So it's done. The CAT is finally out of the bag. If you are one of those who has the calls you aimed for, stop right away. This post is not for you. To the contrary, if you are dejected and disappointed, continue reading. Not clearing CAT in this attempt may not be such a bad thing after all. Each year thousands of aspirants experience what you are feeling right now, and just like them, you broadly have two options: To let go of your CAT/IIM dream or to make up your mind and slog for one more year.
A few years ago, I was in the same situation, and results of CAT' 13 had been announced. I fared miserably. It was so bad that I wouldn't even write my scores here. Not like I had expected 99+ but what I got was way below my expectations. Yet I wasn't really disappointed as I knew I had not given my best shot. I took a resolution that day: Come what may, I will bell the CAT.
What followed was a year of hard work and toil. Numerous classes, tons of tests and countless hours were spent analyzing mocks. The year went by and soon arrived CAT'14. I was way more anxious this time. Reached the exam hall well before time and prayed to God numerous times. I came out of the hall reasonably sure of my chances of cracking CAT this time. The next one month went peacefully doing little productive work. And finally, the D-Day arrived. I would have easily checked the website over 500 times. Each time anyone posted a message on one of those Facebook groups, my heart would skip a beat. I would stare at the system for hours only to get even more agitated. And finally, it arrived in the form of a phone call from one of my friends who had prepared alongside me. I jumped out of my bed and logged on to the website. As I saw my result, I had mixed feelings. My hard work had paid off. My result was a significant improvement over my last year's performance. But in my heart, I knew that it wouldn't be enough to fetch me a seat in the older IIMs. Calls were released a few days later. As expected I got calls from new IIMs only. I went ahead and appeared for the interviews. I was able to crack IIM Ranchi. I was satisfied with it but not happy. There was a voice inside my head that said maybe one more attempt, and I would get what I truly wanted. It was a tough call to make, to go for the birds in the bush or stick with the one in hand. I discussed it with my family and let go of the IIM Ranchi opportunity.
Do you have any gap year during preparation process?
Hi, No I don't have a gap year.
MY PROFILE- 10TH-81%, 12th-75%(west bengal board), btech-8.6(78%), 2yr work ex,….do i have any chance of getting a call from IIM lucknow next yr?if yes at what %?
having gap years of more than 3 years can hinder the chance of getting an iim?
What chances do i have to get into iim ??
Did u give ur 1st attempt while in final year or after final year?
Dealing With Results The Right way!


What is your first thought when you run across that new PF member who has 10 posts, but "100 LV bags" -- an exaggeration of course, but not far from the truth?
What proof does it take for you to fully believe that someone owns the fabulous collection of LV that she so openly brags about but has no pictures of? Or, similarly, the fabulous fashion magazine editor who has fifth grade grammar (again, exaggerations)?
There must be something so gratifying and exciting about exaggerating and sugar coating an otherwise normal (or sub-normal) existence, which is something that the 'net offers with unscrupulous abundance -- and annoys the rest of us who tell it like it is and don't find the point in lying because we are satisfied with our own lives.
Clanalois! Hi hi hi hi hi!
I'm totally the opposite, I don't really need any proof at all! I figure somebody's word is generally pretty good, even on an internet forum... and that's true 99% of the time, right?
I always believe most people, silly perhaps, but that's me.
and I don't come across as very exciting, :-P so I guess ya'll believe me! lol.
lol I know! Me too!
Oh except yesterday I just purchased 20 Chanel bags. Kidding, just the shoes.
but in all seriousness, I agree with Christina.
You poor thing! Even if he is super rich, I still wouldn't go near him with a 10-foot pole, I think he's so unattractive!
His hair (PIECE) is so horrible.
Totally agree! That's exactly how I feel too.
Let me at 'em! I think he's handsome. :worried: :sad2: Too bad his youngest son looks like some kind of deranged fowl.
I tend to be skeptical of any outrageous claims, but other than that really don't think about it too much. If someone needs to build themselves up by saying they have 100 LV's or are sleeping with George Clooney or their dog won Westminster...whatever. I don't take it personally and don't let it affect me. And if any of you really are sleeping with GC, dish!!!!
Cristina Megs had an imposter to as far as handbag pics.......remember the stolen paddy :evil: :evil: .
Iddywho......I just love looking at bags. I can usually tell if they're fake and I don't typically post in their showcases. I won't let fakers ruin my time here at PurseBlog.
I normally don't think anything about it unless maybe if they're like "I'm Kimora Lee!" then I'd think really?
^^^ Don't I wish! Damn GC is hot! Now I must go hop on my private jet to paris to buy a birkin in every color.


text:
\section{Introduction}

Bernstein operators are one of the most important sequences of positive linear operators. These operators were introduced by Bernstein
\cite{Bernstein} and were intensively studied.  For more details on this topic we can refer the readers to excellent monographs \cite{G1} and \cite{G2}.
The
Bernstein operators  are given by
\begin{equation}\label{X} B_{n}:C[0,1]\to C[0,1], \quad B_{n}(f;x)=\displaystyle\sum_{k=0}^n f\left(\frac{k}{n}\right)p_{n,k}(x),  \end{equation}
where
$$ p_{n,k}(x)={n \choose k}x^k(1-x)^{n-k},\,\,  x\in[0,1].$$
It is well known that the fundamental polynomials verify
\begin{equation}\label{et1}
p_{n,k}(x) = (1-x) \ p_{n-1,k}(x) + x \ p_{n-1,k-1}(x), \ \ 0<k< n.
\end{equation}
In a recent paper,   Khosravian-Arab et al. \cite{1} have introduced a sequence of modified Bernstein operators  as follows:
\begin{eqnarray}\label{ne1}
B_n^{M,1}(f,x) = \sum\limits_{k=0}^{n} p_{n,k}^{M,1}(x) \ f\left(\frac{k}{n} \right) , \ \ x \in [0,1],
\end{eqnarray}
\begin{align}\label{et2}
p_{n,k}^{M,1}(x) &= \alpha(x,n) \ p_{n-1,k}(x) + \alpha(1-x,n) \ p_{n-1,k-1}(x), 1\leq k\leq n-1,\\
p_{n,0}^{M,1}(x) &= \alpha(x,n)(1-x)^{n-1},\quad p_{n,n}^{M,1}(x) = \alpha(1-x,n)x^{n-1},\notag
\end{align}
and
\begin{eqnarray*}
	\alpha(x,n) = \alpha_1(n) \ x + \alpha_0(n), \,  n=0,1, \ldots,
\end{eqnarray*}
where $\alpha_0(n)$ and $\alpha_1(n)$ are  unknown sequences.  For $\alpha_1(n)=-1,$ $\alpha_0(n)=1$, obviously, (\ref{et2}) reduces to (\ref{et1}).

A Kantorovich variant of  the modified
Bernstein operators (\ref{ne1}) was introduced and studied in \cite{ana3}.

\section{The modified genuine Bernstein-Durrmeyer operators }
The genuine Bernstein-Durrmeyer operators were introduced by Chen \cite{D2} and Goodman and Sharma \cite{dif_GBD}
 and were studied  by a numbers of
authors (see \cite{ana}, \cite{dif_A2}, \cite{79}, \cite{80},  \cite{ana1}, \cite{143}). These operators are defined as follows:
\begin{align*} &{ U}_{n}(f;x)=(1-x)^n f(0)+ x^n f(1)
+(n-1)
\displaystyle\sum_{k=1}^{n-1}\left(\int_{0}^1 f(t)p_{n-2,k-1}(t)dt\right)p_{n,k}(x),\,\,  f\in C[0,1]. \end{align*}
The genuine Bernstein-Durrmeyer operators are limits of the Bernstein-Durrmeyer operators with Jacobi weights (see \cite{D11}, \cite{D12}, \cite{D100}), namely
$$  U_nf=\displaystyle\lim_{\alpha\to-1, \beta\to -1} M_n^{<\alpha,\beta>}f,\textrm{where} $$
\begin{align*}
&M_n^{<\alpha,\beta>}:C[0,1]\to\Pi_n,\,\, M_n^{<\alpha,\beta>}(f;x)=\displaystyle\sum_{k=0}^n p_{n,k}(x)\frac{\int_0^1w^{(\alpha,\beta)}(t)p_{n,k}(t)f(t)dt}{\int_0^1w^{(\alpha,\beta)}(t)p_{n,k}(t)dt},\\
& w^{(\alpha,\beta)}(t)=x^{\beta}(1-x)^{\alpha},\,x\in(0,1),\,\,\alpha,\beta>-1.
\end{align*}

In this section we introduce a new variant of the genuine Bernstein-Durrmeyer operators as follows:
\begin{align}\label{e1}
&{ U}_n^{1}(f;x)=\alpha(x,n)(1-x)^{n-1}f(0)+\alpha(1-x,n)x^{n-1}f(1)\\
&+(n-1)\displaystyle\sum_{k=1}^{n-1}\left\{\alpha(x,n)p_{n-1,k}(x)+\alpha(1-x,n)p_{n-1,k-1}(x)\right\}\int_0^1p_{n-2,k-1}(t)f(t)dt.\nonumber
\end{align}
Throughout this section we assume $U_n^{1}(e_0)=1$, namely
\begin{equation}\label{e2} 2\alpha_0(n)+\alpha_1(n)=1.\end{equation}
In the following we will consider these two cases:
\begin{equation}\label{e3}
\alpha_0(n)\geq 0, \alpha_0(n)+\alpha_1(n)\geq 0,
\end{equation}
\begin{equation}\label{e4} \alpha_0(n)<0 \textrm{ or } \alpha_1(n)+\alpha_0(n)<0.
\end{equation}
\begin{remark} If the unknown sequences $\alpha_i(n),i=1,2$ verify conditions (\ref{e2}) and (\ref{e3}), it follows that
	$$ 0\leq \alpha_0(n)\leq 1\textrm{ and } -1\leq \alpha_1(n)\leq 1. $$
Thus the sequences $\alpha_i(n),i=1,2$ are bounded and the operator (\ref{e1}) is positive. If the  sequences $\alpha_i(n),i=1,2$ verify conditions (\ref{e2}) and (\ref{e4}), we obtain
	$$ \big(\alpha_0(n)<0,\,\,\alpha_1(n)+\alpha_0(n)>1\big)\textrm{ or }\big(\alpha_1(n)+\alpha_0(n)<0,\,\, \alpha_0(n)>1\big), $$
	hence the operator (\ref{e1}) is not positive.
\end{remark}
Denote $m_{n,k}^{1}(x):={ U}_n^{1}(e_k;x)$, $\mu_{n,k}^{1}(x):={ U}_n^{1}\left((t-x)^k;x\right)$, where $e_k(t)=t^k$, $k=0,1,\dots.$
\begin{lemma}\label{l1}
	The modified genuine Bernstein-Durrmeyer operators (\ref{e1}) verify:
	\begin{itemize}
		\item[i)] $m_{n,0}^{1}(x)=1$;
		\item[ii)] $m_{n,1}^{1}(x)=\displaystyle\frac{1}{n}\left\{xn+(1-2x)(1-\alpha_0(n))\right\}$;
		\item[iii)] $m_{n,2}^{1}(x)=\displaystyle\frac{1}{n(n+1)}\left\{x^2n^2+(4\alpha_0(n)x-2\alpha_0(n)-5x+4)xn\right.
		\left. +2(1-x)(1-2x)(1-\alpha_0(n))\right\}$.
		\end{itemize}
\end{lemma}
\begin{lemma}\label{l2}
	The following statements hold:
	\begin{itemize}
		\item[i)] $\mu_{n,1}^{1}(x)=\displaystyle\frac{1}{n}(1-2x)(1-\alpha_0(n))$;
		\item[ii)] $\mu_{n,2}^{1}(x)=\displaystyle\frac{2}{n(n+1)}\left\{x(1-x)n+(2x-1)^2(1-\alpha_0(n))\right\}$;
		\item[iii)]$\mu_{n,4}^{1}(x)=\displaystyle\frac{12}{n(n+1)(n+2)(n+3)}\left\{x^2(1-x)^2n^2-x(1-x)n\right.\\
		\left.\cdot\left[4\alpha_0(n)(1-2x)^2+23x(1-x)-6\right]+2(1-2x)^4\left[1-\alpha_0(n)\right]
		\right\}.$
	\end{itemize}
\end{lemma}

