text:
\section{Introduction}
A set $A\sbeq \Z$ is called a $B_k$--set, $k\ge 2,$ if
\begin{equation}\label{B_k}
x_1+\dots+x_k=y_{1}+\dots+y_{k}
\end{equation}
with $x_i,y_i\in A$ implies that $x_1,\dots,x_k$ is a permutation of $y_{1},\dots,y_{k}.$ If $A$ is a $B_k$-subsets of $[N]$, then even a  simple argument argument  $\binom{|A|+k-1}{k}=|kA|\le kN$ shows that
$$|A|\le (kk!)^{1/k} N^{1/k}.$$
Currently best bound
 $$|A|\le (1+o(1))(1+\e_k)\frac{k}{2e}N^{1/k}$$
 was proved by Green \cite{green} (see also \cite{obryant} page 14), where $\e_k\rightarrow 0$ as $k\rightarrow \infty$.
 The history of the problem and bibliography can be found in \cite{obryant}.

We call a set $A\sbeq \Z$ a weak $B_k$--set ($B^*_k$--set) if
every solution to (\ref{B_k})
with $x_i\in A$ implies that among numbers $x_1,\dots,x_k,y_{1},\dots,y_{k}$ at least two are equal. In other words $A$ does not contain a solution to (\ref{B_k}) with distinct elements.
It is already non-trivial to prove that  every $B^*_k$--subset of $[N]$ has size $O_k(N^{1/k}).$ It is a fact that there are equations (see Theorem 3.3 in \cite{ruzsa-I}) such that the threshold for the size of a set without solutions in distinct integers is of different order of magnitude.  Ruzsa \cite{ruzsa-I} proved that for every  $B^*_k$--set  $A\sbeq [N]$ we have
$$|A|\le (1+o(1))k^{2-1/k}N^{1/k} \,.$$
Very recently Timmons \cite{timmons} showed that
$$|A|\le (1+o(1))(1+\e_k)\frac{k^{2}}{4}N^{1/k},$$
 where $\e_k\rightarrow 0$ as $k\rightarrow \infty$. On the other hand, for $k\ge 3$ Timmons constructed  a $B^*_k$--subset of $[N]$ with $(1-o(1))2^{1-1/k}N^{1/k}$ elements. Our aim is to prove  the following theorem.

\begin{theorem}
    Let $A\subseteq [N]$ be a  $B^*_k$--set and $N\ge (2 k^{9/2})^k$.
    Then
$$
    |A| \le 16  k^{3/2} N^{1/k} \,.
$$
\label{t:main_introduction}
\end{theorem}

\section{The proof of the main result}

For a finite subset of integers $A$ put
$$\s_k(n) = \s_k(n;A)= |\{(x_1,\dots,x_k)\in A^k: x_1+\dots+x_ k=n\} | \,,$$
$$f(t)=f_A(t)=\sum_{a\in A}e^{-2\pi i at} \,, \quad \quad t\in [0,1]$$
further
$$M_k = M_k (A) =\sum_n \s_k(n)^2=\int_0^1|f(t)|^{2k}dt \,,$$
$$s_k(n) = s_k (n;A) = | \{(x_1,\dots,x_k)\in A^k,\, x_i\not=x_j: x_1+\dots+x_ k=n\} |,$$
$$S_k = S_k (A) =\sum_n s_k (n;A)^2 = \sum_n s_k (n)^2
    =
    $$
\begin{equation}\label{f:S_k_equality}
    =
      | \{ (x_1,\dots,x_k, y_1,\dots,y_k )\in A^{2k}~:~ x_1+\dots+x_ k =  y_1 +\dots+y_k
         ,\, x_i\not=x_j,\, y_i \not=y_j\}|  \,.
\end{equation}
Furthermore, define
\begin{eqnarray*}
S^*_k(A)= | \{ (x_1,\dots,x_k, y_1,\dots,y_k )\in A^{2k}&:&x_1+\dots+x_ k =  y_{1} +\dots+y_{k}
         ,\\ && x_i \not=x_j,\, y_i\not=y_j,\, x_i\not=y_j,\, 1\le i,j\le k \}|  \,.
         \end{eqnarray*}
and for finite subsets of integers $A_1,A_2$ put
\begin{eqnarray*}
S^*_k(A_1,A_2)= | \{ (x_1,\dots,x_k, y_1,\dots,y_k )\in A_1^{k}\times A_2^k &:&x_1+\dots+x_ k =  y_{1} +\dots+y_{k}
         ,\\ && x_i \not=x_j,\, y_i\not=y_j,\, x_i\not=y_j,\, 1\le i,j\le k \}|  \,.
         \end{eqnarray*}
Clearly, $A$ is a  $B^*_k$--set $A$ if and only if $S^*_k (A)=0$

\medskip
Our first lemma can be extracted from Ruzsa's paper \cite{ruzsa-I}.
We will rewrite it for a convenient for us form.

\begin{lemma}\label{l_n:ruzsa}
    Let $A$ be a finite set of integers with $|A| \ge 16 k^4$.
    Then
\begin{equation}\label{e:ruzsa-S_k}
    2^{-k} k!|A|^k \le S_k \le M_k \le 2 S_k \,.
\end{equation}
\label{l:M_k=S_k}
\end{lemma}
\begin{proof}
    If $k=1$, then the result is trivial, thus suppose that $k\ge 2$.
First observed that
\begin{equation}\label{inequality-Mk}
    M_k\ge S_k\ge k!|A|(|A|-1)\dots (|A|-k+1) \ge (5/4)^{-k} k! |A|^k \ge 2^{-k} k!|A|^k
    \,.
\end{equation}
    Ruzsa proved (see inequality (5.8) in \cite{ruzsa-I}) that
$$
    \sum_n (\sigma_k (n) - s_k (n))^2 \le k^4 M_{k-1} \,,
$$
    hence by the H\"{o}lder inequality
\begin{equation*}\label{tmp:03.06.2016_1}
    \sum_n (\sigma_k (n) - s_k (n))^2 \le k^4 M^{\frac{k-2}{k-1}}_k |A|^{\frac{1}{k-1}} \,.
\end{equation*}
Therefore, by the triangle inequality
$$M^{1/2}_k\le S^{1/2}_k+k^2 M^{\frac{k-2}{2(k-1)}}_k |A|^{\frac{1}{2(k-1)}}\,.$$
By the middle inequality in (\ref{inequality-Mk}) and the assumption $|A| \ge 16 k^4$ we see that
$$
    |M^{1/2}_k - S^{1/2}_k|^2 \le k^4 M^{\frac{k-2}{k-1}}_k |A|^{\frac{1}{k-1}}

    \le 2^{-4} M_k

$$
so that
$$
    M_k \le 2 S_k
$$  as required.
\hfill$\blacksquare$
\end{proof}

\bigskip

Observe  that, actually, the inequality (\ref{e:ruzsa-S_k}) can be strengthened to $M_k = S_k (1+o(1))$ for large $|A|$.
Our next lemma provides a  straightforward relation  between $S_k$ and $S_l$ for $l<k$.

\begin{lemma}
    Let $1\le l<k$ and let $A$ be a $B^*_k$--set with $|A| \ge 16 k^4$.
    Then
$$
    S_k \le (\sqrt{2} k)^{2{(k-l)}} |A|^{k-l} S_{l} \,.
$$
\label{l:S_k,S_l}
\end{lemma}
\begin{proof}
    Indeed, counting the number of the solutions to (\ref{f:S_k_equality}), we see that by the assumption on  $A$  we must have $x_i=y_j$ for some $i$ and $j$. There are at most $k^2$ choices for $i$ and $j$ and thus
\begin{equation}\label{ruzsa-k2_my}
    S_k \le k^2 |A| S_{k-1} \le k^2 |A| M_{k-1} \,.
\end{equation}
    Furthermore, by the H\"older inequality and Lemma \ref{l:M_k=S_k}
$$
    M_{k-1}
        =
            \int_0^1 |f(t)|^{2k-2}dt
                \le \B(\int_0^1 |f(t)|^{2k}dt\B)^{\frac{k-l-1}{k-l}}
                        \B(\int_0^1 |f(t)|^{2l}dt\B)^{\frac1{k-l}}
                            \le
                                (2S_k)^{\frac{k-l-1}{k-l}}(2S_l)^{\frac1{k-l}} \,,
$$
hence by (\ref{ruzsa-k2_my})
$$ S_k\le 2^{}k^2|A| S_k^{\frac{k-l-1}{k-l}} S_l^{\frac1{k-l}}$$
and the assertion follows.
\hfill$\blacksquare$
\end{proof}

\bigskip

Using a simple probabilistic argument we prove that the variables  from both sides of (\ref{f:S_k_equality}) can be chosen from disjoint sets.
This allows us to apply a version of a well known theorem of Erd{\H o}s--Ko--Rado, see Theorem \ref{t:EKR} below.

\begin{lemma}\label{l:S_k=S_k(A,A^c)}
 Let $A$ be finite set of integers. Then there exists a set  $A' \subseteq A$ such that
$$
    S^*_k (A) \le
    4^k  S^*_k (A',A\setminus A')\,.
$$\end{lemma}
\begin{proof} Let us pick, randomly, independently, each element of $A$ with probability $1/2.$
    Let  $A'$ be the  random set of chosen elements. Clearly,

\begin{equation*}\label{tmp:04.06.2016_1}
    \mathbb{E} S^*_k (A',A\setminus A')
        = \sum_{x_1+\dots+x_k = x'_1 + \dots +x'_k }2^{-2k}  \,,
\end{equation*}
where the summation is taken over all solutions in the set $A$ with distinct integers.
Whence,
$$\mathbb{E} S^*_k (A',A\setminus A')=4^{-k}S^*_k(A)\,,$$
so that
$$\mathbb{P}\big(\,S^*_k (A',A\setminus A')\ge 4^{-k}S^*_k(A)\, \big)>0\,.$$
Therefore, there is a specific choice of $A'$ such that  $S^*_k (A) \le
    4^k  S^*_k (A',A\setminus A').$

\hfill$\blacksquare$
\end{proof}

\bigskip

For a   $B_k^*$--set  $A$  define
$$
    \mathcal{G}  = \mathcal{G} (A) = \{ j \in [k] ~:~ A \text{ is a $B_j^*$--set} \}
        \quad \quad \mbox{ and } \quad \quad
            \mathcal{X} =  \mathcal{X} (A) = [k] \setminus \mathcal{G} (A) \,.
$$

Timmons \cite{timmons} proved that a large subset of $A$ is a  $B^*_{\lfloor k/2\rfloor}$  or $B^*_{\lceil k/2\rceil}$--set.
We prove that there is a large set $B\sbeq A$ such that  the set $\mathcal{G}(B)$ is very large and  structural. This is a crucial argument in our approach.

