Microsoft has been plugging away at the mobile computing market for almost as long as Windows has been around. Thinking of products like Windows for Pen Computing, or the original Windows CE for handheld devices. At best, the consumers were willing but the platforms were weak.
In Microsoft's case, the problem with those early devices was a stubborn devotion to the look and feel of desktop Windows. Their vision seemed to be that the Windows GUI deserved to be moved to every device, because users understood how it worked. But of course, a desktop interface isn't optimal for a mobile device with a tiny screen and lilliputian keyboard (if any). Tiny hardware platforms deserve software that's optimally designed to work with them.
Pioneering mobile devices like the original PalmPilot and the BlackBerry weren't shackled to a notion of a handheld interface that looked like a desktop, and they did very well. Then came the iPhone, a product from another maker of desktop operating systems. Apple didn't feel obligated to mimic its desktop software design on the iPhone the way Microsoft did, and users seemed to like the result.
Now, Microsoft's share of the mobile computing market is slipping away. Windows Mobile 6 looks pretty feeble next to the iPhone, which is why Windows Mobile 7 has been so greatly anticipated by Microsoft's hardware partners. News is that there has been another delay in Windows Mobile 7, and we're not likely to see it ship until late 2010.
The mobile market isn't going to wait for Microsoft in 2010; far from it. Google's Android platform is starting to make serious inroads into the market with hardware like the Motorola Droid; if the Google Phone rumors are to be believed there may be some big news in early 2010. And who knows what Apple has in store for the iPhone in 2010. In the meantime, the mobile device makers who've stuck with Microsoft and Windows Mobile are going to be tempted to jump ship, rather than wait a year or longer.
At its annual developer conference in Los Angeles on Monday, Adobe secured Flash's future, at least for the near term.
But just because those applications were created as Flash applications does not mean they will be allowed to run as Flash applications.
Flash Professional CS5, to be released as a public beta later this year, will allow developers to create Flash applications using the Flash development platform and then export those Flash apps as native iPhone applications.
That means certain Flash capabilities, such as being able to load another another Flash (.SWF) file or to browse Web content from within exported Flash apps, will not be available. Developers using Apple's tools, however, can browse Web content from within their own apps via the SDK's UIWebKit component.
Adobe's announcement does not change the fact that Flash content on the Web is inaccessible through the iPhone's Safari browser. Flash content on the Web requires Adobe's Flash Player browser plug-in, which relies on a just-in-time compiler and virtual machine to render Flash content. Apple does not allow interpreted code on the iPhone.
James Anthony, co-founder of iPhone game maker Inedible Software, said in an e-mail that since his company has been developing native iPhone applications, its development process won't change at all.
A sudden influx of Flash app conversions may not be entirely welcome, however. iPhone developers have been complaining about how difficult it has become to be noticed among the exploding inventory of Apple's iTunes App Store and more games means more competition.
Apple recently announced that over 85,000 applications are available for the iPhone and that number is likely to pass 100,000 before the end of the year.
Adobe also announced that Google and RIM have joined its Open Screen Project, an initiative make Flash and Adobe AIR available as a consistent runtime environment across a wide variety of devices and platforms. The company said that Flash 10.1 would be available on Google Android, Blackberry, Symbian, Palm webOS and Windows Mobile devices toward the end of the year.
However, company insiders are now striking a more conciliatory tone and acknowledging that Flash may be a better tool for certain jobs than Web technologies and that a lot of developers want to use Flash.
Although Adobe appears to have dispelled many doubts about Flash's future at a time when so many are moving toward open Web technologies, the continued absence of the Flash player on the iPhone will become all the more glaring if Apple, as expected, releases an iTunes-dependent tablet device next year. An Apple tablet could be a showcase device for rich media content, and Adobe will want to make certain that its Flash technology plays a staring role.


text:
WHEN KEEPING IT REAL GOES WRONG: Joe Budden Made a Joke About Being Bi-Sexual to Avoid Getting Cancelled… And Now the Internet is Running With It (WATCH)
Joe Budden was once accused of giving his dog hand jobs and kissing it in the mouth, so we've known that he was pretty open sexually.. but is the internet taking a joke he made during his podcast a little too seriously?
You've probably seen a ton of headlines quickly sweeping social media, claiming that Joe Budden has officially come out as bisexual on his podcast after claiming that he is sexually attracted to both men and women…. however, if you watched more than that 20 second clip that's making the rounds, then you know that this may have actually been taken way out of context.
"I'm bisexual," he said on his show on Thursday. "How do I spread this news? How do I spread the word? Yo, listen, I like guys and girls. Spread the word. I'm down."
The shocking statement had hip-hop fans reacting all over social media, sharing their thoughts on Budden's alleged coming out. However, this is yet another example of why you can't trust everyone's headlines because if you listen to the full podcast convo in full, you'll get that Joe was being sarcastic while discussing the LGBTQ organization that recently deemed rapper DaBaby as "forgiven."
During the episode Joe and his co-hosts questioned how this organization felt that they spoke on behalf of the entire gay community which prompted Joe to joke "who can I make a phone call to? How do I share this news?" basically saying that he'd be "down" to say he's apart of the community in effort to avoid ever having to be "cancelled."
The internet is currently still running rampant with the cut down 20 second clip but you can view that along with the full podcast below (the conversation starts at the 52 second park) for full context.
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November 4, 2021 / Updated November 4, 2021

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Donovan Mitchell historic night
This topic contains 6 replies, has 5 voices, and was last updated by OhCanada- 3 weeks, 3 days ago.
Posted on: Mon, 01/02/2023 - 7:44pm #1258312
Hitster
Donovan Mitchell becoming only the 4th player in the last 60 years to hit over 70 points in an NBA game is a truly historic event. The biggest single game point haul since the late great Kobe's 81 points vs the Raptors nearly 17 years ago. It was almost the perfect storm with Donovan playing 50 mins for his 71 point haul vs the Bulls and the game going into OT..
We've had some big personal hauls recently with Luka hitting 60 and Klay went for 54 last night too. LBJ is still rattling off big numbers and Embeast is near the top of the scoring charts. Donovan was around the top 10 in the scoring list but hadn't been on a hot streak in recent games until last night so if you thought something like this was going o happen he wouldn't have been an obvious candidate to do it.
But a bit like Kobe's masterpiece his team faced a big defecit and Donovan went on a scoring blitz in the 2nd half getting 42 points as he hauled his team back into the game and then had OT to achieve the 70 point barrier. It was as I say the perfect storm as he went on a hot streak and his team mates just gave him the ball.
But he did the feat without an insane 3 point line return. 7 from 15 is hugely impressive but into today's game you might figure it would need someone to hit 10 or more 3's to get the sort of huge return Donovan got.
As I said the conditions were right with a couple of team mates out and playing nsane minutes to chase a game but when you look at the all time greats most of them never went for 70 in a game something that Donovan achieved last night.
Zouldiers
Favorite part about this performance is that they won and he also had 11 rebounds and 8 assists. His 71 points actually mattered.
Posted on: Mon, 01/02/2023 - 10:34pm #1258315
NorrinRadd
That's crazy, first Luka's 60 point triple double and now Mitchell.
OhCanada-
Alot of people will try to discredit these performances and say "the games different" "rules don't allow defending" "pace is much faster today" but in reality all you have to do is watch what these guys are doing. I mean really look at how quickly Mitchell can just change directions while doing multiple crossovers and he doesn't slow down one bit, hes completely under control and balanced at all times not a single thing fundamentally incorrect about what he's doing even on his misses. Its absolutely phenomenal.
Still kinda salty Toronto didn't put together a package to put him next to Siakam and Barnes. And then he ends up in Cleveland next to Garland and Mobley…an even better fit. The one saving grace here is hes struggled against Toronto this year…but the Cavs and Raps are clearly on two different trajectories and its pretty clear Mitchell is a huge difference there.
Posted on: Tue, 01/03/2023 - 1:22am #1258325
Well the game may have changed but Donovan has achieved something and surpassed Devin Booker's 70 point losing effort going back nearly 6 years but that was a losing effort and him possibly chasing the figure. If we get a glut of guys doing this then there may be some logic in the feat has become easier.
I was always surprised none of the record scoring games had gone to OT and this did happen with Mitchell but you can only play the minutes available so I'd not say it lessens his achievement.
60 points has only been achieved by 34 players and 82 times of which Wilt did 34 of them. It has been done 15 times over the last 5 seasons so you could say there have been more instances recently than since Wilt's domination. But a lot depends on game situation as often a player having a dominant game has won it for his team and is sat in the 4th quarter as Kobe was when he'd gone past 60 in one game before the 81 pointer.
We may see more 60 point games going forward but the 70 point figure is still a real landmark and the first for nearly 6 years and only 3rd this century and 5th in nearly 60 years is truly historic.
As a Suns fan I'd forgotten Devin had reached 70 too which was quite embarrassing when I posted initial thread post and David Thompson achieving the feat is a favourite NBA quiz question of mine as he's not a likely initial suggestion unless you know the list. David was a fine player but a more casual fan wouldn't immediately think of him.
Posted on: Thu, 01/05/2023 - 6:25pm #1258354
Gronounours
I feel that more than a sport, basketball (especially the NBA) has become a big show based on individual performance and statistics, where the goal is to generate as much ad revenue and subscriptions as possible.
To me, games are unwatchable. The flow is constantly interrupted by fouls, breaks, and time-outs, which is fantastic for advertisers, but terrible for viewers. Everything is done to boost scoring, so much so that stopping star players is all but impossible. Showtime baby! On the other hand, some teams are built to lose, as the NBA rewards mediocrity, which completely destroys what should be the basis of any sport: the will to win.
Everything is about stats and breaking individual records, as games themselves are too boring. Even when no records have been beaten, stat experts come up with "near-records". How many times do we now read things like "X is only the 3rd under-25 player to register at least 32 points, 13 rebounds, 7 assists, and 5 steals in an away Christmas game over the last 12 seasons"? Every night, new "near-records" are being broken. Who won? Who even cares before the play-offs?
NBA fans gorge on low nutrient, high sugar games; they watch junk sport while eating junk food. I'll take a good 1-0 soccer game over a 71-point performance, any day.
Posted on: Fri, 01/06/2023 - 9:23am #1258357
The players are too rich. Your watching a bunch of pampered millionaires compete and the grit is gone. From a very young age these guys are exposed to a very luxurious lifestyle which can soften most people. The league is soft as hell however the skill level is through the roof due to training methods improving not due to rule changes.
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text:
\section{Introduction}\label{sec:intro}
Lattice Boltzmann Method(LBM) has emerged as an effective approach of Computational Fluid Dynamics(CFD) during the last decades, and it has attracted numerous interests in simulating complex flows. The success of LBM is mainly contributed by several unique advantages. First, the solution of advection in LBM is exact which reduce the numerical diffusion errors in conventional CFD methods~\cite{van2006galilean}. Second, the locality of collision operator guarantees a high parallelization efficiency of LBM codes. Furthermore, microscopic interactions can be better represented in LBM due to the kinetic nature. However, how to impose correct boundary conditions on the fluid-solid interface (FSI) with complex geometries is still an open question. The most common assumption for FSI is non-slip boundary condition in which the fluid velocities at FSI are equal to solid surface velocities. There are mainly three categories of technologies in LBM to achieve non-slip boundary: Kinetic Boundary Conditions (KBC),  partially saturated cells method (PSM) and Immersed Boundary Method (IBM).