In the following we will give a direct estimate for the modified genuine Bernstein-Durrmeyer operator ${ U}_n^{1}$ by means of the first modulus of continuity $\omega(f,\delta)$.
\begin{theorem}
	Let $f$ be a bounded function for $x\in[0,1]$. If $\alpha_1(n)$ is a bounded sequence, then
	$$ \|{ U}_n^{1}f-f\|\leq 2 \left(3|\alpha_1(n)|+1\right)\omega\left(f;\frac{1}{\sqrt{n}}\right) , $$
	where $\|\cdot\|$ is the uniform norm on the interval $[0,1]$.
\end{theorem}
\begin{proof}
	It is known that the modulus of continuity $\omega(f;\delta)$ verifies
	\begin{align}\label{e7} |f(t)-f(x)|\leq \omega(f;\delta)\left(\displaystyle\frac{(t-x)^2}{\delta^2}+1\right). \end{align}
	It follows from (\ref{e2}) that
	\begin{align}\label{ec23}
	|\alpha(x,n)|&=|\alpha_1(n)x+\alpha_0(n)|\leq |\alpha_1(n)|+|\alpha_0(n)|\nonumber\\
	&=|\alpha_1(n)|+\left|\frac{1-\alpha_1(n)}{2}\right|\leq \frac{3}{2}|\alpha_1(n)|+\frac{1}{2}.
	\end{align}
	In a similar way, we get
	$$ |\alpha(1-x,n)|\leq\dfrac{3}{2} |\alpha_1(n)|+\dfrac{1}{2}.$$
	 Therefore,
	using Lemma \ref{l1}, condition (\ref{e2}) and 	chosing $\delta=\displaystyle\frac{1}{\sqrt{n}}$, we get
	\begin{align*} &\left|{U}_n^{1}(f;x)-f(x)\right|\\
	&\leq |{\alpha(x,n)}|(1-x)^{n-1}|f(0)-f(x)| +|\alpha(1-x,n)|x^{n-1}|f(1)-f(x)|\\
	&+(n-1)\displaystyle\sum_{k=1}^{n-1}|\alpha(x,n)|p_{n-1,k}(x)\int_0^1p_{n-2,k-1}(t)|f(t)-f(x)|dt\\
	&+(n-1)\displaystyle\sum_{k=1}^{n-1}|\alpha(1-x,n)|p_{n-1,k-1}(x)\int_0^1p_{n-2,k-1}(t)|f(t)-f(x)|dt\\
	&\leq\left(\displaystyle\frac{3}{2}|\alpha_1(n)|+\frac{1}{2}\right)\omega\left(f;\frac{1}{\sqrt{n}}\right)\left\{(1-x)^{n-1}(nx^2+1)+x^{n-1}(n(1-x)^2+1)\right.\\
	&+(n-1)\displaystyle\sum_{k=1}^{n-1}p_{n-1,k}(x)\int_0^1p_{n-2,k-1}(t)\left(n(t-x)^2+1\right)dt\\
	&+\left.(n-1)\displaystyle\sum_{k=1}^{n-1}p_{n-1,k-1}(x)\int_0^1p_{n-2,k-1}(t)\left(n(t-x)^2+1\right)dt\right\}\\
	&=\displaystyle\frac{1}{n+1}\left(\displaystyle 3|\alpha_1(n)|+1\right)\omega\left(f;\frac{1}{\sqrt{n}}\right)\left[(-2x^2+2x+1)n+4x^2-4x+2\right]\\
	&\leq 2\left(\displaystyle 3|\alpha_1(n)|+1\right)\omega\left(f;\frac{1}{\sqrt{n}}\right).
	\end{align*}
\end{proof}
\begin{remark}\label{r1} If $f\in C[0,1]$, then $\displaystyle\lim_{n\to\infty}\omega\left(f,\frac{1}{\sqrt{n}}\right)=0$. Therefore,  $({ U}_n^{1})_n$ converges uniformly on $[0,1]$ for   $\alpha_1(n)$  a bounded sequence  and $f\in C[0,1]$.
\end{remark}

\begin{theorem}\label{t2}
	Let $\alpha_i(n),i=0,1$ be  convergent sequences that satisfy the conditions (\ref{e3}) and $l_0=\displaystyle\lim_{n\to\infty}\alpha_0(n)$.  If $f^{\prime\prime}\in C[0,1]$, then
	$$
	\displaystyle\lim_{n\to\infty} n\left({ U}_n^{1}(f;x)-f(x)\right)=(1-2x)(1-l_0)f^\prime(x)+x(1-x) f^{\prime\prime}(x),$$
	uniformly on $[0,1]$.
\end{theorem}
\begin{proof}
	Applying the modified genuine Bernstein-Durrmeyer operators ${ U}_n^{1}$ to the Taylor's formula, we obtain
	\begin{align*}{U}_n^{1}(f;x)-f(x)&={ U}_n^{1}(t-x;x)f^{\prime}(x)+\displaystyle\frac{1}{2}{ U}_n^{1}\left((t-x)^2;x\right)f^{\prime\prime}(x)\\
	&+{ U}_n^{1}\left(\xi(t,x)(t-x)^2;x\right), \end{align*}
	where $\xi\in C[0,1]$ and $\displaystyle\lim_{t\to x}\xi(t,x)=0$.

	Using the Cauchy-Schwarz inequality, we get
	$$ n{ U}_n^{1}\left(\xi(t,x)(t-x)^2;x\right)\leq\sqrt{{ U}_n^{1}\left(\xi^2(t,x);x\right)} \sqrt{{n^2 U}_n^{1}\left((t-x)^4;x\right)}. $$
	From Lemma \ref{l2} we have $\displaystyle\lim_{n\to\infty}n^2{ U}_n^{1}\left((t-x)^4;x\right)=12x^2(1-x)^2$.	Since\linebreak $\xi^2(x,x)=0$ and $\xi^2(\cdot,x)\in C[0,1]$, by Remark \ref{r1}, we obtain
	$$ \displaystyle\lim_{n\to\infty}{ U}_n^{1}\left(\xi^2(t,x);x\right)=0 $$
	uniformly with respect to $x\in[0,1]$. Therefore,
	$$ \displaystyle\lim_{n\to\infty}n{ U}_n^{1}\left(\xi(t,x)(t-x)^2;x\right)=0. $$
	Applying Lemma \ref{l2}, the theorem is proved.
\end{proof}

Now, we extend the results from  Theorem \ref{t2} when the sequences $\alpha_i(n)$, $i=0,1$, satisfy the conditions  (\ref{e4}), namely the operator ${ U}_n^{1}$ is nonpositive.

\begin{theorem}\label{t2.5} Let $\alpha_i(n), i=0,1$ be bounded convergent sequences which satisfy  \eqref{e4} and $l_0=\displaystyle\lim_{n\to\infty} \alpha_0(n)$. If $f\in C[0,1]$ and $f^{\prime\prime}$ exists at a certain point $x\in[0,1]$, then we have
	\begin{equation}\label{e5}
	\displaystyle\lim_{n\to\infty} n\left({ U}_n^{1}(f;x)-f(x)\right)=(1-2x)(1-l_0)f^\prime(x)+x(1-x) f^{\prime\prime}(x),\end{equation}
	Moreover the relation \eqref{e5} holds uniformly on $[0,1]$ if $f^{\prime\prime}\in C[0,1].$
\end{theorem}
\begin{proof}
	Applying the modified genuine Bernstein-Durrmeyer operators ${ U}_n^{1}$ to the Taylor's formula, we get
\begin{align*} {U}_n^{1}(f;x)-f(x)&={ U}_n^{1}(t-x;x)f^{\prime}(x)+\displaystyle\frac{1}{2}{ U}_n^{1}\left((t-x)^2;x\right)f^{\prime\prime}(x)\\
&+{ U}_n^{1}\left(\xi(t,x)(t-x)^2;x\right),  \end{align*}
	where $\xi\in C[0,1]$ and $\displaystyle\lim_{t\to x}\xi(t,x)=0$.
	It is sufficient to show that
	\begin{align}
	\displaystyle\lim_{n\to\infty} n{ U}_{n}^{1}(\xi(t,x)(t-x)^2;x)&=0.\label{eG2}
	\end{align}
	Since the operators $ { U}_n^{1}$ are not positive linear operators  we can not use Cauchy-Schwarz inequality and we will introduce new techniques in order to prove the theorem.

	Let $\varepsilon>0$ be given. There exist a $\delta>0$ such that if $|t-x|<\delta$ then $|\xi(t,x)|<\varepsilon$. We denote
	\begin{align*}
	&
	{ K}_1=\left\{i:\left|\frac{i}{n}-x\right|<\delta, i=0,1,2,\cdots ,n\right\},\\
	& { K}_2=\left\{i:\left|\frac{i}{n}-x\right|\ge \delta, i=0,1,2,\cdots ,n\right\}.\end{align*}
	The boundedness of the sequences $\alpha_i(n)$, $i=0,1$ implies that these is a constant $C>0$ such that $|\alpha(x,n)|<C$.

	Let $k\in { K}_1$. Hence $|\xi(t,x)|<\varepsilon$. Therefore we get
	\begin{align}
	&\left|{ U}_n^{1}(\xi(t,x)(t-x)^2;x)\right|\leq C(1-x)^{n-1}|\xi(0,x)|x^2+Cx^{n-1}|\xi(1,x)|(1-x)^2\nonumber\\
	&+ C(n-1)\displaystyle\sum_{k=1}^{n-1}\left\{p_{n-1,k}(x)+p_{n-1,k-1}(x)
	\right\}\int_0^1p_{n-2,k-1}(t)|\xi(t,x)|(t-x)^2dt\nonumber\\
		&\leq C\varepsilon \left\{(n-1)\displaystyle\sum_{k=1}^{n-1}\left[p_{n-1,k}(x)+p_{n-1,k-1}(x)\right]\int_0^1p_{n-2,k-1}(t)(t-x)^2 dt\right.\nonumber\\
	&\left.+(1-x)^{n-1}x^2+x^{n-1}(1-x)^2\right\}=\displaystyle\frac{2\varepsilon C}{n(n+1)}\left\{2nx(1-x)+(1-2x)^2\right\}.
	\label{e6}
	\end{align}

	Let $k\in { K}_2$. We denote $M=\displaystyle\sup_{0\leq t\leq 1}|\xi(t,x)|(t-x)^2$. Then $$|\xi(t,x)|(t-x)^2\leq\displaystyle \frac{M}{\delta^4}\left(\frac{k}{n}-x\right)^4$$
	Moreover, the below upper bound is obtained
	\begin{align}\label{e71}
	&\left|{ U}_n^{1}(\xi(t,x)(t-x)^2;x)\right|\\
	&\leq \displaystyle\frac{MC}{\delta^4}\left\{\displaystyle\sum_{k=1}^{n-1}\left[p_{n-1,k}(x)+p_{n-1,k-1}(x)
	\right]\left(\displaystyle\frac{k}{n}-x\right)^4+(1-x)^{n-1}x^4+x^{n-1}(1-x)^4\right\}\nonumber\\
	&=\displaystyle\frac{CM}{n^4\delta^4}\left\{6x^2(1\!-x)^2n^2+4x(1\!-x)(13x^2\!-13x\!+3)n\!+(1\!-2x)^2(12x^2-12x+1)\right\}.\nonumber
	\end{align}
	Using (\ref{e6}) and (\ref{e71}), it follows
	\begin{align*}
	&\left|{ U}_n^{1}(\xi(t,x)(t-x)^2;x)\right|\leq\displaystyle\frac{2\varepsilon C}{n(n+1)}\left\{2nx(1-x)+(1-2x)^2\right\}\nonumber\\
	&+\displaystyle\frac{CM}{n^4\delta^4}\left\{6x^2(1\!-x)^2n^2\!+4x(1\!-x)(13x^2\!-13x+3)n\!+(1\!-2x)^2(12x^2\!-12x+1)\right\}.
	\end{align*}
	Therefore, the last inequality leads to (\ref{eG2}) and the theorem is proved.
\end{proof}

\section{Better rate of convergence}

In the following we will improve the previous results considering a new genuine Bernstein-Durrmeyer operators that have order of approximation $\displaystyle{ O}\left(n^{-2}\right)$ defined as

\begin{align}\label{U2}
{ U}_n^{2}(f;x)&=(n-1)\displaystyle\sum_{k=1}^{n-1} p_{n,k}^{2}(x)\int_0^1p_{n-2,k-1}(t)f(t)dt\nonumber\\
&+\beta(x,n)(1-x)^{n-2}f(0)+\beta(1-x,n)x^{n-2}f(1).
\end{align}
where
\begin{equation}
\label{e38p}
p_{n,k}^{2}(x)=\beta(x,n)p_{n-2,k}(x)+\gamma(x,n)p_{n-2,k-1}(x)+\beta(1-x,n)p_{n-2,k-2}(x) \end{equation}
and
$$ \beta(x,n)=\beta_2(n)x^2+\beta_1(n)x+\beta_0(n),\,\,\gamma(x,n)=\gamma_0(n)x(1-x),  $$
where $\beta_i(n),i=0,1,2$ and $\gamma_0(n)$ are  unknown sequences. For $\beta_2(n)=\beta_0(n)=1,$ $\beta_1(n)=-2$, $\gamma_0(n)=2$ we obtained the classical genuine-Bernstein-Durrmeyer operators.