\bigskip

\begin{lemma}
    Let $A$ be a $B_k^*$--set.
    Then there is a set $B \subseteq A$,
    $$
        |B| \ge |A| - 2 k^3
    $$
    such that for $\mathcal{X} = \mathcal{X} (B)$, $\G = \G(B)$ we have for any $l$ we have $l \mathcal{X} \cap \G = \emptyset \,.$

    In particular,
\begin{equation}\label{in:X}
    |\X\cap [l]|\le  \big\lfloor\frac{l}2\big\rfloor
\end{equation}
\label{l:structure_X}
  for every $1\le l\le k.$
\end{lemma}
\begin{proof}
We prove the lemma using an iterative procedure. We start with the sets $A_0=A$, $\G_0=\emptyset,$ $\X_0=\emptyset$ and $\S_0=\emptyset.$ Suppose that we have chosen
$A_i, \G_i, \X_i$ and $\S_i.$ If $[k]=\G_i\cup \X_i$ we stop the process, otherwise put  $l:=\min([k]\setminus (\G_i\cup \X_i))$. If $A_i$ contains $k$ pairwise disjoint solutions to the equation
\begin{equation}\label{eq-l}
x_1+\dots+x_{l}=y_1+\dots+y_{l}
\end{equation}
with all variables distinct, and disjoint with $\S_i,$  then we put
\begin{equation}\label{step-1}
A_{i+1}=A_i,\,~ \G_{i+1}=\G_i,\,~ \X_{i+1}=\X_i\cup \{l\},\,~\S_{i+1}=\S_{i}\cup \textsf{Sol}_i\,,
\end{equation}
where $\textsf{Sol}_i$ is the set of all numbers involved in the $k$ disjoint solutions to (\ref{eq-l}).
If this is not the case (there are less than $k$ such solutions), let $\textsf{Sol}_i$ be a maximal collection of pairwise disjoint solutions to (\ref{eq-l}) with distinct variables,
and disjoint with $\S_i$. Then
we put
\begin{equation}\label{step-2}
A_{i+1}=A_i\setminus ( \S_i\cup \textsf{Sol}_i),\,~ \G_{i+1}=\G_i\cup\{l\},\,~ \X_{i+1}=\emptyset,\,~ \S_{i+1}=\emptyset\,.
\end{equation}
Observe that then $A_{i+1}$ is a $B^*_l$--set, and $l\in \G_j,$ for all $ j\ge i+1.$  Thus,
the step (\ref{step-2}) can be applied at most $k$ times, as in each application we add one element to the set $\G_i.$ Therefore, the process must terminate after  $m\le k^2$ iterations. We put $B=A_m, \G=\G_m$ and $\X=\X_m.$ Since
$|\S_i\cup \textsf{Sol}_i|\le 2k^2$
it follows that
$$|B|\ge |A|-2k^3.$$

Next, we prove that $l \mathcal{X} \cap \G = \emptyset \,.$ Suppose that it does not hold. Then there exist $n_1,\dots,n_l\in \X,\, l\le k,$ such that $n_1+\dots+n_l=n\in \G.$
By our construction there are pairwise disjoint solutions in distinct integers
\begin{eqnarray*}
x^{(1)}_1+\dots+x^{(1)}_{n_1}&=&y^{(1)}_1+\dots+y^{(1)}_{n_1}\\
&\dots&\\
x^{(l)}_1+\dots+x^{(l)}_{n_l}&=&y^{(l)}_1+\dots+y^{(l)}_{n_l}.
\end{eqnarray*}
Summing all these solutions up we obtain a solution to the equation
$$x_1+\dots+x_{n}=y_1+\dots+y_{n}$$
in distinct integers  $x_i,y_i\in B$, which contradicts  that $B$ is a $B^*_n$--set.

It remains to prove (\ref{in:X}). Observe that if $l\in \G$ it follows from $2\X\cap \G=\emptyset$ that
$$|\X\cap [l]|\le \big\lceil\frac{l}{2}\big\rceil-1\le \big\lfloor\frac{l-1}{2}\big\rfloor\,,$$ otherwise there are $n_1,n_2\in \X$ such that $n_1+n_2=l,$ which is impossible. Now, let $l\in \X$
and suppose that $|\X\cap [l]|> \lfloor\frac{l}{2}\rfloor$. Let $n$ be the smallest element of $\G$ bigger than $l$. Then
$$\big\lceil\frac{n}{2}\big\rceil-1\ge |\X\cap [n]|=|\X\cap [n-1]|> \big\lfloor\frac{n-1}{2}\big\rfloor\,,$$
which again is a contradiction. This completes the proof.
\hfill$\blacksquare$
\end{proof}

\bigskip

     Clearly, the property $l \mathcal{X} \cap \G = \emptyset$ means that if  $x_1,\dots,x_l\in \mathcal{X}$ such that $x_1+\dots+x_l \in [k]$ then automatically $x_1+\dots+x_l \in \mathcal{X}$.
     Potential  examples of "bad"  $\mathcal{X}$ is the set of even numbers from $[k]$ or $\X=(k/2,k-1]$. However, we do not know any example of a
      dense $B^*_k$--subset of $[N]$ that does not contain a large subset that is $B^*_l$--set for every $l\le k.$

In the proof of the main result we also apply  a variant  of a well--known theorem of Erd{\H o}s--Ko--Rado \cite{ER}, \cite{EKR}.
Let $1\le k,n$, $k< n$ be integer parameters and let $L = \{ l_1< l_2 < \dots < l_r \} \subseteq [0,k]$.
A family $\mathcal{A}$ of subsets of $[n]$ is called $(n,k,L)$--system if,  each of a subset of the family has cardinality $k$ and, for all $A, B\in \mathcal{A}$ from the family we have $|A\cap B|\in L.$ The following theorem was proved in \cite{DEF}.

\begin{theorem}
    Let $\mathcal{A}$ be a $(n,k,L)$--system.
    Then
$$
    |\mathcal{A}| \le \prod_{i=1}^{|L|} \frac{n-l_i}{k-l_i} \,.
$$
\label{t:EKR}
\end{theorem}

Now we are in position  to prove Theorem \ref{t:main_introduction}.
It is a consequence of the following result.

\begin{theorem}
    Let $A$ be a  $B^*_k$--set, $|A| \ge 20 k^{6}$.
    Then
\begin{equation}\label{f:M_k_main}
    M_k (A) \le 2k 8^kk^{3k/2} |A|^k \,.
\end{equation}
\label{t:M_k_main}
\end{theorem}

To see how the theorem above implies Theorem \ref{t:main_introduction} just apply (\ref{f:M_k_main}) and note that by the Cauchy--Schwarz inequality one has
$$
    |A|^{2k} = \Big( \sum_n \sigma_k (n) \Big)^2 \le |kA|\,\sum_n \sigma^2_k (n)
        \le
           2 k 8^k k^{3k/2} |A|^k k N\,,
$$
hence
$$
    |A| \le 16 k^{3/2} N^{1/k}
$$
as required.

\bigskip

\begin{proof}
     Let $B \subseteq A$ be a set given by  Lemma \ref{l:structure_X}. By the Minkowski inequality we have
\begin{eqnarray*}
    M^{1/2k}_k (A)&=&\big(\int_0^1|f(t)|^{2k}dt\big)^{1/2k}\le \big(\int_0^1|f_B(t)|^{2k}dt\big)^{1/2k}+\big(\int_0^1|f_{A\setminus B}(t)|^{2k}dt\big)^{1/2k}\\
    &\le& M^{1/2k}_k (B) + M^{1/2k}_k (A\setminus B)\,.
\end{eqnarray*}
    Since  $|A\setminus B| \le 2 k^{3}, $ it follows that $M^{1/2k}_k (A\setminus B)\le 2k^3$.
    Furthermore, by

    the first inequality in (\ref{e:ruzsa-S_k}), we get

    $$ M^{1/2k}_k (B)\ge \frac12 (20k^6-2k^3)^{1/2}\ge 2k^3 \ge M^{1/2k}_k (A\setminus B)\,,$$
     so that
$$
    M_{k} (A) \le 2^k M_k (B) \,.
$$

    Thus, by Lemma \ref{l:M_k=S_k} it is enough to estimate the quantity $S_k (B).$

       Put $t=\lfloor k/2\rfloor$ and observe that (the formula below works for any $t\le k$)
\begin{equation}\label{S_k-S*_l}
S_t=S_t(B)=\sum_{l=2}^{t}\binom{t}{l}^2(t-l)!S^*_l(B)|B|^{t-l}+t!|B|^t.
\end{equation}
Indeed, notice that from  every solution to the equation
\begin{equation}\label{eq-side-distinct}
 x_1+\dots+x_t = y_1 + \dots+y_t
\end{equation}
in $B$ with $x_i\not=x_j$ and $y_i\not=y_j$, after cancelation of all equal variables from both sides, we obtain for some $l<t,$ a
solution to the equation
\begin{equation}\label{eq-distinct-l}
x_{i_1}+\dots+x_{i_l} = y_{i_1} + \dots+y_{i_l}
\end{equation}
with distinct integers $x_{i_j},y_{i_j}\in B$.
  Conversely, each solution to the equation (\ref{eq-side-distinct})  must be constructed from a solution to (\ref{eq-distinct-l}) for some $2\le l\le t$, and by adding to both sides of the equation the same elements from $B$. This can be done on $\binom{t}{l}^2(t-l)!$ ways, as for a fixed solution $(x_{i_1},\dots,x_{i_l} , y_{i_1}, \dots,y_{i_l})$ we have to chose positions for $x_{i_j}, y_{i_j}$ on $\binom{t}{l}^2$ ways, and then to chose distinct $t-l$ elements from $B$ and order them on the right hand side of the equation on $(t-l)!$ ways. The term $t!|B|^t$ counts the number of solutions with $\{ x_1,\dots,x_t\}=\{ y_1, \dots,y_t\}.$

 Next, applying  Lemma \ref{l:S_k=S_k(A,A^c)} we bound $S^*_l(B)$. Let $B'$ be a set given by Lemma \ref{l:S_k=S_k(A,A^c)}. To estimate $S^*_l(B',B\setminus B')$ observe that every solution to  (\ref{eq-distinct-l}), say,    $(x_{1},\dots,x_{l} , y_{1}, \dots,y_{l}), x_i\in B', y_i\in B\setminus B'$
    corresponds to a set $Z = \{ x_1, \dots, x_l, y_1, \dots, y_l\},$
    and clearly, each such  set with $\sum x_i=\sum y_i,$ gives  $(l!)^2$ solutions to (\ref{eq-distinct-l}).
    Thus, to bound $S^*_l(B', B\setminus B')$ it is sufficient to bound the number of such sets $Z$.
    Denote by $\mathcal{A}_l$ the family of all  sets $Z$ that corresponds to a solution to (\ref{eq-distinct-l}).

    Put $\mathcal{X} = \mathcal{X} (B)$, $\mathcal{G} = \mathcal{G} (B)$.

    By (\ref{in:X}) we have  $|\mathcal{X} \cap [l]| \le \lfloor\frac l2\rfloor$ for every $1\le l\le k.$

Suppose that we have two solutions to (\ref{eq-distinct-l})
    $$
        x_1+\dots+x_a + y_1+\dots+y_{l-a} = x'_1+\dots+x'_b + y'_1+\dots+y'_{l-b}
    $$
    $$
        \tilde{x}_1+\dots+\tilde{x}_a + \tilde{y}_1+\dots+\tilde{y}_{l-a} = \tilde{x}'_1+\dots+\tilde{x}'_b + \tilde{y}'_1+\dots+\tilde{y}'_{l-b} \,,
    $$
    where $0\le a \le l$, $0\le b \le l$, further, $\{x_1,\dots,x_a \} = \{\tilde{x}_1,\dots,\tilde{x}_a \}$,
    $\{x'_1,\dots,x'_b \} = \{\tilde{x}'_1,\dots,\tilde{x}'_b \}$
    and $\{ y_1,\dots,y_{l-a}\} \cap \{ \tilde{y}_1,\dots,\tilde{y}_{l-a}\} = \emptyset$,
    $\{ y'_1,\dots,y'_{l-b}\} \cap \{ \tilde{y}'_1,\dots,\tilde{y}'_{l-b}\} = \emptyset$.
    The above  solutions correspond to some sets $Z_1$, $Z_2 \subseteq [B]^{2l}$ and
    we have $|Z_1 \cap Z_2| = a+b$.

