text:
**Basic Schema Enum**

`{"query": "{__schema{types{name}}}"}`

**Enum Query and Description**

`{"query": "{__schema{queryType{name,fields{name,description}}}}"}`

**Enum Introspection**

```
{"query": "query IntrospectionQuery{__schema{queryType{name}mutationType{name}subscriptionType{name}types{...FullType}directives{name description locations args{...InputValue}}}}fragment FullType on __Type{kind name description fields(includeDeprecated:true){name description args{...InputValue}type{...TypeRef}isDeprecated deprecationReason}inputFields{...InputValue}interfaces{...TypeRef}enumValues(includeDeprecated:true){name description isDeprecated deprecationReason}possibleTypes{...TypeRef}}fragment InputValue on __InputValue{name description type{...TypeRef}defaultValue}fragment TypeRef on __Type{kind name ofType{kind name ofType{kind name ofType{kind name ofType{kind name ofType{kind name ofType{kind name ofType{kind name}}}}}}}}"}
```

**Schemas**
When you interact with GraphQL you do so through the query language. Since this query language is providing an interface to your backend data, it needs a definition of how the data and queries should be structured. This is where the schema comes in, it simply contains the information about what queries are supported. This serves as a validation layer to ensure incoming queries are well formed and supported.

**Types**
Since GraphQL provides an interface to data, it needs a type system to define the different data-types that are supported. The supported types can be found here. Essentially you are looking at things scaler types such as Int, String, Float, Boolean and ID. And a few other types, enum, lists, interfaces.

**Fields**
These are the actual data values that are available in a data Object. In any GraphQL query you will see fields, if you ask for a field, and it is defined in the schema, it will be return to you.

**Arguments**
Just like other query languages, GraphQL provides a mechanism for limiting the data that is returned. Arguments are used for this purpose and are defined in the schema. Here again GraphQL uses the schema to validate a given query, and set of arguments, before being passed to the API responsible for retrieving the relevant data. This forces strong typing and is just another mechanism that prevents injection attacks.

**Mutations**
Sometimes you don't want to query data, you want to modify it. This is where mutations come in. Mutations allow you to define the "functions" that can be executed through GraphQL, including the fields that are modified and the arguments that are allowed.

**Introspection**
This is where GraphQL gets really interesting, even more so if you are doing a security audit. GraphQL can be used to query itself, more specifically, the introspection system allows us to retrieve the full GraphQL schema. This is another piece of well documented information, but not many web app testers seem to be aware of it.

**Source Reference**

* https://github.com/swisskyrepo/PayloadsAllTheThings/tree/master/GraphQL%20Injection
* https://staaldraad.github.io/post/2018-03-16-quick-win-with-graphql/
* https://github.com/doyensec/graph-ql

**Hardening**

* https://github.com/helfer/graphql-disable-introspection
* https://blog.apollographql.com/securing-your-graphql-api-from-malicious-queries-16130a324a6b

redpajama_set_name: RedPajamaGithub


text:
\section{Introduction}

Let $w(n)$ be an additive non-negative integer-valued arithmetic function which is equal to $1$ on primes. For example one can set $w(n)$ to be $\omega(n)$ -- the number of distinct prime factors of $n$ or $\Omega(n)$ -- the number of prime factors with multiplicity. By $E$ we denote the set of natural numbers not representable as $n + w(n)$. For the complement of $E$ we use the notation $E^c$. In this article we are concerned with the lower bound for
\[
\Xi(N) = |[1, N] \cap E|.
\]

\begin{hypo*}
\[
\Xi(N) \gg N.
\]
\end{hypo*}

We show that

\begin{theorem}
\label{main}
\[
\Xi(N) \gg \frac{N}{\log \log N}.
\]
\end{theorem}

The main idea is to consider $n + w(n)$ modulo a prime number. For a prime number $p$ and $r \in \mathbb{Z}/p \mathbb{Z}$ let us denote

\[
a(r) := \sum_{\substack{n \le N \\ n + w(n) \equiv r \pmod p}} 1.
\]

\begin{lemma}
\label{idea}
Let $R$ be a subset of $\mathbb{Z}/ p \mathbb{Z}$. Then
\[
\Xi(N) \ge \sum_{r \in R} (N/p - a(r) - 1).
\]
\end{lemma}
\begin{proof}
Let
\[
N_r := \{n \, | \, n \le N, \, n \equiv r \pmod p\}.
\]
Note that
\[
[1, N] \cap \mathbb{Z} = \coprod_{r \in \mathbb{Z}/ p \mathbb{Z}} N_r, \quad |N_r| \ge N/p - 1, \quad |N_r \cap E^c| \le a(r).
\]
Hence
\[
|N_r \cap E| = |N_r| - |N_r \cap E^c| \ge (N/p - a(r) - 1).
\]
Finally,
\[
\Xi(N) = \sum_{r \in \mathbb{Z}/ p \mathbb{Z}} |N_r \cap E| \ge \sum_{r\in R} |N_r \cap E| \ge \sum_{r \in R} (N/p - a(r) - 1).
\]
\end{proof}

In $\cite{Changa}$ M. E. Changa  studied the distribution of $w(n)$ in a residue ring.
Using the same method we study the asymptotic behavior of $a(r)$.

It turns out that for any fixed $p$
\[
a(r) \sim N/p.
\]

That is the reason we can't prove the Conjecture directly using the observation of Lemma \ref{idea}. Nevertheless, we are able to find the second term in the asymptotic expansion of $a(r)$. Then Theorem \ref{main} follows by an appropriate choice of $p$ and $R$.

Let
\[
G(N) := |\{(n, m) \, : \, n + w(n) = m + w(m), n \le N, m \le N, n \ne m\}|.
\]

\begin{prop} \label{G}
If $w(n) \ll n^{\varepsilon}$ and $0 < \varepsilon < 1$, then
\[
G(N) \gg \Xi(N).
\]
\end{prop}

\begin{proof}
We have $w(n) \le C n^{\varepsilon}$ for some constant $C$.