In the following we suppose ${ U}_n^{2}(e_0;x)=1$, namely
$$ \left(2\beta_2(n)-\gamma_0(n)\right)x^2-\left(2\beta_2(n)-\gamma_0(n)\right)x+2\beta_0(n)+\beta_1(n)+\beta_2(n)=1. $$ This yields
$$
2\beta_2(n)-\gamma_0(n)=0,\,\,
2\beta_0(n)+\beta_1(n)+\beta_2(n)=1.
$$
The above relations lead to
\begin{align*}
{ U}_n^{2}(e_1;x)&=x+\displaystyle\frac{2}{n}\left[2\left(\beta_0(n)-1\right)x-\beta_0(n)+1\right];\\
{ U}_n^{2}(e_2;x)&=x^2+\displaystyle\frac{2}{n(n+1)}\left[4\beta_0(n)nx^2-2\beta_0(n)nx-8\beta_0(n)x^2+\beta_2(n)x^2\right.\\
&-5nx^2+10\beta_0(n)x
-\left. \beta_2(n)x+3nx+7x^2-3\beta_0(n)-9x+3 \right].
\end{align*}
In order to have $\displaystyle\lim_{n\to\infty}{ U}_n^{2}(e_i;x)=x^i$, $i=0,1,2$ we suppose the sequences $\beta_0(n)$ and $\beta_2(n)$ to verify the conditions
$$ \displaystyle\lim_{n\to\infty}\frac{\beta_0(n)}{n}=0\textrm{ and } \displaystyle\lim_{n\to\infty}\frac{\beta_2(n)}{n^2}=0.  $$
We consider  the case $\beta_0(n)=1$ and $\beta_2(n)=n$. Thus  $\beta_1(n)=-n-1$ and $\gamma_0(n)=2n$.
For this particular case the modified genuine Bernstein-Durrmeyer operator becomes
\begin{align}\label{TK2}
\tilde{ U}_n^{2}(f;x)&=(n-1)\displaystyle\sum_{k=1}^{n-1} \tilde{p}_{n,k}^{2}(x)\int_0^1p_{n-2,k-1}(t)f(t)dt\\
&+\left[nx^2-(n+1)x+1\right](1-x)^{n-2}f(0)+\left[nx^2-(n-1)x\right]x^{n-2}f(1),\nonumber
\end{align}
where
\begin{align*}
\tilde{p}_{n,k}^{2}(x)&=\left[nx^2-(n+1)x+1\right]p_{n-2,k}(x)+2nx(1-x)p_{n-2,k-1}(x)\\
&+\left[nx^2-(n-1)x\right]p_{n-2,k-2}(x). \end{align*}

Denote $\tilde{m}_{n,k}^{2}(x):=\tilde{ U}_n^{2}(e_k;x)$, $\tilde{\mu}_{n,k}^{2}(x):=\tilde{ U}_n^{2}\left((t-x)^k;x\right)$, $k=0,1,\dots.$ the moments and central moments, respectively for  the modified genuine Bernstein-Durrmeyer operator $\tilde{ U}_n^{2}$.

\begin{lemma}
	The following statements hold:
	\begin{itemize}
		\item[i)] $\tilde{m}_{n,0}^{2}(x)=1$;
		\item[ii)] $\tilde{m}_{n,1}^{2}(x)=x$;
		\item[iii)] $\tilde{m}_{n,2}^{2}(x)=x^2+\displaystyle\frac{2x(1-x)}{n(n+1)}$.
	\end{itemize}
\end{lemma}
\begin{lemma}
	The following statements hold:
	\begin{itemize}
		\item [i)] $\tilde{\mu}_{n,2}^{2}(x)=\displaystyle\frac{2x(1-x)}{n(n+1)}$,
		\item[ii)] $\tilde{\mu}_{n,3}^{2}(x)=-\displaystyle\frac{6x(1-x)(1-2x)(n-2)}{n(n+1)(n+2)}$,
		\item[iii)] $\tilde{\mu}_{n,4}^{2}(x)=-\displaystyle\frac{12x^2(1-x)^2n}{(n+1)(n+2)(n+3)}+{ O}\left(n^{-3}\right)$,
		\item[iv)] $\tilde{\mu}_{n,5}^{2}(x)=\displaystyle\frac{240x^2(1-x)^2(2x-1)n}{(n+1)(n+2)(n+3)(n+4)}+{ O}\left(n^{-4}\right)$,
		\item[v)] $\tilde{\mu}_{n,6}^{2}(x)=-\displaystyle\frac{240x^3(1-x)^3n^2}{(n+1)(n+2)(n+3)(n+4)(n+5)}+{ O}\left(n^{-4}\right)$.
	\end{itemize}
\end{lemma}
\begin{theorem}
	If $f\in C^{6}[0,1]$ and $x\in [0,1]$, then
	$$ \tilde{ U}_n^{2}(f;x)-f(x)={ O}\left(n^{-2}\right). $$
\end{theorem}
\begin{proof} Applying the modified genuine Bernstein-Durrmeyer operators $\tilde{ U}_n^{2}$ to the Taylor's formula, we obtain
	$$ \tilde{ U}_n^{2}(f;x)-f(x)=\displaystyle\sum_{k=1}^6 f^{(k)}(x)\tilde{ U}_n^{2}\left( (t-x)^k;x\right)+\tilde{ U}_n^{2}\left(\xi(t,x)(t-x)^6;x\right),  $$
	where $\displaystyle\lim_{t\to x}\xi(t,x)=0$.
	We have
	\begin{align}
&	\tilde{ U}_n^{2}(f;x)=(n-1)\left(nx^2-(n+1)x+1\right)\sum_{k=1}^{n-2}p_{n-2,k}(x)\int_0^1p_{n-2,k-1}(t)f(t)dt\nonumber\\
	&+2n(n-1)x(1-x)\sum_{k=1}^{n-1}p_{n-2,k-1}(x)\int_0^1p_{n-2,k-1}(t)f(t)dt\nonumber\\
	&+(n-1)\left(nx^2-(n-1)x\right)\sum_{k=2}^{n-1}p_{n-2,k-2}(x)\int_0^1p_{n-2,k-1}(t)f(t)dt\nonumber\\
	&+\left(nx^2-(n+1)x+1\right)(1-x)^{n-2}f(0)+\left(nx^2-(n-1)x\right)x^{n-2}f(1).
	\label{xx}
	\end{align}
	Let $\varepsilon>0$ be given. There exist  $\delta>0$ such that if $|t-x|<\delta$, then $|\xi(t,x)|<\varepsilon$. We denote
	\begin{align*}
	&{ K}_1=\left\{i:\left|\frac{i}{n}-x\right|<\delta, i=0,1,2,\cdots ,n\right\},\\
	&{ K}_2=\left\{i:\left|\frac{i}{n}-x\right|\ge \delta, i=0,1,2,\cdots ,n\right\}.\end{align*}
	Let $k\in { K}_1$. Since $\left| \xi(t,x)\right| < \varepsilon $,  from (\ref{xx}) we obtain
	\begin{align}
&	\left| \tilde{U}_n^{2}\left(\xi(t,x)(t-x)^6;x\right) \right|
		\leq\displaystyle\frac{\varepsilon n}{4}\left\{(n-1)\sum_{k=1}^{n-2}p_{n-2,k}(x)\int_0^1p_{n-2,k-1}(t)(t-x)^6 dt\right.\nonumber\\
	&+2(n-1)\sum_{k=1}^{n-1}p_{n-2,k-1}(x)\int_0^1p_{n-2,k-1}(t)(t-x)^6 dt\nonumber
	\end{align}\begin{align}
	&+(n-1)\sum_{k=2}^{n-1}p_{n-2,k-2}(x)\int_0^1p_{n-2,k-1}(t)(t-x)^6 dt
	+\left.(1-x)^{n-2}x^6+x^{n-2}(1-x)^6\right\}\nonumber
\\
	&\leq\displaystyle\frac{120\varepsilon x^3(1-x)^3(1+x-x^2)n^3}{(n+1)(n+2)(n+3)(n+4)(n+5)}+{ O}\left(n^{-3}\right).	\label{ec1}
	\end{align}
	Let $k\in { K}_2$. We denote $M=\displaystyle\sup_{0\leq t\leq 1} |\xi(t,x)|(t-x)^6$. Then
	 $$\left| \xi(t,x) \right|(t-x)^6\leq\displaystyle \frac{M}{\delta^6}\left(\frac{k}{n}-x \right)^6.$$
	 Moreover, the below upper bound is obtained
	\begin{align}\label{ec2}
&	\left| \tilde{ U}_n^{2}\left(\xi(t,x)(t-x)^6;x\right) \right|
		=\displaystyle\frac{Mn}{4\delta^6}\left\{\sum_{k=1}^{n-2}p_{n-2,k}(x)\left(\frac{k}{n}-x\right)^6
\right.\\
	&	+2\sum_{k=1}^{n-1}p_{n-2,k-1}(x)\left(\frac{k}{n}-x\right)^6+\sum_{k=2}^{n-1}p_{n-2,k-2}(x)\left(\frac{k}{n}-x\right)^6\nonumber\\
&	+\left.(1-x)^{n-2}x^6+x^{n-2}(1-x)^6\right\}
	=\displaystyle\frac{15Mx^3(1-x)^3}{n^2\delta^6}+{ O}\left(n^{-3}\right)={ O}\left(n^{-2} \right).\nonumber
	\end{align}
	From (\ref{ec1}) and (\ref{ec2}) the proof of theorem is completed.
\end{proof}

In the following we will improve the previous results considering a new\linebreak  genuine Bernstein-Durrmeyer operators that have order of approximation $\displaystyle{ O}\left(n^{-3}\right)$ defined as

\begin{align}\label{K3}
{ U}_{n}^{3}(f;x)&=(n-1)\displaystyle\sum_{k=1}^{n-1} p_{n,k}^{3}(x) \int_{0}^{1}p_{n-2,k-1}(t)f(t)dt\nonumber\\
&+\beta(x,n)(1-x)^{n-4}f(0)+\beta(1-x,n)x^{n-4}f(1),
\end{align}
where
\begin{align*} p_{n,k}^{3}(x)&=\beta(x,n)p_{n-4,k}(x)+\gamma(x,n)p_{n-4,k-1}(x)+\delta(x,n)p_{n-4,k-2}(x) \\
&+\gamma(1-x,n)p_{n-4,k-3}(x)+\beta(1-x,n)p_{n-4,k-4}(x)\end{align*}
and
\begin{align*}
& \beta(x,n)=\beta_4(n)x^4+\beta_3(n)x^3+\beta_2(n)x^2+\beta_1(n)x+\beta_0(n),\\
& \gamma(x,n)=\gamma_4(n)x^4+\gamma_3(n)x^3+\gamma_2(n)x^2+\gamma_1(n)x+\gamma_0(n),\\
&\delta(x,n)=\delta_0(n)(x(1-x))^2.
\end{align*}
Note that $\beta_i(n)$, $\gamma_i(n)$, $i=0,1,\dots,4$ and $\delta_0(n)$ are some unknown sequences. Denote $\tilde{ U}_n^{3}$  the operator (\ref{K3}) with
\begin{align*}
& \beta_0(n)=1,\beta_1(n)=\displaystyle -4-\frac{4}{3}n, \beta_2(n)=\displaystyle 5+\frac{10}{3}n+\frac{1}{2}n^2, \beta_3(n)=-n^2-2n-2,\\
&\beta_4(n)=\displaystyle\frac{1}{2}n^2,\gamma_0(n)=0,
 \gamma_1(n)=\displaystyle 4+\frac{7}{3}n,\,\,\gamma_2(n)=\displaystyle -\frac{19}{3}n-2n^2-8,\\
 & \gamma_3(n)=4n^2+4n+4,
 \gamma_4(n)=-2n^2,\,\, \delta_0(n)=3n^2.
\end{align*}
Let $\tilde{\mu}_{n,k}^{3}(x):=\tilde{ U}_n^{3}\left((t-x)^k;x\right)$, $k=0,1,\dots$ the central moments of $\tilde{ U}_n^{3}$.
\begin{lemma}
	The modified genuine Bernstein-Durrmeyer operator $\tilde{ U}_n^{3}$ verify:
	\begin{itemize}
		\item [i)] $\tilde{\mu}_{n,1}^{3}(x)=\tilde{\mu}_{n,2}^{3}(x)=\tilde{\mu}_{n,3}^{3}(x)=0$;
		\item [ii)] $\tilde{\mu}_{n,4}^{3}(x)=\displaystyle \frac{4x(1-x)(39x^2-39x+10)}{\sum_{k=1}^3(n+k)}+{ O}\left(n^{-4}\right) $;
		\item [iii)] $\tilde{\mu}_{n,5}^{3}(x)=\displaystyle \frac{120(1-2x)x^2(1-x)^2n}{\sum_{k=1}^4(n+k)}+{ O}\left(n^{-4}\right)$;
		\item [iv)] $\tilde{\mu}_{n,6}^{3}(x)=\displaystyle\frac{120x^3(1-x)^3n^2}{\sum_{k=1}^{5}(n+k)}+{ O}\left(n^{-4}\right);  $
		\item [v)] $\tilde{\mu}_{n,7}^{3}(x)=\tilde{\mu}_{n,8}^{3}(x)=\displaystyle{ O} \left(n^{-4}\right); $
		\item[vi)] $\tilde{\mu}_{n,9}^{3}(x)=\tilde{\mu}_{n,10}^{3}(x)=\displaystyle{ O} \left(n^{-5}\right).$
	\end{itemize}
\end{lemma}
The asymptotic order of approximation of $\tilde{ U}_n^{3}$ to $f$ when $n$ goes to infinity is given in the following result:

\begin{theorem}
	If $f\in C^{10}[0,1]$ and $x\in [0,1]$, then
	$ \tilde{ U}_n^{3}(f;x)-f(x)={ O}\left(n^{-3}\right). $
\end{theorem}

\section{Numerical Example}
Some numerical examples with illustrative graphics have been added to validate the theoretical results and also compare the rate of convergence by using Maple algorithms.

\begin{example} Let $g(x)=\displaystyle\sin(4\pi x)+4\sin\left(\frac{1}{4}\pi x\right)$, $n=10$, $\alpha_0(n)=\displaystyle\frac{n-1}{2n}$ and $\alpha_1(n)=\displaystyle\frac{1}{n}$.
	The convergence of the modified genuine Bernstein-Durrmeyer operators is illustrated in Figure \ref{fig:A1}.  Let $\varepsilon_n(f;x)=\left| g(x)-{ U}_n(g;x)\right|$ and $\varepsilon_n^{i}(g;x)=\left| g(x)-\tilde{ U}_n^{i}(g;x)\right|$, $i=1,2,3$ be the error of approximation for  genuine Bernstein-Durrmeyer operators and the modified genuine Bernstein-Durrmeyer operators, respectively. The error of approximation is illustrated in Figure \ref{fig:A2} and for this particular case  the approximation by the modified genuine Bernstein-Durrmeyer operators $\tilde{ U}_n^{i}$, $i=1,2,3$ is better then using classical genuine Bernstein-Durrmeyer operator ${ U}_n$.  Also, in Table \ref{table1} we computed the error of approximation for ${ U}_n$ and $\tilde{ U}_n^{i}$, $i=1,2,3$ at certain points.

\begin{minipage}{\linewidth}
	\centering
	\begin{minipage}{0.44\linewidth}
		\begin{figure}[H]
			\includegraphics[width=\linewidth]{A1}
			\caption{Convergence of the modified genuine Bernstein-Durrmeyer operators}\label{fig:A1}
		\end{figure}
	\end{minipage}
	\hspace{0.05\linewidth}
	\begin{minipage}{0.44\linewidth}
		\begin{figure}[H]
			\includegraphics[width=\linewidth]{A2}
			\caption{Error of approximation by the modified genuine Bernstein-Durrmeyer operators }\label{fig:A2}
		\end{figure}
	\end{minipage}
\end{minipage}
	\begin{tb}\label{table1}\centering
		{\it  Error of approximation  $\varepsilon_n$ and $\varepsilon_n^{i}$, $i=1,2,3$}

		$  $

		\begin{tabular}{|l|l|l|l|l|}\hline
			$x$&$\varepsilon_n(g;x)$&$\varepsilon_n^{1}(g;x)$&$\varepsilon_n^{2}(g;x)$&$\varepsilon_n^{3}(g;x)$ \\  \hline
			$0.10$ & $0.6945330253$  &  $0.5295762286$ & $0.4330397338$ & $0.2812687901$\\  \hline
			$0.15$ & $0.6942110247$ & $0.5933130652$ & $0.4833262822$ & $0.4529855958$ 	\\  \hline
			$0.25$ & $0.1580679909$ & $0.2097384650$ & $0.1632564535$ & $0.1344025490$ 	\\  \hline
			$0.30$ & $0.6879044013$ & $0.7312808277$ & $0.6136368403$ & $0.2177095258$ 	\\  \hline
			$0.40$ & $0.9681814067$ & $0.9948377556$ & $0.8683959826$ & $0.5352250570$ 	\\  \hline
			$0.50$ & $0.0213435310$ & $0.0213436470$ & $0.0022170860$ & $0.0000572989$ 	\\  \hline
			$0.55$ & $0.6243511367$ & $0.6381381849$ & $0.5355754034$ & $0.3459331618$ 	\\  \hline
			$0.70$ & $0.7234749900$ & $0.7601315856$ & $0.6172299990$ & $0.2177088936$ 	\\  \hline
			$0.75$ & $0.1896839607$ & $0.2308635388$ & $0.1663414950$ & $0.1338132004$ 	\\  \hline
			$0.90$ & $0.6796558035$ & $0.5415051330$ & $0.4322424640$ & $0.2822400676$ 	\\  \hline
			$0.95$ & $0.3964880751$ & $0.1546334112$ & $0.194510818$ & $0.0192152324$ 	\\  \hline
		\end{tabular}
	\end{tb}
\end{example}

\begin{example}
	Let
	$ g(x)=\left| x-\frac{1}{4} \right|\cos(4\pi x). $  For $n=10$, $\alpha_0(n)=\displaystyle\frac{n-1}{2n}$ and $\alpha_1(n)=\displaystyle\frac{1}{n}$, the convergence of the modified genuine Bernstein-Durrmeyer operators to  $g(x)$ is shown in Figure \ref{A3}. The errors of approximation  $\varepsilon_n$ and $\varepsilon_n^{i}$, $i=1,2,3$ are illustrated in Figure \ref{A4}.
Also, in Table \ref{table2} we computed the error of approximation for ${ U}_n$ and $\tilde{ U}_n^{i}$, $i=1,2,3$ at certain points.

\begin{minipage}{\linewidth}
	\centering
	\begin{minipage}{0.44\linewidth}
		\begin{figure}[H]
			\includegraphics[width=\linewidth]{A3}
			\caption{Convergence of the modified genuine Bernstein-Durrmeyer operators}\label{A3}
		\end{figure}
	\end{minipage}
	\hspace{0.05\linewidth}
	\begin{minipage}{0.43\linewidth}
		\begin{figure}[H]
			\includegraphics[width=\linewidth]{A4}
			\caption{Error of approximation  $\varepsilon_n$ and $\varepsilon_n^{i}$, $i=1,2,3$ }\label{A4}
		\end{figure}
	\end{minipage}
\end{minipage}
\begin{tb}\label{table2}\centering
	{\it  Error of approximation  $\varepsilon_n$ and $\varepsilon_n^{i}$, $i=1,2,3$}

	$  $

	\begin{tabular}{|l|l|l|l|l|}\hline
		$x$&$\varepsilon_n(g;x)$&$\varepsilon_n^{1}(g;x)$&$\varepsilon_n^{2}(g;x)$&$\varepsilon_n^{3}(g;x)$ \\  \hline
		$0.10$ & $0.0864633606$  &  $0.0482073753$ & $0.0367065261$ & $0.0067324201$\\  \hline
		$0.20$ & $0.1103333385$  &  $0.0961865298$ & $0.0594456124$ & $0.0191120699$\\  \hline
		$0.25$ & $0.0518922812$  &  $0.0436031934$ & $0.0158446516$ & $0.0031661470$\\  \hline
		$0.50$ & $0.2575784301$  &  $0.2575784294$ & $0.2685059808$ & $0.1312442040$\\  \hline
		$0.55$ & $0.2614871004$  &  $0.2604287058$ & $0.3049134784$ & $0.1915072058$\\  \hline
		$0.65$ & $0.1006465455$  &  $0.0976735308$ & $0.0362205580$ & $0.0365602345$\\  \hline
		$0.70$ & $0.3587223234$  &  $0.3466837357$ & $0.1760351064$ & $0.1049635359$\\  \hline
		$0.85$ & $0.3901466578$  &  $0.2963782143$ & $0.1888707949$ & $0.0267144753$\\  \hline
		$0.90$ & $0.1458116388$  &  $0.0029193836$ & $0.0022766453$ & $0.1211619468$\\  \hline
	\end{tabular}
\end{tb}
\end{example}

\begin{example}
	Let  $g(x)=\left(x-\frac{1}{4}\right)\sin(2\pi x)$. The behaviours of the approximations ${ U}_n(g;x)$, $\tilde{ U}_n^{i}(g;x)$, $i=1,2,3$ and their errors  $\varepsilon_n(g;x)$, $\varepsilon_n^{i}(g;x)$ for $n=5,7,10$, $\alpha_0(n)=\displaystyle\frac{n-1}{2n}$, $\alpha_1(n)=\displaystyle\frac{1}{n}$ are illustrated in the Figures \ref{A5}-\ref{A12}.
Also, in Tables \ref{table3}-\ref{table6} we computed the error of approximation for ${ U}_n$ and $\tilde{ U}_n^{i}$, $i=1,2,3$, for $n=5,7,10$ at certain points.
\end{example}

\begin{minipage}{\linewidth}
\centering
\begin{minipage}{0.44\linewidth}
	\begin{figure}[H]
		\includegraphics[width=\linewidth]{A5}
		\caption{Convergence of the genuine Bernstein-Durrmeyer operators  ${ U}_n$  }\label{A5}
	\end{figure}
\end{minipage}
\hspace{0.05\linewidth}
\begin{minipage}{0.43\linewidth}
	\begin{figure}[H]
		\includegraphics[width=\linewidth]{A6}
		\caption{Error of approximation  $\varepsilon_n$  }\label{A6}
	\end{figure}
\end{minipage}
\end{minipage}

$$  $$

\begin{tb}\label{table3}\centering
{\it  Error of approximation  $\varepsilon_n$ for $n=5,7,10$}

$   $

\begin{tabular}{|l|l|l|l|}\hline
	$x$&$\varepsilon_5(g;x)$&$\varepsilon_{7}(g;x)$&$\varepsilon_{10}(g;x)$ \\  \hline
	$0.10$ & $0.0684403678$  &  $0.0678031572$ & $0.0622151561$ \\  \hline
	$0.15$ & $0.0499431989$  &  $0.0531270433$ & $0.0521857868$ \\  \hline
	$0.25$ & $0.0578940551$  &  $0.0463235563$ & $0.0334294267$ \\  \hline
	$0.30$ & $0.1212531914$  &  $0.1072975170$ & $0.0886731506$ \\  \hline
	$0.40$ & $0.1969741168$  &  $0.1851488999$ & $0.1634615511$ \\  \hline
	$0.65$ & $0.1391012080$  &  $0.1078116400$ & $0.0816688494$ \\  \hline
	$0.70$ & $0.2391101684$  &  $0.1978330494$ & $0.1589711006$ \\  \hline
	$0.85$ & $0.3328374955$  &  $0.2808786960$ & $0.2265106612$ \\  \hline
	$0.90$ & $0.2644985309$  &  $0.2206728121$ & $0.1747401754$ \\  \hline
\end{tabular}
\end{tb}

