gravitational collapse occurs on a dynamical timescale to form a protostar.
In the latter, the self-gravity cannot overcome the Lorentz force under conditions of flux
freezing, but gravitational contraction is induced on a longer (ambipolar diffusion) timescale
through neutral-ion slip \citep{nakano72,mouschovias79,shu87,lizano89}. Dynamical collapse
then occurs within a cloud core that has increased its mass-to-flux ratio to a supercritical value
\citep[e.g.][]{mouschovias85,fiedler92, fiedler93,ciolek94,basu94,basu95a,basu95b,nakano98}.

Observationally, it is difficult to directly measure the magnetic field strength in molecular clouds through the Zeeman effect.
\citet{crutcher99} compiled the Zeeman detections of magnetic field strength for 27 dense regions of molecular clouds, in which 22 out of 27 were inferred to be supercritical and five were subcritical \citep[see also][]{nakamura19}.
\citet{shu99} pointed out that a greater fraction would be inferred to be subcritical if
the clouds were assumed to be flattened along the direction of the magnetic field.
Since even subcritical clouds would develop observable supercritical cores through
ambipolar diffusion, the larger question is whether the low density molecular cloud envelopes,
representing the initial conditions of molecular clouds, are supercritical
or subcritical. Indirect measures of the magnetic field strength through polarized emission
or extinction often imply that the magnetic field strength is high \citep[e.g.][]{beltran19,soam19}.
The recent large-scale mapping of the intensity and polarization of Galactic dust emission by the Planck satellite
\citep{planck16} revealed an ordered magnetic field on large scales that is consistent
with sub-Alfv\'enic or at most Alfv\'enic turbulence. When the Davis-Chandrasekhar-Fermi (DCF)
method is applied to the data, the inferred magnetic field strengths imply subcritical
mass-to-flux ratios. This result is consistent with some previous analyses of polarization
and velocity anisotropy in molecular cloud envelopes \citep{cortes05,heyer08}.

Given the above observational results, there is a need to study the gravitational collapse
of cores that arise from both supercritical and subcritical molecular cloud envelopes.
Many numerical simulations have studied the collapse of cores from supercritical initial
conditions \citep[e.g.][]{tomisaka02,banerjee06,tomida15,wurster19}. However, the collapse
process including the accretion phase when starting from subcritical initial conditions
remains relatively unexplored, especially using three-dimensional simulations.
A key difference in the collapse process can arise through a reduced amount of angular
momentum in the ultimately collapsing supercritical core, as well as through the
amount of magnetic flux available in the core.
In an earlier paper \citep[][hereafter, Paper I]{machida18}, we revisited star formation in
a subcritical cloud. We calculated the evolution until about one year after protostar
formation. The prestellar collapse developed structure that was
consistent with many previously calculated
properties of magnetically-supported clouds \citep{mouschovias76a,nakano82,tomisaka88b,tomisaka89,tomisaka90}, and showed a similar efficiency of magnetic braking and magnetic flux loss as in
thin-disk evolutionary models \citep[e.g.][]{basu94,basu95a}. Furthermore, the magnetic braking
led to a decreasing and oscillatory behavior of the angular velocity that had been
seen in analytic models \citep{mouschovias79,mouschovias80}.
In addition, we showed that in a subcritical cloud, a possible outcome is a tiny disk or no disk along with a very weak outflow. This is considerably different from star formation within initially supercritical clouds, and constitutes a different mode of star formation.

Paper I focused mainly on the gas collapsing phase prior to protostar formation and compared results with past studies.
We calculated the accretion phase for only one year following protostar formation in Paper I.
Subsequent to Paper I, this study focuses on the gas accretion phase after protostar formation.
The paper is structured as follows.
The model and numerical settings are described in \S\ref{sec:settings}.
The calculation results are presented in \S\ref{sec:results}.
In \S\ref{sec:discussion}, we discuss the angular momentum and magnetic flux problem and then compare simulation results with observations.
A summary is presented in \S\ref{sec:summary}.

\section{Calculation Models and Numerical Settings}
\label{sec:settings}
Since the calculation models, initial conditions and numerical settings are almost the same as in Paper I, we describe them briefly here. A minor difference is that
the initial prestellar cloud adopted in Paper I is slightly larger and more massive than that adopted in this study.

For the initial state an isothermal sphere with a Bonnor-Ebert density profile is adopted.
We construct the Bonnor-Ebert profile with a central density $7\times10^5\cm$ and an isothermal temperature $T_{\rm iso,0}=10$\,K.
Then, we enhance the cloud density by a factor of two in order to realize a thermally unstable state \citep{matsumoto04,machida10a,machida13}.
Thus, the initial cloud has a central density $n_{c,0}=1.4 \times10^6 \cm$.
The mass and radius of the initial cloud are $M_{\rm cl}=1.0\msun$ and $R_{\rm cl}=5.2\times10^3$\,au, respectively.
Note that the cloud mass and radius adopted in Paper I are $M_{\rm cl}=1.1\msun$ and $R_{\rm cl}=6.2\times10^3$\,au, respectively.

In this study, we assume a rigid rotation of $\Omega_0 = 1.7\times10^{-13}$\,s$^{-1}$ in the initial cloud, and an initially uniform magnetic field $B_0$, which is a parameter in this study.
The magnetic vector is aligned with the rotation vector of the initial cloud, and they are parallel to the $z$-axis.
We adopt three different magnetic field strengths $B_0=330$, 236 and 165$\mu$\,G, which correspond to $\mu_0=0.5$, 0.7 and 1.0, respectively, where $\mu_0$ is the normalized mass-to-flux ratio and is defined as
\begin{equation}
\mu_0 = \left( \dfrac{M_{\rm cl}}{\Phi_{\rm cl}}  \right) / \left(\dfrac{1}{2\pi G^{1/2}} \right).
\label{eq:masstoflux}
\end{equation}
Note that equation~(\ref{eq:masstoflux}) corresponds to the normalized mass-to-flux ratio of the whole cloud at the initial state.
In reality, the ratio is a function of mass and radius (see Fig.~\ref{fig:A1} and Fig.~1 of Paper I).
Thus, we need to pay attention to the difference between the local  and global ratios (for details, see \S\ref{sec:A1}).
The magnitude of the ratio of the thermal to gravitational energy ($\alpha_0$) is set to 0.42 and the ratio of rotational to gravitational energy ($\beta_0$) is set to 0.02.
The models and cloud parameters are summarized in Table~\ref{table:1}.
We prepared seven models ($\mu_0=0.1$, 0.3, 0.5, 1, 2, 3 and 5) in Paper I, while we show the results of three models ($\mu_0=0.5$, 0.7 and 1) in this paper.
Models with $\mu_0=0.5$ and 1 are the almost the same as in Paper I, and the results in the gas collapsing stage are also essentially the same.
In addition to these two models ($\mu_0=0.5$ and 1), we add a new model that has $\mu_0=0.7$, as listed in Table~\ref{table:1}.

The basic equations used in this study are described in Paper I (see eqs.~[3]--[7]), in which the equation of state (EOS) adopted in Paper I (eq.~[8] of Paper I) is replaced by equation~(1) of \citet{machida14b}.
The difference in the EOS between Paper I (eq.~[8] of Paper I) and \citet{machida14b} appears only at a high density of $n\gtrsim10^{18}\cm$, while the EOS in the range $n \lesssim 10^{18}\cm$ is almost the same in the two cases.
In the high density region, the EOS becomes stiff at $\sim 3\times10^{18}\cm$ with a polytropic index $\Gamma=2.0$  \citep{machida14b}, while it becomes stiff at $n \simeq 10^{21}\cm$ with $\Gamma=5/3$ in Paper I.
The former treatment (so-called stiff EOS) is widely used to accelerate the time integration \citep[e.g.][]{tomisaka02,matsumoto04,hennebelle09,joos12,hirano17,machida19} instead of introducing sink particles or sink cells.
Both ohmic dissipation and ambipolar diffusion are not efficient (or do not work well)  in the range $n\gtrsim10^{16}\cm$ \citep{nakano02} with a temperature of $>1000$\,K (for details, see Paper I).
Thus, the stiff EOS of the high-density region ($\gtrsim10^{18}\cm$) does not significantly affect the results, because we wholly cover the magnetic dissipation region.
With the stiff EOS, we can accelerate the time integration with a strong magnetic field \citep[for details, see][]{machida14b, machida15}.

As described in Paper I, both ohmic and ambipolar diffusivities are pre-calculated according to \citet{umebayashi80}, \citet{nakano86}, \citet{nishi91}, \citet{nakano02} and \citet{okuzumi09}, and we prepare a table of them.
The ohmic and ambipolar diffusion coefficients, which are a function of the density, temperature and magnetic field strength, are taken from the table in each time step.
The detailed explanations are given in the Appendix of Paper I.

The simulations are done with our nested grid code \citep[for details, see][]{machida04,machida05a,machida06,machida07,machida10a,machida11a}.
Each grid is composed of ($i, j, k$) = (64, 64, 32) cells, in which a mirror boundary is imposed on the $z=0$ plane.
We use a maximum nineteen levels of nested grid ($l_{\rm max}=19$) for this simulation.
The grid size and cell width of the coarsest grid is $L(l=1)=1.7\times10^5$\,au and $h(l=1)=262$\,au, respectively.
On the other hand, the finest or maximum level of the grid has $L(l=19)=0.64$\,au and $h(l)=0.01$\,au, respectively.
In the numerical code, the hyperbolic divergence cleaning method \citep{dedner02} is adopted to realize a divergence-free field.
The initial Bonnor-Ebert (prestellar) cloud is immersed in the fifth level of the grid ($l=5$), and the boundary is set to surface of the first level of grid ($l=1$).
Thus, the boundary is 16 times farther than the edge of the initial prestellar cloud.
A new level of the grid is generated when needed to ensure the Truelove condition, in which the Jeans wavelength is resolved by at least 16 cells \citep{truelove97}.
{The high-density interstellar medium  ($\sim9.7\times 10^4\cm$)  is included to prevent the Alfv\'en velocity becoming very high outside the Bonnor-Ebert sphere.
}
A high Alfv\'en velocity in a very low-density interstellar medium will significantly slow down the simulation with a small time step. In addition, inclusion of the high-density interstellar medium can reduce the boundary effect because the Alfv\'en waves generated from inside the Bonnor-Ebert sphere never reach the boundary, which is 16 times farther than the edge of the Bonnor-Ebert sphere. Thus, the reflection of Alfv\'en waves at the boundary is suppressed, as described in Paper I.

The outer low-density region does not contribute to self-gravity in our calculation. However, it can accept angular momentum from the core as transferred by magnetic braking \citep{machida13}.
Hence, the external medium sets the efficiency of magnetic braking and along with the magnetic field
strength helps to determine the magnetic braking timescale. The external medium is not rotating
in our simulation. Future work can explore different densities and rotation
rates of the external medium through a parameter study.