    Subtracting our solutions, we get
    \begin{equation}\label{tmp:10.06.2016_1}
        y_1+ \dots +y_{l-a} + \tilde{y}'_1+\dots+\tilde{y}'_{l-b}
            =
                y'_1+\dots+y'_{l-b} +  \tilde{y}_1+\dots+\tilde{y}_{l-a} \,.
    \end{equation}
    Because of  $\{ y_1,\dots,y_{l-a}\} \cap \{ \tilde{y}_1,\dots,\tilde{y}_{l-a}\} = \emptyset$,
    $\{ y'_1,\dots,y'_{l-b}\} \cap \{ \tilde{y}'_1,\dots,\tilde{y}'_{l-b}\} = \emptyset$
    we to see that (\ref{tmp:10.06.2016_1}) is a  solution  with distinct elements from $B$.
       Therefore, $2l-|Z_1 \cap Z_2| \in \mathcal{X}$, so that $|Z_1 \cap Z_2| \in (2l - \mathcal{X})$.
    Putting $L= 2l - \mathcal{X} = \{ l_1 < \dots< l_r\} \subseteq [0,2l]$, $r=|\mathcal{X} \cap [2l]| \le l$,  we see that the family $\mathcal{A}_l$ is a $(|B|,2l,L)$--system.
    Using Theorem \ref{t:EKR}, we obtain
$$
    |\mathcal{A}_l| \le \prod_{i=1}^{|L|} \frac{|B|-l_i}{2l-l_i} \le \frac{|B|^r}{r!}
        \le
            \frac{|B|^{l}}{l!} \,.
$$
    Thus,
$$
    S^*_l (B',B\setminus B') \le \frac{|B|^{l}}{l!} \cdot (l!)^2 = l! |B|^l \,,
$$
    so that by Lemma \ref{l:S_k=S_k(A,A^c)}
$$
    S^*_l (B) \le 4^l l! |B|^l \,.
$$
Therefore by (\ref{S_k-S*_l})
$$S_t(B)\le  4^t t!|B|^t\sum_{l=0}^t\binom{t}{l} =  8^t  t! |B|^t\,.$$
    Applying Lemma \ref{l:S_k,S_l} with $l=t$,  we get
\begin{eqnarray*}
    S_k (B) &\le& (\sqrt{2} k)^{2(k-t)} |B|^{k-t}S_t(B)\\
        &\le&
            8^t  t! (\sqrt{2} k)^{2(k-t)} |B|^{k}\\
                                &\le&
                     2^{k+2t} k^{2k-t} |B|^k\\
                   & \le&
                         k4^{k} k^{3k/2} |B|^k \,,
\end{eqnarray*}
hence by
$$M_k(A)\le 2^k M_k(B)\le 2^{k+1} S_k(B) \le 2  k 8^{k} k^{3k/2} |B|^k \le 2  k 8^{k} k^{3k/2} |A|^k\,,$$
which completes the proof.
\hfill$\blacksquare$
\end{proof}

redpajama_set_name: RedPajamaArXiv


text:
Q: How to get rid of big blank block of space on html mobile site? So iam trying to make a portfolio site for the first time, however i came to test it on mobile and only just realised there is a massive block of white space on the right hand side. But iam struggling to figure out why this is ive tried moving some margins and other css features but cant quite see whats the issue, and its the same problem on all of the pages. Hope someone can help me. (I know its probably something really stupid... )
Image example : https://ibb.co/KXX8dbL
HTML CODE OF JUST index page (issue is same for all other pages)
<!DOCTYPE html>

    <title>Mathews Joy</title>
    <meta charset="utf-8">
    <link rel="stylesheet" href="style.css">
    <meta http-equiv="X-UA-Compatible" content="IE=edge">
    <meta name="viewport" content="width=device-width, initial-scale=1.0">
    <link rel="icon" href="images/MJ.png">

                    Contact Me

                    Certications

                    Data Data Data!

                    MATHEWS JOY

                            "Don't limit yourself.

                             Many people limit themselves to what they think they can do.

                              You can go as far as your mind lets you.

                               What you believe, remember, you can achieve." – Mary Kay Ash

                            "If people are doubting how far you can go,

                             go so far that you can't hear them anymore." – Michele Ruiz

                            "We need to accept that we won't always make the right decisions,

                             that we'll screw up royally sometimes – understanding that failure is not the opposite of success,

                              it's part of success." – Arianna Huffington

                            "You've gotta dance like there's nobody watching,

                             love like you'll never be hurt, sing like there's nobody listening,

                              and live like it's heaven on earth." ― William W. Purkey

                            "Smart people learn from everything and everyone,

                             average people from their experiences,

                              stupid people already have all the answers." – Socrates

                            "Do what you feel in your heart to be right – for you'll be criticized anyway."

                            ― Eleanor Roosevelt

About Me

Student at the University of Lincoln studying Computer Science (first year). A hard-working, responsible and enthusiastic learner. Always motivated with a willingness
            to learn new attributes and obtain new business experiences. My main area of interest is data! specfically data analyst roles and business analyst roles, this has only arised
            recently but as soon as I did research in these fields and talked some some well established professionals, it instantly sparked my interest.

Skills and tools I Have Experience With

SQL

Database communication tool

SQL stands for Structured Query Language. SQL lets you access and manipulate databases.
                    A query language is a kind of programming language that's designed to facilitate retrieving specific information from databases,
                    and that's exactly what SQL does. I have experience using MySQL and SSMS (SQL Server Management Studio).

Python

High-level programming language

Python is an interpreted, high-level and general-purpose programming
                    language. Python's design philosophy emphasizes code readability with its
                    notable use of significant indentation. I have learnt python at university, and have done
                    a couple intermediate/begineer projects including data analysis.

Tableau

Data visualisation

Tableau is a powerful and fastest growing data visualization tool used in the Business Intelligence Industry.
                    It helps in simplifying raw data in a very easily understandable format. I have used this tool to produce
                    clear and easy to understand data visualisations for those with less understanding of the data.

C#

High-level programming language

C# is an object-oriented programming language from Microsoft that aims to combine the computing power
                     of C++ with the programming ease of Visual Basic. My main exposure to this language is through university
                    where I strengthed my OOP skills through making intermediate console applications.

 2021 Created By Mathews Joy

FULL CSS CODE
/* Master Styles */
/* import font google api */
@import url('https://fonts.googleapis.com/css2?family=Poppins&display=swap');
@import url('https://fonts.googleapis.com/css2?family=Satisfy&display=swap');
* {
    font-family: 'Poppins', sans-serif;
    padding: 0;
    margin: 0;
}

@viewport {
    width: device-width;
    zoom: 1.0 ;
}

/* Scroll bar */
::-webkit-scrollbar {
    width: 0;
}
#scrollPath {
    position:Fixed;
    top: 0; right: 0; width:10px; height:100%;
    background: rgba(255,255,255,0.04);
}
#progressbar {
    position:Fixed;
    top: 0; right: 0; width:10px; height:100%;
    background: linear-gradient(to top, silver, aliceblue);
    animation: animate 5s linear infinte;
    z-index: 1;
}
@keyframes animate {
    0%,100%
    {
        filter: hue-rotate(0deg);
    }
    50%
    {
        filter: hue-rotate(360deg);
    }
}
#progressbar:before{
    content: '';
    position: absolute;
    top: 0; left: 0; width: 100%; height: 100%;
    background: linear-gradient(to top, silver, aliceblue);
    filter:  blur(20px);
}
#progressbar:after{
    position: absolute;
    top: 0; left: 0; width: 100%; height: 100%;
    background: linear-gradient(to top, silver, aliceblue);
    filter:  blur(20px);
}

.container {
    display: grid;
    grid-template-columns: 1fr;
}

/* Nav Styles*/
.nav-wrapper{
    display:flex;
    justify-content: space-between;
    padding: 30px;
    box-shadow: 0 2px 8px 0 rgb(0 0 0 / 10%);
}

.left-side{
    display:flex;
}

.nav-wrapper > .left-side > div {
    margin-right: 20px;
    font-size: 0.9em;
    text-transform:uppercase;
}

.nav-link-wrapper {
    color: black;
    height: 22px;
    border-bottom: 1px solid transparent;
    transition: border-bottom 0.5s;
}

.nav-link-wrapper a {
    text-decoration: none;
    transition: color 0.5s;
    color: black;
}

.nav-link-wrapper:hover{
    border-bottom: 1px solid black;
}

.nav-link-wrapper a:hover{
    color:black;
}

.brand {
    color: black;
}
.brand:hover{
    border-bottom: 1px solid black;
}

/* Portfolio Styles */
.portfolio-items-wrapper {
    display: grid;
    grid-template-columns: 1fr 1fr 1fr;
}

.portfolio-item-wrapper {
    position: relative;
}

.portfolio-img-background {
    height: 350px;
    width: 100%;
    background-size: cover;
    background-position: center;

}

.img-text-wrapper {
    position: absolute;
    top: 0;
    display: flex;
    flex-direction: column;
    justify-content: center;
    align-items: center;
    height: 100%;
    text-align: center;
    padding-left: 100px; padding-right: 100px;
}

.img-text-wrapper .subtitle {
    transition: 1s;
    font-weight: 600;
    color: transparent;
    text-align: center;
}

.img-text-wrapper:hover .subtitle {
    font-weight: 600;
    color: white;
}

.img-darken {
    transition: 1s;
    filter: brightness(10%);
}

/* about me */
#parent2 {
    display: flex;
    padding: 5px;
    align-items: center;
    justify-content: center;
    margin-top: 230px;
    height: 350px;
}

.aboutme {
    margin-left: 300px;
    margin-right: 200px;
    font-size: 18px;
    padding: 40px;
    background: #f5f7f8;
    border-radius: 10px;
    height:70%;
    width:100%;
    overflow: auto;
    text-overflow: ellipsis;
}
.aboutme h1 {
    color: #000;
    margin:0 0 30px 0;
    text-transform: uppercase;
    -webkit-text-fill-color: transparent;
    -webkit-text-stroke-width: 0.5px;
}
.aboutme h1:hover {
    -webkit-text-fill-color: black;
}
.pictureofme img{
    width: 300px;
    margin-left: -220px;
    margin-right: 300px;
}

/* Most used sites section */
.wrapper {
    margin: 0;
    padding: 3%;
    box-sizing: border-box;
    background: white;
    margin-top: 10%;
    height: 100%; width: 100%;
}

.wrapper h1 {
    font-size: 40px;
    text-align: center;
    margin-bottom: 60px;
    padding-bottom: 2%;
    text-transform: uppercase;
    color: #000;
    -webkit-text-fill-color: transparent;
    -webkit-text-stroke-width: 0.5px;
}
.wrapper h1:hover {
    -webkit-text-fill-color: black;
}

.tools {
    display: flex;
    text-align: center;
    width:auto;
    justify-content: center;
    flex-wrap: wrap;
}

.tools .websites {
    background: white;
    margin: 5px;
    width: 300px;
    margin-bottom: 50px;
    padding: 20px;
    line-height: 25px;
    position: relative;
    border-radius: 10%;
    box-shadow: 0 2px 8px 0 rgb(0 0 0 / 20%);
}

.tools .websites h3 {
    font-size: 30px;
    text-transform: uppercase;
    margin-top: 50px;
}