\newpage

\begin{minipage}{\linewidth}
	\centering
	\begin{minipage}{0.43\linewidth}
		\begin{figure}[H]
			\includegraphics[width=\linewidth]{A7}
			\caption{Convergence of the modified genuine Bernstein-Durrmeyer operators  ${ U}_n^{1}$ }\label{A7}
		\end{figure}
	\end{minipage}
	\hspace{0.05\linewidth}
	\begin{minipage}{0.43\linewidth}
		\begin{figure}[H]
			\includegraphics[width=\linewidth]{A8}
			\caption{Error of approximation  $\varepsilon_n^{1}$  }\label{A8}
		\end{figure}
	\end{minipage}
\end{minipage}

$$  $$

\begin{tb}\label{table4}\centering
	{\it  Error of approximation  $\varepsilon_n^{1}$ for $n=5,7,10$}

	$  $

	\begin{tabular}{|l|l|l|l|}\hline
		$x$&$\varepsilon_5(g;x)$&$\varepsilon_{7}(g;x)$&$\varepsilon_{10}(g;x)$ \\  \hline
		$0.25$ & $0.0759640671$  &  $0.0559388716$ & $0.0362644403$ \\  \hline
		$0.30$ & $0.1371072386$  &  $0.1171805319$ & $0.0932932589$ \\  \hline
		$0.35$ & $0.1844145994$  &  $0.1666950554$ & $0.1413524766$ \\  \hline
		$0.40$ & $0.2057325249$  &  $0.1923019252$ & $0.1687116616$ \\  \hline
		$0.50$ & $0.1448255593$  &  $0.1453442003$ & $0.1349064978$ \\  \hline
		$0.60$ & $0.0366918591$  &  $0.0179868291$ & $0.0057986703$ \\  \hline
		$0.70$ & $0.2402023843$  &  $0.2045318798$ & $0.1686629702$ \\  \hline
		$0.80$ & $0.3245837174$  &  $0.2807124726$ & $0.2325391597$ \\  \hline
		$0.90$ & $0.1835617165$  &  $0.1497215453$ & $0.1155690815$ \\  \hline
	\end{tabular}
\end{tb}

\newpage

\begin{minipage}{\linewidth}
	\centering
	\begin{minipage}{0.44\linewidth}
		\begin{figure}[H]
			\includegraphics[width=\linewidth]{A9}
			\caption{Convergence of the modified genuine Bernstein-Durrmeyer operators  ${ U}_n^{2}$ }\label{A9}
		\end{figure}
	\end{minipage}
	\hspace{0.05\linewidth}
	\begin{minipage}{0.43\linewidth}
		\begin{figure}[H]
			\includegraphics[width=\linewidth]{A10}
			\caption{Error of approximation  $\varepsilon_n^{2} $ }\label{A10}
		\end{figure}
	\end{minipage}
\end{minipage}

$$   $$

\begin{tb}\label{table5}\centering
	{\it  Error of approximation  $\varepsilon_n^{2}$ for $n=5,7,10$}

	$  $

	\begin{tabular}{|l|l|l|l|}\hline
		$x$&$\varepsilon_5(g;x)$&$\varepsilon_{7}(g;x)$&$\varepsilon_{10}(g;x)$ \\  \hline
		$0.10$ & $0.0764438176$  &  $0.0624790953$ & $0.0432951373$ \\  \hline
		$0.25$ & $0.0345024248$  &  $0.0130565516$ & $0.0000245123$ \\  \hline
		$0.30$ & $0.0990500279$  &  $0.0650077665$ & $0.0375060681$ \\  \hline
		$0.40$ & $0.1914411452$  &  $0.1449016157$ & $0.0994953904$ \\  \hline
		$0.50$ & $0.1740970203$  &  $0.1380269700$ & $0.0987547084$ \\  \hline
		$0.60$ & $0.0439765069$  &  $0.0388439363$ & $0.0284303826$ \\  \hline
		$0.70$ & $0.1215101036$  &  $0.0874936435$ & $0.0605939578$ \\  \hline
		$0.80$ & $0.2110574499$  &  $0.1488955530$ & $0.0977772009$ \\  \hline
		$0.90$ & $0.1561838905$  &  $0.0989074740$ & $0.0557077924$ \\  \hline
	\end{tabular}
\end{tb}

\newpage

\begin{minipage}{\linewidth}
	\centering
	\begin{minipage}{0.45\linewidth}
		\begin{figure}[H]
			\includegraphics[width=\linewidth]{A11}
			\caption{Convergence of the modified genuine Bernstein-Durrmeyer operators  ${ U}_n^{3}$ }\label{A11}
		\end{figure}
	\end{minipage}
	\hspace{0.05\linewidth}
	\begin{minipage}{0.42\linewidth}
		\begin{figure}[H]
			\includegraphics[width=\linewidth]{A12}
			\caption{Error of approximation  $\varepsilon_n^{3}$  }\label{A12}
		\end{figure}
	\end{minipage}
\end{minipage}
$  $

\begin{tb}\label{table6}\centering
	{\it  Error of approximation  $\varepsilon_n^{3}$ for $n=5,7,10$}

	$  $

	\begin{tabular}{|l|l|l|l|}\hline
		$x$&$\varepsilon_5(g;x)$&$\varepsilon_{7}(g;x)$&$\varepsilon_{10}(g;x)$ \\  \hline
		$0.10$ & $0.130304351$  &  $0.060532301$ & $0.020830446$ \\  \hline
		$0.20$ & $0.141691111$  &  $0.080159674$ & $0.039173543$ \\  \hline
		$0.30$ & $0.061291162$  &  $0.037462997$ & $0.020686153$ \\  \hline
		$0.40$ & $0.024416705$  &  $0.017774084$ & $0.010936011$ \\  \hline
		$0.45$ & $0.043687998$  &  $0.031315020$ & $0.019471529$ \\  \hline
		$0.50$ & $0.040509305$  &  $0.029993035$ & $0.019169082$ \\  \hline
		$0.60$ & $0.024027791$  &  $0.011127560$ & $0.004477202$ \\  \hline
		$0.70$ & $0.110487435$  &  $0.062167445$ & $0.031839458$ \\  \hline
		$0.80$ & $0.136082209$  &  $0.064976021$ & $0.026722598$ \\  \hline
		$0.90$ & $0.069748506$  &  $0.012020135$ & $0.006394035$ \\  \hline
	\end{tabular}
\end{tb}

$$  $$

{\bf Acknowledgments.} The work  was financed from Lucian Blaga University of Sibiu research grants LBUS-IRG-2018-04.

$   $

\noindent{\bf References}

redpajama_set_name: RedPajamaArXiv


Women have so much to look forward to. Millennial women can look forward to making less and less than their male counterparts or, if their of an older generation, they can look forward to watching millennials make less and less than their male counterparts.
According to Reuters, a new report from the Office for National Statistics by the Resolution Foundation in the U.K. contains both good news and bad news for the fresh batch of ladies getting stiffed by their employers. While the gender pay gap was on average around 16 percent for the baby boomers, it's dropped to as low as 5 percent for those born between 1981 and 2000. Hurray! Unfortunately, it doesn't last. Booo.
The Guardian reports that the gap sharply widens when women hit their 30s. So, basically, as Millennials age up, they can expect to make 30 percent less than their man counterparts, partly because of the old specter of of baby-making and family-raising, with its accompanying time off.
But she said there were many issues related to working part-time, such as missing out on informal chats in the pub, that needed to be tackled. "I wouldn't want to play down the policy success we've had, but the area where there's probably the most we could do is around the part-time penalties, and the opportunities for promotion and progression, the cultural stuff," Gardiner said.
Much like in the U.S., the cost of childcare remains an issue that the U.K. is grappling with, though a government spokeswoman told the Guardian that beginning in September working parents of children ages 3-4 will be given 30 hours of free childcare in an attempt to make it possible for women to return to work. That's double the previous allotment, but likely not enough to cover the costs for most, leaving women to pay the price as usual.


new brakes, new water pump and fixed the electrical problem with the signal lights in august. new alternator, new battery and rebuilt the air conditioner (it works great now) in october. new tires and alignment in november.


Casual chic is never more apparent than a woman rocking a plain tee and jeans. Luxurious, ultra-soft Pima Cotton ensures supreme comfort, and the stretch knit of the fabric lends itself to the flattering fit of this classic piece. The Peruvian Pima Cotton will caress your body with feathery soft indulgence, making this closet essential irresistible.


Manually Install Java Plugin Firefox - New to Oracle Community? Be sure to check out our FAQ and read through the Community Guidelines.Then, join our Getting Started group, Introduce yourself to community, and start exploring!. Want to offer feedback, or share your ideas?We'd love to hear from you! *Please don't post product-related questions in the feedback space; instead, navigate to or search for an appropriate product. Jun 16, 2017 · Remove the "Java" folder; Empty the Trash on the Mac as usual; Java will be removed completely this way. The Finder based approach is the easier and safer way to uninstall Java from a Mac, though Mac users can also remove Java and JRE via the command line as well.. How To Manually Set Up Your Wired Internet Connection in K / Ubuntu without Network-Manager ~ Ubuntu / Linux blog.
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Adobe Flash Player missing, even though I updated multiple times ... ... is manual install. When clicked, it redirects me to the adobe flash player website, which is still useless. So nothing of what you listed above works.
How To Enable Java Plugin on Firefox 8.0 in Ubuntu 10.04 I hope this article usefull for who can't enable java plugin on firefox .


Jim is a resource and environmental economic practitioner with over 20 years' of postgraduate experience. Since 2006 he has undertaken in excess of 150 consulting assignments.
Cost-benefit analysis, cost effectiveness analysis, and non-market valuation are tools used in most of his projects. A major focus of his work is the integration of environmental values into mainstream decision making and investment.
Jim has experience across a broad range of resource and environmental management issues including water management (allocations, infrastructure investment (urban and rural), water use efficiency, water quality, and stormwater), catchment management, climate change, vegetation management, biodiversity, sustainable agriculture, sustainable development, waste management, development policy, impacts of resource development projects, and natural capital valuation.
Jim has undertaken consulting assignments in all states and territories across Australia as well as numerous international assignments in Tuvalu, Vietnam, Papua New Guinea, Fiji, Myanmar, China, Federated State of Micronesia, and for multinational organisations (e.g. SPREP, UN, FAO, OECD, GIZ, World Bank).
Prior to commencing his consulting career in 2006, Jim was the Director of Economics for the Queensland Department of Natural Resources.


text:
Press freedom in Bahrain three years after #Feb14
By Jason Stern/CPJ Middle East and North Africa Research Associate on February 18, 2014 5:25 PM ET
Three years ago, hundreds of thousands of Bahrainis descended to the streets to demand change. A harsh government crackdown and the turn to violence by some protesters have since dampened the hope lit on February 14, 2011. In this context, we asked Bahrainis and Bahrain observers on Twitter how they think the status of press freedom has changed in the country. We know what we think: The Bahraini government has fallen terribly short of its own rhetoric of reform. But we wanted to hear directly from those who work and live in Bahrain every day.
Below is a Storify of some of the answers we received.
Jason Stern is a senior research associate for CPJ's Middle East and North Africa program. He has a master's in Middle East Studies from George Washington University and a bachelor's in government from Cornell University.
#Feb14
Ahmed Humaidan
Ahmed Ismail Hassan
Ali Abdel Imam
Hussein Hubail
Karim Fakhrawi
Nazeeha Saeed
Short URL: https://cpj.org/x/5971
Saudi control of Arab media, lamented by Khashoggi, shapes coverage of his death
October 30, 2018 2:59 PM ET
It is a cruel irony that Jamal Khashoggi's last unpublished column for The Washington Post was a call for press freedom in the Arab world. His homeland, Saudi Arabia, has spent the last three decades and hundreds of millions of dollars to ensure that never happens....
Undiscoverable: How Al-Jazeera's Snapchat channel disappeared from three Gulf nations
September 10, 2018 12:35 PM ET
Search for "Al-Jazeera" on Snapchat, and the first result that comes up is a ubiquitous publisher channel in the app's famed vertical layout. That is, unless you are in Saudi Arabia, the United Arab Emirates (UAE), or Bahrain. Users in these counties are instead offered a list of stores...
Amid Gulf tensions, press is used as a political pawn
June 8, 2017 5:38 PM ET
Today Bahrain became the latest Gulf nation to put pressure on news outlets amid political tension, when its Interior Ministry announced that anyone publishing support or sympathy for Qatar faces up to five years in prison. The announcement came the day after the United Arab Emirates used the threat...
Bahrain denies accreditation to journalists
May 4, 2017 1:39 PM ET
Bahrain has over the past year refused to grant accreditation to several of its own citizens who report for foreign and independent media, including those working for The Associated Press, Agence France-Presse, France 24, and Monte Carlo Doualiya. It has on multiple occasions not granted media visas to foreign...

redpajama_set_name: RedPajamaCommonCrawl


All forum rules apply to clans and their topics. Apart from those listed in Sharks' original post, some clans make up their own rules as well.
read page 1. 50+ post to be able to join a clan.
how do i know how many posts do i hav??
tradeking09 wrote: how do i know how many posts do i hav??
Look under your avatar on any of your posts.
It is up to date. Some areas don't increase your post count. Posts were recently resynced, so all values should be close to exact. Some are probably off as I moved a topic from a "posts count" zone to a "posts don't count" zone after the resync, but yours should be fine.