\section{Results}
\label{sec:results}
\subsection{Cloud Evolution for a hundred years after Protostar Formation}
We calculate the evolution of subcritical clouds from the prestellar stage until $\sim$500\,yr after protostar formation.
In this section, we focus on the cloud evolution during the gas accretion phase following protostar formation.
The cloud evolution during the gas collapsing stage prior to protostar formation was described in Paper I.

Firstly, we focus on the cloud structure at $t_{\rm ps}\simeq100$\,yr after protostar formation.
Figure~\ref{fig:1} shows the density and velocity distributions for all models (models M1, M07 and M05) about 100\,yr after protostar formation.
Among the models, model M1 has a marginal value of mass-to-flux ratio $\mu_0=1$, while the other two have subcritical values $\mu_0=0.7$ (M07) and 0.5 (M05), respectively.
Although we do not show the cloud evolution and structure for the supercritical case $\mu_0 > 1$, model M1 can be regarded as an alternative to supercritical ($\mu_0 >1 $) models.
\footnote{
We required over one or two years of wall-clock time for the calculations of the main accretion phase.  Thus, we needed to narrow down the number of models.
}

In model M1, a tiny disk with a size $\sim1$\,au appears around the protostar (Figs.~\ref{fig:1}{\it a} and {\it d}) and it drives an outflow as seen in Figure~\ref{fig:1}{\it d}.
The outflow has a well-collimated structure with a speed $\gtrsim 10\km$.
As seen in Figure~\ref{fig:1}{\it d}, the rotating disk is enclosed by the pseudo-disk that has a height $\sim1$\,au at $r_{\rm c}\sim2$\,au, where $r_c$ is the radius in cylindrical coordinates.
In model M1, although the size of the rotating disk is a bit small, the rotationally-supported disk, pseudo-disk, and outflow appear as usually seen in star formation in supercritical clouds \citep[e.g.][]{machida19}.

The structure around the protostar for the subcritical model M07, which has $\mu_0=0.7$, is considerably different from model M1.
In this model, no rotating disk appears by this epoch ($t_{\rm ps} \simeq 100$\,yr).
As seen in Figure~\ref{fig:1}{\it b}, all the velocity vectors on the equatorial plane point to the center without an azimuthal component.
As shown in Paper I, in subcritical clouds the magnetic braking decreases the cloud-scale angular momentum \citep[see also][]{basu94,basu95a,basu95b}.
Thus, in many cases, not enough angular momentum remains to form a rotationally-supported disk in the early accretion stage.
Note that, in a subcritical cloud, the amount of angular momentum introduced into the central region depends on the timing at which the gravitational collapse occurs after sufficient magnetic flux is removed by ambipolar diffusion (for details, see below and Paper I, \citealt{mouschovias79,mouschovias80b}).

As also seen in Paper I, some subcritical models show either no disk or a very tiny rotationally-supported disk just after protostar formation.
During the mass accretion stage, the gas with a (relatively) large angular momentum is expected to fall onto the central region and form a rotationally-supported disk in the absence of magnetic braking on a large scale.
However, in model M07, no rotationally-supported disk appears by this epoch ($t_{\rm ps}=100$\,yr), which indicates that the angular momentum is effectively removed by magnetic braking.
In addition, in model M07, a very weak outflow appears above and below the pseudo-disk, as shown in Figure~\ref{fig:1}{\it e}.
Comparison of Figure~\ref{fig:1}{\it d} with Figure~\ref{fig:1}{\it e} indicates that the outflow density is considerably lower in model M07 than in model M1.
In Figure~\ref{fig:1}, the outflow has a density $\sim 10^{12}\cm$ for model M1, while it has a density $<10^{10}\cm$ for model M07.

Next, we focus on model M05 ($\mu_0=0.5$), which has the strongest magnetic field in the initial state among the models.
As shown in Figure~\ref{fig:1}{\it c}, in this model the disk has a counter-rotation.
Since all prestellar clouds have an anti-clockwise rotation and the rotation vector points in the positive $z$-direction, the disk should have an anti-clockwise rotation when a simple cloud collapse is considered.
However, as seen in Paper I, in subcritical clouds, counter-rotation is frequently realized.
In a subcritical cloud, the magnetic field lines are twisted by the rotation of the initial cloud.
Then, they are swung back by the magnetic tension force and a counter-rotation is realized while decreasing the total angular momentum.
The decrease and oscillation (i.e. clockwise and anti-clockwise rotation) of the angular velocity has been clearly presented in the analytic models of \citet{mouschovias79} and \citet{mouschovias80}.
We demonstrated the counter-rotating disk in the model with $\mu_0=0.5$ in Paper I (see figure 3{\it c} in that paper).
Figure~\ref{fig:1}{\it c} shows that such a counter-rotating disk can be sustained during the early gas accretion phase.
In Figure~\ref{fig:1}{\it f}, the disk-like structure can be confirmed, while the outflow cannot be confirmed on this scale.

Figure~\ref{fig:2} shows the density and velocity distributions at the same epoch as in Figure~\ref{fig:1}, but the spatial scale is different.
On a large scale, models M1 and M05 show a cavity structure on the equatorial plane (Fig.~\ref{fig:2}{\it a} and {\it c}), which is created by an interchange instability \citep{spruit90,lubow95,li96,ciolek98,tassis05}.
The low-density cavity was called the DEMS (Decoupling-Enabled Magnetic Structure) in \citet{zhao11} and \citet{krasnopolsky12}
\footnote{
We discuss the relation between the magnetic cavity in this study and the DEMS in Appendix \S\ref{sec:A1}.
}.
On the other hand, for model M07, there is no cavity around the protostar
\footnote{
No appearance of the cavity for model M07 is also  discussed in Appendices \S\ref{sec:A1} and \ref{sec:B1}.
}.
Figure~\ref{fig:2} bottom panels indicate that all the models show an outflow.
For model M05, no outflow is confirmed on a small scale (Fig.~\ref{fig:1}{\it f}), while the mass ejection occurs instead on a scale of $\sim100$\,au (Fig.~\ref{fig:2}{\it f}).
Among the models, on a scale of $\sim100$\,AU, the outflow is weaker in model M07 than in models M1 and M05.
In addition, all the models show a clear pseudo-disk (Fig.~\ref{fig:2} bottom panels), which is formed in the prestellar cloud stage as shown in Paper I and past works \citep[e.g.][]{mouschovias76a,tomisaka88a,tomisaka89,tomisaka91}.

\subsection{Time Evolution of Protostar, Disk and Outflow}
\label{sec:protostellarmass}
Figure~\ref{fig:3} plots the time evolution of protostellar and disk mass, outflow mass, outflow momentum, and outflow momentum flux.
Figure~\ref{fig:3}{\it a} indicates that all models show a similar evolutionary path of the protostellar mass.
At every time step, the protostellar mass is estimated as
\begin{equation}
M_{\rm ps} = \int_{n>10^{18}\cm, \ {\rm and} \ v_r \, < \, 1 \km} \rho\, dV.
\end{equation}
Thus, we identify the protostar as the region that has a number density $\ge 10^{18}\cm$ and $v_r<1\km$.
The latter condition ($v_r < 1\km$) is imposed so as not to include the outflow driven region near the surface of the protostar \citep{machida14b,machida18,machida19}.
Although the protostellar mass for model M07 is slightly greater than those for models M05 and M1, the protostellar mass for all models is in the range $M_{\rm ps }\simeq 0.03-0.05\msun$ at the end of the calculation ($t_{\rm ps}\simeq500$\,yr).
Therefore, the mass accretion rate is estimated to be $\sim 6\times10^{-5} \msun$\,yr$^{-1}$ ($0.03\msun/500$\,yr), which is in rough agreement with analytic solutions \citep{larson03}.

The disk mass is also plotted by the dotted lines in Figure~\ref{fig:3}{\it a}.
We identify the (rotating) disk with the following criteria \citep{machida10a,joos12,tomida17,machida18,hirano19,machida19}: (1) the number density is in the range $10^8\cm<n<10^{18}\cm$; (2) the azimuthal velocity is greater than the radial velocity by a factor $f_{v}$, i.e. $v_\phi > f_v v_r$, where $f_v=5$ is adopted; and (3) the azimuthal velocity exceeds 90\% of the Keplerian velocity, i.e. $v_\phi > 0.9 v_{\rm kep}$, where $v_{\rm kep}=(G M_{\rm ps}/r)^{1/2}$.
In Figure~\ref{fig:3}{\it a}, the disk mass for models M05 and M1 increases with time and becomes comparable to the protostellar mass, which is also seen in a supercritical cloud \citep{machida19}.
As seen in Figure~\ref{fig:1}, the disk has a density $10^{12}\cm \lesssim n \lesssim 10^{18}\cm$, which roughly corresponds to the magnetically inactive region where both ohmic dissipation and ambipolar diffusion are effective \citep{nakano02}.
Thus, without an effective mechanism of angular momentum transfer due to magnetic effects, the gas accumulates in the magnetically inactive region and the disk mass finally becomes comparable to the protostellar mass \citep{tomida17,machida19}.
When the disk mass approaches the protostellar mass, the gravitational instability occurs and a parcel of gas is transported from the disk to the protostar.
As a result, the disk is self-regulated and has a mass comparable to the protostellar mass as seen in many past works \citep[e.g.][]{vorobyov06}.

The disk mass is comparable to the protostellar mass in models M05 and M1, while no disk appears in model M07.
Thus, the star formation process for model M07 is considerably different from models M05 and M1.
For model M07, the infalling gas directly accretes onto the protostellar surface without going through a circumstellar disk.

We also estimated the outflow mass $M_{\rm out}$ (Fig.~\ref{fig:3}{\it b}), outflow momentum $MV_{\rm out}$ (Fig.~\ref{fig:3}{\it c}), and momentum flux $F_{\rm out}$ (Fig.~\ref{fig:3}{\it d}) for each model.
At every time step, these are calculated as
\begin{equation}
M_{\rm out} = \int_{v_r > v_{\rm thr} } \rho \, dV,
\end{equation}
\begin{equation}
P_{\rm out} \int_{v_r > v_{\rm thr} } \rho \vert v \vert \, dV,
\end{equation}
\begin{equation}
F_{\rm out} = \dfrac{P_{\rm out}}{t_{\rm ps}},
\end{equation}
where the threshold velocity for the outflow is set to $v_{\rm thr}=1\km$.
Figure~\ref{fig:3}{\it b} shows that the outflow mass for models M05 and M1 reaches $\sim0.02\msun$ at $t_{\rm ps}\simeq500$\,yr.
Thus, the outflow mass for these models is comparable to both the protostellar and disk masses.
On the other hand,  the outflow mass for M07 is as small as $\sim10^{-4}\msun$, which is about two orders of magnitude smaller than in models M05 and M1.
The outflow momentum for models M05 and M1 is $\sim10^{-2}-10^{-1}\msun \km$, which is consistent with the typical value of observed outflows around low-mass protostars \citep{wu04}.
The outflow momentum flux for models M05 and M1 is in the range $10^{-4} \lesssim F_{\rm out}/(\msun \km \, {\rm yr}^{-1}) \lesssim 10^{-3}$, which is also in good agreement with the observations around class 0 protostars \citep{bontemps96}.
On the other hand, both the outflow momentum and momentum flux for model M07 are considerably smaller than typical observed values.
Thus, also in terms of the outflow, model M07 is considerably different from the usual star formation process.