.tools .websites p.role {
    font-size: 15px;
    text-transform: uppercase;
    margin: 12px 0;
}

.tools .websites .site_img {
    width: 100px;
    height: 100px;
    border-radius: 50%;
    position: absolute;
    top: -50px;
    left: 50%;
    transform: translateX(-50%);
    background: white;
}

.tools .websites .site_img img {
    width: 100px;
    height: 100px;
    padding: white;
}

/* footer */
.footer {
    background-color:grey;
    text-align: center; color: white;
    padding: 3px;
    position:fixed;
    left:0; bottom:0; width: 100%; height: 20px;
    opacity: 0.5;
    z-index: 1;
}
.copyright {
    float: left
}

/* CONTACT PAGE CSS STYLES */
.connect {
    width: 80%;
    margin:50px auto;
    text-align: center;
    padding-top: 50px;
}

.connect h1{
    color: #4169E1;
}
.connect p{
    margin-bottom: 15px;
}

.contact-box{
    display:flex;
}
.contact-left {
    flex-basis: 60%;
    padding: 40px 60px;
    background: white;
    box-shadow: 0 2px 4px 0 rgb(0 0 0 / 20%);
}
.contact-right {
    flex-basis: 40%;
    padding: 40px;
    box-shadow: 0 2px 4px 0 rgb(0 0 0 / 20%);
}

.input-row {
    display:flex;
    justify-content: space-between;
    margin-bottom: 20px;
}

.input-row .input-group {
    flex-basis: 45%;
}

input{
    width:100%;
    border:none;
    border-bottom: 1px solid black;
    outline:none;
    padding-bottom: 5px;
}

.textarea{
    width: 100%;
    padding: 10px;
    outline: none;
    border:1px soild black;
    box-sizing:border-box;
}

label {
    margin: 6px;
    display:block;
    color: purple;
}

button{
    border: none;
    outline: none;
    width: 100%;
    height: 35px;
    border-radius: 30px;
    margin-top: 20px;
    box-shadow: 0 2px 4px 0 rgb(0 0 0 / 20%);
}

.contact-left h3{
    color: forestgreen;
    font-weight:600;
    margin-bottom:30px;
}

.contact-right h3{
    color:forestgreen;
    font-weight:600;
    margin-bottom:30px;
}

tr td:first-child {
    padding-right: 20px;
}
tr td{
    padding-top: 20px;
}

.contacts {
    display: flex;
    justify-content: space-around;
    padding: 10px;
    font-size: 18px;
    padding-bottom: 200px;
}

.contacts .facebook {
    color: blue;
}
.contacts .instagram {
    color: orangered;
}
.contacts .linkedin {
    color: steelblue;
}
.contacts .gmail {
    color: red;
}

/* Certications Page */
.title-box {
    margin:auto 50px;
    text-align: center;
    margin-top: 90px;
    padding-bottom: 20px;
}

.title-box h1{
    color: purple;
}

.certications-box {
    width: 200px;
    height: 198px;
    border-radius: 4px;
    margin-bottom: 30px;
    box-shadow: 0 2px 4px 0 rgb(0 0 0 / 20%);
    padding: 20px;
    position: relative;
}

.certications-box img{
    width: 100px;
    position: absolute;
    top: 20px;
    right: 20px;
    border-radius: 4px;
    transition: .5s;
}

.certications-box h4{
    margin-top: 25px;
    margin-bottom: 5px;
    color: #2196f3;
}

small {
    color: #555;
}

.break-box {
    margin: 50px auto 20px;
    border-radius: 3px;
    box-shadow: 0 2px 4px 0 rgb(0 0 0 / 20%);
}

.certications-box p{
    text-align: center;
    font-size: 16px;
}

.certications-row {
    display: grid;
    grid-template-columns: auto auto auto;
    justify-content: space-around;
    flex-wrap: wrap;
    margin: auto;
    padding: 60px;
}

.certications-box img:hover{
    width: 198px;
}

/* Video Text */
.banner2 {
    position: absolute;
    height: 100vh;
    width: 100%;
    overflow: hidden;
    display:flex;
    justify-content: center;
    text-align: center;
}

.banner2 video{
    width: 100%; height: 100%;
    object-fit: cover;
    top: 0;
    left: 0;
}

.banner2 h2 {
    top: 0; left: 0; width: 100%; height: 100%;
    position: absolute;
    background: #fff;
    font-size: 30vw;
    text-transform: uppercase;
    text-align:center;
    line-height: 45vh;
    color: #000;
    mix-blend-mode:screen;
}

.banner3 {
    position: absolute;
    height: 100vh;
    width: 100%;
    overflow: hidden;
    display:flex;
    justify-content: center;
    text-align: center;
}

.banner3 video{
    width: 100%; height: 100%;
    object-fit: cover;
    top: 0;
    left: 0;
}

.banner3 h2 {
    top: 0; left: 0; width: 100%; height: 100%;
    position: absolute;
    background: #fff;
    font-size: 20vw;
    text-transform: uppercase;
    text-align:center;
    line-height: 45vh;
    color: #000;
    mix-blend-mode:screen;
}

/* Scroll to top button */
.scrollTop {
    position: fixed;
    bottom: 800px;
    height: 60px;
    width: 40px;
    right: 40px;
    background: #fff url(images/up.png);
    border-radius: 50%;
    background-size: 40px;
    background-position: center;
    background-repeat: no-repeat;
    cursor: pointer;
    z-index: 10;
    visibility: hidden;
    opacity: 0;
    transition: 0.5s;
}

.scrollTop.active {
    bottom: 40px;
    visibility: visible;
    opacity: 1;
}

/* POWERPOINT */
.powerpoint {
    padding: 90px;
}

/* THANK YOU PAGE */
.thank-you {
    justify-content: center;
    text-align: center;
    font-size: 230%;
    padding-top: 18%;
}

/* ANALYSIS PAGE */
.twitter {
    display: grid;
    padding: 90px;
    margin: auto;
    width: 66%;
    grid-template-columns: auto auto auto;
    justify-content: space-between;
    flex-wrap: wrap;
}

.data #main-header{
    padding-right: 17%;
    padding-left: 17%;
    margin-left: auto;
    margin-right: auto;
    padding-top: 4%;
    font-size: 50px;
    text-align: center;
    color: #000;
    text-transform: uppercase;
}
.data #main-header:hover {
    -webkit-text-fill-color: transparent;
    -webkit-text-stroke-width: 0.5px;
}

.data .data-inner {
    padding-right: 25%;
    padding-left: 25%;
    margin-left: auto;
    margin-right: auto;
    padding-top: 3%;
    padding-bottom: 5%;
}

.data .data-inner #first-header{
    color: green;
}
.data .data-inner #second-header{
    color: salmon;
}
.data .data-inner #third-header{
    color: blue;
}

.data .data-inner  img{
    display: block;
    padding: 4%;
    margin-left: auto;
    margin-right: auto;
    width: 68%;
}

.data .data-inner  iframe{
    display: block;
    padding: 4%;
    margin-left: auto;
    margin-right: auto;
    width: 68%;
    height: 330px;
}

/* SCREEN LOADER */
.loader {
    position: fixed;
    z-index: 99;
    top: 0;
    left: 0;
    width:100%;
    height:100%;
    background: white;
    display:flex;
    justify-content: center;
    align-items:center;

}
.loader > img {
    width: 100px;
}
.loader.hidden{
    animation:fadeOut 1s;
    animation-fill-mode: forwards;
}
@keyframes fadeOut{
    100%{
        opacity: 0;
        visibility: hidden;
    }
}

JAVASCRIPT FULL
// For Loading screen
window.addEventListener('load', function(){
    const loader = document.querySelector(".loader");
    loader.className += " hidden";  // class loaderhidden
});

// For the hover animations at start of the page
const portfolioItems = document.querySelectorAll('.portfolio-item-wrapper');

portfolioItems.forEach(portfolioItem => {
    portfolioItem.addEventListener('mouseover', () => {
        portfolioItem.childNodes[1].classList;
        portfolioItem.childNodes[1].classList.add('img-darken');
    })

    portfolioItem.addEventListener('mouseout', () => {
        portfolioItem.childNodes[1].classList.remove('img-darken');
    })
})

// For Progress bar
let progress = document.getElementById('progressbar');
let totalHeight = document.body.scrollHeight - window.innerHeight;
window.onscroll = function(){
    let progressHeight = (window.pageYOffset / totalHeight) * 100;
    progress.style.height = progressHeight + "%";
}

// Custom cursor
const cursor = document.querySelector('.cursor');

document.addEventListener('mousemove', e => {
    cursor.setAttribute("style", "top: "+(e.pageY - 10)+"px; left: "+(e.pageX - 10)+"px;")
})

document.addEventListener('click', () => {
    cursor.classList.add("expand");

    setTimeout(() => {
        cursor.classList.remove("expand");
    }, 400)
})

// Scropp up top button
window.addEventListener('scroll', function(){
    var scroll = document.querySelector('.scrollTop');
    scroll.classList.toggle("active", window.scrollY > 500)
})

function scrollToTop(){
    window.scrollTo({
        top: 0,
        behavior: 'smooth'
    })
}

A: You have to use media query to make responsive layout for mobile device check this article for media query https://www.w3schools.com/cssref/css3_pr_mediaquery.asp
also add this inside your universal selector
*{
  width: auto;
  overflow-x: hidden;
}

by setting width to auto all element will take all available space and by adding overflow-x:hidden it will hide element which overflow the viewport or screen
you can make responsive image grid by putting following code
.row {
  display: flex;
  flex-wrap: wrap;
  padding: 0 4px;
}

/* Create four equal columns that sits next to each other */
.column {
  flex: 25%;
  max-width: 25%;
  padding: 0 4px;
}

.column img {
  margin-top: 8px;
  vertical-align: middle;
  width: 100%;
}

/* Responsive layout - makes a two column-layout instead of four columns */
@media screen and (max-width: 800px) {
  .column {
    flex: 50%;
    max-width: 50%;
  }
}