My membership doesn't appear on my account / the system doesn't recognise me as a member.
This can sometimes happen when a customer has multiple accounts. If the account associated with the login you have used does not have a membership attached then please contact the Box Office. If you are concerned that your membership is not listed or you can't book as a member during Priority Booking, please contact our Box Office or Development teams. Do not register a new account as this will treat you as a new customer.
I am at the seating plan and I can't get the seats I want, how do I select a different date?
To choose a different performance of the same production, click on 'Select another performance' to the left of the seating plan (or below it on most mobile phones).
I have tried looking at a number of dates but there doesn't seem to be any seats available to select, is the production sold out?
This means that there are no tickets available to buy online. However we may have seats available through our Box Office on 020 7359 4404.
Returned tickets may become available online, in person or over the phone and we will also release tickets weekly through Almeida Rush, you can find out more here.
Why have I been put in an online queue when trying to book tickets on your website?
An online waiting room is a way to limit traffic flow onto the website during busy periods such as Priority Booking and ensure that every customer has a fair and smooth booking experience. Without the queue in place, customers may have difficulty accessing the site or completing their transactions when there are a certain number of consecutive users. The queue only comes into effect when a certain amount of traffic hits the website, and so will only operate during particularly busy periods, such as when tickets for a new production go on sale.
A certain time before tickets go on sale you may be taken to a pre-queue where a number will be allocated to you. These numbers are not distributed on a first-come first-served basis and do not indicate where your place will be when you are taken to the main booking queue.
Once you've entered the queue you don't have to do anything else and provided you don't click the 'take me out of the queue' link your position should be held. You will be allocated a time (usually 10 minutes) to enter the website, log in and select your seats. However you can lose your place or have your number 'rejected' if you try to join the queue more than three times using the same browser. Also, if you have forgotten your log in details you may be taken to the back of the queue if you need to reset your password and follow the reset password link. This is why we recommend you check your log in details and have them ready before big on-sale events.
I am trying to make a group booking but am unable to select more than nine seats.
The maximum number of seats that can be purchased in any one transaction is nine, even if you are purchasing tickets across a number of different productions. This allows us to offer the best service possible to those making group bookings, and prevents individuals reselling large numbers of tickets through unauthorised agents.
If you would like to book more than nine tickets in one transaction please contact our Box Office on 020 7359 4404.
I am trying to book a ticket at a concessionary rate but the only options are Student, Under 30s, Job Seekers Allowance or Over 65.
The concessionary rates that we offer are for Students, those claiming Job Seekers Allowance, Over 65s and the companions of Deaf and disabled patrons.
We also offer discounted tickets for Under 25s, Under 30s, and those that live or work in the Islington area.
I am under 25, how do I take advantage of the Under 25s concession?
The dates of performances with Under 25s tickets available will be listed under Dates & Tickets info on each production page. Please note sometimes the date that these go on sale. To book these tickets, you first need to enter the promo code UNDER25 at the top right of the seating plan once you've chosen your date. This will reveal on the seating plan the Under 25s seats that are available to book. Tickets will need to be collected from Box Office on the presentation of a valid ID.
I am trying to book a concessionary ticket, but this option does not seem to be available.
Please ensure you are booking for a performance on which concessions are valid. Concessions are available Monday to Thursday and on all matinees. They are not valid on weekend evening performances and aren't applicable in the final week of the production. The Under 65 concession is also not available in the penultimate weekend of performances. Concessions are only available on seats in the second price band (£28 / £32) for evening performances; for matinees concessions are available on the £39.50 tickets as well.
I am unable to find an £10 or £20 seat using the concession rate.
Concessionary tickets are £25, so if you would like to book a £10 or £20 ticket you can do so without applying a concession.
I am booking for a captioned performance and would like to know which seats give the best sightlines of the captioning screen.
Our password system is case sensitive – please check your Caps Lock is not turned on.
If you continue to have problems you can request a password reminder using the Forgot Password function.
I've asked for a password reminder but I've not received this by email.
I am unable to edit my account details, after inputting new details they do not seem to save.
Before completing my purchase, will I see an order confirmation page?
After clicking 'Add to basket' you will be taken to your Shopping Basket where you can review your order. You can also find your basket located in the top right of the menu bar, or in the top menu when looking on a mobile device or small window. You will also have a final opportunity to review your order before clicking 'Buy now' at the checkout stage. Please do not press the back button once you've input your payment details.
My booking session has timed out, will my tickets still be held?
Tickets are held in your basket for 10 minutes. If you do not complete your booking within this time and your session times out you may need to start the booking process again.
If the seats you wanted no longer seem to be available, first check whether they are still in your basket. If they are not, they may be locked in your session. Please wait for 30 minutes before trying to book again.
When trying to make payment I am receiving an error message.
Please ensure that the address you are entering is the billing address for your card and that you have entered it as it appears on your statement. For security reasons we cannot take payment without the correct billing address.
We accept all major credit and debit cards - Amex, Mastercard, Solo, Visa Debit, Visa Credit and Visa Electron – unfortunately we do not accept Diners Card.
I have booked tickets online but I've not received an email confirmation.
I would like to change my data protection settings / stop receiving emails from you.
Go to the 'Your Preferences' section of your online account. Here you can choose how and if we contact you - by Post, Email, Phone and whether you're happy to receive information from Similar Organisations.
To change your data protection settings log into your account. From there you can change the 'Post', 'Email', 'Phone' and 'Similar Organisations' settings to 'yes' or 'no'.
Before logging out of your account please click 'Save Changes' to ensure that your new settings are saved.
I'm on your e-list, but haven't received recent emails from the Almeida Theatre.
Our database may suggest you did not wish to receive emails from us (i.e. we don't have permission according to your Data Protection settings). To add yourself to the e-list simply log into your account go to 'Your Preferences' and tick 'by email'. Before logging out of your account please click 'Save Changes' to ensure that your new settings are saved.
I am trying to create a new login / sign up to the e-list but my password is not being accepted.


French cryptographic money selection and use are set to get a minor lift from one year from now, as the French Prudential Supervision and Resolution Authority (ACPR), an administrative branch of the Banque de France has allowed consent for tobacco shops in the nation to offer bitcoin from January 1, 2019.
As indicated by a news report from Europe 1, the shops being referred to, which ordinarily offer lottery tickets and cigarettes will now start to offer bitcoin available to be purchased by means of an organization with the French Fintech startup Keplerk.
The organization with Keplerk likewise incorporates a nearby money enroll programming provider,which will give the foundation to pitching bitcoin to cigarette shop clients. The shops will pitch a voucher to clients, which can be reclaimed for bitcoin by means of Keplerk's crypto wallet. As per Keplerk, this denotes the first run through anyplace on the planet that physical shops will offer bitcoin to the overall population.
As per Keplerk, the task will be financed charging a 7 percent commission expense on each exchange. The organization further uncovered that it has been attempting to anchor the fundamental administrative authorization and corporate associations for over eighteen months.
French money related controllers have a long-standing doubt of digital forms of money and have cautioned more than once about the risks of putting resources into crypto. On Wednesday, the French national bank underlined its distrust of crypto, expressing that the ACPR conceded the authorization in its very own autonomous limit, which ought not be interpreted as meaning that it regulates the Keplerk venture.
As indicated by Europe 1, the ACPR's authorization was allowed not in light of French administrative kind disposition to crypto, but rather essentially in light of the fact that controllers in the nation feel that the development of bitcoin into a worldwide money is unavoidable. To them, it is smarter to acknowledge the truth of far reaching purchaser interest for bitcoin and to control it however much as could reasonably be expected than to be totally let well enough alone for the circle.


text:
Disciplines History European History
Voices Revived
The Spaniards An Introduction to Their History
by Americo Castro (Author), Willard F. King (Translator), Selma Margaretten (Translator)
Trim Size: 6 x 9
Request an Exam or Desk Copy Recommend to Your Library (PDF) RightsLink Rights and Permissions Buying Options
This ambitious book by Américo Castro is not simply a history of the Spanish people or culture. It is an attempt to create an entirely new understanding of Spanish society. The Spaniards examines how the social position, religious affiliation, and beliefs of Christians, Moors, and Jews, together with their feelings of superiority or inferiority, determined the development of Spanish identity and culture. Castro follows how españoles began to form a nation beginning in the thirteenth century and became wholly Spanish in the sixteenth century in a different way and under different circumstances than other peoples of Western Europe.
The original material of this book (chapters II through XII) was translated by Willard F. King, and the newly added material (preface, chapters I, XIII, and XIV, and appendix) was translated by Selma Margaretten.
This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1971.
Américo Castro was a Spanish cultural historian, philologist, and literary critic who challenged some of the prevailing notions of Spanish identity.
"An invaluable book for historians and Hispanists alike, one in which Castro fully explains his 'rules of the game' (in the preface and chapter I) and then proceeds brilliantly to develop his main thesis concerning the reality of Spanish history."—Manuel Duran, Yale University
Art of Suppression
Pamela M. Potter
Beyond Reason
Karol Berger
Making New Music in Cold War Poland
Lisa Jakelski
Cinema and the Wealth of Nations
Lee Grieveson
From 1989, or European Music and the Modernist Unconscious
Seth Brodsky
Russian Opera and the Symbolist Movement, Second Edition
Simon Morrison
Edmund Burke and the Conservative Logic of Empire
Daniel O'Neill
The Curious Humanist
Johannes von Moltke
Contesting Indochina
M. Kathryn Edwards
Moral Communities
Mark D. Steinberg