\subsection{Density and Velocity Profiles}
Figure~\ref{fig:4} left panels plot the density and radial and azimuthal velocity on the equatorial plane along the $x$-axis for model M07.
In Figure~\ref{fig:4}{\it a}, the sudden increase of the density around $0.03-0.05$ au corresponds to the protostellar surface.
Outside the protostar, the density scales roughly $\propto r^{-1.5}$ (expansion wave) and then
$\propto r^{-2}$, which both correspond to analytic self-similar solutions \citep{shu77,hunter77}.
In addition, a slight wave-like pattern is seen in the range $\sim 0.1-10$\,au, which is caused by the inhomogeneous distribution of the magnetic field (see below).
On the other hand, the density profile is rather smooth in the range $\gtrsim 10$\,au.

We can also confirm the protostellar surface from the radial velocity profile (Fig.~\ref{fig:4}{\it b}), in which the sudden increase of the radial velocity roughly corresponds to the protostellar surface.
The azimuthal velocities have a local peak just outside the protostar (Fig.~\ref{fig:4}{\it c}).
For this model (model M07), the angular momentum on the cloud scale is largely removed by magnetic braking during the prestellar cloud stage.
Therefore, although the rotational motion eventually becomes prominent just outside the protostar,  the rotation velocity ($\vert v_\phi\vert \lesssim 3\km$) is much less than the radial velocity ($\vert v_r \vert \lesssim 25\km$).
However, the rotational motion causes torsional  Alfv\'en waves that generate toroidal fields above and below the protostar.
The gradient in the toroidal field can drive the outgoing flow (see below).

The density and velocity profiles along both the $x-$ and $y-$axes for model M05 are plotted in Figure~\ref{fig:4} right panels.
The profiles for model M05 are considerably different from those for model M07.
The protostellar surface is located around $\sim 0.03-0.05$\,au (Fig.~\ref{fig:4}{\it d}).
Outside the protostar, the density has a complex profile in the range $0.05 -30$\,au.
As seen in Figure~\ref{fig:1}{\it c}, the rotating disk exists around the protostar for model M05.
The rotating disk gradually evolves with time and its size reaches $\sim2$\,au at the end of the calculation.
The disk evolution can be confirmed in Figure~\ref{fig:4}{\it f}, in which the azimuthal velocity suddenly drops at $0.1-2$\,au.
It should be noted that the initial cloud has a positive azimuthal velocity and positive angular momentum, i.e. the rotation vector points in the positive $z$-direction as described in \S\ref{sec:settings}.
Thus, the azimuthal velocity would normally stay positive during the star formation process.
Nevertheless, the azimuthal velocity and angular momentum for this model are negative in a wide range, as seen in  Figure~\ref{fig:4}{\it f}.
The negative rotation (or negative angular momentum) is introduced by the swing back of the magnetic field (or magnetic tension force), and the cloud develops a counter-rotation motion at the center, as explained in Paper I.

Figures~\ref{fig:4}{\it e}  and {\it f} indicate that the radial velocity is much less than the azimuthal velocity inside the rotating disk.
In other words, the rotating disk corresponds to the region where $\vert v_\phi \vert \gg \vert v_r \vert$ is realized.
The azimuthal velocity becomes nearly zero as the distance from the protostar increases.
On the other hand, the radial velocity oscillates around $v_r \sim 0$ outside the disk.
The oscillation in the radial velocity is caused by the interchange instability, which is often seen in the disk formation simulations \citep{seifried11,li13,joos12,machida14a,matsumoto17,vaytet18}.

\subsection{Magnetic Flux Loss}
\label{sec:fluxloss}
Figure~\ref{fig:5} shows the plasma beta (left) and magnetic field strength (right) on the equatorial plane for model M05.
In the figure, we can confirm a bipolar-like structure along the $y$-axis, inside which the magnetic field is strong.
This region corresponds to the density cavity seen in Figure~\ref{fig:2}{\it c}.
We call the region inside the white curve in the Figure~\ref{fig:5} left panel the magnetic cavity.
As described in Appendix \S\ref{sec:A1}, the cavity corresponds to the region called the Decoupling-Enabled Magnetic Structure (DEMS) in \citet{zhao11} and \cite{krasnopolsky12}.
The velocity vectors point outward in the magnetic cavity, which means that (low-density) gas flows out from the central region.

The magnetic cavity is caused by the interchange instability \citep{li96, tassis05}.
For this model (M05), the rotating disk forms as shown in Figures~\ref{fig:1}{\it c} and \ref{fig:4} right panels.
Inside the disk, both ohmic dissipation and ambipolar diffusion are effective, because the disk has a high surface density \citep{machida07}.
Thus, the magnetic flux accumulates near the outer edge of the disk.
In Figure~\ref{fig:5} right panel, we can confirm a ring-like structure at $r\sim1-2$\,au, roughly corresponding to the disk outer edge where the magnetic flux accumulates.
Thus, the magnetic field becomes strong near the disk outer edge, around which the interchange instability tends to occur because the magnetic pressure gradient becomes greater than the pressure gradient \citep{spruit90,lubow95}.
Then, the magnetic flux interchanges with the gas and it leaks from the disk \citep{ciolek98}.
The leaked magnetic flux pushes aside the gas and the density cavity is created \citep{li96}.

Since the magnetic field is coupled with the gas outside the disk, the outward motion seen in the magnetic cavity (Fig.~\ref{fig:5} left panel) means that magnetic flux moves outward.
By this process, the excess magnetic flux is removed from the disk.
The complex profiles of density and velocity seen in Figure~\ref{fig:4} are attributed to the interchange instability and subsequent leak of the magnetic flux \citep{li96}.

Figure~\ref{fig:6} top panels show the profile of magnetic field strength for models M07 (left) and M05 (right).
In both models, the magnetic field in the range $\lesssim 2-3$\,au gradually decreases as time proceeds, while it slightly increases in the range $3\,{\rm au} \lesssim r \lesssim 100$\,au.
The decrease and increase rate of the magnetic field is greater in model M05 than in model M07.
Around the protostellar surface ($r\sim0.01$\,au), the magnetic field decreases from $B_z \simeq 500$\,G ($t_{\rm ps}=2.5$\,yr) to $\simeq25$\,G ($t_{\rm ps}=471.9$\,yr) for model M05.
On the other hand, for model M07, it decreases from $B_z\simeq400$\,G ($t_{\rm ps}=3.5$\,yr)  to $\simeq200$\,G ($t_{\rm ps}=500.3$\,yr).

The ratio of the magnetic flux to the mass is plotted against the distance from the protostar in  Figure~\ref{fig:6} middle  panels.
At each radius, the ratio can be calculated as
\begin{equation}
\dfrac{\Phi(r)}{M(r)} = \dfrac{\Delta S B_z (r)}{\Delta S \Sigma(r) }
= \dfrac{B_z(r)}{\Sigma(r)}
= \sqrt{\pi G} \dfrac{B_z(r)}{c_s(r) \rho(r)^{1/2}},
\label{eq:ratio}
\end{equation}
where $\Delta S$ is a small area, and the surface density and scale height are defined as $\Sigma=\rho h$ and $h=c_s/(\pi G \rho)^{1/2}$ \citep{scott80,saigo98,machida05a}.
In equation~(\ref{eq:ratio}), we ignored the magnetic effect when estimating the disk scale height, which is discussed in Appendix \S\ref{sec:C1}.
Figure~\ref{fig:6} middle  panels indicate that the magnetic flux moves outward.
The mass-to-flux ratios normalized by the critical value are plotted in Figure~\ref{fig:6} bottom panels, which indicate that the normalized ratios far from the protostar are almost the same as those of the initial clouds.
As shown in Figure~\ref{fig:4}, for model M05, the disk has a size $0.1-2$\,au.
Thus, with time, the magnetic flux decreases inside the disk and increases outside the disk.
This indicates that the magnetic flux gradually leaks from the disk.
The removal of the magnetic flux is also seen in model M07, while the time variation of the magnetic flux is small compared with model M05.
As shown in Figure~\ref{fig:1}{\it b}, no (rotating) disk appears in model M07.
Both ohmic dissipation and ambipolar diffusion become efficient inside the disk, because the disk surface density is high.
Since the magnetized fluid stays in the disk for a long duration, the magnetic fields (or charged particles) are gradually decoupled from neutral particles.
Thus, the existence of the disk greatly contributes to the removal of the magnetic flux.

We calculated the cloud evolution only for about 500\,yr after protostar formation.
During the calculation, the magnetic field around the protostar or inside the disk continues to decrease.
The magnetic flux is also introduced into the central region with the infalling gas.
Thus, the removal and introduction of magnetic field may be balanced in a subsequent evolutionary stage.
We need further longer-term calculations to reach more conclusions about the magnetic flux loss from the disk.

\subsection{Evolution of Protostellar System for 500 years}
In supercritical clouds, the protostar is surrounded by a rotationally-supported disk that drives the protostellar outflow.
It is believed that the formation of a rotationally-supported disk and the appearance of bipolar outflows are common in the typical star formation process.
On the other hand, the star formation process induced in a subcritical cloud seems to have a remarkable diversity.
In this subsection, we confirm whether some curious features that appeared in the subcritical cloud at the protostar formation epoch (or $t_{\rm ps} \sim100$\,yr) can be sustained during the main accretion stage.

Figure~\ref{fig:7} shows the density and velocity distributions for all models at $t_{\rm ps}\simeq500$\,yr after protostar formation.
With this figure, we revisit the characteristics of each model in the following discussion.

In model M1 (Fig.~\ref{fig:7} left panel), the star formation process is similar to that seen in a supercritical cloud, with a small disk and a large cavity appearing around the protostar.
The radius of the rotating disk at the protostar formation epoch is about 0.5\,au, while that at $t_{\rm ps}\sim500$\,yr is $\sim2$\,au.
Thus, although the disk grows slightly, it remains quite small.
Outside the disk, the density cavity that is created by the interchange instability and the leak of the magnetic flux is sustained to this epoch (Fig.~\ref{fig:7}{\it d}, {\it f}).
In addition, the protostellar jet does not disappear by this epoch (Fig.~\ref{fig:7}{\it a}).
Thus, the protostar formation process for model M1 is almost the same as seen in a supercritical cloud.