/* Responsive layout - makes the two columns stack on top of each other instead of next to each other */
@media screen and (max-width: 600px) {
  .column {
    flex: 100%;
    max-width: 100%;
  }
}

check this article for responsive grid images https://www.w3schools.com/howto/howto_css_image_grid_responsive.asp

redpajama_set_name: RedPajamaStackExchange


text:
Classic North American Super Nintendo
The Super Nintendo Entertainment System, also known as Super Nintendo, Super NES, or SNES, was a 16-bit video game console released by Nintendo in 1990. In Japan and South-East Asia, the equivalent was known as the Super Famicom (aka SFC).
The SNES is Nintendo's second home console, following the Nintendo Entertainment System. Whereas the earlier system had struggled in the PAL region and large parts of Asia, the SNES proved to be a global success, albeit one that could not match its predecessor's popularity in Southeast Asia and North America—due in part to increased competition from Sega's Mega Drive console (released in North America as the Genesis. Despite its relatively late start, the Super Nintendo Entertainment System became the best-selling console of the 16-bit era.
The Original NES was grey and sported a section for inserting game cartridges directly in the center of the console, so that the cartridge faces upright, with artwork facing the gamer. On the console are two controller ports and a button for starting gameplay and a button for ejecting the inserted cartridge.
1 Controls
2 Chrono Titles for Super Nintendo
3 Emulation
4 Other Square Titles for the Super Nintendo
Controls[edit]
Controlling the on-screen characters is achieved through the use of a hand-held device known simply as a "controller", which plugs into the front of the console via a long, thin cord. Controllers for the SNES originated as gray in color with light purple and dark purple buttons. The colors varied as new versions of the console reached the market. After the production of the Game Cube made emulation of Super Nintendo video games possible, a new controller that matched the port holes on the new console was created. These controllers were purple in color with red, green, and yellow buttons similar to the original Game Cube controller.
Top: SNES Controller for the Game Cube. Bottom: Traditional SNES controller.
Both controllers allow control of an on-screen character's movement via the D-Pad (Directional Pad) on the left side of the controller, which is shaped like a cross, with each direction corresponding with the proper compass direction. (Up, Down, Left, and Right). On the right side, four buttons are featured in a rhomboidal pattern. From the top left to the bottom right, the keys are Y, X, B, and A. Y and X are light purple and A and B are dark purple. A Start and Select button are featured in the center of the controller, and an L and R button on the top rim near where the cord connects to the controller.
The functions of the button vary between games. However, universally, the Start Button pauses games, allows entrance into specific maintenance menus, or helps progress dialogue. Select, although mostly unused, sometimes assists with restarting the game emulation if pressed in conjunction with Start. The A button typically allows the progression of dialogue, menus, and other generally choosing options. In Chrono Trigger, the B-button allows the player to dash or allow the character to run faster.
Chrono Titles for Super Nintendo[edit]
Chrono Trigger - (Originally)
Radical Dreamers: Nusumenai Hōseki - for the Satellaview accessory.
Chrono Trigger: Crimson Echoes - emulated consoles only.
Emulation[edit]
An Emulator is a program that allows console video games to be played on Personal Computers. The name emulator literally refers to the fact that the console's video game playing behavior is emulated. Super Nintendo Emulators, such as Snes9x and ZNES, allow games such as Chrono Trigger and Radical Dreamers: Nusumenai Hōseki to be playable on computers. Generally illegal, as the games played upon them are illegally acquired copies, use of emulation is permissible when one owns original copies of the games played on them and has no reasonable way to play the game on the original console, or wishes to emulate the game to receive screenshots. Legal specifics regarding Video game console emulators differs with each project, and the Terms of Use for each emulator is also detailed by the creators.
Chrono Trigger: Crimson Echoes was designed exclusively for the emulator ZNES. As a fan-made game, the only way to play it is through emulation.
Other Square Titles for the Super Nintendo[edit]
Romancing SaGa
Hanjuku Hero: Aa, Sekaiyo Hanjukunare
Alchest
Front Mission: Gun Hazard
Super Mario RPG: Secret of the Seven Stars
Tactics Ogre: Let Us Cling Together
Treasure of the Rundras
Wikipedia: Super Nintendo Entertainment System
Nintendo's "Classic System" page on the SNES
Gallery[edit]
A Chrono Trigger cartridge for the SNES.
A Radical Dreamers cartridge for the SNES with a protective dust trap along the teeth.
The Satellaview accessory attached to a Super Famicom.
Retrieved from "https://www.chronowiki.org/w/index.php?title=Super_Nintendo_Entertainment_System&oldid=40211"

redpajama_set_name: RedPajamaCommonCrawl


I've heard it over and over, "they grow so fast". Not until Norah did I realize how true this is. As I packed up her newborn clothes that she only got to wear once before she grew out of them, I couldn't help but feel a little sad. Was I so focused on the future and making sure she was reaching milestones that I forgot to live in the present? Each day she does something crazy that makes me think, "Whoa, kid! Slow down!"
This is my reminder to slow down and live in the present. She will only be this little once and I don't want to miss a single moment.


text:
An environmental clean-up crew works to remove gasoline fuel from an ETP pipeline spill in Darby creek in Tinicum Township, Pa. (Kimberly Paynter/WHYY)
Kimberly Paynter / WHYY
Sunoco's 12-inch pipeline leaked 33,000 gallons of gasoline into creek, PHMSA says
Ageing pipeline, which has leaked before, will be used to temporarily carry natural gas liquids
Jon is an experienced journalist who has covered a wide range of general and business-news stories for national and local media in the U.S. and his native U.K. As a former Reuters reporter, he spent several years covering the early stages of Pennsylvania's natural gas fracking boom and was one of the first national reporters to write about the effects of gas development on rural communities. Jon trained as a general news reporter with a British newspaper chain and later worked for several business-news organizations including Bloomberg News and Market News International, covering topics including economics, bonds, currencies and monetary policy. Since 2011, he has been a freelance writer, contributing Philadelphia-area news to The New York Times; covering economics for Market News, and writing stories on the environment and other subjects for a number of local outlets including StateImpact. He has written two travel guidebooks to the European Alps; lived in Australia, Switzerland, Israel, and Saudi Arabia, and visited many countries including Ethiopia, Peru, Taiwan, and New Zealand. Outside of work hours, Jon can be found running, birding, cooking, and, when weather permits, gardening in the back yard of a Philadelphia row home where he lives with his partner, Kate.
September 4, 2018 | 11:33 AM
An environmental clean-up crew works to remove gasoline fuel from an ETP/Sunoco pipeline spill in Darby creek on June 21, 2018 in Tinicum Township, Pa. (Kimberly Paynter/WHYY)
An 81-year-old pipeline that Sunoco plans to convert for natural gas liquids leaked more than 33,000 gallons of gasoline into a creek near Philadelphia in June because of an unspecified pipe failure, according to new data from a federal agency.
The Pipeline and Hazardous Materials Safety Administration released a spreadsheet disclosing details of its investigation into the spill that was first reported by a member of the public on June 19 at Darby Creek near Philadelphia International Airport.
The data show that 798 barrels, or 33,516 gallons, of gasoline were "unintentionally" released by the pipeline that runs from Point Breeze near Philadelphia to the Montello terminal at Sinking Spring near Reading, Berks County.
A section of the 12-inch pipeline, which was manufactured and installed in 1937 and has leaked at least twice before in its history, will be used temporarily as part of the new Mariner East 2 natural gas liquids pipeline until construction on delayed sections of the line is completed, Sunoco has said.
About two-thirds of the spill, or 509 barrels, was recovered, leaving a net loss of 289 barrels or 12,138 gallons, according to the PHMSA data. The pipeline had been shut down for routine maintenance the day before the leak was reported, and was restarted with a new section to replace the leaking pipe on July 1.
PHMSA said it first learned of the spill on the evening of June 19 from a "private citizen" who reported a petroleum odor at Darby Creek near where it flows under route 291 a few miles west of the airport.
"The control center immediately notified field operations of the complaint and personnel were dispatched to the area to investigate," the report said.
It does not specify any environmental damage but affirms soil contamination and a need for long-term remediation.
"Product recovery and site remediation efforts continue," the agency said in a narrative accompanying the data table. "The failed pipe was fully excavated, removed and replaced."
PHMSA said it will file another report when it has received information on the cause from a third-party that is doing a metallurgical analysis of the failed pipe.
Sunoco, a unit of Energy Transfer Partners, did not immediately respond to a request for comment. In July, it said it will use the 12-inch line to carry natural gas liquids from Wallace Township in Chester County to Middletown Township in Delaware County, a distance of about 25 miles, for a temporary period while Mariner East 2 is being completed.
Rick Kuprewicz, an independent pipeline expert, said he reviewed the integrity of the 12-inch line for West Goshen Township, one of the municipalities where Sunoco plans to utilize the line, but that his report is not yet public.
Kuprewicz said the leak at Darby Creek is not likely to have been caused by the age of the line, "knowing what I know about pipe steel."
The multibillion dollar, cross-state pipeline is now at least 18 months behind its original schedule after construction caused a string of delays, including dozens drilling mud spills statewide and sink holes in Chester County. The incidents prompted three shutdowns ordered by two regulators and a judge. The company plans to use the older line so that it can start to meet customer orders for propane, butane and ethane by the end of September.
The addition of the 12-inch line to ME2, albeit temporarily, has fueled the fears of pipeline safety campaigners who say the old line adds to the dangers of leaks or explosions of the highly volatile liquids to be carried by the line.
"Once again, Sunoco has had an accident on its 12-inch Point Breeze to Montello pipeline," said Eric Friedman, a member of Del-Chesco United for Pipeline Safety, a coalition of community groups in Delaware and Chester Counties. "And once again, it has demonstrated an inability to detect that a leak is occurring.
"It took Sunoco seven days after the public's report of a leak to even confirm that it was its pipeline that was leaking," Friedman said. "Had this accident involved hazardous, highly volatile liquids, the result could have been catastrophic."
In 2015, the line leaked an unspecified quantity of gasoline at Edgmont Township in Delaware County, prompting local officials to write to the PUC expressing "serious safety concerns." In 1987, the pipeline spilled about 70,000 gallons of gasoline in West Whiteland Township, Chester County.
Delaware Watershed
Mariner East: A pipeline project plagued by mishaps and delays
Pipelines: The new battleground over fracking
New study finds climate change will dramatically alter Earth's ecosystems


The effective use of business intelligence has the power to support and grow any business. The key is effective use of business intelligence.
Business intelligence has a long history in supporting business, from the days of filing cabinets full of information to computer storage and data warehousing. If you're interested, click here to read more information on the history of business intelligence.
These days, business intelligence is a broad term referring to the technology, the applications and the practices that collect, integrate and analyze business information, with a goal of supporting decision-making processes. Effective business intelligence tools can give you various views of your business operations – historical, current and future or predictive views.
But like many other components of your business, rather than rushing in by finding a business intelligence solution, it's best to start by developing a valuable strategy that can then be executed on.
The basic purpose of business intelligence is to provide the information that allows you to analyze the business, adjust course if needed, and make decisions that support strategic goals. So, the first step in an effective business intelligence strategy is to develop vision and goals for the strategy.
• What does your business need to evolve and improve?
• What data can support that growth?
• What is it you want to accomplish with your strategy?
It's important to know where you want to go before starting down the road.
Whatever the size of your business, it's important to build an effective team to develop and implement the strategy.
There are some key components to consider when building your team.
The first consideration is to ensure there is an Executive sponsor, often the Chief Financial Officer. The sponsor needs to value the data and understand the benefits of it to the business. The sponsor will be your voice at the Executive table, will support any funding decisions needed and will help remove any roadblocks to implementing the strategy.
It's also important that the rest of the organization sees that the Executive finds value in the strategy. This will help with support and buy-in across the business.
The Executive sponsor can also provide the corporate view of the key measures that need to be gathered and analyzed.
Which leads to another key component, having a cross-functional team. It's important to bring together subject-matter experts from various parts of the organization, which will provide different views into the information that needs to be gathered. Different levels of the organization will give you a strategic view, a tactical view and an operational view of the information that needs to be gathered and how it will be used.
A cross-functional team also ensures there are advocates for the strategy throughout the organization, and provide you with an expert in each area of the organization, as team members will be able to understand the information.
Once you have your vision and goals established, and your team is in place, it's time to determine the information needed to support the strategy. After all, business intelligence is about analytics and data, and they need to be effective to support the strategy.
Again, your cross-functional team will provide value by working together to determine the key performance indicators (KPIs) with a view across the business.
• What are the main analytics that you want to track and where will you get that information?
• What are your industry's KPIs that you want to benchmark your business against?
• What is your company's historical data that's important to analyze in order to track progress?
• Who will be using the information and how can it best be delivered to them?
From this important conversation, your team will be able to develop custom KPIs for your business. These company-specific metrics are what you will track, report, and monitor. The best decisions will be made by understanding who will use the data and how they will use it, which in turn determines the type of information needed and the frequency of information gathering.
It's also key to ensure the data is gathered and presented in a way that makes it easy for all areas of the business to understand, digest and act on the information.
Consider small steps, if that works for your business. Perhaps you don't need to track every measure at the outset. Choose a few KPIs and track and report them, gather feedback on the information, and adapt if necessary before tackling all the KPIs.
Only once you have your strategy in place and your key metrics determined are you able to think about a technology solution that supports your strategy. That's because business intelligence is not just a technology initiative. The hard work the team has done to this point will ensure you're in the best position to find the right tool and implement it successfully.
Your cross-functional team will again be key in this decision. While the technology experts can provide key answers to questions such as number of servers required, or security of the data, the other stakeholders can provide input into how they will use the data to ensure the solution meets their needs. The entire business can have input into the best solution.
After the solution is chosen, be sure the team supports implementation and tracks progress on a regular basis.
Once your business intelligence strategy is implemented and is being used, it's important to step back regularly and analyze the decisions made using the data.
• Did the data provide the right information, at the right time?
• Did the data support effective decision-making?
• Is there additional information needed?
• Is there information that wasn't valuable or relevant, that doesn't need to be gathered any longer?
• What can be done differently the next time a decision is made using the data?
• What went right and what went wrong?
• Stepping back to answer such questions allows the business intelligence strategy to adapt to suit the needs of the business.
There isn't a one-size-fits-all business intelligence strategy for every organization, but these steps provide a solid framework for any type or size of business to develop and implement a strategy that works. It's important to be able to gather important data and use it to make valid business decisions. The variety and volume of information available provides huge potential for data-driven insights, which in turn can help grow your business.
Author Bio: Danielle Canstello is party of the content marketing team at Pyramid Analytics. They provide enterprise level analytics and BI platform. In her spare time, she writes around the web to spread her knowledge of the marketing, business intelligence and analytics industries.