Let us denote
\[
g(n) := |\{ m \, : \, m + w(m) = n, m \le N \}|.
\]

Note that if $n \le N - C N^\varepsilon$, then $n + w(n) \le N$. Hence
\[
\sum_{n \le N} g(n) = \sum_{\substack{n \ge 1 \\ n + w(n) \le N}} 1 \ge N - C N^\varepsilon.
\]

We have
\[
G(N) \ge \sum_{n \le N} \binom{g(n)}{2} = \sum_{n \in [1, N] \cap E^c} \binom{g(n)}{2} \ge \sum_{n \in [1, N] \cap E^c} (g(n) - 1) \ge
\]
\[
(N - C N^\varepsilon) - |[1, N] \cap E^c| = \Xi(N) - C N^{\varepsilon} \gg \Xi(N).
\]
\end{proof}

In $\cite{Erdos1}$, P. Erd\H{o}s, A. S\'ark\H{o}zy, C. Pomerance showed that if $w(n)$ is the number of distinct prime factors of $n$, then

\[
G(N) \ge N \exp(-4000 \log \log N \log \log \log N)
\]
for $N$ large enough.

So Theorem \ref{main} in view of Proposition \ref{G} improves this bound and gives

\[
G(N) \gg \frac{N}{\log \log N}.
\]

\section{Lemmas}

\begin{lemma}[Perron's formula] \label{Perron}
Let
\[
F(s) = \sum_{n = 1}^{\infty} \frac{a(n)}{n^s},
\]
where the series converges absolutely for $\operatorname{Re} s > a \ge 0$, and let
\[
\sum_{n = 1}^\infty \frac{|a_n|}{n^\sigma} \ll (\sigma - a)^{-\alpha}
\]
as $\sigma \rightarrow a + 0$ for some $\alpha > 0$.
 Then for every $b > a$, $x \ge 2$ and $T \ge 2$ we have
\[
\sum_{n \le x} a(n) = \frac{1}{2 \pi i} \int_{b - iT}^{b + iT} F(s) \frac{x^s}{s} ds + R(x),
\]
where
\[
R(x) \ll \frac{x^b}{T(b-a)^\alpha} + 2^b \left( \frac{x \log x}{T} + \log \frac{T}{b} + 1 \right) \max_{x/2 \le n \le 3x/2} |a(n)|.
\]

\end{lemma}
\begin{proof}
See, for example, $\cite[\text{Theorem}~7,\text{p.}~20]{Changa_book}$ or $\cite[\text{Theorem}~1,\text{p.}~64]{Karatsuba}$.
\end{proof}

\begin{lemma}[M. E. Changa]
\label{Chang}
Let $f(n)$ be a complex valued arithmetic function such that $|f(n)| \le 1$, let the following equality hold for $\operatorname{Re} s > 1$:
\[
\sum_{n = 1}^\infty \frac{f(n)}{n^s} = (\zeta(s))^\alpha H(s),
\]
where $\alpha \in \mathbb{C}$, $|\alpha| \le 1$,
and  the function $H(s), s = \sigma + it$, is analytic in the domain $\sigma > 1 - \frac{c_1}{\log  T} , |t| \le T$ for every sufficiently large $T$, and let the bound $H(s) \ll \log^{c_2} T$ hold in this domain. Then
\[
\sum_{n \le x} f(n) = \frac{H(1)}{\Gamma(\alpha)} x \log^{\alpha - 1} x + O(x \log^{\operatorname{Re} \alpha - 2} x).
\]
Here constant in $O$ depends only on $c_1, c_2, C$.
\end{lemma}
\begin{proof}
See $\cite[\text{Lemma}~3.1]{Changa}$.
\end{proof}

\begin{lemma} \label{Siegel0}
Let $T \ge 3$. If $\chi$ is a complex character modulo $k$ and $s = \sigma + i t$, then $L(s, \chi)$ has no zeroes in the domain
\[
\operatorname{Re} s = \sigma \ge 1 - \frac{c_3}{\log k T}, \, \, |t| \le T .
\]
If $\chi$ is a real character modulo $k$ and $s = \sigma + i t$, then $L(s, \chi)$ has no zeroes in the domain
\[
\operatorname{Re} s = \sigma \ge 1 - \frac{c_3}{\log k T}, \, \, 0 < |t|  \le T .
\]
\end{lemma}
\begin{proof}
See $\cite[\text{Theorem}~2,\text{p.}~124]{Karatsuba}$
\end{proof}

\begin{lemma}
\label{Siegel}
Let $3 \le X$. There exists at most one $3 \le k \le X$ and at most one real primitive character  $\chi_1$ modulo $k$ for which  $L(s, \chi_1)$ has a simple real zero $\beta_1$ such that
\[
\beta_1 \ge 1 - \frac{c_4}{\log X}.
 \]
\end{lemma}
\begin{proof}
See $\cite[\text{Corollary}~2,\text{p.}~131]{Karatsuba}$.
\end{proof}

We call a prime number $p < X$ unexceptional if  $L(s, \chi)$ has no real zeroes on the interval
\[
\left[ 1 - \frac{\min(c_3, c_4)}{\log X}, +\infty \right)
 \]
for every character $\chi$ modulo $p$. Otherwise we call $p$ exceptional. Note that the notion of being exceptional depends on $X$. Lemma \ref{Siegel} implies that there exist at most one exceptional $p < X$.