Next, we focus on model M07 (Fig.~\ref{fig:7} middle panels).
In this model, the rotating disk does not appear in the early accretion phase (Figs.~\ref{fig:1} and \ref{fig:2}).
We do expect that the rotating disk will appear in a further evolutionary stage, because parcels of gas with greater angular momentum will later fall onto the central region.
However, no disk appears by the end of the simulation (Figs.~\ref{fig:7}{\it e} and {\it h}).
On the other hand, the outflow continues to be driven till the end of the calculation (Fig.~\ref{fig:7}{\it b}), even though it is weaker than in models M05 and M1 (Fig.~\ref{fig:3}).

For model M07, the angular momentum is largely removed by the magnetic braking during the prestellar stage, and thus no rotating disk appears (Paper I).
The magnetic dissipation (ohmic dissipation and ambipolar diffusion) is not very effective without the disk, because  the gas density around the protostar is too low to switch on the magnetic dissipation (Paper I).
In addition, since the radial velocity dominates the azimuthal velocity (Fig.~\ref{fig:4}), the gas directly falls onto the protostellar surface.
Thus, there is not enough time to dissipate the magnetic field until the infalling gas reaches the protostar.
As a result, the magnetic field is largely coupled with the neutral gas in the infalling envelope.
Note that inefficient magnetic dissipation occurs even for model M07 (for details, see Appendix \S\ref{sec:B1}).
Therefore, the remaining small amount of angular momentum continues to twist the magnetic field lines that can drive the outflow  \citep[e.g.][]{uchida85,Lynden-Bell03,machida08}.

Figure~\ref{fig:8} shows a three-dimensional view of the outflow and magnetic field lines for model M07.
The figure indicates that the magnetic field lines are strongly twisted inside the outflow, even though rotational motion is not apparent in the region around the protostar in Figures~\ref{fig:1} and \ref{fig:2}.
Note that the rotational (or azimuthal) velocity is actually confirmed in Figure~\ref{fig:4}{\it c}.
For this model, the angular momentum is also transported by the outflow
and no disk forms in the main accretion stage.
The magnetic field is coupled with the neutral gas and the outflow continues to eject the angular momentum as long as no disk appears. In other words, no disk forms unless the outflow, which transports the angular momentum, disappears.

Finally, we describe model M05.
For this model, a counter-rotating disk appears at the protostar formation epoch.
As shown in Paper I, a subcritical cloud can have both positive (anti-clockwise) and negative (clockwise) rotations during the prestellar stage, due to the magnetic braking.
If a rapid cloud collapse is induced when the central part has a negative rotation, a counter-rotating disk forms around a newly-born protostar (Paper I).
Figure~\ref{fig:7}{\it j} shows that the counter-rotating disk is sustained for at least $\sim500$\,yr, during which the disk has a size $\lesssim 3$\,au.
The outflow also sustains for $\sim 500$\,yr after protostar formation (Fig.~\ref{fig:7}{\it c}).
Thus, the counter-rotating disk and outflow system does not transiently appear only  at the protostar formation epoch.

For model M05, the outflow should have the same rotation direction as the disk, because the outflow is driven by the rotating disk.
Figure~\ref{fig:9} shows the rotation velocity perpendicular to the $y=0$ plane for this model.
In the figure, the positive and negative velocity along the line of sight are colored by red and blue, respectively.
Figure~\ref{fig:9}{\it d} indicates that the rotation direction of the outflow at its root is the same as that of the disk.
Both the disk and outflow have a clockwise rotation  near the outflow driving region.
However, on a large-scale, the positively (or anti-clockwise) rotating outflow encloses the clock-wise rotating outflow (Fig.~\ref{fig:9}{\it c}).
Furthermore, on a large scale of $\sim1000$\,au (Fig.~\ref{fig:9}{\it b}), the positive and negative rotations are nested in the outflow.
This nested rotation is attributed to the envelope having both positive and negative rotations.
As described in Paper I, the prestellar cloud has both positive and negative rotations because the moment of inertia at each radius is different.
The outflow has a wide opening angle and sweeps the envelope gas that has a different sign of the angular momentum.
In summary, since the infalling gas has both positive and negative signs of the angular momentum (Fig.~\ref{fig:9}{\it a}), the outflow also has both signs of the angular momentum, as seen in Figure~\ref{fig:9}{\it b} and {\it c}.
Figures~\ref{fig:7} and \ref{fig:9} show that the outflow having nested rotations also survives for $\sim500$\,yr and reaches $\sim1000$\,au.

\section{Discussion}
\label{sec:discussion}
\subsection{Angular Momentum and Magnetic Flux Problems}
Star formation occurs through a process of removing excess internal energy, angular momentum and magnetic flux.
Without this removal, the prestellar cloud cannot collapse to form a star.
The removal of internal energy has been elaborately investigated in one-zone and one-dimensional calculations \citep{larson69,masunaga00}.
Magnetic flux loss and its role in disk formation has been demonstrated in axisymmetric thin-disk calculations \citep{dapp10,dapp12}.
However, the removal of angular momentum and magnetic flux needs to be investigated in multi-dimensional calculations, because the centrifugal and Lorentz forces have an anisotropic nature
and are closely coupled to each other.
Hence, we should further investigate the removal of magnetic flux and angular momentum (the so-called angular momentum and magnetic flux problems) with three-dimensional nonideal MHD simulations.

In recent years, the angular momentum transport and magnetic flux loss were investigated by state-of-the-art three-dimensional simulations \citep{machida07,tomida15,wurster18}.
Simulations have shown that the angular momentum is largely removed from the rotationally-supported disk by both magnetic braking and a magnetic outflow \citep{tomisaka02,joos12}, and the magnetic field also dissipates in the disk due to ohmic dissipation and ambipolar diffusion \citep{tomida15,tsukamoto15b, masson16,vaytet18}.
Thus, the rotationally supported disk plays a significant role for resolving both the angular momentum and magnetic flux problems.
Since the gas collapse slows once the rotationally-supported disk forms, the magnetic braking and magnetic dissipation timescales become shorter than the dynamical (or collapse) timescale.
Then, the angular momentum is significantly transported in both disk outer and inner edges by magnetic effects, while the magnetic field dissipates in the intermediate region of the disk \citep{machida14b,machida19}.
It should be noted that supercritical clouds were adopted as the initial state in almost all recent simulation studies, as described in \S\ref{sec:intro}.

On the other hand, the removal process of magnetic flux and angular momentum in subcritical clouds differs from that in supercritical clouds.
In the subcritical case, the Lorentz force prevents an initial rapid collapse.
The cloud core does not collapse until its mass-to-flux ratio rises to a marginally
supercritical value, due to ambipolar diffusion.
During this time, the cloud contracts very slowly and establishes a disk-like configuration \citep{mouschovias76a,tomisaka88a,tomisaka88b,tomisaka89,tomisaka90,tomisaka91}.
During the quasi-contraction phase, the magnetic flux is removed on a cloud scale of $10^3-10^4$\,au.
Even after a rapid collapse begins, a large amount of magnetic flux remains because the cloud collapse occurs when the cloud self-gravity just exceeds the Lorentz force, i.e. the core is
marginally supercritical.

On the other hand, during the quasi-contraction stage, the angular momentum on the cloud scale is largely removed by the magnetic braking \citep{basu94,basu95a,basu95b}.
When too much angular momentum is transported during this stage, the opposite sign of the angular momentum (or counter-rotation) is introduced into the cloud center by the swing back of the magnetic field \citep{mouschovias79,mouschovias80}.
As a result, in a subcritical cloud, a large amount of magnetic flux and a small amount of angular momentum remains just before the rapid collapse begins.
Like the models of \citet{mouschovias79,mouschovias80}, our models are embedded in
a nonrotating environment. This enhances the ability of magnetic braking to create a
counter-rotation. The ultimate outcome of whether the core develops no disk, a directly-rotating
disk, or a counter-rotating disk then depends upon the timing of exactly when the core
becomes supercritical with $\mu \gtrsim 1$ and begins a rapid collapse, since the rotation
rate is undergoing a decaying oscillatory evolution. When the rapid collapse begins, the
rotation rate rises rapidly in magnitude regardless of which sign it has at that time.
The models that develop disks have a magnitude of the rotation rate $\sim 10^{-15}$ s$^{-1}$ at the
time that rapid collapse begins. This is similar in magnitude to the background rotation
rate adopted by \citet{basu94,basu95a,basu95b} in their studies of magnetic braking in
the prestellar stage, based on Galactic differential rotation in the solar neighborhood.
However, if the surrounding interstellar medium has a significantly greater rotation
rate, then the result of a counter-rotating collapse may not be realized even in subcritical
clouds. We will conduct a parameter study in the future to explore this.

Our study focuses on the gas accretion phase of a protostar that is born in a subcritical cloud.
As described above, the magnetic field is very strong and the angular momentum is very small when the protostar forms.
A very small amount of angular momentum causes either no disk or the appearance of a very tiny rotating disk around protostar.
Without the disk, the dissipation of the magnetic field on a small scale ($\lesssim 100$\,au) is not effective, because
(1) the gas density is not high enough to prevent  the penetration of cosmic-rays and the disk temperature is not high enough to cause the thermal ionization of alkali metals \citep{nakano02}, and
(2) the dissipation timescale of magnetic field does not become significantly shorter than the contraction timescale of the cloud.
Therefore, a large amount of  magnetic flux is introduced into the central region or  small disk.

With a large amount of advected magnetic flux, the interchange instability tends to occur \citep{spruit90,lubow95,li96,ciolek98}.
As shown in \S\ref{sec:results}, the strong magnetic field interchanges with the gas and is violently expelled from the central region.
When a (tiny) disk emerges, both ohmic dissipation and ambipolar diffusion produce an inhomogeneous distribution of magnetic field \citep[e.g.][]{machida19}, which promotes the occurrence of the interchange instability.
Through this process, the magnetic flux leaks from the disk \citep{zhao11,krasnopolsky12} and the magnetic field strength near the protostar gradually decreases, as shown in Figure~\ref{fig:6}
\footnote{
The quantitative estimate of the leaked magnetic flux  is described in Appendix \S\ref{sec:A1} and \ref{sec:B1}.
}.

\subsection{Is there a Corresponding Object in Observations?}
This study shows that when a star forms in a subcritical cloud, the system can
be characterized by
\begin{itemize}
\item a protostar that has no disk or a very tiny disk.
\item a very weak outflow.
\item a cavity or inhomogeneous density distribution in the infalling envelope or pseudo disk, which is produced by the interchange instability and the leak of the magnetic flux.
\item a rotation direction of the disk and outflow that is opposite to the rotation of the infalling envelope.
\item an outflow that has different signs of rotation in different places.
\end{itemize}
If an observed object has one or some of these features, it is consistent with the possibility of star formation in a subcritical cloud.
However, the above features can also be observed for the supercritical case.
For example, recent studies indicate that a counter-rotating envelope can appear when the Hall effect works well in the star formation process \citep{krasnopolsky11,tsukamoto15,tsukamoto17}, although the parameter space within which the Hall effect becomes effective is fairly limited  \citep{koga19,wurster19}.
Furthermore, the interchange instability can be also seen in both ideal and nonideal MHD simulations starting from a supercritical state \citep{seifried11,zhao11,joos12,krasnopolsky12,matsumoto17,zhao18,machida19}.
To make firm conclusions, we need highly precise observations to directly determine the magnetic field strength in molecular clouds.