It was good to get away from everyday cares, if only for a little while. My husband is going to Beijing for five weeks, and while I do my best not to think of it, I know the day of departure is looming.
So I was glad for the time together in Eureka Springs, where so many before us have come to tap into the area's healing powers. We had no agendas, no list of 'must dos', taking each day and meal and experience as it came. We visited a few of the area's natural wonders, including some of its natural springs that once were the source of Ozarka bottled water, before the company moved its operations to Texas. We took in a few of the shops, antique stores as well as 'vintage' stores; the latter we found were 'vintage' in name only as none carried vintage wares.
Here in Eureka, it's the antique stores who offer vintage goods. I could have had a vintage Barbie case for a mere $45 and I saw sheets of vintage photos for ninety percent less. It made me sad to think that no family member had wanted to keep these old Victorian portraits and photos for their own sakes. Perhaps the person who left behind the photos for the pearly gates left behind no remaining family. Either way, it's a sad thought.
Darting in and out of quaint little Victorian shops to keep out of the rain, my husband's eye fell on an interesting book title. "How to Profit from the Coming Rapture: Getting Ahead When You're Left Behind". I believe it may offer tongue in cheek advice to help readers laugh at those worries in life that never transpire but make us anxious all the same. Maybe somewhere in those pages, it teaches the importance of telling the truth, like when to call yourself 'vintage' and when it's time to stop calling yourself Ozarka.
We were fortunate to stay at a place that was true to the words written about it. And, because it was grounded in truth, it became more than claimed to be. Mt. Victoria Inn was simply the best part of my Eureka Springs visit. Each day I came to borrowed 'home' after a day of exploring to immerse myself in simple pleasures, while soaking up the ambiance of comfortable elegance around me.
On the outside veranda, I let the breeze caress my face and carry away my worries; I allowed myself to get lost in a good book or watching a good movie while curled snug in my borrowed bed; and I enjoyed life and wrote about it while others prepared my meals. And food always tastes better when prepared by another's capable and gifted hands.
Without dipping even my smallest toe in the famed local waters, I found relief from my worries. Somehow, like that Texas company who left behind everything but the name, I need to carry something of this healing place with me. But I want substance over form; something that is not in name only.
On the verge of beginning my own journey to Mississippi, I'm so glad I took the time to stop packing and track down your blog. I'd seen your URL once before, but didn't pursue it. Today I did, and found your lovely post.
Like you, I've been gifted with a few days with no agenda, no list of "must-do's". I hope at the end I'm also gifted with your sense of relief and release. As you suggest, the key is truth-telling – perhaps one reason that I've always found refreshment in the blues.
And thank you for adding me to your blogroll. I'm honored.
I've never considered the blues as a source of refreshment — but I see this is so. As sadness weighs me down, I move more slowly, which allows me to breathe more deeply. And all that stillness and deep breathing helps me biirth whatever trouble I'm carrying…. just like a screaming baby, I release it to te world.
Thank you for taking time to visit and leaving a calling card. You're writing is as lovely as your site — I will visit regulary, as it points to a world where truth lives. My life and my blogroll are mere signposts, pointing others to something greater.
Safe travels. And may you return refreshed, full of sacred souvenirs.


Have you ever experienced a collision repair business scheduling system that works to perfection? I can't say that I have, even though I've worked with or seen many different systems.
I've seen both extremes, from managers who schedule based on the height of the stack of scheduled estimates to complex custom automated systems costing over $1 million. Of course, the latter works far better than the former, but neither is perfection. The reason is that we work in an industry with an incredible amount of variables, including job variances, hidden damage, parts issues, insurance claim issues, staff issues, weather and market conditions, and on and on. You understand. The key is determining what is right for your operation.
Let's take a look at some scheduling concepts and key factors.
The concept is that of taking in a set number of cars per day or per week. The assumption is that the size of the jobs averages out and therefore the schedule remains consistent and controllable. This is a very simplistic system. Some consolidators use this philosophy. Since the size of the jobs varies it is wise to give a shop manager some authority to make adjustments. If you're looking for a new system to start with or one that is the easiest to grasp, this is a good choice. A good option for this plan is to also schedule the number of vehicles leaving to control a steady work flow. Assuming your work in process (WIP) is at an appropriate level, the number of cars leaving on average should match the number of cars arriving.
This is the same philosophy as the plan above except it is more precise in understanding the size of jobs scheduled. In theory, this is a more accurate way of scheduling. A big variable is scheduling a job that does not yet have a complete and thorough estimate. This system requires more effort to log the number of flat-rate hours for each job. Your management system may do it for you. If you are looking for more precise data than simply relying on numbers of cars, this could be a good methodology for you. It could be handled through some management systems or a simple log, such as a spreadsheet, or even a written document.
WIP can be measured by number of vehicles, dollars of work in process, or flat rate hours of work in process. This methodology relies on a specific WIP or an ideal range, and adjusting the amount of incoming work to maintain that WIP. This will be more complex than the above plans. Your management system may provide the data for you. The beauty in this system is that it addresses maintaining a consistent WIP in addition to scheduling incoming vehicles. In other words, it will help prevent your WIP from getting away from you. This is a good solution, especially if your management system provides the data.
Some shops allow for some specific variables. A good example would be tow-ins. The idea is to assume you will receive a certain number each week or day. Often they are more likely to appear after a weekend or holiday. Plan for it.
Some shops have a specific priority relationship with a dealer or insurer and reserve a certain number of schedule spots for them each day or week. Some also use this philosophy for unexpected drop offs—those customers who simply bring their cars in and tell you to fit it in when you can. These are the people who are hard to schedule out because they often would rather leave the car at the shop than drive or store it themselves. Often we choose to take on such jobs rather than risk losing the customer to a competitor.
Seasonal adjustments can be prudent for many shops. For example, for those of us in states with significant ice and snow, we often see an increase in severity as well as in unexpected tows. In this case, it's wise to adjust the amount of scheduling capacity accordingly.
With rare exception we all have our busy and slow times. You can count on the marketplace changing on a regular basis. Customers tend to understand this. Perhaps the weather or economy make it obvious. Perhaps it's because they shop around. I find it wise to adjust scheduling philosophy accordingly, especially understanding the variables we deal with and knowing that scheduling is not a perfect science. When it is slow, try to capture every job as promptly as possible. I am more inclined to risk overscheduling to some reasonable extent, knowing that it will be hard to get more jobs tomorrow and that any job that is a no-show or total loss will be hard to replace. In the busy season, I prefer to slightly under-schedule. In those times I am more confident that a lost job will be easier to replace. I also know that in busy times it is easy to let WIP get out of control, getting us in trouble with customers and insurers.
For many years, we've talked about the importance of making our weekly schedules as consistent as possible, taking in the same number of jobs later in the week as we do at the beginning. For many of us, the benefits are intuitively obvious. Repairers know it, industry consultants and experts know it, and most insurers know it. Yet we still seem to struggle with taking more work early in the week and scheduling light for the later part. I understand the concerns over weekend rental expense. But, have you calculated the lost revenue and expense of inconsistent work volume? It makes it worth our while to find creative solutions to take in more of our repair jobs later in the week.


text:
News 30 August 2017
Stockholm World Water Week 2017: IHE Delft to assess water management needs in Iraq
Iraqi minister of Water Resources, Dr Hassan Janabi, signed a renewed version of a Memorandum of Understanding with director Johan van Dijk of IHE Delft. The Iraqi minister and IHE Delft will continue their cooperation for another five years.
The signing took place in the stand of IHE Delft at the Stockholm World Water Week on 29 August.
IHE Delft will initially support the ministry by assessing their needs in relation to development of staff expertise and performance improvement.
Iraqi minister Dr Hassan Janabi (left) and IHE Delft director Johan van Dijk, talking about the details of the signing ceremony.
A second step will be developing capacity building programmes, resulting from the initial needs assessment.
The two parties also commit to improve water resources in Iraq through integrated and optimal use of water resources management, with a special emphasis on transboundary water management and water for agriculture.
The MoU is a follow-up of the first MoU, which was signed early 2014.
Assessment of needs
On the occasion of signing the MoU, Dr Hassan Janabi said to be very happy to continue the cooperation. 'IHE Delft updated the skills of our people at the ministry. We have also done joint modelling exercises and assessment of the needs of our ministry.'
The MoU is mainly about capacity building within the ministry, but we will look for further enhancement of our cooperation', the minister added.
This news item was originally published on the website of IHE Delft.
• IHE Delft to lead AFMA-based flood resilience project for Alexandria, Egypt, 27 July 2017
• IHE Delft receives Coca-Cola grant for women and water for change in communities project, 19 June 2017
• Water education institute IHE Delft starts new life at age 60, 28 April 2017
IHE Delft
www.un-ihe.org