\begin{lemma}
\label{short}
For every sufficiently large $X$, the interval
\[
\left[ X - X^{4/5}, X \right]
\]
contains at least two prime numbers.
\end{lemma}
\begin{proof}
See $\cite{Cons_primes}$ or $\cite[\text{Theorem}~2,\text{p.}~98]{Karatsuba}$.
\end{proof}

\begin{lemma}[Borel–Carathéodory theorem]
\label{Bor}
Let $R > 0$, and let the function $f(s)$ be analytic in the circle $|s - s_0| \le R$. Moreover assume that $\operatorname{Re} f(s) \le M$ on the circle $|s - s_0| = R$. Then
in the disk $|s - s_0| \le r < R$ we have
\[
|f(s) - f(s_0)| \le 2(M - \operatorname{Re} f(s_0)) \frac{r}{R - r}.
\]
\end{lemma}
\begin{proof}
See, for example, $\cite[\text{Lemma}~4,\text{p.}~35]{Karatsuba}$.
\end{proof}

\begin{lemma} \label{L=O}
Let $\chi$ be a non-principal character modulo $k$. Then the following bound holds in the domain $|\sigma - 1| \le c / \log k T$, $|t| \le T$:
\[
L(s, \chi) = O(\log k T).
\]
\end{lemma}

\begin{proof}
Let us denote $S(t) = \sum\limits_{n \le t} \chi(n)$. We have
\[
\sum_{n = N + 1}^{M} \frac{\chi(n)}{n^s} = \int_{N}^M \frac{d S(t)}{t^s} = \frac{S(M)}{M^s} - \frac{S(N)}{N^s} + s \int_{N}^M
\frac{S(t) \, d t}{t^{s + 1}}.
\]
As $M$ approaches infinity, we find that
\[
L(s, \chi) = \sum_{n = 1}^{N} \frac{\chi(n)}{n^s} - \frac{S(N)}{N^s} + s \int_{N}^\infty  \frac{S(t) \, d t}{t^{s + 1}}.
\]
Hence
\[
L(s, \chi) - \sum_{n = 1}^{N} \frac{\chi(n)}{n^s} = O(k N^{-\sigma}) + O(k T \sigma^{-1} N^{-\sigma}).
\]
If $n \le k T$, then
\[
|n^{-s}| = n^{-\sigma} \le n^{-1} (k T)^{c / \log k T} \ll n^{-1}.
\]
If we take $N = k T$, we obtain
\[
L(s, \chi) = O(\log k T).
\]
\end{proof}

\begin{lemma} \label{log L}
Let $T \ge 3$, let $\chi$ be a non-principal character modulo $k$, and let $L(s, \chi)$ be nonzero in the domain
\[
\sigma \ge 1 - \frac{3c}{\log k T}, \, \, |t| \le 2 T;
\]
then on the boundary of the domain
\[
\sigma \ge 1 - \frac{c}{\log k T}, \, \, |t| \le T
\]
we have $\log L(s, \chi) \ll \log \log k T$.
\end{lemma}

\begin{proof}
If $\sigma \ge 1 + c/\log k T$, then
\[
|\log L(s, \chi)| = \left| \sum_{p} \sum_{m=1}^\infty  \frac{\chi^m(p)}{m p^{m s}} \right| \le \log \zeta(\sigma) \ll \log \frac{1}{\sigma - 1} \ll \log \log k T.
\]

Using Lemma \ref{L=O}, we obtain
\[
\operatorname{Re} \log L(s, \chi) = \log |L(s, \chi)| \le C' \log \log k T.
\]
for $|\sigma - 1| \le 3c/\log{k T}$, $|t| \le 2 T$.

Thus, setting $s_0 = 1 + c/\log k T + i t$, $R = 3 c / \log k T$, $r = 2c / \log k T$ in Lemma \ref{Bor}, we find that
\[
|\log L(s, \chi) - \log L(s_0, \chi)| \le 2 (C' \log \log k T - O(\log \log k T)) \ll \log \log k T.
\]
for $|s - s_0| = r$
\end{proof}

\begin{lemma}
\label{L_main}

Let $\chi$ be a non-principal character modulo $k$ and $\log k = o(\log x)$. Assume that $L(s, \chi)$  has no zeroes in the domain $\sigma \ge 1 - \frac{3c}{\log k T}, \, \, |t| \le 2 T$ for $T > C$.
Let $\alpha \in \mathbb{C}$, $|\alpha| \le 1$.
Let $f(n)$ be a complex valued arithmetic function, such that $|f(n)| \le 1$ and  let
\[
\sum_{n = 1}^\infty \frac{f(n)}{n^s} = (L(s, \chi))^\alpha H(s),
\]
for $\operatorname{Re} s > 1$. Let $H(s), s = \sigma + it$ be analytic in the domain $\sigma > 1 - \frac{3c}{\log k T} , |t| \le T$ for each $T > C$. Moreover, let $H(s) \ll \log^{c_5} T $ in this domain.

Then
\[
\sum_{n \le x} f(n) \ll x \exp\left( -c_6 \frac{\log x}{\sqrt{\log x} + \log k} \right).
\]
Here the constant in Vinogradov symbol depends only on $c, c_5, C$ and does not depend on $\chi$.
\end{lemma}

\begin{proof}

Substituting  $b = 1 + 1/\log{x}$, $\log T = \sqrt{\log{x}}$ into Perron's formula (Lemma \ref{Perron}), we obtain

\[
\sum_{n \le x} f(n) = \frac{1}{2 \pi i} \int_{b - i T}^{b + i T} (L(s, \chi))^\alpha H(s) \frac{x^s}{s} ds + R(x),
\]
where
\[
R(x) \ll x \exp(-c_7 \sqrt{\log x}).
\]

Let $\beta := 1 - c/\log k T$ and consider the contour $\Gamma$ consisting of segments joining in succession the points  $\beta + iT, \beta - iT, b - iT, b + i T, \beta + iT$.

Note that $(L(s, \chi))^\alpha H(s) \frac{x^s}{s}$ is well-defined and holomorphic in the interior and on the sides of $\Gamma$.

On the sides of $\Gamma$ we have
\[
|(L(s, \chi))^\alpha| = |e^{\alpha \log L(s, \chi)}| \le e^{|\log L(s, \chi)|} \ll \log^{c_8} k T,
\]
here we used Lemma \ref{log L}.