Recently, Keplerian disks were observed around some class 0 protostars by ALMA \citep[e.g.][]{hara13,sakai14,ohashi14,aso15, hirota17,okoda18}, whereas Keplerian disks were also not confirmed in some other class 0 protostars \citep{yen15,tobin15}.
The limited spatial resolution of ALMA constrains determination of the disk size.
Although it is difficult to observe a disk with a radius $\lesssim 10$\,au, the lack of
significant sized disks around some
class 0 protostars may be a proof of star formation in a subcritical cloud.
To precisely constrain the disk size, we need to wait for further high-resolution observations.

We next describe several objects that have features that are consistent with
star formation in a subcritical cloud.
Using ALMA, \citet{tokuda14} observed MC27 or L1521F, which was believed to be a starless core before the ALMA era \citep{onishi02}, and found a $0.1\msun$ protostar associated with a very compact bipolar outflow.
In addition, an arc or cavity-like structure is also confirmed far from the Spitzer source (or protostar).
Furthermore, the protostar possess a tiny disk with a size $\sim10$\,au and a mass of $\sim10^{-4}\msun$  \citep{tokuda17}, even though there exists a very massive envelope around the protostar and the object is undoubtedly in the main accretion phase.
Although the cause of the curious features could be undetected small-scale turbulence or being the birth site of a multiple system \citep{tokuda18}, our work shows that these features are consistent with star formation in a subcritical cloud.

\citet{kawabe18} observed two protostars for which the outflow mass and mass loss rate are extremely low.
Since the dynamical timescale, which is estimated from the outflow, is as short as $\sim100$\,yr, they infer a very young protostar.
In addition, a Keplerian disk cannot be observed for these objects.
A weak outflow and no detection of the rotating disk can be explained by star formation in a subcritical cloud.
Future observations should determine details of the star formation process for these objects.

\cite{louvet16} showed the counter-rotation between a Keplerian disk and protostellar jet around a classical T Tauri star \citep[see also][]{cabrit06}.
That system is of course more evolved than the one shown in this study.
Using the SMA archival data, \citet{takakuwa18} found a counter-rotation between the Keplerian disk and infalling envelope around a class I protostar (IRAS 04169+2702).
The Keplerian disk has a size $\sim200$\,au.
Although we cannot justify the formation of such large-sized and/or late time counter-rotating disks without further long-term simulations, these objects are possible candidates of star formation in subcritical clouds.
\citet{aso19} also observed six class 0 objects that are not associated with an observed disk.
Nevertheless, these objects have massive envelopes, but the outflow activities seem to be very weak.
These objects may also be candidates for star formation in subcritical clouds \citep[see also][]{hirano14}.

\section{Summary}
\label{sec:summary}
Subsequent to Paper I, this study has focused on the gas accretion stage of star formation in subcritical clouds.
The star formation process in a subcritical cloud differs from that in a supercritical cloud in
ways that are schematically presented in Figure~\ref{fig:10}. There we classify the star formation process into three cases of supercritical, subcritical case 1, and subcritical case 2.

The star formation process in the supercritical case is shown in Figure~\ref{fig:10}{\it a}.
For this case, the protostar is surrounded by a rotationally-supported disk that drives both a high-velocity collimated jet and a slow-velocity wide-angle outflow.
The angular momentum is transported on the disk scale by the magnetic effects of magnetic braking and outflows, while the magnetic field dissipates inside the disk.
Many recent observations seems to support this usual star formation process.

On the other hand, for the subcritical case, a large amount of angular momentum is transported out to the interstellar medium before the gravitational collapse begins.
A part of the angular momentum is also transported by the outflow, and the remaining angular momentum can contribute to the formation of a tiny disk.
In this case, a large amount of magnetic flux is also introduced into the central region. The magnetic flux trapped in the disk finally gives rise to the interchange instability and is ejected from the central region.

We further classified star formation in a subcritical cloud into two cases.
The first one is shown in Figure~\ref{fig:10}{\it b}.
For this case, a protostar possesses a tiny disk that drives a weak outflow.
In addition, the swing back of the magnetic tension force in a cloud scale produces a counter-rotating disk and outflow, in which the rotation vector of the disk and outflow is opposite to that of the prestellar core.
In addition, there exists a cavity-like structure, which is created by the interchange instability and the leak of the magnetic flux into the pseudo-disk or infalling envelope.
In the cavity, the magnetic pressure is high, and the thermal pressure, which is proportional to the gas density, is low.
The second subcritical case is shown in Figure~\ref{fig:10}{\it c}.
For this case, although no disk appears, the rotational motion produces torsional Alfv\'en waves that can drive a very weak outflow.

It is very difficult to definitively identify a protostellar system that is born in a subcritical cloud. However, we have identified several unique collapse channels that can arise in the
case of subcritical initial conditions. In the ALMA era, we hope to identify objects that
can be explained through these scenarios. In doing so we can better understand the role of
magnetic fields in constraining the star formation process.

\section*{Acknowledgements}
We have benefited greatly from discussions with ~K. Tomida and ~T. Nakano.
We thank ~S. Okuzumi  for supplying the data of coefficients of ohmic dissipation and ambipolar diffusion.
The present research used the computational resources of the HPCI system provided by (Cyber Sciencecenter, Tohoku University; Cybermedia Center, Osaka University, Earth Simulator, JAMSTEC) through the HPCI System Research Project (Project ID:hp160079, hp170047, hp180001,hp190035).
The present study was supported by JSPS KAKENHI Grant Numbers JP17K05387, JP17H02869,  JP17H06360 and  17KK0096.
Simulations reported in this paper were also performed by 2017, 2018 and 2019 Koubo Kadai on Earth Simulator (NEC SX-ACE) at JAMSTEC.
This work was partly achieved through the use of supercomputer system SX-ACE at the Cybermedia Center, Osaka University. SB was supported by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada.

redpajama_set_name: RedPajamaArXiv


text:
Q: Finding order of elements order-wise in product of groups. This is in continuation of earlier post here. Though still not found two such $16$-length product groups, still want to learn the process of finding correct pair of such product groups.
Goal is to show that two $16$- length groups formed by four groups' products, are not isomorphic; though they have same number of elements order-wise.
Let, $G= C_{8}\times C_2\times C_1\times C_1$, and $H= Q_8\times C_2\times C_1\times C_1$
First, need to know if both $G,H$ have $16$- length products.
Next, need show two products $G,H$ have the same number of elements order-wise.
Last part is to show these two groups are not isomorphic, i.e. $G\ncong H.$
Request inputs for first part, as assume that $C_1$ has only identity element that does not add to length of group product.
For second part, my attempt:
So, Cartesian product need be formed
$G$ has components $C_8, C_2, C_1.$
Number of elements of order $8$ in $C_8=2,$ given by $r, r^7,$
Number of elements of order $4$ in $C_8=2,$ given by $r^2, r^6,$
Number of elements of order $2$ in $C_8=1,$ given by $r^3,$
Number of elements of order $1$ in $C_8=1,$ given by $r^0=e.$
Second consider $C_4$:
Number of elements of order $4$ in $C_4=2$ given by $r_4, r_4^3,$
Number of elements of order $2$ in $C_4=1,$ given by $r_4^2,$
Number of elements of order $1$ in $C_8=1,$ given by $r_4^0=e.$
Now, form Cartesian product of two groups : $$C_8=\{e_{C_8}, r_{C_8}, r_{C_8}^2, r_{C_8}^3, r_{C_8}^4, r_{C_8}^5, r_{C_8}^6, r_{C_8}^7\},$$
$$C_4:\{e_{C_4}, r_{C_4}, r_{C_4}^2, r_{C_4}^3, $$
$$CP_{C_8\times C_4}= \{(r_{C_8}^0, r_{C_4}^0), (r_{C_8}^0, r_{C_4}^1), ..., (r_{C_8}^7, r_{C_4}^3) \}$$
But $e$ can pair only with other $e$.
So, get :
$$CP_{C_8\times C_4}= \{(r_{C_8}^0=e_{C_8}, r_{C_4}^0=e_{C_4}), (r_{C_8}, r_{C_4}),  (r_{C_8}^1, r_{C_4}^2),
(r_{C_8}^1, r_{C_4}^3), $$
$$(r_{C_8}^2, r_{C_4}),
(r_{C_8}^2, r_{C_4}^2),
(r_{C_8}^2, r_{C_4}^3),$$
$$(r_{C_8}^3, r_{C_4}),
(r_{C_8}^3, r_{C_4}^2),
(r_{C_8}^3, r_{C_4}^3),
 ... \}$$
Or, a total of ($3\times 7+1= 22$) elements in the Cartesian product.
But, need know order of these elements pair-wise.
Seems a long exercise, is there a shortcut?
For last part, think if above is correct, then can use the property that $C_8\ncong Q_8$.

A: The direct product of two abelian groups is abelian. Thus
$$G= C_{8}\times C_2\times C_1\times C_1$$
is abelian. However, since $Q_8$ is nonabelian, $Q_8\times A$ is nonabelian for any group $A$. Thus
$$H= Q_8\times C_2\times C_1\times C_1$$
is nonabelian.
For any groups $K$ and $L$ with $K\cong L$, we have that $K$ is abelian if and only if $L$ is abelian.
Thus the groups $G$ and $H$ cannot be isomorphic.