The simplest KBC is the bounce-back scheme: fluid molecules which contact with the solid surface are reflected back to the fluid domain with opposite velocity. It has been proven that the bounce-back scheme holds the second-order accuracy of LBM in space. However, the bounce-back scheme can only be applied when FSI lies exactly at the nodes or middle of two neighbouring nodes (half-way bounce-back). Otherwise, the real FSI is replaced by an approximated stairwise boundaries which may damage the accuracy of LBM. The idea of using interpolation on distribution functions to reduce geometrical errors is firstly introduced by Bouzidi et al~\cite{bouzidi2001momentum}. This interpolated bounce-back scheme is improved by Yu et al~\cite{yu2003viscous} in which the treatments on distributions are unified regardless of the position of FSI. Filippova~\cite{filippova1998grid} proposed other interpolation scheme and further modified by Mei et al.~\cite{mei1999accurate} to improve the numerical stability. It is found that the relative errors of mentioned interpolation schemes depend on viscosity~\cite{peng2016implementation}, Ginzburg~\cite{ginzburg2003multireflection} developed a multireflection boundary condition which is viscosity-independent. Information at three neighbouring nodes is needed in the multireflection boundary condition. However, there may not always have enough information to implement interpolations in practice, thus Tao et al.~\cite{tao2018one} introduce an one-point second-order curved boundary condition recently. Guo et al.~\cite{guo2002extrapolation} reconstituted the distributions at closest solid nodes by equilibrium and non-equilibrium part, the velocity, density and non-equilibrium are extrapolated from the fluid domain, also known as non-equilibrium extrapolation scheme. All KBCs share some common characters like sharp interfaces, no fluid inside of solids, direct modification on distributions.

The original PSM proposed by Noble et al.~\cite{noble1998lattice,cook2004direct} is designed for particulate flows. The basic idea is mixing the effects of fluid and bounce-back on FSI by volume average. The weighting strategy depends on solid volume fraction where $0$ means fully Saturated and $1$ means fully bounce-back. The biggest advantage of PSM is the smooth transition between fluid and solid nodes, and no refilling algorithms are needed for moving boundaries which is very common for KBCs. Also, the locality and flexibility of PSM are highly desirable for complex flows. For instance, PSM is coupled with Discrete Element Method (DEM)~\cite{feng2007coupled} for dense particulate flows and also for general shaped particles~\cite{galindo2013coupled,galindo2015micro} by using the sphero-polyhedron technique~\cite{galindo2012breaking,galindo2009molecular,galindo2010molecular,galindo2013strength}. Recently, PSM is modified by Zhang et al.~\cite{zhang2017efficient} with Multi-Relaxation model and an efficient particle contact detection strategy.

IBM proposed by Peskin~\cite{peskin2002immersed} also attracted lots of attention due to its flexibility and robustness. Fluid feels solid boundaries by an external force field. Feng et al.~\cite{feng2004immersed} combined IBM with LBM firstly, the penalty method is employed to link flows and particle motions. The IBM is enhanced by Luo et al.~\cite{luo2007modified} where velocity distributions at the boundary layer are introduced to improve the accuracy near particle surfaces. The idea of momentum exchange is also combined with IBM to avoid user-defined parameters in penalty methods~\cite{niu2006momentum}. Wu et al.~\cite{wu2009implicit} notice that the non-slip condition is not exactly satisfied in explicit IBMs, thus an implicit velocity correction based IBM is proposed. Most of IBMs have a diffuse interface due to the smoothed external force field, the sharp interface can also be achieved in IBM as shown in~\cite{kang2011comparative}.

As mentioned, the sharp interface can only be found in KBCs and servral IBMs, thus KBCs are surposed to be more accurate. Here we presented an improved version of KBC where the ideas of interpolated bounce-back schemes and non-equilibrium extrapolation scheme are combined, the proposed scheme shows better accuracy at high Reynolds number and less dependency on solids positions which may crucial in many appilcations.

The structure of the paper is organized as follows: Sec.~\ref{sec:lbm} describes the basics of LBM. Sec.~\ref{sec:bc} explains the ideas and approximations of proposed scheme. And validations are presented in Sec.~\ref{sec:benchmark} with several well-defined benchmark cases. Finally Sec.~\ref{sec:conclusion} presents conclusions from the present work.

\section{Lattice Boltzmann method for fluid}\label{sec:lbm}
Flows are solved by the Lattice Boltzmann Method~\cite{galindo2012numerical,galindo2013lattice} with the D2Q9 model where spaces are divided into square lattices and the velocity domain is discretized into 9 discrete velocity vectors as follows:

\begin{equation*}
\resizebox{0.5\hsize}{!}
{$\overrightarrow{e}_i = \left\{
  \begin{array}{l l l}
    0, & \quad \text{$i$ = 0,}\\[0.5ex]
    (\pm1,0,),(0,\pm1), & \quad \text{$i$ = 1 to 4,}\\[0.5ex]
    (\pm1,\pm1), & \quad \text{$i$ = 5 to 8,}\\
  \end{array} \right.$}
\end{equation*}

Based on the Chapman-Enskog expansion of the Boltzmann equation, an evolution rule is applied to every distribution function~\cite{mohamad2011lattice}:
\begin{equation}
f_i(\overrightarrow{x}+\overrightarrow{e}_i\delta{t},t+\delta{t}) = f_i(\overrightarrow{x},t) + \Omega_{col},
\end{equation}
where $f_i$ is the probability distribution function, $\overrightarrow{x}$ is the position of the local lattice, $\delta{t}$ is the time step and $\Omega_{col}$ is the collision operator. The most widely used form of $\Omega_{col}$ is the so-called Bhatnagar-Gross-Krook (BGK) collision operator: $\Omega_{col} = \frac{\delta{t}}{\tau}(f^{eq}_{i}-f_i)$, with $f^{eq}_{i}$ the equilibrium distribution given by,
\begin{equation}
f^{eq}_{i} = \omega_i\rho \bigg(1 + 3\frac{\overrightarrow{e}_i \cdot \overrightarrow{u}}{C^2} + \frac{9(\overrightarrow{e}_i \cdot \overrightarrow{u})^2}{2C^4} - \frac{3u^2}{2C^2}\bigg),
\label{eq:feq}
\end{equation}
where $C=\delta{x}/\delta{t}$ is the characteristic lattice velocity ($\delta{x}$ is the lattice size), here we choose $C=\delta{x}=\delta{t}=1$. The weights are $\omega_0=4/9$, $\omega_i=1/9$ for $i=$1 to 4, and $\omega_i=1/36$ for $i=$5 to 8.

The BGK collision operator assumes that the collision only depends on a dimensionless relaxation time $\tau$, where $\tau=3\nu+0.5$. However, It's found that the simulations become unstable when the value of $\tau$ is close to 0.5~\cite{galindo2013coupled}. Therefore, the BGK collision operator is only suitable for flow at relatively low Reynolds numbers. To overcome this limitation, the multiple relaxation time (MRT) collision operator is adopted in this study as follows:

\begin{equation}
\Omega_{col} = \mathbf{\hat{M}^{-1}\hat{S}}(m^{eq}_{i}-m_i),
\label{eq:mrt}
\end{equation}
with $m_i=\mathbf{\hat{M}}f_i$, where $\mathbf{\hat{M}}$ is a matrix used to transform the probability distribution function $f_i$ to velocity moments linearly. For the D2Q9 model, the moments are arranged as: $m_0=\rho$; $m_1=e$; $m_2=\epsilon$; $m_{3,5}=j_{x,y}$ are components of the momentum $\overrightarrow{j}=(j_x,j_y)=\rho \overrightarrow{u}$; $m_{4,6}=q_{x,y}$ are related to components of the heat flux $\overrightarrow{q}=(q_x,q_y)$; $m_7=p_{xx}$; and $m_8=p_{xy}$ are related to the components of the strain-rate tensor.  The equilibrium moments are the functions of conserved moments (density $\rho$ and moment density $\overrightarrow{j}$) and the non-conserved moments are given by~\cite{lallemand2000theory},
\begin{equation}
\begin{array}{cc}
m^{eq}_1=e^{eq}=\rho(-2+3\overrightarrow{j}\cdot\overrightarrow{j}), & m^{eq}_2=\epsilon^{eq}=\rho(1-3\overrightarrow{j}\cdot\overrightarrow{j}), \\[2ex]
m^{eq}_4=q_x^{eq}=-j_x, & m^{eq}_6=q_y^{eq}=-j_y, \\[2ex]
m^{eq}_7=p_{xx}^{eq}=\frac{{j_x}^2-{j_y}^2}{\rho}, & m^{eq}_8=p_{xy}^{eq}=\frac{j_x j_y}{\rho},
\end{array}
\end{equation}
the transformation matrix is defined as:
\begin{equation}
\mathbf{\hat{M}} = \begin{bmatrix}
       \phantom{-}1 & \phantom{-}1 & \phantom{-}1 & \phantom{-}1 & \phantom{-}1 & \phantom{-}1 & \phantom{-}1 & \phantom{-}1 & \phantom{-}1          \\[0.3em]
       -4&-1 &-1 &-1 &-1 & \phantom{-}2 & \phantom{-}2 & \phantom{-}2 & \phantom{-}2          \\[0.3em]
       \phantom{-}4 &-2 &-2 &-2 &-2 & \phantom{-}1 & \phantom{-}1 & \phantom{-}1 & \phantom{-}1          \\[0.3em]
       \phantom{-}0 & \phantom{-}1 & \phantom{-}0 &-1 & \phantom{-}0 & \phantom{-}1 &-1 &-1 & \phantom{-}1          \\[0.3em]
       \phantom{-}0 &-2 & 0 & \phantom{-}2 & \phantom{-}0 & \phantom{-}1 &-1 &-1 & \phantom{-}1          \\[0.3em]
       \phantom{-}0 & \phantom{-}0 & \phantom{-}1 & \phantom{-}0 &-1 & \phantom{-}1 & \phantom{-}1 &-1 & \phantom{-}1          \\[0.3em]
       \phantom{-}0 & \phantom{-}0 &-2 & \phantom{-}0 & \phantom{-}2 & \phantom{-}1 & \phantom{-}1 &-1 &-1          \\[0.3em]
       \phantom{-}0 & \phantom{-}1 &-1 & \phantom{-}1 &-1 & \phantom{-}0 & \phantom{-}0 & \phantom{-}0 & \phantom{-}0          \\[0.3em]
       \phantom{-}0 & \phantom{-}0 & \phantom{-}0 & \phantom{-}0 & \phantom{-}0 & \phantom{-}1 &-1 & \phantom{-}1 &-1
     \end{bmatrix}
     \label{eq:M}
\end{equation}