By residue theorem, we have
\[
\int_{\Gamma} (L(s, \chi))^\alpha H(s) \frac{x^s}{s} ds = 0.
\]

Estimating the integral trivially on the sides of $\Gamma$, we obtain
\[
\int_{b - i T}^{b + i T} (L(s, \chi))^\alpha H(s) \frac{x^s}{s} ds \ll x \exp\left( -c_6 \frac{\log x}{\sqrt{\log x} + \log k} \right).
\]
This concludes the proof.

\end{proof}

Let us set $e(z) := \exp(2 \pi i z)$. By $\mathbb{P}$ we denote the set of prime numbers.

\begin{lemma}
\label{F_{t, p, u}}
Let $u(n)$ be a completely multiplicative function such that $|u(n)| \le 1$ for all $n$.
Set
\[
L(s, u) := \sum_{n \ge 1} \frac{u(n)}{n^{s}}.
\]

Then for $\operatorname{Re} s > 1$ we have
\[
\sum_{n \ge 1} \frac{e \left( \frac{w(n) t}{p} \right) u(n)}{n^s} = (L(s, u))^{e(t/p)} F_{t, p, u}(s).
\]
Here $F_{t, p, u}(s)$ is holomorphic on $\operatorname{Re} (s) > 1/2$. Moreover, for every $\epsilon > 0$, there are $0 < b_{1, \epsilon} < b_{2, \epsilon}$, such that in the half-plane $\operatorname{Re} (s) > 1/2 + \epsilon$ we have
\[
b_{1, \epsilon} < |F_{t, p, u}(s)| < b_{2, \epsilon}.
\]
And  $b_{1, \epsilon}$ and $b_{2, \epsilon}$ do not depend on $p, t$, and $u$.

In particular there exist constants $0 < b_1 < b_2$ such that
\[
b_1 \le |F_{t, p, u}(1)| \le b_2
\]
for every $p$, $t$ and $u$.

\end{lemma}

\begin{proof}
Set
\[
 F_{t, p, u}(s) = (L(s, u))^{-e(t/p)} \sum_{n \ge 1} \frac{e \left( \frac{w(n) t}{p} \right) u(n)}{n^s} .
\]
By assumption, $w(n)$ is an additive function and $w(q) = 1$ for $q \in \mathbb{P}$.
Thus for $\operatorname{Re} s > 1$, we have
\[
\sum_{n \ge 1} \frac{e \left( \frac{w(n) t}{p} \right) u(n)}{n^s} = \prod_{q \in \mathbb{P}}
\left( 1 + \frac{e(t/p) u(q)}{q^s} + \frac{e\left( \frac{w(q^2) t}{p} \right) u(q)^2}{q^{2s}} + \ldots \right)
\]
and
\[
L(s, u) = \prod_{q \in \mathbb{P}} (1 - u(q) q^{-s})^{-1}.
\]

Therefore,
\[
\log F_{t, p, u}(s) = \sum_{q \in \mathbb{P}} e(t/p) \log(1 - u(q) q^{-s}) + \log \left( 1 + \frac{e(t/p) u(q)}{q^s} + \frac{e\left( \frac{w(q^2) t}{p} \right) u(q)^2}{q^{2s}} + \ldots \right).
\]

Let us denote
\[
h_{q, t, p, u}(s) := \sum_{j \ge 2} \frac{e\left( \frac{w(q^j) t}{p} \right) u(q)^j}{q^{j s}}.
\]

This series converges uniformly on  $\operatorname{Re}(s) > 1/2 + \epsilon$. So $h_{q, t, p, u}(s)$ is analytic in the half-plane $\operatorname{Re}(s) > 1/2$. In addition, $h_{q, t, p, u}(s) = O(q^{-2 \sigma})$.

For $\operatorname{Re} s > 1$ we have
\[
\log F_{t, p, u}(s) = \sum_{q \in \mathbb{P}} e(t/p)(-u(q) q^{-s} - u(q)^2 q^{-2s}/2 - \ldots)  + \]
\[
(e(t/p) u(q) q^{-s} + h_{q, t, p, u}(s)) +
\sum_{j \ge 2} \frac{(-1)^{j + 1}}{j} (e(t/p) u(q) q^{-s} + h_{q, t, p, u}(s))^{j}.
\]

If $\operatorname{Re} s \ge 1/2 + \epsilon$, we obtain
\[
\log F_{t, p, u}(s) \ll \sum_{q \in \mathbb{P}} q^{-2 \sigma} \ll_{\epsilon} 1.
\]
So $|\log F_{t, p, u}(s)| \le C_\epsilon$. Hence

\[
e^{-C_\epsilon} \le F_{t, p, u}(s) \le e^{C_\epsilon}.
\]

\end{proof}

\section{Main results}

Fix a large $N$. Let $X = X(N)$ be a number that we will choose later. Let $p$ be an unexceptional prime lying in the interval $[X - X^{4/5}, X]$. By Lemmas  \ref{Siegel} and \ref{short} such $p$ exists.