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text:
Differentiate between Prokaryotic and Eukaryotic cells
SECTION - III
Attempt any THREE questions: (8 x 3 = 24)
(a) Differentiate between Prokaryotic and Eukaryotic cells.
Ans. PROKARYOTIC AND EUKARYOTIC CELLS:
Biologists have divided cells into two types: prokaryotic and eukaryotic.
The differences between these two types of cells are mainly based upon the structure of their nuclei.
Prokaryote
(i) Eukaryotes have a very well defined nucleus, in which nuclear material (chromosomes or DNA) is enclosed in a double nuclear membrane.
(ii) Those possessing eukaryotic cells are called eukaryotes.
(iii) Eukaryotes includes all other unicellular or multicellular organisms such as animals, plants, fungi and protista. (Containing all membrane bounded organelles)
(iv) Ribosomes compared of eukaryotes 80S.
(v) The cell wall of plants is generally made up of cellulose.
(vi) Eukaryotic cells are given in diagram.
(i) In prokaryotic cells, however the genetic material (DNA) is without any nuclear membrane covering and is directly submerged in the cytoplasm.
(ii) Organisms possessing prokaryotic cells are called prokaryotes.
(iii) Prokaryotes include bacterial and blue green algae. Prokaryotic cells generally lack many of the membrane bounded structures found in eukaryotic cells, For Example, mitochondria, endoplasmic reticulum, chloroplast and Golgi apparatus are absent in prokaryotic cells.
Since there is no nuclear membrane, a prokaryotic cell has no distinct nucleus and its DNA molecule is directly suspend in cytoplasm.
(iv) Prokaryotes have small sized ribosomes 70S.
In prokaryotes mitosis is missing and the cell divides by binary fission. Because of their simpler structure, it was widely accepted for a long time that prokaryotic cells represent a more primitive stage of evolution than eukaryotic cells Perhaps the most distinctive features of the prokaryotic cell is its cell wall, composed of polysaccharide chains bound covalently to shorter chains of amino acids forming.
Peptidoglycan and Murein.
(v) The entire cell wall is often regarded as a single huge molecule or molecular complex called Sacculus or murein and is differently structured than that of a bacterium.
(vi) Diagrams of prokaryotic.
(b) Explain the nutrition in fungi.
Ans. NUTRITION IN FUNGI:
All fungi lack chlorophyll and are heterotrophs (obtaining carbon and energy from organic matter).
They obtain their food by direct absorption from the intermediate environment and are thus absorptive heterotrophs.
(1) Saprotrophs:
Most fungi are saprotrophs (or saprobes), decomposers that obtain their food (energy, carbon and nitrogen) directly from dead organic matter.
They secrete out digestive enzyme which digest dead organic matter, and all organic molecules thus produced are absorbed back into the fungus.
Saprobic Fungi anchor to the substrate by modified hyphae, the rhizoids.
Fungi are the principal decomposers of cellulose and lignin, the main components of plant cell walls (most bacterial cannot break them).
Extensive system of fast growing hyphae provides enormous surface for absorptive mode of nutrition.
Saprobic fungi, along with bacteria, are the major decomposers of the biosphere, contributing to the recycling of the elements (C, N, P, O, H etc) used by living things.
(2) Parasites:
Some fungi are parasites.
Haustoria:
Parasitic fungi absorb nutrient directly from the living host cytoplasm with the help of special hyphal tips called hustoria.
They may be obligate or facultative.
(i) Obligate Parasites:
Obligate parasites can grow only on their living hosts and cannot be grown on available defined growth cultures medium.
Various mildews and most rust species are obligate parasites.
(ii) Facultative Parasites:
Facultative parasites can grow parasitically on their host as well as by themselves on artificial growth media.
(3) Predators:
Some fungi are active predators.
(i) Oyster Mushroom (Pleurotus Ostreatus) is a carnivorous (predatory) fungus:
It paralyses the nematodes (that feed on this fungus), penetrate them, and absorb their nutritional-contents, primarily to fulfil its nitrogen requirements.
It fulfills its glucose requirements by breaking the wood.
(ii) Arthrobotrys:
Some species of arthrobotrys trap soil nematodes by forming contricting ring, their hyphae invading and digesting the unlucky victim. Other predators have other adaptations, such as secretion of sticky substances.
(4) Mutualistic Symbiotic:
Fungi form two key mutualistic symbiotic association (associations of benefit to both partners).
They are lichens and mycorrhizae.
(i) Lichens:
Lichens are mutualistic and have symbiotic associations between certain fungi mostly Ascomycetes and imperfect fungi, and few Basidiomycetes (about 20 out 15000 species of lichens) and certain photoautotrophes either green algae or a cyanobacterium, or some times both.
Most of the visible part of lichens consist of fungus and algal components are present within the hyphae.
Fungus protects the algal partner from strong light and desiccation and itself gets food through they courtesy of alga.
Lichens can grow at such place where neither of the components along can even at harsh places such as bare rocks etc.
Lichens vary in colour, shape, overall appearance, growth form.
Bioindicators: They are ecologically very important as bioindicators of air pollution.
(ii) Mycorrhizae:
Mycorrhizae are mutualistic association between certain fungi and roots of vascular plants (about 97% of all kinds of vascular plants).
The fungal hyphae dramatically increase amount of soil contact and total surface area for absorption and help in the direct absorption of phosphorus, zinc, copper and other nutrients from the soil into the roots. Such plants show better growth than those without this association.
The plant, on the other hand, supplies organic carbon to fungal hypahe.
There are two main types of mycorrhizae
(a) Endomycorrhizae:
Endomycorrhizae, in which the fungal hyphae penetrate the outer cells of the plant root, forming coils, swellings and minute branches, and also extend out into surrounding soil;
(b) Ectomycorrhizae:
Ectomycorrhizae in which the hyphae surround and extend between the cells but do not penetrate the cell walls of the roots. These are mostly formed with pines, firs etc.
However, the mycelium extend far out into the soil in both kinds of mycorrhizae.
Fungi grow best in moist habitats, but are found wherever organic matter is present.
Temperature and pH:
They survive in dry conditions in some resting stage or by producing resistant spores.
They can also tolerate a wide range of pH from 2 - 9, a wide temperature range, and high osmotic pressure such as in concentrated salt/sugar solutions as in jelly, jam etc.
These features also help them in their survival on land.
Reserve food Material:
Fungi store surplus food usually as lipid droplets or glycogen in the mycelium.
Differentiate between Prokaryotic and Eukaryotic cells Reviewed by SaQLaiN HaShMi on 9:39 AM Rating: 5
Explain the structure and function of cell wall?
(a) Explain the structure and function of cell wall?
Ans. CELL WALL:
The outer most boundary in most of the plant cells is cell wall.
The cell wall of plant cell is different from that of prokaryotes, Both in structure and chemical composition.
It is secreted by protoplasm of the cell.
Its thickness varies in different cells of the plant.
(1) Composition and Structure:
It is composed of three main layers:
Primary wall
Secondary wall
Middle Lamella
(i) Middle Lamella:
The middle lamella is first to be formed in between the primary walls of the neighboring cells.
(ii) Primary Wall:
The primary wall is composed of :
Cellulose and some deposition of
Pectin (gelling agent) and
Hemicelluloses
Cellulose molecules are arranged in a criss-cross arrangement. The primary wall is a true wall and develops in newly growing cells.
(iii) Secondary Wall:
The secondary wall is formed on its inner surface and is comparatively thick and rigid.
Chemistry it is composed of:
Inorganic salts
Cutin
Lignin (complex polymer) etc.
Prokaryotic cell wall lacks cellulose; its strengthening material is peptidoglycan or Murein.
Fungal cell wall contains chitin.
(2) Functions:
Cell wall is very important.
It provides a definite shape to the cell and keep it rigid.
It does not act as a barrier to the materials passing through it.
(b) Write importance of pea family?
Ans. ECONOMIC IMPORTANCE: (PEA FAMILY)
(i) High-Protein:
The family is of considerable importance as a source of high protein food, oil, and forage as well as ornamentals and other uses.
Main importance lies in the pulses, belonging to this family, which are used as food, some important and common species of pulses yielding plants are:
These pulses are rich in protein contents.
(ii) Forage Crop of Horses:
(Medicago sativa) Alfalfa is one of the worlds best forage crop for horses.
(iii) Fodder Crops:
Vicia. Melilotus and Trifolium are also cultivated as main fodder crops.
Many trees of this family provide excellent timber for building, furniture and fuel.
Main timber plants are Butea, Dilbergia etc.
(iv) Vegetable Oil:
Seeds of Arachis hypogea peanut are edible and also used for extraction of peanut oil which after hydrogenation is used as a vegetable oil.
(v) Indigo Dyes:
Indigo dyes are obtained from Indigofera tinctoria and Butea monosperma, yielding yellow dye from flowers.
(vi) Medicines:
Many plants of this family are important for medicines.
These include Glycyrrhiza glabra for cough and cold.
Clitoria ternatea is used against snake bite.
(vii) Weights:
The red and white seeds of Abrus precatorious are used by jewelers as wights called "ratti".
(viii) Ornamental:
Some important ornamental plants include Lathyrus, Lupinus, Clitoria, Butea etc.
Explain the structure and function of cell wall? Reviewed by SaQLaiN HaShMi on 9:09 AM Rating: 5
Biology Part 1 Intermediate - Solved Guess Paper No. 1 Short Questions
Biology Intermediate Part - 1 (11th Class)
Guess Paper No. 1
Total Marks: 83 (Subjective Type) Time Allowed: 3:10 hours
Q.2 Write answers of any Eight questions: (8 x 2 = 16)
(i) Which process is most important at individual level organization?
Ans. Coordination between different organ and systems is most important at individual level organization. An individual cannot survive without it.
(ii) Differentiate between organic and inorganic molecules?
Ans. Organic: The molecules containing both carbon and hydrogen together are called organic molecules.
Inorganic: The molecules without carbon and hydrogen together are called inorganic molecules.
(iii) Why are amino acids so reactive and form new peptide bonds?
Ans. Amino acids have two most reactive groups at both ends. Amine group at one end has Hydrogen atom and carboxylic group at the other end have OH group. So amino acids are reactive at both ends and can easily form new peptide bonds.
(iv) Give two functions of proteins?
Ans. (i) They build many structures of the cells like cell membrane.
(ii) All enzymes are protein in nature. These enzymes control the metabolism of cell.
(v) What is energy of activation? what is its relation with enzyme?
Ans. The minimum amount of energy required to start a reaction is called activation energy. Enzyme decreases the activation enzyme. So reaction takes place in less time.
(vi) What is induced fit model? Who did propose it?
Ans. This model was proposed Koshland in 1959. He describes that when a substrate combines with an enzyme, it induces changes in the enzyme structure. These changes enable the enzyme to perform its catalytic activity. This is also called "Hand Glove" model.
(vii) Give salient features of cell theory?
Ans. (i) All organisms are composed of one or more cells.
(ii) All cells arise from pre-existing cells.
(iii) Cell is the basic structural and functional unit of all the organisms.
(viii) What is resolution of eye? How can the resolution of eye be improved?
Ans. The human eye can differentiate between two points, which are at least 1.0 mm apart. This is known as resolution of eye. The resolution of eye can be improved by the use of microscopes.
(ix) What is virion? Name its different parts?
Ans. The complete virus is called virion. It is composed of central core, Capsid, and envelop. Virion is outside the living organism.
(x) Why are retroviruses so dangerous and drugs do not kill them?
Ans. The retroviruses change their RNA into DNA by enzyme reverse transcriptase. This DNA is incorporated in the DNA of host in form of provirus. So it cannot destroy in this form.
(xi) What are three types of bacteria on the basis of shape? Give differences among them?
Ans. The three types of bacteria are cocci, bacilli and spirilla. Cocci are spherical or oval bacteria. Bacilli are rod shaped bacteria. The spiral shaped bacteria are spirally coiled.
(xii) Name a parasitic amoeba what disease does it cause?
Ans. Entamoeba histolytica is an intestinal parasite. It causes amoebic dysentery in humans
(i) How are Foraminifer source of lime stone?
Ans. Dead Foraminiferans sink to the bottom of the ocean. They form grey mud, this grey mud gradually transformed into chalk. The old and dead Foraminiferans are changed into limestone deposits.
(ii) Differentiate between Ectomycorrhlizae and Endomycorrhlizae?
Ans. In case of Endomycorrhizea, the fungal hyphae penetrate into the cell wall of the plant root. In case of Ectomycorrhlizae, the hyphae surround and extend between the cells. But they do not penetrate into the cell wall of the root cells.
(iii) Give two terrestrial adaptations in fungi?
Ans. Fungi develop extensive system of fast spreading hyphae. The hyphae penetrate into the substrate. Thus they increase the contact and the surface area for absorption. The cell wall of hyphae
is made up of chitin.
(iv) Why is adiantum called as maiden hair ferm?
Ans. The stipe (stalk) and rachis of leaf of adiantum are black, smooth and shiny. Hence it is called maiden hair fern.
(v) Why did the gymnospers have naked seed and it failed to form fruit?
Ans. the megasporophlls cover ovule. These sporophylls are not folded or joined at the margins to from an ovary. That is why, seed are naked on megasporophyll. So it could not develop fruit.
(vi) What are protozoa and metazoa ?
Ans. Metazoa includes all multicellular animals like man.Protozoa includes all unicellular animals like amoeba amoeba.
(vii) What is pseudocoelom and pseudocoelomate?
Ans. The animals with false coelom developed from blastocoel are called pseudocoelomate. The space between the body wall and the digestive tube is called pseudocoelom.
(viii) What is Ark-e-Gulab? Give its uses?
Ans. The petal of rose give Ark-e-Gulab on distillation with water. This Ark-e-Gulab is used for curing eye disease and for many other purposes.
(ix) Differentiate between polyp and medusa?
Ans. Polyp is a tube like structure. It reproduces asexually. While medusa is an umbrella like structure. It reproduce sexually.
(x) What is principal function of xylem?
Ans. The principal function of xylem in the plants is the upward transportation of water and solutes.
(xi) What is NADP? Give its significance?
Ans. NADP is nicotine amide dinucleotide phosphate. Hydrogen is produced by the splitting of water. It reduces NADP* (Nicotine Amide Dinucleotide phosphate) to NADPH + H+. The NADPH2 has reducing power.
(xii) What is photophosphorylation?
Ans. The synthesis of ATP due to light energy is called photophosphorylation. Its mechanism is chemiosmosis.
Q.4 Write answers of any SIX questions: (6 x 2 = 12)
(i) What is peristalsis?
Ans. Peristalsis is wave of contraction of the circular and longitudinal muscle which is preceded by wave of relaxation to squeeze the food down into the digestive canal.
(ii) What is constipation?
Ans. It is other extreme condition. In this case, excessive water is absorbed.
(iii) What is common thing between photorespiration and photosynthesis?
Ans. Both the photorespiration and photosynthesis occurs in the presence of light. Both uses RuBP as their reactant.
(iv) What are air sacs in birds? Give their function?
Ans. The lungs of birds have developed several extensions called air sacs. These airs sacs help in the movement of air.
(v) What are lenticels? What is lenticular transpiration?
Ans. The loss of water vapours through the lenticels is called lenticular transpiration. Lenticels are aerating pores in the bark of some plants.
(vi) What are haparin and histamine?
Ans. The Basophils produce heparin. It is substance that inhibits the clotting of blood. These cells also produce histamine. The histamine participates in the allergic reactions.
(vii) What is haemolymph? Can you call it blood?
Ans. The haemolymph is a colourless fluid flow in the haemocoel of the insects. It lacks RBC or haemoglobin, so it is colourless. Blood the insects. Blood means red colour. But still it may be called blood.
(viii) What is Histoplasmosis? How does its infection spread?
Ans. It is a serious infection of lungs. It is caused by inhaling spores of a fungus. This fungus is common in soil contaminated with bird's feaces.
(ix) Define Cardiac Cycle?
Ans. It is the sequence of events, which take place during the completion of one heartbeat. Heartbeat involves three distinct stages.
(i) Relaxation phase-diastole.
(ii) Atria contract-atrial systole.
(iii) Ventricles contract-ventricular systole.
Biology Part 1 Intermediate - Solved Guess Paper No. 1 Short Questions Reviewed by SaQLaiN HaShMi on 9:20 AM Rating: 5
Biology Part 1 Intermediate - Solved Guess Paper No. 1 MCQS
Total Marks: 17 (Objective Type) Time Allowed: 20 minutes
Q. 1 You have four choices for each objective type question as A, B, C and D. The choice which you think is correct; fill that circle in front of that question number. User marker or pen to fill the circles. Cutting or filling two or more circles will result in zero mark in that questions.
(i) Following structure is not concerned with lipid metabolism:
(A) SER (B) Glyoxisome
(C) Mitochondria (D) None of these
(ii) Nucleoli are not:
(A) Darkly stained (B) Membranous
(C) Variable in number (D) Factory of ribosome
(iii) Total animals, which have been discovered so far are:
(A) 0.5 million (B) 1.5 million
(C) 2.5 million (D) 3.5 million
(iv) Word vaccination was first used by:
(A) Edward Jenner (B) Louis Pasteur
(C) Robert Koch (D) C. Linnacus
(v) Which of the following is not an infectious disease?
(A) Polio (B) Typhoid
(C) Rabies (D) Cancer
(vi) Which is considered as small virus?
(A) Polio virus (B) Retrovirus
(C) Small pox (D) HIV
(vii) Feature not related to lytic cycle:
(A) Adsorption (B) Penetration
(C) Injection (D) Induction
(viii) Polio virus most commonly affects:
(A) Peripheral nerves (B) Spinal cord
(C) Brain (D) None of these
(ix) In small pox, areas which contain pus are called:
(A) Pustules (B) Scars
(C) Pocks (D) None of these
(x) Which of the following disease can develop autoimmunity?
(A) Influenza (B) Hepatitis
(C) Measles (D) Herpes simplex
(xi) Following statement is incorrect about HIV:
(A) Enveloped virus (B) Attached to WBC through receptor
(C) Transcriptase converts RNA into DNA (D) None of these
(xii) Hepatitis is caused by:
(A) Virus (B) Toxic agents
(C) Drugs (D) All of these
(xiii) HAV is:
(A) DNA enveloped (B) DNA non-enveloped
(C) RNA enveloped (D) RNA non-enveloped
(xiv) Type of hepatitis, which causes chronic liver disease is:
(A) Hepatitis A (B) Hepatitis B
(C) Hepatitis C (D) Hepatitis D
(xv) Antibiotics cannot kill:
(A) Streptococcus pneumonia (B) Staphylococcus
(C) Hepatitis virus (D) Tuberculosis bacteria
(xvi) Which one of the following is not related to cloning?
(A) Replacement of the nucleus of zygote, by another nucleus of the same organism
(B) Separation of an embryo to form more embryos
(C) The individual resulting have the similar biological make up
(D) Removal of the piece if DNA or gene from the cell and incorporating another gene or piece of DNA in its place
(xvii) Human beings can't digest cellulose because:
(A) Cellulose is hard to chew
(B) Cellulose can't be absorbed from small intestine after its digestion
(C) Cellulose can't be digested because of its composition
(D) Cellulose can't be digested because we lack enzyme to digest it
(i) (D) (ii) (A) (iii) (C) (iv) (B)
(v) (D) (vi) (A) (vii) (D) (viii) (C)
(ix) (A) (x) (C) (xi) (D) (xii) (D)
(xiii) (D) (xiv) (C) (xv) (C) (xvi) (A)
(xvii) (D)
Biology Part 1 Intermediate - Solved Guess Paper No. 1 MCQS Reviewed by SaQLaiN HaShMi on 9:45 AM Rating: 5