In Eq.~\ref{eq:mrt}, $\mathbf{\hat{S}}$ is the diagonal relaxation matrix in velocity moments. The kinetic viscosity is related to $\mathbf{\hat{S}}$, the diagonal elements of $\mathbf{\hat{S}}$ is given as:
\begin{equation*}
\resizebox{0.45\hsize}{!}
{$s_{i,i} = \left\{
  \begin{array}{l l l}
    0.3, & \quad \text{$i$ = 0,3,5}\\[0.5ex]
    1.5, & \quad \text{$i$ = 1,2}\\[0.5ex]
    1.2, & \quad \text{$i$ = 4,6}\\[0.5ex]
    \frac{1}{3\nu+0.5}, & \quad \text{$i$ = 7,8}\\
  \end{array} \right.$}
\end{equation*}

Here the Mach number is defined as the ratio of the maximum velocity to $C$. When $Ma\ll1$, the LBE can be used to recover the Navier-Stokes equation. More detail can be found in~\cite{mohamad2011lattice}. The macroscopic fluid properties such as density $\rho$ and flow velocity $\overrightarrow{u}$ can be determined by the zero-th and the first order moment of the distribution function:
\begin{equation}
\begin{array}{ll}
\rho(\overrightarrow{x}) &= \sum_{i=0}^{8} f_i(\overrightarrow{x}),\\[2ex]
\overrightarrow{u}(\overrightarrow{x}) &= \frac{1}{\rho(\overrightarrow{x})} \sum_{i=0}^{8} f_i(\overrightarrow{x})\overrightarrow{e}_i ,
\end{array}
\end{equation}

\section{fluid-solid interface boundary conditions}\label{sec:bc}
\begin{figure}[t]
\begin{centering}
\includegraphics[width=0.8\linewidth]{ibb}
\caption{Schematic of the bounce back role at FSI, where ``s" for the closest solid node, ``w" for wall, ``f" for the boundary node, ``ff" for the neighbouring fluid node of ``f", ``d" for the depart position where molecules arrive to ``f" at next time step.}
\label{fig:ibb}
\end{centering}
\end{figure}
The no-penetration non-slip boundary condition needs to be imposed on the fluid-solid interface properly. There are mainly two categories of boundary schemes can satisfy the requirements. Firstly, macroscopic boundary conditions where macroscopic properties are modified, such as velocity corrected immersed boundary method in which the effects of boundaries are replaced by a smoothed external force field for fluid. In the second category, the distribution functions are used directly to impose boundary conditions. Here we consider the later one since it can maintain a sharp interface and fit the kinetic nature of LBM.

The computational nodes are divided into fluid nodes and solid nodes, the fluid nodes which are close to the solid boundary are further identified as boundary nodes (Fig.~\ref{fig:ibb}). Since the uniform-sized mesh is used in classic LBM, the curved boundaries generally locate between boundary nodes and solid nodes. Thus the distribution functions at boundary nodes which streamed from solid nodes are missing, the key task is to determine missing distribution functions properly.

The simplest solution is the bounce-back role where molecules depart from $f$ with velocity $\bm{e}_{i'}$ hit on wall and return back to node $f$ with opposite discrete velocity ($\bm{e}_{i}$). It is clear that the wall is assumed to be located at the middle point between point $s$ and $f$ regardless of the actual position. This assumption leads to stairwise boundaries which damage the second order accuracy of LBM. Therefore, Bouzidi et al~\cite{bouzidi2001momentum} proposed an interpolated bounce-back scheme to reduce geometrical errors. As shown in Fig.~\ref{fig:ibb}, molecules depart from $d$ with velocity $\bm{e}_{i'}$ will end up to node $f$ after bounce-back on the wall, the position of $d$ depends on $q=\abs{\bm{x}_f-\bm{x}_w}/\abs{\bm{x}_f-\bm{x}_s}$. For $q \leqslant 0.5$, the distribution function after collision $f^{+}_{i'}(\bm{x}_d,t)$ can be linearly interpolated using the information at node $f$ and $ff$. For $q>0.5$, $d$ lies between $f$ and $w$ where no information of distributions are known. Also, the exploration can be used but it's unfavourable due to numerical stability issues and unbounded errors. After steaming, molecules depart from $f$ with velocity $\bm{e}_{i'}$ will end up to $d$, thus $f_{i}(\bm{x}_f,t+\delta{t})$ can be determined based on $f_{i}(\bm{x}_d,t+\delta{t})$ and $f_{i}(\bm{x}_ff,t+\delta{t})$. Bouzidi's scheme can be summarized as:

\begin{equation}
f_{i}(\bm{x}_f,t+\delta{t}) = 2qf^{+}_{i'}(\bm{x}_f,t) + (1-2q)f^{+}_{i'}(\bm{x}_{ff},t) + 6\omega_{i'}\rho_{0}\frac{\bm{e}_i \cdot \bm{u}_{w}}{C^2}, \quad \text{$q \leqslant 0.5$}
\label{eq:q_less}
\end{equation}

\begin{equation}
f_{i}(\bm{x}_f,t+\delta{t}) = \frac{1}{2q}(f^{+}_{i'}(\bm{x}_f,t)+ 6\omega_{i'}\rho_{0}\frac{\bm{e}_i \cdot \bm{u}_{w}}{C^2}) + \frac{2q-1}{2q}f_{i}(\bm{x}_{f},t), \quad \text{$q > 0.5$}
\label{eq:q_larger}
\end{equation}
where $\bm{u}_w$ is the wall velocity, notice that the term in Eq.~\ref{eq:q_less} and~\ref{eq:q_larger} which including $\bm{u}_w$ indicates the momentum exchange due to the moving wall~\cite{ladd1994numerical}.

Yu et al~\cite{yu2003viscous} proposed an unified interpolated bounce-back scheme regardless of the value of $q$. The idea is to evaluate distributions at wall $f_{i'}(\bm{x}_w,t+\delta{t})$ first, then the bounce-back role is applied, the missing distributions at $f$ after streaming $f_{i}(\bm{x}_f,t+\delta{t})$ is interpolated between $f_{i}(\bm{x}_w,t+\delta{t})$ and $f_{i}(\bm{x}_ff,t+\delta{t})$. Yu's scheme can be summarized as:
\begin{equation}
f_{i}(\bm{x}_w,t+\delta{t}) = qf^{+}_{i'}(\bm{x}_f,t) + (1-q)f^{+}_{i'}(\bm{x}_{ff},t) + 6\omega_{i'}\rho_{0}\frac{\bm{e}_i \cdot \bm{u}_{w}}{C^2},
\end{equation}

\begin{equation}
f_{i}(\bm{x}_f,t+\delta{t}) = \frac{1}{1+q}(f_{i}(\bm{x}_w,t+\delta{t}) + \frac{q}{1+q}f_{i}(\bm{x}_{ff},t+\delta{t}),
\end{equation}

\subsection{velocity interpolation based bounce-back scheme}\label{sec:vibb}
Beside of interpolated bounce-back schemes, Guo et al~\cite{guo2002extrapolation} introduced a non-equilibrium extrapolation boundary condition, where virtual distributions at solid node $s$ are decomposed into equilibrium part $f^{eq}_{i}(\bm{x}_s,t)$ and non-equilibrium part $f^{neq}_{i}(\bm{x}_s,t)$. $f^{eq}_{i}(\bm{x}_s,t)$ can be determined by Eq.~\ref{eq:feq} with $\bm{u}_s$ and $\rho_s$. Both $\bm{u}_s$ and $f^{neq}_{i}(\bm{x}_s,t)$ are extrapolated from fluid nodes $f$ and $ff$. Since the fluctuation of density is of order $O({Ma}^2)$, $\rho_s$ is approximated as $\rho_s=\rho_f$. The main idea behind Guo's scheme is the fact that the distributions are dominated by the equilibrium part since the variations of $f^{neq}$ are one order smaller than $f^{eq}$. Thus it is safe to extrapolate $f^{neq}$ with second order accuracy~\cite{guo2002extrapolation}.

Here we combine the idea of interpolated bounce-back and non-equilibrium extrapolation/interpolation together. As shown in Fig.~\ref{fig:ibb}, the unkown $f_{i}(\bm{x}_f,t+\delta{t})$ is determined by bounce-back role:
\begin{equation}
f_{i}(\bm{x}_f,t+\delta{t}) = f^{+}_{i'}(\bm{x}_d,t) + 6\omega_{i'}\rho_{0}\frac{\bm{e}_i \cdot \bm{u}_{w}}{C^2},
\label{eq:eqneq}
\end{equation}
where $f^{+}_{i'}(\bm{x}_d,t)$ is given as:
\begin{equation}
f^{+}_{i'}(\bm{x}_d,t) = f^{eq}_{i'}(\rho_d,\bm{u}_d) + f^{neq}_{i'}(\bm{x}_d,t),
\label{eq:eqneq}
\end{equation}
$\rho_d$ is extrapolated/interpolated as
\begin{equation}
\rho_d = 2q\rho_f + (1-2q)\rho_{ff},
\label{eq:rhod}
\end{equation}
And $f^{neq}_{i'}(\bm{x}_d,t)$ is handled in the same way and rescaled by density ratio:
\begin{equation}
f^{neq}_{i'}(\bm{x}_d,t) = 2q(f^{+}_{i'}(\bm{x}_f,t)-f^{eq}_{i'}(\bm{x}_f,t))\frac{\rho_d}{\rho_f} + (1-2q)(f^{+}_{i'}(\bm{x}_{ff},t)-f^{eq}_{i'}(\bm{x}_{ff},t))\frac{\rho_{d}}{\rho_{ff}},
\label{eq:neqd}
\end{equation}

As shown in Guo's scheme, velocities play the most important roles in determining unknown distributions. Fortunately, both $\bm{u}_w$, $\bm{u}_f$ and $\bm{u}_{ff}$ are known. $\bm{u}_d$ in Eq.~\ref{eq:eqneq} can be evaluated by linear interpolation separately:
\begin{equation}
\resizebox{0.6\hsize}{!}
{$\bm{u}^{*}_d = \left\{
  \begin{array}{l l}
    \text{$2q\bm{u}_f + (1-2q)\bm{u}_{ff}$}, & \quad \text{$q \leqslant 0.5$,}\\[3ex]
     \text{$\frac{1-q}{q}\bm{u}_f + \frac{2q-1}{q}\bm{u}_w$}, & \quad \text{$q > 0.5$,}\\[0.ex]
  \end{array} \right.$}
  \label{eq:bouzidi}
\end{equation}
or linearly interpolated between $\bm{u}_w$ and $\bm{u}_{ff}$ regardless of $\bm{u}_{f}$:
\begin{equation}
\bm{u}^{**}_d = \frac{1-q}{1+q}\bm{u}_{ff} + \frac{2q}{1+q}\bm{u}_w,
\label{eq:neqd}
\end{equation}
$\bm{u}_d$ is calculated by weighted averange as shown in Fig.~\ref{fig:interpolation}:
\begin{equation}
\bm{u}_d = \frac{1}{3}\bm{u}^{*}_d + \frac{2}{3}\bm{u}^{**}_d,
\label{eq:neqd}
\end{equation}