\begin{theorem} Under assumptions above,
\[
a(r) = \frac{N}{p} + 2\frac{N}{p} \operatorname{Re} \left(e \left(\frac{-r}{p}  A_1 \,  \right) \right) + B_1(r) + B_2(r) + B_3(r).
\]
Here
\[
A_t = \frac{F_{t, p}(1) \, (1 - \frac{p}{p-1}d_{t, p}(1))}{\Gamma(e(t/p))} \log^{e(t/p) - 1} N,
\]
\[
d_{t, p}(s) :=  \left(1 + \frac{e \left( \frac{t}{p} \right)}{p^s} + \frac{e \left( \frac{w(p^2) t}{p} \right)}{p^{2s}} + \ldots\right)^{-1},
\]
\[
F_{t, p}(s) = \prod_{q \in \mathbb{P}} \left(1 + \frac{e \left( \frac{t}{p} \right)}{q^s} + \frac{e \left( \frac{w(q^2) t}{p} \right)}{q^{2s}} + \ldots\right) \left(1 - \frac{1}{q^s} \right)^{e(t/p)},
\]
\[
B_1(r) \ll B_1 := p N \exp\left( -c_6 \frac{\log N}{\sqrt{\log N} + \log p} \right),
\]
\[
B_2(r) \ll B_2 := N \log^{\cos(2 \pi / p) - 2} N
\]
and
\[
B_3(r) = 2 \frac{N}{p} \sum_{t=2}^{(p-1)/2} \operatorname{Re} \left( e \left(\frac{-r}{p} \right) A_{t} \right) \ll B_3 := \frac{N}{p^3} \sum_{t=2}^{(p-1)/2} t \log^{\operatorname{cos}(2\pi t / p) - 1} N.
\]
Moreover
\[
\left|A_1 \right| \asymp p^{-2} \log^{\cos(2\pi/p) - 1} N.
\]
\end{theorem}

\begin{proof}

Applying discrete Fourier transform, we obtain
\[
a(r) = \sum_{\substack{n \le N \\ n + w(n) \equiv r \pmod p}} 1 = \frac{1}{p} \sum_{\substack{n \le N \\ t \in \mathbb{Z} / p \mathbb{Z}}}
e \left( \frac{(n + w(n)) t}{p}\right) e \left( \frac{-r t}{p} \right).
\]
Let $k, t \in \mathbb{Z}/p\mathbb{Z}$. Set
\[
S_t := \sum_{n \le N} e \left( \frac{w(n) t}{p} \right),
\]
\[
S_{k, t} := \sum_{\substack{n \le N \\ n \equiv k \pmod p}} e \left( \frac{w(n) t}{p} \right),
\]
\[
S_{t, \chi} := \sum_{n \le N} e \left( \frac{w(n) t}{p}\right) \chi(n) .
\]

Then
\[
a(r) = \frac{1}{p} \sum_{t, k \in \mathbb{Z}/p \mathbb{Z} } e \left( \frac{(k - r) t}{p} \right) S_{k, t}.
\]

Note that
\[
S_{k, 0} = \frac{N}{p} + O(1),
\]
\[
S_{0, t} = S_t - S_{t, \chi_0},
\]
\[
S_{k, t} = \frac{1}{p-1} \sum_{\chi} \overline{\chi(k)} \, S_{t, \chi}, \, \text{if} \, \, \, k, t \ne 0 .
\]

Putting $u \equiv 1$ in Lemma \ref{F_{t, p, u}}, we obtain
\[
\sum_{n \ge 1} \frac{e \left( \frac{w(n) t}{p} \right)}{n^s} = (\zeta(s))^{e(t/p)} F_{t, p}(s).
\]
Here $F_{t, p}(s) := F_{t, p, u}(s)$.

Now applying Lemma \ref{Chang}, we see that
\[
S_t = \frac{F_{t, p}(1)}{\Gamma(e(t/p))} N \log^{e(t/p)-1} N + O(N \log^{\operatorname{cos} (2 \pi t / p) - 2}N).
\]

Lemma \ref{F_{t, p, u}} gives us
\[
\sum_{n \ge 1} \frac{e \left( \frac{w(n) t}{p} \right) \chi(n)}{n^s} = (L(s, \chi))^{e(t/p)} F_{t, p, \chi}(s).
\]

If $\chi$ is non-principal, then using Lemma \ref{L_main} we see that
\[
S_{t, \chi} = O\left(N \exp\left( -c_6 \frac{\log N}{\sqrt{\log N} + \log p} \right)\right).
\]

Note that $c_6$ and constant in $O$ do not depend on $\chi$.

Therefore, if $k, t \ne 0$, then we have
\[
S_{k, t} = \frac{S_{t, \chi_0}}{p-1} + O\left(N \exp\left( -c_6 \frac{\log N}{\sqrt{\log N} + \log p} \right)\right),
\]

there $\chi_0$ is the principal character modulo $p$. Let us denote
\[
d_{t, p}(s) :=  \left(1 + \frac{e \left( \frac{t}{p} \right)}{p^s} + \frac{e \left( \frac{w(p^2) t}{p} \right)}{p^{2s}} + \ldots\right)^{-1}.
\]
 We have

\[
\sum_{n \ge 1} \frac{e\left(\frac{w(n) t}{p}\right) \chi_0(n)}{n^s} =
d_{t, p}(s) \sum_{n \ge 1} \frac{e \left( \frac{w(n) t}{p} \right)}{n^s} =
(\zeta(s))^{e(t/p)} F_{t, p}(s) d_{t, p}(s) .
\]

Using Lemma \ref{Chang}, we obtain
\[
S_{t, \chi_0} = \frac{F_{t, p}(1) d_{t, p}(1)}{\Gamma(e(t/p))} N \log^{e(t/p)-1} N + O(N \log^{\operatorname{cos} (2 \pi t / p) - 2}N),
\]

Putting all together we obtain
\[
a(r) = \frac{N}{p} + \frac{1}{p} \sum_{t \not\equiv 0 \pmod p} e (-rt/p) S_{0, t}  +
\frac{1}{p (p-1)} \sum_{t \not\equiv 0 \pmod p} S_{t, \chi_0} \sum_{k \not\equiv 0 \pmod p} e \left( \frac{(k - r) t}{p} \right) + B_1(r).
\]
Here
\[
B_1(r) \ll p N \exp\left( -c_6 \frac{\log N}{\sqrt{\log N} + \log p} \right).
\]

Thus
\[
a(r) = \frac{N}{p} + \frac{1}{p} \sum_{t \not\equiv 0 \pmod p} e(-rt/p) (S_t - S_{t, \chi_0} - S_{t, \chi_0}/(p-1)) + B_1(r) =
\]
\[
\frac{N}{p} + \frac{1}{p} \sum_{t \not\equiv 0 \pmod p}  \left(S_t - \frac{p}{p-1} S_{t, \chi_0} \right) e(-rt/p) + B_1(r).
\]