SMASHWELD 316. SMASHWELD 316 Topflex Conjunto semiautomtico para soldagem MIGMAG Manual de Instrues Ref. : Smashweld 316 Smashweld 316 Topflex Mar 17, 2014 Ok so ESAB is viable here in Canada. I found their site and it does appear that I would be able to get parts and stuff for it. ESAB Smashweld 180 Thoughts? by Greg From KW Mon Mar 17, 2014 7: 46 pm. Seamed nice and quiet its actually smaller than I thought it would be. Its made in Sweden and came with the manual Smashweld 4000T welding machines are designed to operate with PSF405 3M (Euroconnector type) torches Quality accessories for the quality welder ESAB offers a wide range of accessories.
Smashweld Mig Adaptor For Linde& LTec Mig Welding Machines. SMASHWELD 316. SMASHWELD 316 Topflex Conjunto semiautomtico para soldagem MIGMAG Manual de Instrues Ref. : Smashweld 316 Apr 18, 2008 ESAB smashweld 180 Discussion in 'Shop Talk' started by billyj, Apr 24, 2005. Apr 24, 2005# 1 FYI and anyone else that may own the older ESAB model a company in California took over that end of the business.
Now I'll wait till california wakes up and give them a call. I did this on my Smashweld 180 a few esab smashweld 180 manual I want to run gas less wire. How do I swap polarity? Welding Tools question ESAB offers a wealth of product support resources, including a range of technical and service publications, from Safety Data Sheets and downloadable product manuals to process certifications.
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Parts come off the router and are sorted by type onto rolling carts. These parts then flow to either edgebander, bore dowel insert or are put directly into a sort preceding the assembly table for those parts such as cabinet backs that don't need to be doweled or banded. On a good day we cut 30 sheets on the router, but parts don't reach the edgebander fast enough that I can leave it on continuously.
As a result I am having to run a full batch which sits in front of the bander until all sheets are done, then I batch everything through the bander. We are able to machine and sort both those parts that need no further machining after the router (e.g. backs) as well as parts that need only to be doweled after leaving the router (e.g. nailers) but it really doesn't speed things up very much.
I have considered small batches but the waste is pretty significant, especially given that I am running a lot of prefinished plywood so all parts have to be oriented with respect to grain direction.
I have also considered a second router. For those of you running two routers, is the output sufficient that you can run your bander nonstop without cooking your glue?
Also, is there some third option that I haven't considered?
We have a setting on our bander that kicks back the heat so it does not burn. Saves restarting from room temp.
I think most experienced craftsmen could beat a cnc to the bottom of a stack of plywood.
When we process 1 sheet on the CNC, whilst it is machining the previous panels are sorted, horizontally bored, edged and the scrap put in the bin. And we are not exactly breaking our backs to do this, unlike the panel saw. Also all holes are already drilled ready for comfimat screw assembly and any hardware required.
Our machining is by far the most efficient part of our operation with out a doubt, just ask our second year apprentice who operates the CNC.
I'd say about 30 sheets it about right and my machine is programed down, one so its not wearing its self out and the other is it more than keeps up with assembly.
Marty, to be clear I can do 50 sheets a day. Cut and bored (ready for assembly with all necessary holes, what we call milling), and cleaned up.
Are you saying with a CNC the same guy is also banding that same amount in a day (the 30 sheets) or is banding done by another person? I'm guessing banding with my small bander would take another day so if we are including banding I'm done to 25 sheets a day. But if we are talking two guys, I'm still at 50 a day. Just trying to get an apple to apple comparison.
Banding at the same time, same guy.
My real surprise and something we didn't really consider was the cleanliness, you are always on top of the waste.
I would like to see an "experienced craftsman" beat a cnc to the bottom of a stack doing radius works, ellipse work, cut out letters etc.
I have done both traditionally and with a cnc and wouldn't want to go back to try and do things manually.
We used to use and Altendorf then Martin slider to cut our parts. Between the yield, accuracy and speed you can't beat a router.
It is hard to compare because you will change the way you do things. If you add automatic unloading (and loading if needed) it can cut a lot, dead dead accurate into the thousandths of an inch. If you get the right front end software there is no head scratching and miss cut parts. Your yield should go up also. I also found that we could have one guy who could run the saw efficiently and a second and third that could get by. A router is significantly easier to run. We have several people that can put out the same quantity and quality. The statement I will make and the one I have heard over and over is, "we should have done this sooner".
If you are past 50 sheets a day than there are other options but depending on what you are making a router is hard to beat up until then.
Yours is a straw man argument. Nothing was said of radius/ellipse/letter work and I doubt that Robert is doing this sort of work. For me, and obviously you, a CNC makes business sense, but if Robert is a one man shop and doesn't want the hassle that comes along with hiring people, taking on more volume, etc, then I think that a valid argument can be made against purchasing a CNC in his case.
Are you able to pendulum process? Do you have a pusher installed on your machine? Or are you cutting, labeling, and offloading on the spoilboard?
When we bought our router 1-1/2 years ago we were having a problem, the router couldn't keep up with the rest of the shop. We didn't buy a pusher and wished we had. So I built a sort of manual pusher system. I will attach photos. It allowed us to load and run another sheet while I label and offload the sheet I just ran on my secondary table. I estimated that we gained %40 on our output.
We made a table at the end of the router. And what I call a "Rake" that sits over the sheet after its cut. It has a rope attached to it. At the end of the table is a pulley and we simply pull the sheet off of the spoilboard and onto the table. Works pretty slick.
I wasn't trying to bash your CNC. If it works for you great.
I already knew a CNC machine was not for me for various reasons.
5)I'm just an ornery cuss that likes doing things the old fashioned way and hates computers. I'd rather sit in front of saw then a computer programming it.
Thank you everyone for your responses. I know they are great machines, just not for me, but it's fun to know I'm not missing out on too much productivity at the same time.
I was the op, just posted under my first name accidentally. We have a scissor lift immediately in front of the cnc table and a shop built 5' x 10' workbench immediately after the table.
As soon as the cnc stops, and I mean the very second it stops (the bit better still be spinning) we cut off the vacuum. We then press a button on the control upon which the machine parks itself at the offload end of the table. After pressing the button the operator positions himself at the scissor lift which by this time will be at a height slightly above the table. The operator tilts the sheet so that the front edge of the sheet lands flush on the spoil board. The operator then pushes the new sheet, onto the table which in the process pushes the cut sheet onto the offload table. Its important that the offload table be at least 5' wide, preferably larger because the cut sheet has a tendency to want to expand when there are a lot of smaller pieces which could result in some falling on the floor to either side of the table.
Its also important that the new sheet ride on its front edge at a sufficient angle that the pressure forces this edge flat (if say, perhaps, you are dealing with slightly cupped sheet of plywood). By sliding the new sheet on in this way you clean off the dust and chips which fall along with the recently cut sheet.
The operator then acknowledges to the router that the next sheet is loaded. Total downtime for the machine is around 30 seconds. The operator then labels the parts on the offload table (their configuration stays pretty consistent to that in which they were cut so they are easy to lablel). After labeling, parts are sorted onto carts by type.
However, rather than load these parts onto a cart I would rather feed them straight into the edge bander. This would minimize handling and also eliminate the feast or famine situation that I now have in my operations following the router.
I know that one person mentioned a feature on his bander that allowed him to maintain above room temp, but even at this it seems that you are still processing in batches, albeit smaller, but still batches.
I think that, in our system, a single operator could operate both cnc machines as well as contribute to labeling and sorting/banding parts on the offload table. The question the becomes whether this output would sufficiently supply the so that it could run full tilt until the routers were done with the job.
The thing about the edgebander is that it is the highest capacity machine in most operations but unless you can run it in tandem with the router you don't realize this high capacity and rather it becomes a bottleneck with a kitchen full of parts sitting in front of it.
Robert - pay no attention to that. This site is full of guys who think that their CNC router distinguishes them from the masses and become emotional when someone says that they can go through sheets faster on a slider (which is true).
We average 30 sheets per day. The edge bander sits next to the cnc. the sorting rack is stationed at the end of the bander we cut, including all joinery, hinge holes drawer glide holes everything, no secondary operation, edge band, sort into racking on wheels, with 1 man. and working at a normal pace. I too could cut panel rout bore and sort 50 sheets per day on a good day ,but not 7 days a week 52 weeks a year for 30 years. also we too, use a non journeyman to perform this operation, freeing up my limited supply of journeyman, so they can use their skills in other areas. From a business point of view it seems ludacris not to automate this process.
I have always been amused by the 50 sheet vs 40 sheet per day arguments.
How do you sell 50 sheets per day?
Cris you miss his point. He neither has nor wants journeymen employees, he is a journeyman and likely enjoys the process and has made a viable business of it. It makes no sense to say that to not have a router would be ludacris just because in your case it is ludacris. There are large factories for which the idea of not having a fully automated million dollar finishing line would be ludacris, so therefore it is ludacris that you do not have a fully automated finishing line, right?
AGC funny you should bring that up I will be looking into a spray machine at IWF this summer still hand apply glazes and stain but very interested in automating application of clear.
I think it's great for those of you who can make use of CNC routers. For myself it is just not the way we want to go. I don't have the long term belief in the economy to support taking on the overhead and I have built a solid group of men that the CNC would have to replace and I don't want to replace them. The CNC won't call in sick, but neither will it help me out when I'm in a pinch by doing me a favor of unloading a lumber truck when I am not available and bringing it up to my shop. There is give and take with the machine and it is just not for us but I know it's the only way for some of you guys and I'm glad it's making you a lot of money.
I hear you Cris but you get my point. That said, I would be interested in hearing the outcome of your decision as I am at some point going to have to make a change in the way we finish.
We have zero automation in finish but, assuming that we are looking at similar equipment, why are you going to use it only for automating the clear?
The majority of the color in our stained product is sprayed on rather than wiped. Cefla, Makor and Superfici each make a small flatline that will spray the stain, sealer, topcoat as well as paint. I have never seen one of these in operation but as I understand it you can purchase multiple "heads" which contain your guns and hoses, which makes it easy to move from paint to clear.
Also, don't listen to the salesman if he is trying to incorporate a brush sander as they will not account for the portion of the sanding that he claims and will leave the majority to be done by hand.
Does anyone have a "ball-park" price for finishing lines? Say, from the low-end and up? I know that is a wide range, but if they start at over 100K I will self-eliminate my business at this time. If much less, then a trip to IWF this summer might be worth the trip.
I think Makor makes a sprayer that's under 100k. You can later add an oven which I don't have the volume to justify at this time......that said, I would never consider buying a used flatline but I would definitely consider a used oven.
I have also thought about installing a hanging line, which would never be automated bc the cost would be prohibitive but it would be a definite upgrade from where we are now (spray everything flat in an automotive paint booth, wait for it to dry, flip it over, etc).
Some ppl say that edge coverage is an issue and while I have never seen a machine in operation I have sold high end factory cabinets (woodmode) and there is quite a bit of texture on their edges as a result of the flatline. The hang line would allow for sufficient edge coverage as well as cut drying time in half.
I think kitchen shops have a different take on productivity over commercial only shops. Our output varies considerably from day to day. The CNC panel saw can cut a tremendous amount in a day if it is stack cutting. Beats the hell out of a slider. But all you end up with is a huge pile of parts, many of which need drilling, notching, curved corners etc. I personally don't mind seeing a machine sitting idle part of the day, employees are another matter. We don't use carts, I think they are likely to be wasteful. Depending on your shop size, a lot of time can be spent returning them to the start of the process. Our software allows us to separate plain rectangular parts and send to the CNC panel saw as optimized sheets. The panel saw cuts blanks for the PTP and stacks them on the conveyors that are a short ride away from the PTP. I'm not a great fan of PTP machines for panel work but got this one cheap and needed a quick increase in output. The router "only" cuts about 40 sheets a day. Operator starts @ 6:00am. If cutting primarily rectangles it can cut more but much of our work involves curves. Lots of small parts that need to be onion skinned or tabbed. Operator labels, & sorts, moves stacks via conveyor to their next operation. Then gets a different material quite a few times a day. Banding doesn't start until a few hours after routing. The machine will automatically go to idle if no parts are run. It has a small pot that doesn't take long to come back up. The pot has automatic filling.
People seem to think the way they are doing something is better/best. Might be/for them. Comparing how many sheets can be cut on a 10" saw/slider to how many come off a router isn't any where near a valid comparison.
PS I'm in the market for a laminar type case clamp, will be selling my Gannomat 260 clamp.
Thanks for the advice, I have gained much from reading your posts. That said, have you seen the p2p machines that accept the panel fed vertically? The alignment is automatic and they also do the horizontal boring/dowel insertion. Its a different kind of machine really.
A CNC doesn't replace good men it allows them to put out more work per day. You can't run a quality high production cabinet business with fools at the controls.
Author, you said, "On a good day we cut 30 sheets on the router, but parts don't reach the edgebander fast enough that I can leave it on continuously".
It seems you do not have sufficient capacity at router to keep the edgebander busy always. One option which you already considered is to increase the router capacity. Another option is to optimally batch and sequence parts on router in order to improve busy time of the edgebander. The next option is overtime at the edgebander. Is any loss of time on the edgebander a loss of sales for you currently?


there's a non-monetary reason for the company to do what it does.
Has your department ever been called a "cost center"? That's another way of saying "we will outsource your work to as soon as you start asking too much money." You are disposable. A cog in the machine. But the ramifications here are so much broader, because if IT isn't the driver of business, then all IT decisions will be monetary decisions.
On the other hand, we can easily name companies that heavily rely on their IT for business success. Google, GitHub, Etsy, Netflix, Spotify… We know them, because they're very active members of our community. They speak, share, collaborate, contribute, while internally, each one of them is pushing the boundaries of their technology.
I was never the smartest guy in the room. From the first person I hired, I was never the smartest guy in the room. And that's a big deal. And if you're going to be a leader - if you're a leader and you're the smartest guy in the world - in the room, you've got real problems.
Jack's right, and his words apply to everyone - not only "leaders". You always want to be around people who are better than you. If you dig through the stories of most successful people, they always reference somebody who inspired them, who they learned tons from.
You want to work for a company that has a diverse set of top-notch specialists. People passionate about their work, who continuously pursue mastery. People who's contributions will inspire and motivate you to develop your own skills. People who will be happy to share their knowledge.
Simon's talk is well worth watching to understand how much the "why" we do things matters. You should also grab his book "Start with Why" to dive deeper into the matter.
Too many times important initiatives are explained in monetary terms, which don't mean anything to most people working on them. If the company makes an extra million, are we actually going to receive any of it? Not likely.
What you want instead is a business pursuit you can believe in - big or small, like getting the world rid of malaria, or making awesome tools for developers. You want to be part of something good being done for others, where money comes back almost as a side effect.
It goes without saying, that in order for a company to become a Geek Heaven, the bottom layers need already to be catered for. You certainly won't feel any good working at a place, where you may get fired any minute, you're getting peanuts for your work or which is physically unsafe.
A lot of companies these days do very good on the bottom layers of the pyramid, but very few succeed in the upper ones.
There's a clear business case for building companies, where geeks are happy.
You're a geek. You're doing a job that's highly in demand these days and will remain so for the nearest future. Use that to your advantage and "vote with your feet" for companies that you truly feel great working for. Find the criteria for what makes your very own Geek Heaven, and if you haven't found it yet, move on.
Designed, developed, handed over to QA for testing. Then all hell breaks loose. "How do I test it?" "Where's the documentation?" "This is broken; not it's not, it's not our component." "I'm not signing this off!" Or my personal favorite: "I've other priorities to test now. I'll get to your stuff tomorrow." for three days in a row. Keeping QA separate from development teams is a recipe for trouble, friction and lots of missed opportunities. It has to stop.