We choose above interpolation scheme because of the following observation: $\bm{u}_w$ and $\bm{u}_{ff}$ are supposed to be more accurate since they are not affected by the unknown distributions. Thus $\bm{u}^{*}_d$ which including $\bm{u}_{f}$ is assigned with less weight. Notes that above boundary scheme cannot be recovered to the bounce-back scheme when $q=0.5$. However, Peng et al~\cite{peng2016implementation} report that errors of linear interpolated bounce-back increase with $q$, thus recovering to bounce-back scheme do not guarantee a better accuracy. Later, we will show this inconsistency have trivial effects on results.
\begin{figure}[t]
\begin{centering}
\includegraphics[width=0.8\linewidth]{interpolation}
\caption{Schematic of velocity interpolation schemes.}
\label{fig:interpolation}
\end{centering}
\end{figure}

\section{Benchmark and discussion}\label{sec:benchmark}
\subsection{Poiseuille flow with a moving wall}\label{sec:poiseuille}
To evaluate the accuracy of the proposed boundary condition with well-defined geometries, the Poiseuille flow with a moving wall is chosen as the first benchmark case as shown in Fig.~\ref{fig:poiseuille}. The bottom wall is fixed and halfway bounce-back is applied, while the top wall is moving with $u_{top}$ and different boundary conditions are tested. The fluid is initially rest and driven by a constant body force $g$ along the x-direction. The analytical solution for steady state is given as\citep{peng2016implementation}
\begin{equation}
u_x = -\frac{g}{2\nu}y^2+\bigg(\frac{g}{2\nu}H + \frac{u_{top}}{H}\bigg)y,
\label{eq:exact}
\end{equation}
where $H$ is the height of the channel and $y$ is the vertical coordinate. A $L \times L$ domain size is used and the top wall is placed above the highest lattices with distance $q$. $q$ varies between 0 and 1. Since $H$ varies with $q$, the Reynolds number is defined as $Re=u_{top}L/\nu$. The parameters are chosen as: $L=60$, $g=1.0\times 10^{-6}$, $u_{top}=0.01$. Two values of viscosity are used $\nu=0.1$ and $\nu=0.01$ which correspond $Re=6$ and $60$.

Simulated velocity profile are compared with the analytical solution in Fig~\ref{fig:vel_re60} at $Re=60$ and $q=0.8$. Overall, all boundary schemes provide reasonable results. However, the proposed scheme shows a better accuracy compared with Bouzidi and Yu's scheme in the zoom-in view (Fig~\ref{fig:vel_zoom_re60}). Previous studies~\cite{peng2016implementation} indicate that errors depend on the value of $q$, Fig.~\ref{fig:error_re6} and Fig.~\ref{fig:error_re60} show errors vary with $q$ at $Re=6$ and $Re=60$. Here the error is defined as:$\left| (u_s - u_e)/u_e \right|$ where $u_s$ is simulated velocity and $u_e$ is the exact value from Eq.~\ref{eq:exact}. At low $Re$, all three schemes show identical pattern at small $q$ while the proposed scheme shows slightly less error at large $q$. In practice, the global error mainly depends on the maximum local error, thus a small improvement on maximum local error can still considerably increase the overall accuracy. At high $Re$, it is clear that the proposed scheme performs much better, especially at large $q$. Furthermore, errors decrease with increasing $q$ when $q>0.5$ and almost one order magnitude smaller than other schemes. Peng et al~\cite{peng2016implementation} argue that quadratic interpolation schemes have better consistency than linear schemes since quadratic schemes have converging error at $q=0$ and $q=1$. The proposed scheme also shows significant improvements in terms of consistency at high $Re$. These improvements are mainly due to the usage of $\bm{u}_w$ which eliminate the unphysical slipping on boundaries. To investigate the effect of $\tau$, $q$ is fixed to $0.8$ and $\tau$ varies between $0.5$ and $1$ which is the typical range of $\tau$ in practices. As shown in Fig.~\ref{fig:error_tau}, the proposed scheme shows less dependence on $\tau$ than others.

\begin{figure}[t]
\begin{centering}
\includegraphics[width=0.8\linewidth]{poiseuille}
\caption{Schematic of Poiseuille flow with a moving wall.}
\label{fig:poiseuille}
\end{centering}
\end{figure}

\begin{figure}[t]
\begin{centering}
\includegraphics[width=0.8\linewidth]{vel_re60}
\caption{Simulated velocity profile at $Re=60$ and $q=0.8$.}
\label{fig:vel_re60}
\end{centering}
\end{figure}

\begin{figure}[t]
\begin{centering}
\includegraphics[width=0.8\linewidth]{vel_zoom_re60}
\caption{A zoom-in view of Fig.~\ref{fig:vel_re60}.}
\label{fig:vel_zoom_re60}
\end{centering}
\end{figure}

\begin{figure}[t]
\begin{centering}
\includegraphics[width=0.8\linewidth]{error_re6}
\caption{Errors as a function of $q$ at $Re=6$.}
\label{fig:error_re6}
\end{centering}
\end{figure}

\begin{figure}[t]
\begin{centering}
\includegraphics[width=0.8\linewidth]{error_re60}
\caption{Errors as a function of $q$ at $Re=60$.}
\label{fig:error_re60}
\end{centering}
\end{figure}

\begin{figure}[t]
\begin{centering}
\includegraphics[width=0.8\linewidth]{error_tau}
\caption{$\tau$ effect on errors at $q=0.8$.}
\label{fig:error_tau}
\end{centering}
\end{figure}

\subsection{Cylindrical Couette flow}\label{sec:couette}
Another classic benchmark is the cylindrical Couette flow which involves curved boundaries as shown in Fig.~\ref{fig:couette}. Two cylinders are placed at the centre of the domain ($L \times L$), where the inner cylinder rotating with a constant angular velocity $\omega_1$ and the outer cylinder is fixed. To evaluate the order of accuracy of the proposed scheme, the radius of cylinders are set as $R_1=L/4.8$ and $R_2=L/2.4$. The analytical solution for steady state is given as
\begin{equation}
\frac{u_r}{\omega_1 R_1} = \frac{R_1 R_2}{R_2^2-R_1^2}\bigg(\frac{R_2}{r}-\frac{r}{R_2}\bigg),
\label{eq:exact2}
\end{equation}
where $u_r$ is the velocity component which perpendicular to the radial direction and $r$ is the radial distance from the centre of cylinders. Four values of $L$ are used in simulations: $20, 40, 80, 160$ and viscosity varies with $\omega_1$ to fix Reynolds number as $Re=6$ and $60$.

The relative errors against resolutions are plotted on a log scale in Fig.~\ref{fig:error_vs_l_re6} and Fig.~\ref{fig:error_vs_l_re60} for $Re=6$ and $Re=60$ respectively. The results of Yu's scheme are also presented as a comparison. The results confirm that interpolated bounce-back schemes are generally second-order accuracy. The proposed scheme shows more accurate at all resolutions. Compared to Fig.~\ref{fig:error_re6} in which all schemes have identical errors at low $Re$, it is surprising that the proposed scheme performs better regardless of $Re$. This superiority can be explained by the fact that errors increase with $q$ thus little improvements for large $q$ can significantly increase accuracy. It can be also found in Fig.~\ref{fig:error_re6} and~\ref{fig:error_re60} that the accuracy of the proposed scheme is slightly better than second-order, especially at high resolution. The errors are found linearly increased with $Re$ as shown in Fig.~\ref{fig:error_vs_re} ($L=160$), but the proposed scheme shows less dependence on $Re$ where errors of Yu's scheme increases dramatically at high $Re$ in comparison.
\begin{figure}[t]
\begin{centering}
\includegraphics[width=0.8\linewidth]{couette}
\caption{Schematic of cylindrical Couette flow.}
\label{fig:couette}
\end{centering}
\end{figure}

\begin{figure}[t]
\begin{centering}
\includegraphics[width=0.8\linewidth]{error_vs_l_re6}
\caption{Errors as a function of resolutions at $Re=6$.}
\label{fig:error_vs_l_re6}
\end{centering}
\end{figure}

\begin{figure}[t]
\begin{centering}
\includegraphics[width=0.8\linewidth]{error_vs_l_re60}
\caption{Errors as a function of resolutions at $Re=60$.}
\label{fig:error_vs_l_re60}
\end{centering}
\end{figure}

\begin{figure}[t]
\begin{centering}
\includegraphics[width=0.8\linewidth]{error_vs_re}
\caption{Errors as a function of Reynolds number.}
\label{fig:error_vs_re}
\end{centering}
\end{figure}

\subsection{Magnus effect}\label{sec:magnus}
To further validate the proposed scheme for more complex flows, simulations of a rotating particle immersed in a Poiseuille flow are also carried out. Non-equilibrium extrapolation scheme is used for the left velocity inlet and zero velocity gradient outlet for the right side. Zero velocity gradient is achieved by simply modify all distributions at the boundary equal to the distributions at closest fluid nodes. The top and bottom boundaries are set as solid walls. The particle spins with a constant angular velocity $\omega$. An additional lift force acts on the particle due to the rotation. This phenomenon is due to the well-known Magnus effect. To speed up the convergence of equilibrium state, the fluid field is initialized to the Poiseuille flow as $u_x= 4U\frac{y}{L}(1-\frac{y}{L})$, where $U$ is the unperturbed mainstream speed (along with the x-direction). A lift coefficient, which indicates the magnitude of the lift force, can be obtained as $C_L = \frac{F_y}{\rho_f U^2 R}$ depending on the lift force $F_y$. Here, the Reynolds number is defined as $Re=\frac{2 U R}{\nu}$. Another dimensionless number is the spin number $S_{pa}=\frac{\omega R}{U}$. The domain size is $L=400$ and radius of the particle $R=10$. Fluid properties are fixed as $U=0.05, \nu=0.02$. Fig.~\ref{fig:spa_vs_cl} shows the lift coefficient varying with the spin number at $Re=20$. It also shows an excellent agreement with the results of Kang et al.~\cite{kang1999laminar} and Ingham and Tang~\cite{ingham1990numerical}.

\begin{figure}[t]
\begin{centering}
\includegraphics[width=0.8\linewidth]{spa_vs_cl}
\caption{Lift coefficient $C_L$ as a function of the spin number $S_{pa}$.}
\label{fig:spa_vs_cl}
\end{centering}
\end{figure}

\section{Concluding remarks}\label{sec:conclusion}
A velocity interpolation based Bounce-Back scheme has been developed in this study. We combine the ideas of interpolated bounce-back schemes and non-equilibrium extrapolation scheme. The proposed scheme is validated by numbers of well-defined benchmark cases including Poiseuille flow with a moving wall, cylindrical Couette flow and Magnus effect. It is shown that the proposed scheme provides better accuracy at high Reynolds number and less dependency on solids positions which may crucial in many applications.