Now we have
\[
a(r) = \frac{N}{p} + \frac{N}{p} \sum_{t \not\equiv 0 \pmod p} \frac{e(-rt/p) F_{t, p}(1) \, (1 - \frac{p}{p-1}d_{t, p}(1))}{\Gamma(e(t/p))} \log^{e(t/p) - 1} N + B_1(r) + B_2(r).
\]
Here
\[
B_2(r) = O\left( N \log^{\cos(2 \pi / p) - 2} N \right).
\]

Let us denote
\[
A_t := \frac{F_{t, p}(1) \, (1 - \frac{p}{p-1}d_{t, p}(1))}{\Gamma(e(t/p))} \log^{e(t/p) - 1} N,
\]
\[
B_3(r) = \frac{N}{p} \sum_{t=2}^{p-2} e(-rt/p) A_t.
\]

Then
\[
a(r) = \frac{N}{p} + 2\frac{N}{p} \operatorname{Re} \left( e \left(\frac{-r}{p} \right) A_{1} \right) + B_1(r) + B_2(r) + B_3(r).
\]

We have
\[
B_3(r) = 2 \frac{N}{p} \sum_{t = 2}^{(p-1)/2} \operatorname{Re} \left( e \left(\frac{-r t}{p} \right) A_{t} \right).
\]

Note that
\[
\left|1 - \frac{p}{p-1}d_{t,p}(1) \right| \asymp \left|(1 - p^{-1}) - \left( 1 - \frac{e(t/p)}{p} + \frac{e(t/p)^2 - e(w(p^2) t / p)}{p^2} + O(p^{-3}) \right) \right| =
\]
\[
\left|(1 - p^{-1}) - \left(1 - \left(1 + \frac{2 \pi i t}{p} + O(t^2 / p^2)\right) p^{-1} + \theta p^{-2}\right)\right| = 2 \pi i \frac{t}{p^2} + 2 \theta p^{-2} + O\left( \frac{t^2}{p^3} \right) \ll \frac{|t|}{p^2},
\]
here $|\theta| \le 1$. If $t = 1$, we obtain
\[
\left|1 - \frac{p}{p-1}d_{t,p}(1) \right|  \gg p^{-2}.
\]

Since $\Gamma(s)^{-1}$ is an entire function and $|F_{t, p}(1)| \le b_2$, it follows that
\[
\left| A_{t} \right| \ll \frac{t}{p^2} \log^{\cos(2\pi t/ p) - 1} N.
\]

Hence
\[
B_3 \ll \frac{N}{p^3} \sum_{t=2}^{(p-1)/2} t \log^{\operatorname{cos}(2\pi t / p) - 1} N.
\]

Since
$|e(1/p) - 1| \ll p^{-1}$ and $\Gamma(1) = 1$, it follows that
\[
\left|\Gamma(e(1/p))^{-1} \right| > C_{\Gamma}
\]
for some constant $C_{\Gamma} > 0$ and $p$ large enough. Further we have $\left| F_{t, p} (1) \right| \ge b_1$. Hence
\[
\left|A_1 \right| \gg p^{-2} \exp((\cos(2\pi/p) - 1) \log \log N).
\]

This concludes the proof.

\end{proof}

\begin{proof}[Proof of Theorem \ref{main}]

Let $r$ belong to $R \subset \mathbb{Z}/p \mathbb{Z}$ iff
\[
2\frac{N}{p} \operatorname{Re} \left( e \left(\frac{-r}{p} \right) A_{1} \right) < 0.
\]
Note that
\[
\left| \left\{ r : \operatorname{Re} \left( e \left(\frac{-r}{p} \right) A_{1} \right) \le -\frac{1}{2} \left| A_{1} \right|\right\} \right| \asymp p.
\]

Thus, substituting such $R$ into Lemma \ref{idea}, we obtain
\[
\Xi(N) \gg \sum_{r \in R} \frac{N}{p} - a(r) - 1 \gg -\sum_{r \in R} \left(  2\frac{N}{p} \operatorname{Re} \left( e \left(\frac{-r}{p} \right) A_{1} \right) + O(B_1 + B_2 + B_3 + 1) \right) \gg
\]
\[
N \left|A_{1}\right| + p O(B_1 + B_2 + B_3 + 1).
\]

Note that
\[
\frac{X^2}{p^2} \le 1 + 5 X^{-1/5}.
\]

Let us choose $X = \alpha^{-1} \sqrt{\log \log N}$, we obtain
\[
N \left|A_1\right| \gg N p^{-2} \exp \left( ((\cos(2\pi/p)) - 1) \log \log N \right) \gg N p^{-2} \exp\left( - \frac{2\pi^2}{p^2} \log \log N \right) \gg
\]
\[
 N X^{-2} \exp\left( - \frac{2\pi^2}{X^2}  (1 + 5 X^{-1/5}) \log \log N \right) \gg
\]
\[
 N X^{-2} \exp\left( - \frac{2\pi^2}{X^2} \log \log N \right) \gg \alpha^2 \exp \left(- 2\pi^2 \alpha^2 \right) \frac{N}{\log \log N}.
\]

Let us choose $\alpha$ such that $p B_3 \le 0.1 \, N \left|A_1\right|$. That is
\[
\tilde{C} \, \sum_{t=2}^{(p-1)/2} t \log^{\operatorname{cos}(2\pi t / p) - 1} N \le   \exp \left(- 2 \pi^2 \alpha^2 \right)
\]
for some constant $\tilde{C}$.