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Ryan Poles' First-Ever Bears Signing Is So On Brand
Ryan Poles needed some time to get situated as Chicago Bears GM. Most of the futures contracts the team handed out to players they'll want around for training camp were already handed out. Now that he is in the building and running the show, it was a matter of waiting for when he'd make his first official move. That finally arrived on February 11th when the Bears signed another futures deal with Willie Wright.
Eric Edholm of Yahoo Sports was the first on the news. What makes the signing rather perfect is that Wright is an offensive lineman. Poles himself played offensive line in college and briefly in the NFL. From the moment he took over last month, he made it clear that the line would be a major focal point for him moving forward. Nobody can ever say he's not a man of his word after this move. An excellent way to set the tone for this offseason.
Bears are signing ex Browns/Falcons Willie Wright to a futures deal, per source
New Bears GM Ryan Poles' first? Not sure
— Eric Edholm (@Eric_Edholm) February 11, 2022
*Watch #58
Wright was an undrafted free agent out of Tulsa in 2019 by the Cleveland Browns.
Though he failed to make their roster, he did end up with the Atlanta Falcons a year later. Interestingly that was the final season Chris Morgan was the offensive line coach. Now he runs the show in Chicago. So the signing makes a bit more sense now. The common scouting reports on Wright were a quick, athletic blocker with good hand technique. Unfortunately, his size (6'2, 300 lbs) and below-average power led to him going undrafted.
This is likely why teams planned for him to move from offensive tackle to center. A position that is a bit kinder to undersized linemen. He never got a chance to work with Morgan after 2020 though. The coaching staff was fired the following offseason. Now he'll get a second chance, thanks to Ryan Poles and the new regime in Chicago.
Tags: bears brand FirstEver poles Ryan signing
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Collective Memories
Transformation of Local Music
Dr. Carol Babiracki will present the first lecture in the Music, Media and Culture series October 7, 7:30 p.m., MMaP Gallery. Her topic is "Transnational Tribals and the Transformation of Local Music in India."
Carol Babiracki is an Associate Professor of Music, History and Culture in the Fine Arts Department of Syracuse University. Before joining Syracuse, she taught on the faculties of Brown and Harvard Universities, and holds a Ph.D. from the University of Illinois at Urbana-Champaign. She has spent many years in India doing field research, with a focus on village expressive culture in the state of Jharkhand over a twenty-five year period. Her publications have appeared in the journal Asian Music and in the books Women's Voices Across Musical Worlds, Shadows in the Field: New Perspectives on Field Research in Ethnomusicology, Comparative Musicology and the Anthropology of Music, Ethnomusicology and Modern Music History, and The Western Impact on World Music. She is currently completing a monograph about the role of Mundari music history and performance in the autonomy movement that resulted in Jharkhand statehood in 2000.
Dr. Babiracki will also be making informal presentations in three classes this week. These classes have been opened to members of the university community and the public, although space is limited in some cases.
Tues., October 7, School of Music Video Conferencing Room, 9-11:30 am: Presentation in Problems and methods in ethnomusicology: on fieldwork issues in village India.
PUBLIC LECTURE: Tues.,October 7, 7:30-9:00 pm, Public lecture (MMaP Gallery). Reception to follow. "Transnational Tribals and the Transformation of Local Music in India"
Thurs., Oct. 9, Science building room 2101 at 10:30-11:45a.m., In Introduction to Folklore class "Studying traditional dance: Mundari dance, including a dance workshop & some flute tunes"
Thurs., Oct. 9, Education building room 4008 at .2:00-3:15, In Folklore Research Methods class. "Advocacy in Fieldwork. Defining 'human rights' in Jharkhand"
For further information, call 737-2051 or email kharriswalsh@mun.ca or bdiamond@mun.ca
Posted by Dale Jarvis at 9:27 AM


Thanks for joining me on this journey about the life of a working mom trying to find the balance in being more like Christ, raising an idiosyncratic child and living a life I love!
I love being able to wear matching shirts with my boys. We have matching pj's for the holidays and I love them.
Awe how cute. I love it!
Your shirts are adorable. I wish I had memories like this with my daughter. Although she is 33 now, I may still get them.
Yes!! Get them. Order some shirts and take some photos.
She is so lucky to have you in her life. Nothing beats when serves Christ as a center of a fanily.
Yes definitely! Without God, I am nothing!
I love your matchy matchy outfit !! This is way too cute mama !!
Yesterday when I saw this post i saved this. Still now 5 times I have read it. Don't sympathise with me but I lost my mom when I was 16 and dad when I was 23 now I'm 25. I don't don't have a family. I knew how much my ma loved me that's why I can feel the depth of your post.
🤗 I always want her to know how much she is loved and I am happy to know that you know how much your mother loves you.
From your aspirations for your daughter, I can tell that you are a wonderful mother. You are fortunate to have each other.
Nothing more important that modeling Christ's love to our children! Blessings!!!
Ah this is so sweet. I have a daughter too & love your message. Also, how good are those t-shirts?!
Very beautiful and expressive quote! You guys looks great together. I love those matching tees with cute message.
What a beautiful message. Your daughter is very lucky to have such a kind and loving mother. Keep up the great work!
You are such a great mom and she is really lucky to have you. Being a mom is not so easy, I am really admires you.
She is so fortunate to have a dedicated mom like you! Great job. Those shirts are awesome.
those matching shirts are adorable! I would like to find something similar for my son and myself, thanks for reminding me!
Aww, This is the sweetest thing I've read today. You are an inspiring mom. Never forget to show our love for our children each day.
Love the matching t-shirts, beautiful message!
So lovely to see people express their joy and happiness when the world is so full of sadness. Lovely to read this.


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Biville-la-Rivière és un municipi francès situat al departament del Sena Marítim i a la regió de Normandia. L'any 2007 tenia 106 habitants.

Demografia

Població
El 2007 la població de fet de Biville-la-Rivière era de 106 persones. Hi havia 44 famílies de les quals 12 eren unipersonals (12 homes vivint sols), 8 parelles sense fills, 16 parelles amb fills i 8 famílies monoparentals amb fills.

La població ha evolucionat segons el següent gràfic:

Habitants censats

Habitatges
El 2007 hi havia 52 habitatges, 44 eren l'habitatge principal de la família, 7 eren segones residències i 1 estava desocupat. Tots els 51 habitatges eren cases. Dels 44 habitatges principals, 33 estaven ocupats pels seus propietaris, 9 estaven llogats i ocupats pels llogaters i 2 estaven cedits a títol gratuït; 1 tenia una cambra, 5 en tenien tres, 15 en tenien quatre i 23 en tenien cinc o més. 33 habitatges disposaven pel capbaix d'una plaça de pàrquing. A 27 habitatges hi havia un automòbil i a 14 n'hi havia dos o més.

Piràmide de població
La piràmide de població per edats i sexe el 2009 era:

Economia
El 2007 la població en edat de treballar era de 70 persones, 51 eren actives i 19 eren inactives. De les 51 persones actives 48 estaven ocupades (25 homes i 23 dones) i 3 estaven aturades (1 home i 2 dones). De les 19 persones inactives 4 estaven jubilades, 7 estaven estudiant i 8 estaven classificades com a «altres inactius».

Activitats econòmiques
Dels 6 establiments que hi havia el 2007, 2 eren d'empreses de fabricació d'altres productes industrials, 3 d'empreses de comerç i reparació d'automòbils i 1 d'una empresa financera.

Poblacions més properes
El següent diagrama mostra les poblacions més properes.

Referències

 Résumé statistique Fitxa resum de dades estadístiques de Biville-la-Rivière a l'INSEE.
 Évolution et structure de la population Fitxa amb el detall de dades de Biville-la-Rivière a l'INSEE
 France par commune  Dades detallades de tots els municipis de França accessibles a partir del mapa.

Municipis del Sena Marítim

redpajama_set_name: RedPajamaWikipedia


Roll Cooling. The cooling of work rolls is an important process in the hot rolling technology and cannot be taken as a marginal issue. The Heat Transfer and Fluid Flow Laboratory designs cooling of rolls to reach their long working life while rolled product is still well heat treated.
Let Qr( ) be the radial heat flow rate at the radial location r within the pipe wall. Then, in the end view shown above, the heat flow rate into the cylindrical shell is Qr ( ) , while the heat flow rate out of the cylindrical shell is Qr r ( +∆ ).
COOLING TOWER—a structure designed for air cooling of hot liquid; as used in the pulp and paper industry it is a vertical tower/ usually square in cross section, with wooden slats on all four sides, and designed for spraying hot water at the top, allowing the descending water to exchange heat with a rising column of cooler air.
Heat Flow and Diagrams Lab. Quick Look. Grade Level: 12 ( 12) Time Required: ... Have students then set up the design that was discussed and agreed upon in the previous step for measuring how fast heat flows through two different materials (aluminum and steel in this example).
A diagram of toilet paper manufacturing process. now perforated, and may be scented, embossed, or colored. Recently, toilet paper manufacturers increased the number of sheets on a roll, allowing consumers to replace the roll less frequently.
business unit in this issue of the Diagram which are designed to reduce energy consumption. ... 40 Roll service Nothing works without rolls 42 43 Review / Imprint ... and two eight-roller mills (MDDO). The new South Amman Mills plant operates four purifiers of type MQRF.
Conduction is the passing of heat energy between two objects that are in direct, physical contact. It is one of the three types of heat transfer, the other two being convection and radiation.
Cold rolling speeds vary but modern mills operate at exit speeds as high as 3000 m per minute. A modern complex including melting furnaces, DC casting facilities, pre-heat furnaces, hot mill, cold mill and annealing furnaces involves a very large capital investment which can only be fully justified on financial grounds if a big market is assured.
To remove particulate from the system, some systems have in-line or side stream (preferred method) filtration units. The in-line filters of the flow, where the side stream takes 10% or less of the system flow rate. There are two types of pumps used in a hot oil system.
based oil for cold mills, is delivered at a controlled temperature to spray headers. After being sprayed, the coolant is collected and returned to the main holding reservoir through a filtration system. Systems custom designed with the coolant flow rate, cleanliness and heat dissipation meeting the special requirements of the rolling mill.
• Process Flow Diagram – PFD (simplified version of the P&ID) Most industries have standardized the symbols according to the ... Heat Exchanger. Building the P&ID. The P&ID will use symbols and circles to represent each instrument and how they are inter-connected in the process. Thermometer.
TECHNICAL RUBBER COURSE Mixing Technology & Machinery Robert Dickstein. Main Topics ... THE MILL) Main Mixer Metal Temperature Heat Transfer Optimum Material Flow (Stick-Slip) Temperature Control - Maximum Productivity - Optimum Quality. Main Metal Temperature & Interfacial friction effects.
Heat imparted to the material, due to the work of grinding, is related to the time it is held within the chamber and the air flow characteristics. Impact grinding is most efficient with dry, low-fat ingredients, although many other materials may be reduced in size by proper screen selection and regulated intake.
Two-Roll Arrangement. Weld rolls must be capable of closing the tube with enough pressure to upset the edges, even with the welder shut off and the edges cold. This requires large horizontal components of force, as suggested in Figure 6.
Three drying processes occur at the same time: (1) flow of heat from the surface of the drying cylinder to the paper (contact drying), (2) cooling of the paper as heat is used to evaporate the water in it (flash drying), and (3) flow of heat from the surrounding air to the paper (convection drying).
Computer Numerical Control for my RF Mill/Drill, version 2.2 ... that is a roll of toilet paper to the right of my mill. 1 You are free to distribute this article but not to change it. R. G. Sparber Janu Page 2 of 27 ... The A driver/motor path receives signals from two places on the BOB.
Heat Transfer B 51 (3) (2007) 251–274), we have developed a simplified 2D numerical model to analyze the heat and flow patterns on the cross section of two-roll-mill flow under the assumption of infinite length in the third (vertical) direction.