\section*{Acknowledgement}\label{sec:Acknowledgement}

\bibliographystyle{elsarticle-num}

redpajama_set_name: RedPajamaArXiv


text:
Belgians Gallery
Choose from 91 pictures in our Belgians collection for your Wall Art or Photo Gift. Popular choices include Framed Prints, Canvas Prints, Posters and Jigsaw Puzzles. All professionally made for quick delivery.
Congo/Cartoon/Punch/1906
Train Derailed/1914
WWI Poster, Belgian & Allies Aid League
A Little Belgian Refugee by Charles Dana Gibson
Elisabeth, Queen of the Belgians
A Belgian refugee adopted by a British woman
King Leopold III - King of Belgium
King of the Belgians
Queen of the Belgians
Leopold I of Belgium (1790-1865). The first King of the Bel
Quex Park VAD patients & staff in hall of house
Battle Plan/Waterloo
VAD hospital patients and staff in the hall of Quex House in March 1915. The hall was used as a recreation space for the patients. A Ward of the hospital was beyond the door on the left, in the Drawing Room. A notice on the door says NO ONE TO ENTER WARD WITHOUT..... (rest obscured). The patients include British soldiers (wearing the patients uniform of hospital blues - blue serge jacket & trousers, white shirt and red tie) and Belgian patients. The latter wore their uniform or civilian clothing. The Belgians include Oscar Van Audenhove, a soldier from Ghent who painted the background to one of the Museum dioramas while at Quex (he is sitting behind the table). The nurse second from the left is Mary E Holmes, who worked as the Matron of the Hospital in 1915. The nurse three from the right is Fanny Watson, a local woman who worked as a VAD nurse at Quex throughout the War. This room remains largely unchanged at Quex House today. The furniture in the photograph is still in the room, as is the mirror on the wall. The Quex Park VAD Hospital opened on 15 October 1914 and closed on 31 January 1919. The hospital was run by Kent/178, the Birchington Detachment. The Commandant was Hannah Powell-Cotton (1881-1964), wife of Major Percy HG Powell-Cotton (1866-1940) of Quex Park, founder of the Powell-Cotton Museum. Major Powell-Cotton was the VAD Transport Officer for the Isle of Thanet area, responsible for organising the transport of patients from the stations to the local hospitals. Date: 1915
© The Powell-Cotton Museum Collection / Mary Evans Picture Library
Cl鯠de M鲯de 1912
Malvina Longfellow, 1915
WW1 - Decorated Belgian aeroplanes - Charlie Chaplain
WW1 - Subsidiary wars in Africa - Northern Rhodesian rifles
WW1 - Belgian Cavalry in action
Belgian refugees accommodated at Alexandra Palace, WW1
WW1 - Belgians destroy railways to hamper German advance
BELGIUM. Laeken. Church of Saint Walpurgis. Facade
ALBURQUERQUE, Enrique Fernᮤez de la Cueva, Duke
World War I. Invasion of Belgium (1914). Detachment
LEOPOLD I of Belgium (1790-1865). King of Belgium
EYCK, Hubert van (1370-1426). The Ghent Altarpiece
American actress Malvina Longfellow(1889-1962), pictured in The Bystander in 1915 at the time of her London debut in Lady Lever's play The Torches of Fate'. The play was performed at the Vaudeville Theatre, in aid of the fund for distressed Belgians in Belgium during World War One. The Bystander lauded her pro-Belgian credentials in the assumption of this charitable role. Date: 1915
MAETERLINCK, Maurice (1862-1949). Belgian writer
Planispheric astrolabe. 1569. Manufactured in golden
First World War (1914). Ypres bombing (Belgium)
Helmet with visor. It belonged to Charles V. SPAIN
WEYTS, Petrus. The Charles V in a storm
VAN STRYDONCK, Guillaume. The Little Master is
VAN EYCK, Hubert and Jan. Ghent Altarpiece
Civitatis Orbis Terrarum. Ghent
BREE, Mathieu I. Van. Portrait of Cuvier
Belgium. Bruges. City Hall
Entry of Belgian troops into Bruges, 1918 by Matania
Emile Cammaerts
Emile Leon Cammaerts (1878-1953), Belgian poet, playwright and writer. He wrote a biography of King Albert I of Belgium and became Professor of Belgian Studies at the University of London. Married to the actress Miss Tita Brand, he is pictured here in uniform as a member of the United Arts Corps during the First World War. Date: 1915
Tatler cover - Queen of the Belgians, WW1
Destruction of the bridge at Li觥, Belgium
King Albert I of Belgium and his consort, Queen Elisabeth
With the Belgians at La Panne
An extremely rare porcelain coffee cup - WWI
The poor Belgians have suffered greatly - WWI
Unconquerable The King of the Belgians
German prisoners captured by Belgians, WWI
King Albert of the Belgians
Sketch cover - King George V & Albert I, end of WW1
Algerian cavalry in West Flanders, 1914
Tatler cover - King Albert of Belgium


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text:
President, Foreign Minister of Madagascar congratulate India on its 76th Independence Day, call India an inspiration
Celebrations of the 76th Independence Day of India in Antananarivo, Madagascar were marked by unfurling of the Indian National Flag by Ambassador Abhay Kumar which was attended by the Indian community in Madagascar. Ambassador also hosted a reception on the occasion of the 76th Independence Day of India, in which the President of the Senate of Madagascar H.E. Mr. Herimanana Razafimahefa was the Chief Guest.
It was also attended by Minister of Agriculture, Minister of Mines, Minister of Transport, besides the Ambassadors and the Head of International Organisations in Madagascar.
Speaking on the occasion of the reception hosted at the Embassy's Residence, Ambassador Abhay Kumar said:
"India attained her Independence on 15 August 1947 and we are celebrating 75 years of its independent journey as progressive India through an initiative called: Azadi Ka Amrit Mahotsav. The initiative recognizes the glorious history of India's people, culture and achievements and the philosophy of 'Vasudhaiva Kutumbakam' which means the whole Earth is a family. I am happy to see this core Indian philosophy in practice in the form of donation to Madagascar of 50 computers, 15000 bicycles and 5000 tonnes of rice from India."
"I would like to thank the members of Indian Community, who are the representatives of India in Madagascar, for their cooperation with the Indian Embassy. The Indian community in Madagascar has its roots in the state of Gujarat. The Community not only plays a crucial role economically, but also enriches Madagascar's cultural and social diversity. The Embassy organized an exhibition on the history of Indian Diaspora in Madagascar in March 2021. Recently a Centre for Indian Diaspora was opened in Antananarivo in July 2022. I believe it will go a long way in improving the understanding of the history, journey, role and contributions of Indian diaspora in Madagascar", Ambassador said.
The Chief Guest of the evening, the President of the Senate of Madagascar H.E. Mr. Herimanana Razafimahefa
said: " On behalf of His Excellency Mr. Andry Rajoelina , President of the Republic of Madagascar, on behalf of the Government and the people of Madagascar, and on my own behalf, I would like to express our warmest congratulations to Her Excellency Mrs. Droupadi MURMU, President of the Republic of India, to His Excellency Narendra Modi , Prime Minister of the Republic of India, as well as to the people of India on the occasion of this great celebration."
Highlighting the relationship between India and Madagascar, the President of Senate said: "India has always stood by Madagascar in difficult times, both in supporting the Malagasy Government in its efforts to cope with the severe weather, and during the severe drought that has led to food insecurity for the population in the southern regions. "
"India today is a source of inspiration and a leader in development. Indeed, through the Security and Growth for All Policy (SAGAR), which aims to ensure peace and stimulate development for all, India has become a strategic partner in the Indian Ocean region ", noted the Senate President.
The celebrations also saw performances from yoga and Hindi languages students and cultural performances by members of ITEC and ICCR alumni in Madagascar.
Congratulating India on the occasion, Madagascar's President Andry Rajoelina sent a congratulatory tweet saying: "My warm greetings to you PM @narendramodi
and the people of India on the occasion of 75th anniversary of India's Independence.
My gratitude for standing with Madagascar during the time of need."
PM Narendra Modi thanked the Hon'ble President of Madagascar on Twitter and responded: "Thank you President Andry Rajoelina for wishing us on our Independence Day. As a trusted developmental partner, India will always work with Madagascar for the welfare of our people. @SE_Rajoelina #IndiaAt75"
Foreign Minister of Madagascar also congratulated people of India and tweeted: "MEA @drsjaishankar. Madagascar is grateful to India's friendship and initiatives to strengthen bilateral relations.
My warm greetings to you and the people of India on this special day 75th anniversary of India's Independence."
EAM Dr. S. Jaishankar responded by tweeting —"Thank you for your greetings FM @RichardJRand. Our SAGAR vision for a secure and prosperous Indian Ocean Region will guide the #IndiaMadagascar bilateral relationship."


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A key feature in Microsoft Office 2013 is the ability to easily save documents as PDF files.
Information Services recommends upgrading to the latest version of Microsoft Office, which fully supports saving as PDF. Employees may contact us to have us do the upgrade or borrow a DVD from the Help Desk and do it themselves. Students may download the latest version from Microsoftonline.com.
BishopApps (Google Docs) automatically converts all document files into PDF before printing. You can also download any online document in PDF format. Since you can upload many different file types into BishopApps, you can easily use this tool to convert documents to PDF format.
While editing a document, open the File menu.
In the Export to PDF dialogue box set your preferences and click theExport button.
Your browser will then automatically download the output as a PDF file (or open a PDF file directly, depending on how your browser is configured to handle PDF). After the file is downloaded, you can use the PDF file as you please.
Pages, Numbers, and Keynote are the Mac's equivalents of Word, Excel, and PowerPoint, respectively. All three have the same basic instructions for saving/exporting a PDF file, with a few variations.
Open or create the document you wish to export as a PDF.
Click "File" and select "Export" from the drop-down menu.
Select the PDF tab at the top of the new pop-up box, select the Image Quality of your choosing (Good, Better, Best.) Click "Next".
Enter a Save As title, choose export location, then click the blue "Export" button.
Note: You can also export a Pages document in Word (.docx) format by selecting Export to -> Word from the File menu, shown above.
Select the PDF tab at the top of the new pop-up box, select the Image Quality of your choosing (Good, Better, Best.) and select Layout of choosing (Sheet View or Page View.) Click "Next".
Note: You can also export a Numbers document in Excel (.xlsx) format by selecting Export to -> Excel from the File menu, shown above.
Select the "PDF" tab at the top of the new pop-up box. Select choices for Export (Slides or Slides With Notes) and preferences for Options, and select the Image Quality of your choosing (Good, Better, Best.) Click "Next".
Adobe Reader is a free program for viewing and printing of PDF documents.It includes a browser plugin for displaying PDF documents within Firefox and other Web browsers.
Go to the Adobe Reader download page.
After answering Steps 1-3, click the yellow Download now button.
*Note: you may need to enable pop-ups.
After installation, you should notice that the Adobe Reader plugin becomes a part of your browser, allowing you to view PDF's from browsers like Internet Explorer and Netscape. Mozilla Firefox, SeaMonkey and Opera will detect the browser plugin if Adobe Reader is installed, and the Adobe Reader installer will install the plugin automatically if you install Adobe Reader after your web browser.
Select Tools > Internet Options > Programs (tab) > Manage Add-ons.
Find and select Adobe PDF Reader.
Make sure Enabled is selected.
Can't view a PDF on the Web? Try this first.