redpajama_set_name: RedPajamaCommonCrawl


text:
#619 2nd floor 80 feet road, Koramangala 6th block near sony world signal Bangalore - 560095
info@doctordreams.in
MD-MS
Nobel Medical College
About Nobel Medical College
Nobel Medical College Teaching Hospital (P) Ltd. an affiliated to Kathmandu University was founded in 2004. It is located in Biratnagar, one of the major academic hubs of eastern part of Nepal. Its key objective is to impart international standard medical education to the meritorious students of Nepal and abroad enrolled for both medical and paramedical courses. Nobel Medical College, recognized by the Nepal Medical Council (NMC), Ministry of Education, Nepal and Ministry of Health, Nepal, has constantly maintained its academic standards as per the requirements of other Medical councils and Universities across the globe. The Institution is equipped with internationally renowned faculties who are professionally committed in the medical field. Their selfless devotion and genuine contribution have always been supportive towards getting recognition of Medical Councils in the world.
Nobel Medical College is listed in the International Medical Education Directory (IMED) and World Directory of Medical Schools (WDOMS).
#619 2nd floor 80 feet road ,koramangala 6th block near sony world signal, Bangalore 560095
Call to +91-9035061122 / 9035061133
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Tution fees INR
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text:
Family Selection of Child-Care Centers
The Influence of Household Support, Ethnicity, and Parental Practices
Bruce Fuller
Susan D. Holloway
Xiaoyan Liang
Accumulating evidence shows that young children benefit developmentally by participating in quality childcare centers and preschools. But we know little about which family characteristics and home practices influence parents' selection of a center-based program. This article reports on the influence of the family's social-structural attributes, ethnicity, and parental practices on the likelihood of selecting a center-based program, after taking into account economic characteristics. The odds that parents enroll their child in a center-based program are greatest when mothers are more highly educated, when the child is older, and when less plentiful (nonpaternal) social support is available to the mother, such as from a resident grandparent. Ethnic differences in the propensity to select centers were found, even after family economic and structural variables were taken into account: African-American families were more likely than white or Latino families to use center-based care. Parental practices linked to the child's early literacy development and close supervision were related to the likelihood of center selection. Selection processes must be more carefully taken into account as researchers attempt to isolate the discrete effects of children's participation in centers and preschools.
This article was originally printed in Child Development by Wiley-Blackwell
Suggested citationFuller, B., Holloway, S. D., & Liang, X. (1996, December). Family selection of child-care centers: The influence of household support, ethnicity, and parental practices [Article]. Policy Analysis for California Education. https://edpolicyinca.org/publications/family-selection-child-care-centers