We have
\[
\sum_{t=2}^{(p-1)/2} t \log^{\operatorname{cos}(2\pi t / p) - 1} N  =
\sum_{2 \le t < p/4} t \log^{\operatorname{cos}(2\pi t / p) - 1} N  + O(p^2 \log^{-1} N).
\]

Note that
\[
\frac{5 \pi^2}{X^2} \le \cos \frac{2\pi}{p} - \cos \frac{4\pi}{p} \le \cos \frac{4\pi}{p} - \cos \frac{6\pi}{p} \le \ldots
\]

Therefore,
\[
\sum_{2 \le t < p/4} t \log^{\operatorname{cos}(2\pi t / p) - 1} N  \le
\sum_{2 \le t < p/4} t \log^{\frac{-5 \pi^2 (t - 1)}{X^2}} N \le
\]
\[
2 \sum_{t = 1}^{\infty} t \exp \left(-5 \pi^2 \alpha^2 t \right) = \frac{2 \exp(-5 \pi^2 \alpha^2)}{\left( 1 - \exp(-5 \pi^2 \alpha^2) \right)^2}.
\]

Clearly, for $\alpha$ large enough, we have
\[
\frac{2 \exp(-5 \pi^2 \alpha^2)}{\left( 1 - \exp(-5 \pi^2 \alpha^2) \right)^2} \le 0.5 \, \tilde{C}^{-1} \exp \left(- 2\pi^2 \alpha^2\right).
\]
Obviously,
\[
p^2 \log^{-1} N = o(1).
\]
Thus we obtain
\[
p B_3 \le 0.1 N \left| A_{1} \right|
\]
for $\alpha$ large enough. Note that $\alpha$ does not depend on $N$. Hence
\[
N \left|A_{1}\right| \gg \frac{N}{\log \log N}.
\]

Obviously, $pB_1 = o \left( N / \log \log N \right)$ and $pB_2 = o \left( N / \log \log N \right)$.

Therefore,
\[
\Xi(N) \gg N \left|A_{\frac{p+1}{2}}\right| \gg \frac{N}{\log \log N}.
\]

\end{proof}

I am grateful to Vitalii V. Iudelevich for setting the problem and Alexander B. Kalmynin for valuable discussions.

redpajama_set_name: RedPajamaArXiv


text:
https://www.instagram.com/eudiplomacy/
http://twitter.com/eu_eeas
https://www.youtube.com/user/EUExternalAction?feature=mhee
http://www.flickr.com/photos/eeas/
http://www.facebook.com/EuropeanExternalActionService
Check all our newsletters
EU in the World
EEAS homepage > Human Rights & Democracy > Search
Documents, Press Material
Regions Middle East & North Africa (MENA) (12)
Countries Algeria (3) Angola (3) Benin (3) Botswana (3) Burkina Faso (3) Burundi (3) Cameroon (3) Central African Republic (3) Comoros (3) Congo (Brazzaville) (3) DR Congo (Kinshasa) (3) Djibouti (3) Egypt (3) Equatorial Guinea (3) Eritrea (3) Eswatini (3) Ethiopia (3) Gabon (3) Gambia (3) Ghana (3) Guinea-Bissau (3) Iran (5) Iraq (4) Japan (6) Lesotho (3) Liberia (3) Libya (3) Madagascar (3) Malawi (3) Mali (3) Mauritania (3) Mauritius (3) Mozambique (3) Myanmar (Burma) (5) Namibia (3) Niger (3) Nigeria (3) Rwanda (3) Sao Tome and Principe (3) Senegal (3) Seychelles (3) Sierra Leone (4) South Africa (3) South Sudan (3) Sudan (3) Tanzania (3) Tchad (3) Vatican City and the Holy See (3) Venezuela (5)
Topics Common Foreign & Security Policy (CFSP) (2) Counter-Terrorism (1) Countering disinformation (1) Crisis Response (1) Culture (2) Development Cooperation (5) EU Global Strategy (1) EU International Cyberspace Policy (1) EU information in Russian (1) Global Tech Panel (1) Humanitarian & Emergency Response (5) Military and civilian missions and operations (1) Multilateral Relations (3) Refugee protection & Migration (2) Sanctions policy (4) Trade (1) Water Diplomacy (1)
(-) Remove Human Rights & Democracy filter Human Rights & Democracy
Organisations African Union (AU) (1) Foreign Affairs Council (9) UN Geneva (3) UN New York (2) UN Rome (2) UNESCO (2) Vienna - international organisations (1)
(-) Remove Annexes filter Annexes
Community gatherings & markets
Conference/seminar (2) Apply Conference/seminar filter
Conferences & conventions
Fairs & shows
EU Financed Projects
Europe Day
European Development Days
Intercultural dialogue
International, European Days and Anniversaries (1) Apply International, European Days and Anniversaries filter
Thematic series
EU project positions
International positions
Traineeships in Delegations
News stories (174) Apply News stories filter
Voices and views (1) Apply Voices and views filter
(-) Remove Council Conclusions filter Council Conclusions
Factsheets (5) Apply Factsheets filter
HR/VP speeches (28) Apply HR/VP speeches filter
Joint Press Releases (5) Apply Joint Press Releases filter
Joint Statements (30) Apply Joint Statements filter
Op-Eds (1) Apply Op-Eds filter
Petition responses (1) Apply Petition responses filter
Remarks (20) Apply Remarks filter
Statements by the HR/VP (36) Apply Statements by the HR/VP filter
Statements by the Spokesperson (160) Apply Statements by the Spokesperson filter
Statements on behalf of the EU (34) Apply Statements on behalf of the EU filter
Civil Society and Media (2) Apply Civil Society and Media filter
Environment and Climate Action
Multisector
Public Health and Social Protection
Editorial team... EEAS Press Team (15) Press and information team of the Delegation to the UN in Geneva (1) Strategic Communications (7)
Post date... 2016 (3) 2017 (1) 2018 (10) 2019 (9)
Sustainable Europe by 2030: Council adopts conclusions
The Council today adopted a set of conclusions on the implementation by the EU of the United Nations' 2030 Agenda on Sustainable Development and its 17 Sustainable Development Goals (SDGs). They are considered essential for ending poverty and ensuring a peaceful, healthy and secure life for
Author: EEAS Press Team - Publication date: 10/12/2019
Democracy: EU adopts conclusions
The Council today adopted conclusions on democracy. The conclusions underline that in today's world, democracy is being challenged and called into question. While democracy remains strong in many countries, in others there is a growing trend towards authoritarianism. The Council notes that the
Annual report on the EU guidelines on promoting compliance with international humanitarian law (IHL)
International Humanitarian Law ("IHL"), which seeks to limit the effects of armed conflict and to protect civilians and others not taking part in hostilities, is a cornerstone of modern international law. Nevertheless, despite States' universal acceptance of its rules and principles,
Author: Strategic Communications - Publication date: 27/09/2019
For a torture-free world: Council reinforces EU policy towards third countries on torture and other cruel, inhuman or degrading treatment
The Council today adopted the following conclusions on the revised Guidelines on EU policy towards third countries on torture and other cruel, inhuman or degrading treatment or punishment:
Supporting the Sustainable Development Goals across the world
The Council today adopted conclusions welcoming the publication of the first joint synthesis report of the EU and its member states on ''Supporting the Sustainable Development Goals across the world'' as an important contribution to EU reporting at the High Level Political Forum
The European Union's Global Strategy: Three years on, moving forward
Editorial Sections: EEAS United Nations (UN) Common Foreign & Security Policy (CFSP) EU Global Strategy Regional policies Security, Defence & Crisis Response Counter-Terrorism Crisis Response Military and civilian missions and operations Multilateral Relations Human Rights & Democracy
Sustainable development: Council adopts conclusions
The Council today adopted a set of conclusions concerning the implementation by the EU of the United Nations' 2030 Agenda on Sustainable Development, which was established in 2015 and comprises a set of 17 Sustainable Development Goals (SDGs). Given the horizontal nature of the 2030 Agenda, its
Iran: Council extends by one year sanctions responding to serious human rights violation
The Council today extended until 13 April 2020 its restrictive measures responding to serious human rights violations in Iran.
Human rights: Council adopts conclusions on EU priorities in UN human rights fora in 2019
The Council today adopted conclusions on EU priorities in UN human rights fora in 2019. It reaffirms the EU's commitment to promoting and protecting human rights, democracy and the rule of law, which also play a key role in ensuring peace and sustainable security.
Women, peace and security: Council adopts conclusions
The Council adopted conclusions on women, peace and security (WPS). The Council recalls the commitments of the European Union and its member states to the full implementation of the WPS agenda, which consists of UN security council resolution 1325 and its follow-up resolutions, ensuring that it is
European Union External Action
EEAS Building, 9A Rond Point Schuman
Contact the EEAS
Visit the EEAS
Questions about the EU
Quick Network Access