I spend New Year's Eve with Snow, watching DVDs and eating potato stew and leftover Lebkuchen. At midnight we watched the fireworks from my balcony for about ten minutes and burned a few sparklers before the cold drove us back in. The thermometer in front of my bedroom window had gone down to -8°C the last few nights, which means -10 or colder away from the house, and today I finally lost patience with the cold and turned on the heating in all rooms. (I know they say you should not turn on the heating in rooms where you dry the washing, but come on, 12°C and 30 per cent humidity?) So now the temperature is a comfortable 16°C all around, and cozy 18°C in the living room.
Yes, the flat has some problems with heating. But it's cool in summer, which is more important to me.


Woomera Reserve Playground is located in the south-east corner of Woomera Reserve in Little Bay. You can access the playground via two paths – one from Noora Avenue and the other from Nurla Avenue. The playground is fenced and partially covered with a shade sail. There's a range of play equipment on site for children of all ages. A concrete bike path is located next to the playground which is perfect for younger children learning to ride a bike or scooter.


text:
from functools import reduce

def _composed_doc(fs):
    """
    Generate a docstring for the composition of fs.
    """
    if not fs:
        # Argument name for the docstring.
        return 'n'

    return '{f}({g})'.format(f=fs[0].__name__, g=_composed_doc(fs[1:]))

def compose(*fs):
    """
    Compose functions together in order:

    compose(f, g, h) = lambda n: f(g(h(n)))
    """
    # Pull the iterator out into a tuple so we can call `composed`
    # more than once.
    rs = tuple(reversed(fs))

    def composed(n):
        return reduce(lambda a, b: b(a), rs, n)

    # Attempt to make the function look pretty with
    # a fresh docstring and name.
    try:
        composed.__doc__ = 'lambda n: ' + _composed_doc(fs)
    except AttributeError:
        # One of our callables does not have a `__name__`, whatever.
        pass
    else:
        # We already know that for all `f` in `fs`, there exists `f.__name__`
        composed.__name__ = '_of_'.join(f.__name__ for f in fs)

    return composed

__all__ = [
    'compose'
]

redpajama_set_name: RedPajamaGithub


text:
Q: Property of the sequence of primes Let $p_n$ denote the $n$-th prime number. Does anyone know a proof of the following property?
$$\forall n, n', \ p_n p_{n'} \geq p_{n+n'}$$
I'm surprised I can't find anything on this while I believe it should be something people could find interesting (if it's true). The case $n=1$ (i.e. $p_n=2$) is equivalent to Bertrand's postulate.

A: Assume $n\leq m$ (here I use $m$ instead of $n'$). By Rosser's theorem we have that $p_np_m>n\ln n\cdot m\ln m=nm\ln n\ln m$. For $n,m>8$ we have $nm\geq\frac{n+4}{2}\cdot m=\frac{1}{2}nm+2m\geq 2n+2m$. We further have for $n>e^2$ $\ln n\ln m>2\ln m=\ln m+\ln m\geq\ln n+\ln m$, so $p_np_m>nm\ln n\ln m> 2(n+m)(\ln n+\ln m)>2(n+m)\ln nm>2(n+m)\ln(n+m)=(n+m)\ln(n+m)+(n+m)\ln(n+m)>(n+m)\ln(n+m)+(n+m)\ln\ln(n+m)>p_{n+m}$ where last equality is one mentioned here and holds for $n+m\geq 6$.

A: We can use a few explicit improvements over Bertrand found on Wikipedia:

[Nagura 1952] For $x\ge 25$ there is a prime between $x$ and $\frac 65 x$.

Hence if $p_{n}\ge \left(\frac 65\right)^n$ and $p_{n'}>23$ then there are $n$ primes between $p_n'$ and $p_{n}p_{n'}$. Together with finitely many checks for $p_n\le p_{n'}\le 23$ this settles all cases with one of the primes being $<100$ (or equivalently: where at least one of $n,n'$ is $\le 25$). Actually, we need only handle the case that at least one of $n,n'$ is $\le 5$ (i.e. one of $p_n,p_{n'}$ is $\le 11$), because the rest is dealt with by the following nice  estimate for the $n$th prime:

For $n\ge 6$, we have $n(\ln(n\ln n)-1)<p_n<n\ln(n\ln n)$

Hence $$p_np_{n'}>nn'(\ln(n\ln n)-1)(\ln(n'\ln n')-1)$$
and $$p_{n+n'}<(n+n')\ln((n+n')\ln(n+n')) $$
As we may even assume $n\ge n'\ge6$, we find
$$\begin{align} p_{n+n'}&<2n\ln(2n\ln(2n))\\&=2n\ln((2n+\ln2)\ln n)\\&<2n(\ln 3+\ln(n\ln n))\\&<3n\ln(n\ln n))\end{align}$$
and
$$\begin{align}p_np_{n'}&>6n(\ln(n\ln n)-1)(\ln(6\ln 6)-1)\\&
>13n(\ln(n\ln n)-1)\end{align} $$
So that all we need to complete the proof is
$$ 10\ln(n\ln n)>13$$
which is the case because $n\ln n\ge 6\ln 6>10$

redpajama_set_name: RedPajamaStackExchange


A 250ml bottle of our extremely gentle natural bubbles for both hair and body. It has a faint hint of lavender, which is calming just before bed time. Natural and 71% organic too. Free from harmful additives, chemicals, perfume and other unnecessary stuff. We test extensively on severe eczema skin for weeks before our products are released. The packaging, designed by Esther Hall from Cat & Owl Design, features several woodland animals including a moose, a beaver and a bear.
Our brand new Eco-friendly reed diffuser in our trademark Lemongrass scent. Unlike other reed diffusers the carrier liquid in our diffuser is made from renewable sources. And of course the scent is 100% pure essential oil. Generous size of 120ml in thick bottomed glass bottle. The bathroom is no longer the only place where you can enjoy our famous Lemingrass scent - now you can enjoy it in the rest of your home too.
If you would like to buy both our Peppermint Shampoo and the matching Peppermint Conditioner - this is one to go for. Both bottles are 250ml. One click and save £2.00 in the process.


text:
How Salts in Drinking Water Can Affect Health
26 Oct 2020 | 23:47 pm (IST)
Water is the elixir of our lives and our survival depends on it. Unfortunately, water is soon becoming a scarce commodity and scientists warn of disasters of epic proportions, if we fail to save water.
Besides water scarcity, another major issue faced by today's world is its contamination. It is hard to get 'pure drinking water' these days and we all know that 80 per cent of the diseases, infections, allergies are waterborne.
How Pure Is Your Water?
The purity of water is often measured by estimating the amount of Total Dissolved Salts (TDS) present in the water. TDS comprises inorganic salts like magnesium, calcium, potassium, sodium, bicarbonates, chlorides and sulfates, besides fluoride, arsenic, chromium, perchlorate, heavy metals, bacteria and viruses, depending on the source.
In these days and times, water has become quite contaminated with the presence of various disease-causing viruses, bacteria and other pollutants than beneficial minerals.
If you are worried how clean is your drinking water, go for a simple TDS testing. It can be done at home with the help of small digital TDS testing meter.
What Is TDS?
Total Dissolved Salts is a concentration of positively charged and negatively charged ions in water and it will provide a general idea about the quality of water for our regular drinking needs.
Total dissolved salts are measured in milligrams per unit volume of water or parts per million (PPM). For drinking water, the maximum concentration level set by The Bureau of Indian Standards is at 500 ppm.
High or Low TDS Affects The Taste:
Water with high levels of TDS around 1000 ppm is considered unfit for human consumption. High levels of TDS are caused due to the presence of potassium, chloride and sodium and toxic ions in larger amounts. It is also undesirable to drink as it may taste salty, metallic or bitter.
Low levels of TDS, 100 ppm may have a flat or diluted taste to it and unpalatable.
How TDS Affects Health:
High levels of TDS means it is unfit for consumption and several diseases like nausea, lung irritation, rashes, vomiting, dizziness etc., Drinking water with elevated amount of TDS for longer periods will expose body to various chemicals, toxins and may cause chronic health conditions like cancer, liver, kidney failures, nervous system disorders, weaken immunity and may also cause birth defects in the new born.
Several studies suggest that consuming water with low TDS may cause mineral leaching from healthy tissues in the body.
What You Can Do?
Test your drinking water to know the levels of TDS. If you have a water purifier at home, change filters periodically.
If you don't have a water purifier, drink only boiled water. Boiling water kills several viruses and bacteria and can save health from various infections.


text:
Andreaea julicaulis är en bladmossart som beskrevs av C. Müller 1898. Andreaea julicaulis ingår i släktet sotmossor, och familjen Andreaeaceae. Inga underarter finns listade i Catalogue of Life.

Källor

Sotmossor
julicaulis

redpajama_set_name: RedPajamaWikipedia


A ''dream come true'' for a West Point graduate is to be nominated by the President to become the next Secretary-of-the-Army.
On Tuesday, April 4th our next 1ST TUESDAY speaker will be President Trump's choice for the next Secretary of the Army, TN State Senator MARK GREEN! [see link below] WHAT TIMING! This will be a historic day at 1ST TUESDAY. Need I saw more?
As usual, doors at Waller Law [511 Union Street -27th floor] open at 11am. Event lunch is at 11:30, $20 for Members -- $25 for Guests. Lunch must be pre-ordered Monday. A large crowd is expected. Soooo, if you too would like to ''JOIN US'' please DON'T hesitate. Secure seating at 1st Tuesday Nashville and click on ''JOIN US''.
Pass the word and share with those you know. See you on Tuesday, April 4th for 1ST TUESDAY with the Secretary-to-be !!


We're Not Stupid! is our way of engaging with the wider world about political issues. The People page is a place to document and archive our interactions with the people, who may not feel as though they have a voice in the obscure, deceptive world of political rhetoric and doublespeak.
The initial aim is to talk to Bradfordians, and ask them to send a message to the people in power. Below are their messages.