text:
NV77/Shutterstock
CO₂ shortage: why a chemical problem could mean more empty shelves
Published: September 20, 2021 12.04pm EDT
Mark Lorch, University of Hull
Mark Lorch
Professor of Science Communication and Chemistry, University of Hull
Mark Lorch does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.
University of Hull provides funding as a member of The Conversation UK.
As far as the environment goes, carbon dioxide is probably public enemy number one. This makes it all the more ironic that the UK is currently suffering from a shortage of the gas, which experts warn will affect a variety of industries, most notably food and drink.
In the right setting, CO₂ is an extremely useful gas. When added to beverages it gives them their fizz. Trap it in high pressure bubbles in sweets and you get popping candy. Compress it in a cylinder and you have a fire extinguisher. Freeze it and you produce dry ice which is used to keep medical materials (including COVID vaccines) chilled during transport.
The microbial organisms that cause food to perish need oxygen to survive, so packaging salad leaves with CO₂, not oxygen, keeps them fresh. Meanwhile, in the meat industry, high concentrations of the gas are used to replace oxygen in the air animals breathe, rendering them unconscious before they are slaughtered.
Given our need for CO₂ in one area, and the excess of it in another, the obvious question is: why don't we simply pull carbon dioxide out of the air? The simple answer is that, despite its detrimental impact, there's relatively little carbon dioxide in the air. Though we have 50% more of it in our air than before the industrial revolution, CO₂ still only makes up 0.04% of air content.
This makes CO₂ extremely difficult to "find" and then remove from the air. There's plenty of work going on to capture the gas from the air, with a view to countering CO₂ emissions, but at the moment this isn't a viable source of the gas for industry.
Instead, the main source of CO₂ for industrial uses is from the production of nitrogen-based fertilisers, which produces CO₂ as a byproduct. And with fertiliser production on hold in the UK due to the skyrocketing price of gas, which is used heavily in fertiliser plants, the knock-on effect is a shortage in CO₂. So to explain the current CO₂ shortage, we really need to look at how nitrogen-based fertilisers are made.
Read more: Gas price spike: how UK government failures made a global crisis worse
Capturing nitrogen
Nitrogen plays a critical role in the biochemistry of every living thing. It is also the most common gas in our atmosphere. But nitrogen gas is largely inert, which means plants and animals can't extract it from the air. Consequently, a major limiting factor in agriculture has always been the availability of nitrogen.
In 1910, the German chemists Fritz Haber and Carl Bosch changed all this when they combined nitrogen and hydrogen into ammonia. This in turn can be used as a crop fertiliser, eventually filtering up the food chain to us.
Today, about 80% of the nitrogen in our bodies comes from the Haber-Bosch process, making this single chemical reaction probably the most important factor in the population explosion of the past 100 years.
Carl Bosch and Fritz Haber, the fathers of modern fertilisers. Mikel Agirregabiria/flickr, CC BY-NC-SA
About 78% of our atmosphere is nitrogen, so finding this ingredient for the Haber-Bosch process is easy. But the other component, hydrogen gas, is not so readily available. There's plenty of hydrogen about, most obviously as the H in H₂O and CH₄ (methane), but breaking the bonds between the hydrogen and oxygen in water or carbon in methane requires a huge amount of energy.
The main way it's currently produced is by a process known as methane steam reforming. This works by starting with natural gas – which is becoming far more expensive in the UK – and then heating it to about 1,000℃ in the presence of water. The end products are hydrogen gas (H₂) and CO₂.
These are separated for their respective uses. Unfortunately, the amount of CO₂ produced by the fertiliser industry far exceeds the quantity needed by other industries. So most fertiliser plants don't bother capturing it.
The fossil fuels used in fertiliser production and the CO₂ it creates as a byproduct makes it particularly unfriendly to the environment. Hence a big part of the decarbonisation agenda is to produce hydrogen cleanly for use in fertilisers and fuel. One of the simplest ways to achieve this is via the electrolysis of water, using clean sources of electricity.
Meanwhile, as carbon capture technologies develop, we may see carbon dioxide extracted directly from the air for use in industrial processes. But that's a long-term solution, and so isn't going to help any time soon.
But there are alternatives to CO₂ that might help in a pinch. The most obvious is nitrogen gas, which can be used in the same way as CO₂ to preserve food or stun animals. Likewise, because nothing burns in nitrogen, it can be used to suppress fires – just like CO₂ fire extinguishers.
The UK government has been holding crisis talks with the US owner of two of the UK's largest nitrogen fertiliser plants, both currently inactive. Perhaps persuasion will see them fire back to life. But the CO₂ shortage has nonetheless exposed the complex chemical supply chains upon which we rely for our fizzy drinks and packaged salads.
CO2 shortage
Nitrogen fertiliser


"The volunteers from Safe Passage UK looked for me at the youth centre and found me. They asked if we had family in the UK and if I would be happy to go and live with them. They spoke to my Aunty but then it took a very, long time for me to come here, about 4 months, and then I left for England on the train.
When I saw my Aunty and Uncle at the station, I felt that was the best time ever. I felt very safe and very, very happy. Now I live in Manchester in my Aunty's house and I have my own bedroom and I am at school. I was a bit nervous but it's very good and interesting and it's nice to meet new friends.
To help change lives and provide protection to people like Jabir, donate here.
Sixteen-year-old Tarek travelled from Syria to Calais alone to join his friend and find his Uncle in the UK, leaving his mother and unborn sister behind in Syria. He spent six long months in the camp waiting for a chance to get his passage to safety.


text:
Centrolene litorale är en groddjursart som beskrevs av Pedro M. Ruiz-Carranza och Lynch 1996. Centrolene litorale ingår i släktet Centrolene och familjen glasgrodor. Inga underarter finns listade i Catalogue of Life.

Källor

Externa länkar

Glasgrodor
litorale

redpajama_set_name: RedPajamaWikipedia


text:
Blunting Neoliberalism: Tripartism and Economic Reforms in by L. Fraile
By L. Fraile
This quantity is likely one of the first books to think about the influence of tripartism around the constructing international. It covers eight case experiences from Africa, Asia, jap Europe and Latin the USA, targeting advancements because the Nineties. those experiences convey that tripartism has the impact of decreasing the social impression of neoliberal economics reforms.
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Additional info for Blunting Neoliberalism: Tripartism and Economic Reforms in the Developing World
Example text
In South Africa, there was tripartite involvement in preparing the country's offer to the WTO in 1993, including agreement on a tariff-reduction timetable, and in preparing subsequent negotiations of bilateral trade agreements. NEDLAC's Industry and Trade Chamber has regularly discussed industrial policies and negotiated a new Competition Policy Act in 1998. Tripartism appears to be associated with a cautious, gradual approach to privatization. Slovenia, Singapore, South Africa and Uruguay, all cases of relatively strong tripartism, conform to this pattern and have retained a significant state presence in the economy.
There had been some failed Lydia Fraile and Lucio Baccaro 23 attempts at policy concertation before, including consultations over labour legislation reform in 1996. In response to the crisis and the need for an IMF rescue package, the government created a new institution, the Tripartite Commission, which negotiated a comprehensive social pact in 1998. The pact was tied to a tough structural adjustment package and involved numerous agreements on a wide range of policies, including labour legislation, employment policy, social protection, wage policy and price controls, corporate governance, and bank and public sector restructuring.
Pizzorno (eds), The Resurgence of Class Conflict in Western Europe since 1968, London: Macmillan. , 1958, The Great Transformation, Boston: Beacon Press. , 2005, Inequality and Prosperity: Social Europe vs. Liberal America, Ithaca, NY: Cornell University Press. , 1997, 'Still Engaging in Corporatism? Recent Italian Experience in Comparative Perspective', European Journal of Industrial Relations, vol. 3, no. 3, 259–78. ', in M. Rhodes and Y. Mény (eds), The Future of European Welfare: A New Social Contract?
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text:
Walesa to Trump: US no longer moral, political world leader
By AFP Aug 29, 2019 in World
Poland's freedom icon Lech Walesa on Thursday said the United States was "no longer the main global power" in political and moral leadership ahead of a visit by President Donald Trump.
Trump is due in Poland on Sunday for ceremonies marking 80 years since the outbreak of World War II.
"President Trump, I urge you to regain the position of world leader for the USA," Walesa said in an interview published in Thursday's edition of Poland's centrist Rzeczpospolita daily.
"The world needs the leadership of the USA. Moral and political leadership, not only economic and military leadership," added Walesa, a Nobel Peace laureate.
Walesa led the Solidarity labour movement that brought a peaceful end to communism in Poland in 1989 and became its first post-war democratically elected president in 1990.
Working as a shipyard electrician in the Baltic port city of Gdansk, he stunned the communist bloc and the world when he led a 1980 strike by 17,000 shipyard workers.
The communist regime was forced to grudgingly recognise Solidarity as the Soviet bloc's first and only independent trade union after it gained millions of followers across Poland in the wake of the Gdansk strike.
"I have a message for President Trump: The United States was for years a good empire that led the world. Today the USA is no longer the main global power," Walesa told Rzeczpospolita.
"It still has military advantage, economically you are still ahead of others, but morally and politically the USA is no longer the world leader," he added.
Shunned by Poland's controversial right-wing government, Walesa said he would not be taking part in Sunday ceremonies in Warsaw marking the WWII anniversary.
Aside from Trump, few other major leaders are expected in the Polish capital, as French President Emmanuel Macron and German Chancellor Angela Merkel are not coming, while Russian President Vladimir Putin was not invited.
According to the Polish presidency, around 40 foreign delegations are expected, half of them led by heads of state.
More about Poland, US, Politics, Trump, Walesa
Poland US Politics Trump Walesa


"Good stuff -- sorta like Yanni backed up by Pop/Rock musicians"
"Beautiful Melodies and Cinematic Landscapes ... painted by Synthesizers"
Antherius is a composer, multi-instrumentalist, and producer of "Instrumental Pop/Rock" and "Progressive New Age" music. His synth-based instrumentation includes acoustic and electric guitars, brass and string sections, celestes, a cathedral-resident leslie organ, drum sets, orchestral and ethnic percussions, along with complex ambient textures.
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Q: CodeIgniter: login password match I'm curious about a good way to do login with CodeIgniter.
I am currently trying the following:
- Take a user's email and password from the login form
- Encrypt that password, and compare it to the one in the DB.
However it returns false. I believe it is because the encryption method creates a new encrypted password every time.
I believe this is a good thing, but the only other way I can see to do a login is as follows:

*

*When the user submits the form to login, the form is validated

*The user in the DB with a matching username (or email address) is pulled and stored in a variable.

*The password that was pulled out is then decrypted and compared with the user trying to login

I am uncomfortable with this because it requires me to store an unencrypted password in a variable, potentially requiring a good hacker to only know a user's email address.
Suggestions?

A: When user register you can store password & it's salt by using php crypt i.e. crypt($password, $salt) where $password is user entered password & $salt is random string.
Now, At the time of login

*

*When the user submits the form to login, the form is validated

*The user in the DB with a matching username (or email address) is pulled.

*The password that was pulled out is take into $hashed_password & user entered into the $password then compare
if (crypt($password, $hashed_password) == $hashed_password)
{
//successful login
}else{
//Invalid username/password
}

A: You chould also use the form_validation rules using
$this -> form_validation -> set_rules('passconf', 'Re-enter', 'required|matches[password]');
#the rules set as the 3rd parameter of the set_rules function have matches


This page displays sold house prices for Cavendish Road in Bradford.
Cavendish Road in Idle, Bradford consists predominantly of terraced houses. Properties on Cavendish Road typically have values around £100,000 - £150,000, with larger terraced houses and townhouses valued at around £150,000.
Map showing Cavendish Road in Bradford.