I just bought a new digital video camera, and the research was quite exhausting!
Before I get to the product review, there are a few things you should know about digital video cameras, and playing your recordings.
Sure, you can buy an expensive HDMI cable and plug it straight in your High Def TV, and you'll be utterly amazed at the quality.
On the flip side, you can always buy a Mac and use iMovie and this entire blog post can be irrelevant. If that was the case, the title would have been called Consumer Digital Video Cameras Camcorder.
Teaching a course from How to Choose a Video camera to Producing a DVD playable on your TV or Blu-Ray player requires much more than a single Blog post.
These two topics are inter-related so I am going to attempt it, but I will follow up with future more detailed articles if the demand is there.
Media Format. Choose the media format of the camera. You can choose from DV tapes, Hard Drive, Flash disk or even memory sticks!
Video Format. Choose the final video format of the files. File formats includes MPEG2, AVI, raw DV or AVCHD (a high def compressed file like MTS or MP4). You have to decide what you plan on doing with the video files. Are you burning DVDs for sale? Just viewing them on a computer? Or uploading to YouTube?
Batteries. Get a spare battery (adds $80 -$120 to your budget), or buy from a 3rd party battery retailer. Make sure you rotate your batteries. Like the cliche, if you don't use it, you'll lose it. Leaving a battery unused will kill the battery after 1 year or more and will no longer hold a charge.
Record. This is recording the video footage, with the best possible light and sound.
Capture. This process is copying the media from the camera to the computer.
Edit. You have to scan you video clips, and possibly trim them.
Convert. The video format you record is probably different than the format required to make the DVD.
Author. This is the process where you make menus, chapters, and add any fancy stuff like titles, credits and transitions.
Copying. If you plan on selling your final product, then you'll need to mass produce the DVD including the cover label.
At the end, I bought the Canon Vixia HG20, and here are some explanations to my decisions.
NOTE: The term "HD or high def video" refers to videos with a display resolution of either 1280×720 (720p) or 1920×1080 (1080i or 1080p which is full HD). YouTube only supports 720p HD resolution with a 16:9 widescreen with an aspect ratio and 24fps frame rate. Some default settings are set to 30 fps. The old video standard was 720×480 or 640×480 (4:3 ratio).
Storing the video files requires disk space, but if you use DV tapes, you can store them on tapes and off-site. Much cheaper than an external HD. You do practice disaster recovery, don't you?
Some cameras have a viewfinder and/or LCD display while recording. The LCD mode may be hard to view in bright sunlight from my experience.
My original Canon was a DV camera. The reason why I didn't buy another DV camera was DV cameras take 1 hour minimum to copy 1 hour of "tape" to your computer with a Firewire cable connected. Basically you have to "playback" the entire video.
The Hard drive and Flash based models are at the mercy of the the USB 2.0 connection, which copies at 400Mb/sec… which is fast. Faster than 1 hour per hour of video with 1394 Firewire, so I am happy. When I record a track meet and publish it on my Blog, the faster the better.
Editing a video from a DV based camera is easy with Windows Movie Maker or other commercial software.
The standard DVD uses the MPEG-2 format. It is compressed and not great for frame by frame analysis.
If you want to get fancy using Converting or Authoring techniques, without the headache of converting files to compatible DVD formats, you are probably better off buying a $50-100 software package like Nero 9 or Pinnacle Studio. There are literally hundreds of software packages out there.
Everyone is going towards the AVCHD video format, which is 1920×1080 (MXP, FXP, XP), but the standard setting is 1440×1080 SP mode, which still looks fantastic. The higher the resolution, the longer it will take to "convert" the file formats to a lower setting.
NOTE: Converting AVCHD files requires a "good" powerful computer, and it can take hours.
The software that comes with the Camera is the ImageMixer SE. It allows you to simply make a DVD playable onto a regular DVD or Blu-Ray player. There are no special effects to this software other than making a simple menu for your different chapter selection. It is limited to about 40 minutes per single sided DVD-R disc.
If you are using a DV method, the simplest program is using Windows Movie Maker in Windows XP. The file format is a lower quality streaming video (not a frame by frame one) but all the older videos on this blog uses this method. It is very easy to capture, edit and trim the videos, add a Title or credits page, and add fancy transitions, like fade in/fade out between scenes. You can also dub or overlay extra audio clips.
Otherwise, consider buying a $50-100 software package like Nero 9 or Pinnacle Studio that will create a fancy DVD. Of course, there are higher end software products over $1000 that professionals use.
If you have a Blu-Ray player at home, then recording the video in the highest quality and burning them in AVCHD mode using a regular DVD-R will yield fantastic results. This is the big selling point today. You can get about 40 minutes on a single 4.7Gb DVD. Otherwise, you will need an Authoring program that will downsize, compress and convert your video. If you do, I hope you have a powerful computer.
As for copying or mass producing your final DVD, try using LightScribe technology. These are essentially a 2 sided DVD. One side is for the data, and the other is for the "silkscreen" label by simply "burning" the image using a Lightscribe DVD burner. The DVD burners are as low as $28, and the discs are inexpensive.
There's no need to mess around with sticky labels that can produce "bubbles" and look very unprofessional.
In my opinion, in about 5 years, AVCHD, Blu-Ray optical discs, Solid State & Flash Disk drives will become the norm. Until then, you can choose depending on your budget as older technologies still exist.
I hope this helps you in your decision on what camera to buy. If you have any questions, please comment below. Good Luck.
Looks like a pretty snazzy camera.
Congrats on the new purchase as it is not only excellent camera but convenient. (You forgot to mention the tripod) I'm a Canon person, also, though I've shot a ton of surf footage with Sony's and Panasonic's. What are going to be the primary uses for your camera? Track meets, your athletes' training sessions and tutorials I presume?
You're costing me money when I read your articles. Example: I purchased Jack Daniels' 2nd ed. "Daniels' Running Formula" based on your recent article. That wasn't so bad except I came across another book I had been holding off on but went ahead and finally bought it, Tim Noakes' 4th ed. "Lore of Running." My brain is already cooking from Chapter 1 in Noakes' book. Gotta love it. So far, I appreciate Daniels' presentation and attitude towards running even though I prefer to set up a personal program for the sprinting distances.
My main 3 goals with the camera are filming track meets, shooting video for training DVDs, and filming seminars. We actually finished filming a "40 Yard Dash" video, which I'll promote for sale shortly.
As far as spending money, well, at least you're helping stimulate the economy with your recent spending.
In short, what is the best camera for the money ($300 to $600) that you can use straight out the box (without having to buy a better lens or other pricey accessories) for recording sprinters from start to finish, then being able to slow it down so one can clearly critique their form?
2) it records to tape, but in raw DV format. You will need a firewire 1394 connection. With raw DV, you can easily capture to your computer in AVI format, which supports frame-by-frame (thus, analysis). A compresses video format makes it look fuzzy.
You can easily use Windows Movie Maker and easily create WMV files for Youtube or even email the file, since it's small (14Mb per minute).
Of course, if you have a Mac, then this is a very easy solution for you with iMovie & QuickTime.


text:
Das Belgische Statistikamt (STATBEL), früher Generaldirektion der Statistik und der Wirtschaftsinformation (GDSWI), davor Statistisches Landesamt (SLA), ist Teil des belgischen Föderalen öffentlichen Dienstes Wirtschaft, K.M.U., Mittelstand und Energie. Es hat seinen Hauptsitz im World Trade Center (Gebäude III) in Brüssel (boulevard Simon Bolivar 30).

Das STATBEL veranstaltet Erhebungen bei belgischen Haushalten und Unternehmen, wertet behördliche Datenbanken (z. B. das Nationalregister) aus bzw. bearbeitet sie, und übermittelt Daten an belgische und internationale Behörden und Organisationen wie OECD und Eurostat.

Auf seiner Website (statbel.fgov.be) veröffentlicht Statbel Zahlenreihen, Pressemitteilungen und Studien. Dort können auch Datenbanken abgerufen werden.

Aufgaben und Aufträge
Grundaufgabe des BELSTAT ist das Sammeln, Verarbeiten und Verbreiten relevanter, verlässlicher und sachkundig gedeuteter Zahlen zur belgischen Gesellschaft.

Unter 'Sammeln' versteht man das Einholen von Daten bei gesellschaftlichen und wirtschaftlichen Aktoren. Dies erfolgt anhand unmittelbarer bzw. indirekter Befragungen. Bei Erhebungen wird die zu untersuchende Grundgesamtheit unmittelbar von Erhebungsbeauftragten befragt, während bei indirekten Erhebungen behördliche Register (Datei der Sozialsicherheit, MwSt.-Register, Zentralregister der Unternehmen…) benutzt werden. Letztere Arbeitsweise wird zunehmend eingesetzt, da sie den Arbeitsaufwand und die Kosten für  Unternehmen  bzw. Privatpersonen verringert.

'Verarbeiten' von statistischen Daten beinhaltet in erster Stelle ein kritisches Bewerten der gemachten Angaben.
BELSTAT validiert die Antworten (prüft sie auf Gediegenheit und Wahrscheinlichkeit) und macht aus den Grunddaten Übersichtstabellen und Statistiken.

BELSTAT macht seine Arbeitsergebnisse allen interessierten Gruppen zugänglich:
 Staatsbehörden (alle belgischen politischen Körperschaften auf jeglicher Ebene, und auch internationale Einstellungen und Organisationen)
 Geschäftswelt (alle Unternehmen ungeachtet deren Größe oder Ziele)
 Gesellschaft (Forscher, Journalisten, Dozenten, Studenten und Bürger im Allgemeinen)

BELSTAT veröffentlicht statistische Informationen über:
 die Haushalte (Bevölkerungszahlen, Haushaltsbudget, Zeitverwendung, Reiseverhaltensmuster…)
 die Industrie, das Baugewerbe, den Handel und sonstige Dienstleistungen (Daten aus Erhebungen bei Unternehmen)
 die Konjunktur, in Form von Indizes (z. B. Verbraucherpreisindizes) und  Wirtschaftsindikatoren zu Industrieproduktion, Investitionen, Ausfuhr, Beschäftigung, Einzelhandel und dem Dienstleistungssektor…

Erhebungen
BELSTAT macht Erhebungen u. a. über Arbeitskräfte, über Einkommen und Lebensbedingungen, über die Struktur und Verteilung der Löhne, über die Struktur der Unternehmen, ferner die Landwirtschaftserhebung, den Zensus 2011 (die erste gemeinsame Volkszählung in den EU-Mitgliedstaaten) und das Haushaltsbudget.

Zudem wirkt die Generaldirektion an einigen wichtigen Erhebungen anderer Organisationen mit. Beispiele dafür sind die Gesundheitserhebung des Wissenschaftlichen Instituts Volksgesundheit und die Zeitbudgeterhebung der Forschungsgruppe TOR der Freien Universität Brüssel (VUB). Auch andere staatliche Einrichtungen können die methodologische Expertise von BELSTAT nutzen.

Weblinks
 Website der Generaldirektion Statistik und Wirtschaftsinformation

Einzelnachweise

Organisation (amtliche Statistik)
Wissenschaft und Forschung in Belgien
Behörde (Brüssel)

redpajama_set_name: RedPajamaWikipedia


LGBTQ Affirmative Therapists Guild of Utah - Plan B Theatre - The Ice Front - Note: 2nd Sat.
Plan B Theatre - The Ice Front - Note: 2nd Sat.
The actors of the Norwegian National Theatre find themselves in an uneasy truce with Nazi cultural authorities during the German occupation of Norway. When they are forced to perform a Nazi propaganda piece, conscience comes face to face with The Final Solution.
THE ICE FRONT questions what it means to be an artist, to be a patriot, to be human.
Post-Performance Salon: A 1 hour Guild-specific Salon Discussion will follow this production, to provide an opportunity for members of the Guild to discuss the play with the Playwright (Eric Samuelsen), Director (Jerry Rapier), and Actors (Kirt Bateman, Roger Dunbar, Ariana Farber, Stephanie Howell, Jay Perry, Topher Rasmussen, Robert Scott Smith, Emilie Starr, Christy Summerhays).