text:
Community Calendar for Dec. 17
The Hartselle City Council has rescheduled its second regular meeting of December for Dec. 17 at 8:30 a.m. in the city hall auditorium. The council will not meet on Dec. 23.
The Morgan County Commission will hold a rescheduled meeting Thur., Dec. 18, at 9 a.m. in the County Commission Boardroom on the Fifth Floor of the Morgan County Courthouse, 302 Lee St. NE in Decatur. This meeting will replace the Dec. 23 meeting.
Morgan County school students will be dismissed at noon on Dec. 19.
The 10th annual Chappell Karate Basket Brigade will be Sat., Dec. 20 at 11 a.m. at the OWO Recreation Center at 906 Roberts Drive in Hartselle. If anyone would like to make a tax-deductible donation, donations are still being accepted. Also, anyone who would like to volunteer to package the food into boxes and/or help deliver them, please contact Amanda Bussey at 256-612-4438.
Hartselle Parks and Recreation is hosting a Candy Cane Hunt Dec. 21 at 2 p.m. at Pavilion 4 at Sparkman Park. Bring a basket and a sack of candy canes. Children will hunt by age groups (ages 3 and under, 4-5, 6 and older). Prizes will be given to those who find the specially marked candy canes. Hot chocolate and cookies will be served. The event is free, but participants are asked to register by Dec. 18.
Dec. 22-Jan. 5
Hartselle City Schools will close for the Christmas holidays. All Morgan County Schools and the Central Office will be closed in observance of the Christmas/New Year's Holiday from Dec. 22 through Jan. 2, 2015.
Fifth and sixth graders are invited to join a New Year's Party at Sparkman Civic Center Jan. 2 from 7-9 p.m. There will be music, dancing, party favors and snacks to celebrate the New Year. Please register and pay the $10 fee per child at Sparkman Civic Center no later than Dec. 30.
Morgan County teachers will return for Teacher Workday on Jan. 5, 2015. Students will be welcomed back for the second semester on Jan. 6, 2015.
Festival of the Cranes Returns to Wheeler National Wildlife Refuge Jan. 10, 2015. This is a One Day Event for the Birds.
Start the New Year off right by joining the Women's Connection Luncheon Fri., Jan. 9, 2015, at 11 a.m. at the Decatur Country Club located at 2401 Country Club Road. Humorous speaker, Carol Frey, will share tips for those cooking ruts and relationship ruts in "A Perfect Welcome into a Not So Perfect Home." Bring your favorite hostess tip and your humorous disasters to share around the table. Cost is $15 with no dues or membership required. For reservations and complimentary nursery, contact Clarice at (256) 301-9196, (256) 341-7129 or email cekkess@charter.net or Stephanie at (256) 686-2876 or email stephanieroybal06@yahoo.com. Reservations must be received by Jan. 5.
The 8ers Square Dance club in Decatur will host a beginner square dancing class starting Jan. 16 at the Decatur Aquadome, 1202 Fifth Ave. in Decatur. The class will be held from 7:30-9:30 p.m. Two free trial nights will be held Fri., Jan. 16 and 23. No special clothes are required. For more information, call 256-353-1759 or 256-340-0532 or visit www.8ers.com-8ersfromdecatur.
Priceville Elementary School will have its board member appreciation breakfast Jan. 30 from 7:45 to 8:30 a.m.
PES will have its annual Winterfest starting at 5 p.m. for food and 6 p.m. for games.
March 23-27
Hartselle and Morgan County schools will close for spring break March 23-27.
All month
Water Aerobics classes will meet on Monday, Wednesday and Thursday from 6:50 to 7:50 a.m. beginning June 2. The fee is $25 per month or $5 per visit.
Morgan County Humane Society, located at 86 Gum Springs Cut Off Road, is a no-kill animal shelter. It meets the second Tuesday of every month at 6:30 p.m. at the shelter. For more information, call 256-773-7222.
Volunteer entertainment is needed at Columbia Cottage in Hartselle. Gospel or country singers, instrumentalists, comedians, speakers, home schoolers, children or youth groups are welcome. Contact Penny Vest at 751-4809 or 502-1491.
A cancer support group meets on the first Monday of each month at 6 p.m. at the Pleasant Place building. Any person with any type of cancer is invited to attend. For more information, call 784-5694.
Hartselle's New Beginnings Quilt Guild meets on the second Thursday of each month at the Farm Service Agency office on Alabama 36 west of downtown Hartselle. It is open to all who are interested in quilt making, The guild is focused on beginning quilt makers to help them learn how to make a new block each month and new techniques used to make them. For more information, call 482-3971.
Weight Watchers classes meet on Mondays at 5 p.m. and 6:30 p.m. and Tuesdays at 9 a.m. at Sparkman Civic Center with weigh-ins beginning 30 minutes prior to each meeting. Call 1-800-651-6000 for more information.
The Decatur IAAP Chapter meets the second Tuesday of each month at Decatur Chamber of Commerce at 5:30 p.m. No reservations are required. Administrative/clerical professionals and students are invited. For more information, call Cindy Anders at 351-1623 or email cindyanders@aol.com.
Baton classes meet Mondays at 5 p.m. The class is for age 6 and older. The fee is $40 per month.
Youth tumbling classes meet Mondays at 4 p.m. at Sparkman Civic Center. The class is for ages 3-12. The fee is $40 per month.
Priceville Palace hosts a big band swing dance with the Sophisticated Swingers on the first Friday of each month at 7:30 p.m. Every Saturday night Glenn Wood and the Crosscut Band is featured. A free couples dance class is held on the first and third Saturdays from 6 to 7 p.m. You do not have to have a partner to participate. For more information, call 256-353-4362.
All mothers of active duty reserve or honorably discharged military service members are invited to attend monthly meetings of Blue Star Mothers of America, Inc. The Morgan County Chapter meets the first Tuesday of every month at 7 p.m. at East Highland Baptist Church in Hartselle.
The Hartselle Chapter of Alcoholics Anonymous meets Mondays at 8 p.m.; Tuesdays at 5:30 p.m.; Wednesdays at noon and 8 p.m.; Thursdays at 5:30 p.m.; Fridays at 7 p.m. and Saturdays at 7 p.m. The Friday meeting is a smoking meeting. The meetings take place at 527 South Sparkman Street. Call 773-3031 for information.
A "North Alabama Board Gamers" group is forming. You can join the group or just get more information online at www.meetup.com/NorthAlabamaBoardgamers.
TOPS – Interested in learning how to lose weight? Join Taking Off Pounds Sensibly (TOPS.) every Monday at 3 p.m. at First Christian Church, Hartselle. For more information, contact Doris Chapman 773-9358
The VFW Ladies Auxiliary Post 2214 hosts a dance every Tuesday from 7-10 p.m. at 112 Veterans Drive in Cullman with the "Always Country Band" featuring Jerrold Burns from Country Boy Eddie's Band. Admission is $4. For information, call 796-9111.
Hartselle Kiwanis Club meets the first and third Tuesday of the month at noon at Sedona Steak House.
Hartselle's Rotary Club meets every Tuesday at noon at Sedona Steak House.
Sparkman Civic Center offers birthday bash celebrations. Cost is $100. It includes party room at Sparkman Civic Center, themed invitations, themed decorations, plates, cups, napkins, eating utensils, party favors, games, activities and two party coordinators. All you need to supply is cake and refreshments. Space is limited, so register early. Party days are Monday through Friday from 6 to 8 p.m. or Saturday from 10 a.m. to noon. For more information, call 256-773-2581.
Women's yoga classes will meet on Monday nights at 6:15 p.m. at Sparkman civic center. The fee is $25 per month.
The Hartselle Hope AL-Anon Family Group, located at 527 Sparkman St. in Hartselle, meets Mondays at 8 p.m., Tuesdays at 5:30 p.m., Wednesdays at noon and 8 p.m., Thursdays at 5:30 p.m., Fridays at 7 p.m. and Saturdays at 7 p.m. The Ala-Teen Family Group meets Fridays at 7 p.m. For more information, call 1-888-425-0775.
AARP Chapter 1831 meets the first Tuesday of every month except July, at the Christ Our Redeemer Lutheran Church, located 721 Pickens St. SW in Hartselle, at 10 a.m.
Falkville VFW, located at 784 Culver Road, hosts bingo every Tuesday and Thursday night at 6:30 p.m. For more information, call 256-784 5747.
Dale Serrano Dance Studio meets Monday nights at Sparkman Civic Center. For more information, call 205-822-6378.
Weight Watchers meets on Monday nights with weigh-in at 5 p.m. followed by a meeting at 5:30 p.m. The fee is $13 per week. For more information, call Weight Watcher at 1-800-651-6000.
Women's aerobics classes meet Tuesday and Thursday mornings from 7:45 to 8:45 a.m. at Sparkman Civic Center. The fee is $25 per month.
Senior Nutrition Center, also known as the Hartselle Senior Center is the place for friendly visiting, serious Rook and Canasta, a loud game of Texas spinner dominoes, sing-a-longs, informative chats and so much more. The center is open from 8 a.m. to 1 p.m. Monday through Friday. Groups also participate in evening supper bus trips. Registered participants are welcome to stay for lunch provided by the Commission on Aging. For more information or for transportation, call Dan Price at 256-773-0786.
Hartselle Civitan Club meets the first and third Monday at 6 p.m. in Sparkman Civic Center Room 10. The club works with Civitan International to support and work with people in our community with mental and physical disabilities and support the Civitan International Research Center in Birmingham. Civitan is the only civic club with a research center. Hartselle Civitan Club was responsible for starting the Special Needs Accessible Playground located directly behind the Sparkman Civic Center. Along with Woodmen of the World, they also do the Avenue of Flags along U.S. 31 in Hartselle. For more information, contact secretary Rita Sims at 256-773-5904.


text:
Kenny Rogers legendary country music singer dead at 81
in Celebrity/Actor who died, Who Important Died Today
Kenny Rogers (Kenneth Ray Rogers), the legendary country and western music, was born on August 21, 1938, and died on March 20, 2020. He was an American singer, songwriter, actor, record producer, and entrepreneur.
Kenny Rogers got elected to the Country Music Hall of Fame in 2013.
Dead at 53 is Anne Heche following a car crash one week ago.
Peter Aykroyd, Emmy nominated 'SNL' actor-writer, dead at 66
Rogers was particularly popular with country audiences but also charted more than 120 hit singles across various music genres, topped the country and pop album charts for more than 200 individual weeks in the United States alone. He sold over 100 million records worldwide during his lifetime, making him one of the best-selling music artists of all time.
Kenny Rogers, died Friday night, according to a statement posted by his family. Known for such hits as "The Gambler," "Lady," "Islands in the Stream," and "Lucille," Rogers died peacefully at home in Sandy Springs, Ga., of natural causes at 10:25 p.m., the statement said.
In all, Kenny Rogers had 24 No. 1 hits and was the winner of six CMA Awards and three Grammys, the family's statement said.
Kenny Rogers legendary country music singer dead at 81 1
Raised in public housing along with seven siblings, Kenny was born in Houston, Texas. He had his first gold single at age 20 with a song called "That Crazy Feeling" under the name Kenneth Rogers.
He then joined a jazz group, the Bobby Doyle Trio, as a standup bass player. His breakthrough came in 1966 when asked to join a folk group called the New Christy Minstrels. The band reformed as First Edition and scored a pop hit with the psychedelic song, "Just Dropped In (To See What Condition My Condition Was In)." After the group disbanded in 1974, Rogers pursued a solo career, and his 1977 hit "Lucille" crossed over to the pop charts and earned the crooner his first Grammy.
"The Gambler," written by Don Schlitz, came out in 1978, which became Rogers' signature song he later developed into a series of television movies in that he starred.
One of his biggest hits was "Lady," written by Lionel Richie, a chart-topper for six weeks straight in 1980. Other singles included "You Decorated My Life," "Every Time Two Fools Collide," with Dottie West, "Don't Fall In Love with a Dreamer" with Kim Carnes, and "Coward of the County."
Over the years, Rogers collaborated with several female duet partners, most notably, Dolly Parton. The two paired at the suggestion of the Bee Gees' Barry Gibb, who wrote "Islands in the Stream."
"Barry was producing an album on me, and he gave me this song," Rogers told the Associated Press in 2017. "And I went and learned it and went into the studio and sang it for four days. And I finally looked at him and said, 'Barry, I don't even like this song anymore.' And he said, 'You know what we need? We need Dolly Parton.' I thought, 'Man, that guy is a visionary.'
"From the moment she marched into that room, that song never sounded the same," Rogers added. "It took on a whole new spirit."
Rogers and Parton toured together, leading to an HBO concert special. The two later recorded "You Can't Make Old Friends" in 2013. That same year, Rogers was a winner of the CMA's Willie Nelson Lifetime Achievement Award and got inducted into the Country Music Hall of Fame.
He received a total of 10 awards from the Academy of Country Music. According to the Recording Industry Association of America, Rogers sold more than 47 million records in the United States alone.
He was a superstar for six decades before retiring from touring in 2017 at the age of 79. Despite his crossover success, Rogers always preferred to be thought of as a country singer.
"You either do what everyone else is doing, and you do it better, or you do what no one else is doing, and you don't invite comparison," Rogers told The Associated Press in 2015. "And I chose that way because I could never be better than Johnny Cash or Willie or Waylon at what they did. So I found something that I could do that didn't invite comparison to them. And I think people thought the mind desired to change country music. But that was never my issue."
Last May, Rogers was admitted to a Georgia hospital for dehydration, amid rumors that his overall health was failing. In 2018, health problems prompted Keny Rogers to call off shows during what pointed out his farewell concert tour.
A statement from the singer's management at the time stated that "Kenny Rogers has been working through a series of health challenges. He has now to cancel all performances through the end of the year to focus on recuperation,"
"I didn't want to take forever to retire," Rogers was quoted as saying. "I've thoroughly enjoyed this opportunity to say farewell to the fans over the past two years on 'The Gambler's Last Deal' tour."
In addition to his musical craft, Rogers had a chain of restaurants called Kenny Rogers Roasters and was a partner behind a riverboat in Branson, Mo.
He was involved in several charitable causes, including the Red Cross and MusiCares.
His wife, Wanda, survive rogers, and his sons Justin, Jordan, Chris and Kenny Jr., as well as two brothers, a sister, and grandchildren, nieces, and nephews, his representative said.
The family is planning a private service "out of concern for the national COVID-19 emergency," a statement posted early Saturday read. The also stated, that there a plans for a public memorial later date.
Source: FoxNews | Top
Tags: Kenny RogersKenny Rogers AgeKenny Rogers AlbumsKenny Rogers And Dolly PartonKenny Rogers And Lionel RichieKenny Rogers And Lionel Richie LadyKenny Rogers Early SongsKenny Rogers Endless LoveKenny Rogers Evening StarKenny Rogers I Don't Need YouKenny Rogers Islands In The Stream LyricsKenny Rogers On The Road AgainKenny Rogers Roasters MenuKenny Rogers Roasters Near MeKenny Rogers Singapore
Famous movie actress Anne Heche died at 53: Anne Celeste Heche was born on May 25, 1969, starting her acting career at...
Peter Aykroyd, an Emmy-nominated actor and writer on "Saturday Night Live" for the 1979-80 season who later worked with an...
Jean-Paul Belmondo, star of 'Breathless,' dead at 88
PARIS (AP) — Jean-Paul Belmondo was the star of the iconic French New Wave film "Breathless." His crooked boxer's nose...
Sunni Welles, TV Actress and Bill Cosby Accuser, Dead at 72
Sunni Welles became one of around 60 women who came forward with sexual assault, rape, drugging, and other sexual misconduct...
Playwright Terrence McNally 81, is dead from coronavirus-related complications


This is interesting there are interviews with folks who helped create Facebook and discussion of twitter. They talk on how its based partly on slot machines in casinos in terms of psychology.
How notifications are a huge draw and how the pause to show number of notifications is made that way to build anticipation. What scares me is the builders used social media to exploit emotions by the way its programmed.
I confess there is good feeling seeing notifications.


Many plants actually love these tricky spots!
If you have an area of your garden that's in full or dappled shade there are many different and interesting plants that you can grow with great success. Dappled shade is when light conditions are still fairly good, but overhanging branches and foliage filter the strong sunlight out.
Many plants favour and indeed prefer shady spots to grow and thrive. They are protected from direct sunlight which can cause young foliage to scorch and very often the soil retains moisture for longer because the heat of the sun doesn't dry it out.
The range of plants that can be grown include spring bulbs, perennials and shrubs and by carefully selecting the plants you can easily create an attractive woodland-style border that will provide colour and interest for most of the year.
Planting while the soil is still moist and mixing in some garden compost to improve the soil will help new plants settle in for the summer. For the first growing season it's important to water around the roots in dry weather to make sure the plants establish well.


text:
// Copyright (c) 2017 Ubisoft Entertainment
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
namespace Sharpmake
{
    public static partial class Options
    {
        public static class AndroidMakefile
        {
            public class AppPlatform : StringOption
            {
                public AppPlatform(string option)
                    : base(option)
                {
                }
            }

            public enum ArmMode
            {
                [Default]
                Thumb,
                Arm,
            }

            public class CompilerFlags : Strings
            {
                public CompilerFlags(params string[] options)
                    : base(options)
                {
                }
            }

            public class CompilerExportedFlags : Strings
            {
                public CompilerExportedFlags(params string[] options)
                    : base(options)
                {
                }
            }

            public class ExportedDefines : Strings
            {
                public ExportedDefines(params string[] defines)
                    : base(defines)
                {
                }
            }

            public enum GroupStaticLibraries
            {
                Enable,
                [Default]
                Disable,
            }

            public class PrebuiltStaticLibraries
            {
                public PrebuiltStaticLibraries(string moduleName, string libraryPath, ArmMode armMode = ArmMode.Thumb)
                {
                    ModuleName = moduleName;
                    LibraryPath = libraryPath;
                    Mode = armMode;
                }

                public string ModuleName { get; set; }
                public string LibraryPath { get; set; }
                public ArmMode Mode { get; set; }
            }

            public enum StandardLibrary
            {
                [Default]
                System,
                GAbiPP_Static,
                GAbiPP_Shared,
                StlPort_Static,
                StlPort_Shared,
                GnuStl_Static,
                GnuStl_Shared,
            }

            public enum ShortCommands
            {
                Enable,
                [Default]
                Disable,
            }

            public class SupportedABIs : Strings
            {
                public SupportedABIs(params string[] options)
                    : base(options)
                {
                }
            }

            public class ToolchainVersion : StringOption
            {
                public ToolchainVersion(string value)
                    : base(value)
                {
                }
            }
        }
    }
}


Looking for a great small business opportunity? Maybe an Allegra Network full-service print franchise is right for you!
Allegra Network, one of the largest printing franchises in the world, links more than 400 locations in the United States, Canada, and Japan.
The company has consistently rated among Entrepreneur Magazine's Annual Franchise 500® and was ranked 90th among America's top global franchises.
Allegra Network's premier brand, Allegra Print & Imaging, offers full-service print and graphic communications services including full-color printing, graphic design, digital color copying, mailing services, high speed output and online file transfer.
As printing sales continue to grow, the company's median sales and profits have increased over the past 10 years due to the comprehensive support its franchisees receive in the key areas of technology, operations and marketing.


Once you've written the Project Initiation Document with sufficient information you need to get it approved. This usually means distributing it via the PMO to all the Stakeholders listed on the Distribution List within the PID and other interested parties such as Operations or HR for Resources. You will usually need to email the PID to all those listed and ask for comments back.
If your company has one, this stage will often be lead by the ITQA Team who will compile the comments and lead the Informal and Formal Reviews. The latter are meetings which the Stakeholders and Interested Parties will attend to discuss the PID in further detail. It is only after these stages are complete that your PID will be of a sufficient standard to be approved and passed onto the Programme Board for funding.
Depending on the complexity and size of your project these stages can be completed in anything from 5 Informal and 4 Formal Reviews for a $12 million project (not mine but one a colleague was managing!) through to simple email approvals with no Reviews for a project with a budget of $100,000.
However whatever the size of the project you need to be aware that there may be problems raised which have nothing to do with your project which relate for example to matters such as a shortage of resources or lack of finance. And unless you know what other projects are coming up you often won't realise that these problems are there until you circulate the PID and people start raising problems upon discovering the impact your project will have on their teams.
For example I once worked at a company where two enormous projects were in the pipeline both of which utilised the same resources and timeframes. Until both those project's circulated their PID's, no-one realised that one project would need to be prioritsed over the other due to lack of resources. However by the time this had happened a great deal of work had already been done on both projects, one of which essentially had to be put on hold until more resources could be recruited and trained up.
It can be tempting to miss certain people who are perceived as being difficult from this stage because you know they will raise too many issues. However this would be extremely shortsighted. Get them involved at this stage and get their objections resolved now. Leaving it until later will simply cause even bigger problems, and make you look unprofessional.
The best thing when writing a PID is to talk to as many people in the various departments as you can. Find out what their upcoming workload is like, what other projects are in the pipeline, whether the company perceives your project as a priority and whether there are enough experienced resources to work on your project.


text:
Title: James Turner
Subject: Jesse Franklin, David Stone (politician), Montfort Stokes, Governors of North Carolina, William Hawkins (governor)
12th Governor of North Carolina
December 6, 1802 – December 10, 1805
Benjamin Williams
Nathaniel Alexander
United States Senator
March 4, 1805 – November 21, 1816
Jesse Franklin
Montfort Stokes
(1766-12-20)December 20, 1766
Southampton County, Virginia
January 15, 1824(1824-01-15) (aged 57)
Democratic-Republican
James Turner (December 20, 1766 – January 15, 1824) was the 12th Governor of the U.S. state of North Carolina from 1802 to 1805. He later served as a U.S. senator from 1805 to 1816.
Turner was born in Southampton County, Virginia; his family moved to Warren County, North Carolina in 1770. Raised in a family of farmers, Turner served in the North Carolina volunteer militia during the American Revolutionary War in 1780. He served under Nathanael Greene alongside Nathaniel Macon, with whom he formed a lasting friendship and political alliance.
In 1798, Turner was elected to the North Carolina House of Commons; he served there from 1799 to 1800, and served in the North Carolina Senate from 1801 to 1802. In 1802, the General Assembly elected John Baptista Ashe governor, but he died before he could assume office; Turner was chosen in his place and sworn in on 5 December 1802. He served the constitutional limit of three one-year terms and, at the end of this time as governor, was elected to the United States Senate when Montfort Stokes resigned before serving the term to which he had been elected.
Turner served as a senator for eleven years, re-elected to a second term in 1810, resigning due to ill health in 1816. During his time in office, he supported the administration of James Madison during the War of 1812.
Turner was married three times; first to Marian Anderson in 1793 (they had four children), then to Ann Cochran in 1802, with no children, and finally to Elizabeth Johnston in 1810 (resulting in two children). Turner died in 1824 and is buried on his "Bloomsbury" plantation in [[
Virginia, Raleigh, North Carolina, Charlotte, North Carolina, Tennessee, South Carolina
Virginia, Isle of Wight County, Virginia, Suffolk, Virginia, Greensville County, Virginia, Hampton Roads
Franklin County, North Carolina, Vance County, North Carolina, Northampton County, North Carolina, Halifax County, North Carolina, Race (United States Census)
North Carolina, United States Senate, Robert Byrd, David Stone (politician), Orange County, Virginia
David Stone (politician)
North Carolina, United States Senate, Jesse Franklin, United States House of Representatives, Bertie County, North Carolina
United States Senate, North Carolina, Lunenburg County, Virginia, American Revolutionary War, Andrew Jackson