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Human Rights Tribunals
Canada's Human Rights Tribunal (CHRT) was originally established to adjudicate complaints of housing and employment discrimination. Unfortunately, its lax evidentiary standards and wide jurisdictional reach have made it easy for its benign mission to metastasize into a vehicle for stifling critical discussion of Islam.
The CHRT was established in 1977 and is charged with enforcing the Canadian Human Rights Act (CHRA). The CHRA includes a hate speech provision or what that Act calls "hate messages." Section 13 proscribes the communication of "any matter that is likely to expose a person or persons to hatred or contempt by reason of the fact that that person or those persons are identifiable on the basis of a prohibited ground of discrimination." Originally, covering communications made "telephonically," the provision was expanded to include communication over the Internet post 9/11.
Parallel human rights acts, commissions, and tribunals also exist in the Canadian provinces. Four provinces, Alberta, British Columbia, Saskatchewan, and the Northwest Territories, have a "hate speech" provisions similar to the CHRA, though some are even broader in scope in terms of the types of communications they cover. (See, for example Saskatchewan Human Rights Code's Section 14, which covers essentially any mode of communication.)
In Europe, individuals who are charged with "hate speech" are at least brought into court and afforded the due process rights of a criminal defendant. By contrast, in Canada, the Tribunal's lax rules of procedure and evidence enable plaintiffs to pursue claims that would never survive in a standard court of law.
Examples of this procedural unfairness include:
No Standards of Evidence - CHRT judges may receive and accept evidence that they "see fit", irrespective of whether such evidence is or would be admissible in a court of law.
No Right to Cross-examine - Defendants are not always permitted to confront their accusers.
Asymmetric Cost Burden – The government funds the plaintiff, while even a defendant who prevails cannot be awarded costs.
No Standing Requirements – 3rd parties not involved in the alleged offence may nonetheless file complaints, further encouraging predatory suits from plaintiffs with agendas.
Rules Lack Certainty – The CHRT may, on its own initiative or at a party's behest, "dispense with compliance with any Rule" in the interest of time or efficiency.
The situation is summed up in the CHRT's nearly 100% conviction rate. In three decades of federal human rights commission cases, only one defendant in a Section 13 complaint that went beyond the discovery phase has been acquitted.
Frequently called a "kangaroo court" and "Star Chamber," the CHRT has been at the center of a number of prominent efforts to silence speech regarding Islam. As with other uses of the legal system to silence speech, the harm is in the process itself. For even if charges are eventually dropped, defending oneself in the tribunals can be costly.
In 2006, Syed Soharwardy, a Calgary imam, filed a complaint with the Alberta Human Rights Commission (the Provincial counterpart of the federal CHRT) against Ezra Levant for reprinting the Danish Mohammed cartoons in his magazine. It is telling that Sowahardy had previously gone to the police three times to demand Levant's arrest, without success. As Levant observes: Sowahardy "only had to ask the willing enforcers of the human rights commission once."
In 2007, the Canadian Islamic Congress (CIC) subjected Canada's Maclean's magazine to "triple jeopardy," lodging an identical complaint against it in three different jurisdictions for publishing "flagrantly Islamophobic" articles. The claims were ultimately dismissed, but not before Maclean's was obliged to spend significant sums for its defense, prompting the CIC to boast that it had "increase[d] the cost of publishing anti-Islamic material."
Change is sorely needed. In October 2008, Dr. Richard Moon, tasked by the Canadian Human Rights Commission to consider the most appropriate mechanisms for addressing hate speech, produced a report recommending that Section 13 be repealed and that hate speech on the Internet be left to criminal courts. In September 2009, a CHRT panel found Section 13 unconstitutional for violating the freedom of expression, although that decision is being appealed and has no precedential effect. Even some of the CHRT's creators have now turned against it. (e.g., Alan Borovoy, chief of the Canadian Civil Liberties Association: "A free culture cannot protect people against material that hurts.") At the legislative level, conservatives and some liberal members of parliament have called for the repeal or review of Section 13.
Recent Developments:
In November of 2011, MP Brian Storseth's "private members" bill, Bill C-304, calling for the repeal of Section 13, was endorsed by Canada's Minister of Justice, Rob Nicholson. In endorsing the bill, Nicholson significantly increased the likelihood that the bill would move forward. In February 2012, the bill passed a 158-to-131 vote, which moved it on to the Standing Committee on Justice and Human Rights. In June 2012, the bill passed its third reading in the House of Commons and was sent to the Canadian Senate.
Since then, the bill has been stuck in the Senate.
As Section 13 is under political attack, two judicial challenged are pending in the Canadian court system (the Whatcott and Lemire cases).
The Legal Project provides financial assistance to commentators haled before the CHRT for their legitimate discussion of Islam. We also continue to monitor developments and publicize the problem through articles, blogs, and publicly available reports.
Adam Liptak – "Hate Speech or Free Speech? What Much of West Bans is Protected in U.S." – A comparison of the Canadian and U.S. approaches to free speech jurisprudence.
Kathy Shaidle – "Canada's Human Rights Kangaroo Court" – A look at the investigative tactics employed by the Canadian Human Rights Commission.
Joseph Brean – "Scrutinizing the Human Rights Machine" – How the CHRT has strayed from its original mandate.
Ezra Levant – "What a Strange Place Canada Is" – A look at how Canada's human rights laws have been manipulated by Islamists.
Hilary White – "Mark Steyn Case Wakes Up Canadian Press To Human Rights Tribunals' Threat to Free Speech" – A look at how the CHRT has stacked the deck in favor of plaintiffs seeking to exploit its relaxed rules of procedure and evidentiary standards.
Rebecca Walberg – "Confronting the Speech Police" – How the CHRT and provincial tribunals have fostered a culture of victim-hood and identity politics.
The Canadian Human Rights Tribunal and its Provincial Counterparts: Rules of Procedure and Available Remedies – Jeffrey Azarva, The Legal Project.
"Report to the Canadian Human Rights Commission Concerning Section 13 of the Canadian Human Rights Act and The Regulation of Hate Speech on the Internet" – University of Windsor Professor Richard Moon's recommendations on the role of Section 13 in addressing Internet hate speech.
"Freedom of Expression and Freedom from Hate in the Internet Age" – The Canadian Human Rights Commission's 2009 special report to parliament.
The Canadian Human Rights Commission – The official website of the Canadian Human Rights Commission, the body charged with investigating and referring complaints to the CHRT.
The Canadian Human Rights Tribunal – The official website of the CHRT.
© 2022 The Middle East Forum.


The Rose is a beautiful bag that you can carry on your arm, or over the shoulder, even convert to adjustable if you so desire.
An exterior pocket that can be closed with a thumb or magnetic closure.
A zippered closure on top makes everything accessible yet secure.
An Optional removable shoulder strap.
Pattern includes 32 pages of easy step-by-step instructions with color photos to help you through each step. Pattern also includes printable pattern pieces with seam allowances included.


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5 ways cops know when UR texting and driving
By Maryalene LaPonsie Posted : January 20, 2016
https://www.insurance.com/auto-insurance/auto-insurance-basics/cops-know-ur-texting-driving.html
No one needs to tell Americans they shouldn't text while driving. They already know it.
In fact, 98 percent of those surveyed by AT&T in 2013 said it isn't safe to send a text or email while driving. Yet, nearly half of respondents said they text while driving, and four in 10 said it's a habit. Even states with the best drivers aren't immune to this problem.
If people won't stop texting and driving for their own safety, states are hoping drivers will put down their phones to avoid a ticket and fine. Currently, 46 states and the District of Columbia have banned texting while driving, according to the Insurance Institute for Highway Safety. Of those, 14 won't allow drivers to use handheld phones at all behind the wheel.
Despite the laws, some drivers keep on texting and driving. Maybe they think they won't be caught. Maybe they're wrong.
5 ways to get busted for texting
In Michigan, the law that bans texting while driving has been on the books since 2010, but the problem persists.
"I see it probably at least once a day," says Steve Bukala, chief of police in Lowell, Michigan.
Bukala notes the practice seems to occur more frequently on the highway than on city roads.
Here are five ways the police know when your eyes are on your phone rather than the road.
1. They see the phone on your steering wheel.
"A lot of [people] aren't even concerned about hiding it," Bukala says. "They usually have their phone right on the steering wheel."
Bukala thinks it's not hard for police officers to drop behind a car and confirm someone is texting.
Don't assume your tinted windows are going to hide your phone either.
2. You are constantly looking down.
Do you think you're sneaky keeping your phone on your lap or on a center console, rather than on the steering wheel? Constantly looking down and to the side, especially if you have only one hand on the steering wheel, can be a dead giveaway.
Bukala says his officers need to actually see the phone before they can pull someone over for texting and driving, but that doesn't mean you can't be pulled over for other things. If the cops think you're texting, they may look to see what else you're doing wrong.
While Michigan is one of five states where police don't stop motorists for "primary enforcement" of texting laws, most states with anti-texting legislation do allow officers to pull over a driver for a texting offense alone.
3. The glow from your screen gives you away at night.
The soft glow from your screen makes it possible to type at night; it also makes it possible for police to see who has a cellphone on in the car. While that's not a giveaway that you're texting, as with looking down constantly, it may attract some unwanted attention.
4. Cops on bikes can peer inside your car.
Officers on bikes or motorcycles may be the most likely to hand out cellphone tickets.
"I really notice it in the summer when I'm on my motorcycle," Bukala says. That's because it's easy to pull up alongside a car and peer in the window, especially at stop lights. Then it doesn't matter whether or not your cellphone is in your lap; the police have a clear view.
5. The police are watching you from above.
Cops in some states are upping their game, literally. The U.S. Department of Transportation issued grants in 2012 to Connecticut and Massachusetts to help them develop new ways of cracking down on texting and driving. Those methods include setting up spotters on overpasses to look for texting drivers and notify nearby patrol cars.
In 2013, New York invested $1 million into its efforts to thwart distracted drivers, including those texting. The state's initiative includes the deployment of elevated SUVs that provide a better view into the vehicles around them, giving police a chance to identify those trying to multi-task on the road.
What's the damage? Points, fines and auto insurance premiums
Penalties for texting and driving vary by state. Michigan cellphone tickets come with a $100 fine and two points on your license for a first time offense, Bukala says. Other states may also have fines and/or points attached to violations.
If your state considers texting while driving to be a moving violation, it could be seen by your insurer as a minor infraction. Some insurers disregard a minor violation when it comes to policy renewal, but may discontinue any good driver discount you previously enjoyed. Other insurers may raise your rates with only one ticket on your record, and multiple infractions almost always result in a rate hike.
However, the damage from cellphone tickets doesn't end there. There's also your car insurance to think about.
In some states, texting tickets aren't counted as moving violations, but other states, including Arizona, consider texting and driving to be a moving violation. "All violations fall into one of two categories: minor violations and major violations," explains Charlotte Burr, co-owner of AZ Insurance Team in Tempe, Arizona. Most insurance companies consider cellphone tickets a minor violation, but that doesn't mean they don't come without a price. "If someone has a minor violation, it may raise their premiums a little -- maybe 10 to 20 percent."
Texting while driving may also be the basis for more serious charges, such as careless driving or reckless endangerment, if someone's phone use leads to an accident. Those can be major violations, racking up more points and higher auto insurance premiums.
Of course, the cost of car insurance is relatively minor compared to the price someone else might pay because you couldn't wait to read or send a text. "In 2013 alone, 3 million people died from distracted driving collisions," Burr says. "It's impossible when you're looking at [your phone] to pay attention driving."
Avoid the temptation to do something that could get a person killed: turn off the ringer and keep your phone tucked in the glove compartment or purse while driving. Because even if you think you can get away with texting and driving, the cops are onto you.
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