redpajama_set_name: RedPajamaCommonCrawl


studies of grasshopper playing baseball.
Damn, I don't check your blog for a few days and look what happens...these are really cool!!
Yeah I agree with Moro!
All of these are really good!
Very nice. Love these characters so much and would love to see more of them.
Hey Leo, I need a noun for the Chades challenge. Also, your bugs are great! I always have a tough time getting gesture and design into a drawing, and I usually have to focus on one or the other. How do you do it, man??
Moro: Thanks for checking out my blog!How's everything going?
enjae lee: Thank you so much! lovely work in your blog.
pavementmouse: thanks for the kind words. I will try to post more!!!
paul abadilla: Hey bro! How are you?....I need to talk to you about that lecture you guys want from James. I'll call you soon.
munchanka: Well, your stuff is awesome and really gestural man! I don't think you need feedback. Anyways, I usually try to get the gesture right with a really broad marker first on a separated piece of paper. Just the idea that I really want to focus on. After getting the idea down I start my final design. For the challenge how about some fun crocodiles??
wow! real nice! love those shapes!


text:
De gevlekte knolvezelkop (Inocybe pseudohiulca) is een paddenstoel uit de familie Inocybaceae. Hij komt voor langs lanen en boswegen op voedselrijke leem of kleigrond onder eik en beuk.

Kenmerken
Hoed
Vaak grote, gedrongen vruchtlichamen met een diameter tot circa 8 cm. De kleur is strogeel tot olijfgeel met spitse umbo. In het midden van de hoed een vergankelijke grijzige sluier. De hoed is plakkerig, daarom vaak bedekt met aarderesten. De rand is heeft soms een witte zoom.

Steel
De steel is zwakvezelig-breekbaar. Knollen vaak diep in de grond, daardoor makkelijk af te breken

Geur
De geur is zoetig, honingachtig en wordt later spermatisch.

Smaak
Hij is eetbaar maar kan makkelijk worden verwisselt met ander giftige soorten.

Sporen
De sporen zijn hoekig en zijn vrij groot (tot 13 micron). Cystidia meestal halsloos, knotsvormig, subglobulos of subfusiform, op de hals relatief dikwandig (tot ca. 3 µm).

Voorkomen
In Nederland komt hij zeer zeldzaam voor. Hij staat op de rode lijst in de categorie 'Ernstig bedreigd'.

Inocybaceae
Schimmelsoort

redpajama_set_name: RedPajamaWikipedia


text:
Best Sample Essays, Free Research Papers, Dissertation Samples
How to Write the Best Research Paper
How to Write the Best Term Paper
Research Paper on Sales Promotion and Public Relations
Posted on July 21, 2012, 3:03 am, by admin, under Sample research papers.
Promotion and Public Relations
Within the scope of this research, we will consider a company that does business in E-commerce, namely Amazon. The e-commerce activities of retail companies have been the subject of substantial examination, certainly more than other e-commerce sectors. Observers have been able to gain an especially clear perspective of the successes and failures associated with retail-focused e-commerce. This perspective reveals that customer service, a willingness to change a failing e-commerce strategy, and measures to determine what specific products are most appropriate for e-commerce are keys to retail e-commerce success.
We can write a Custom Research Paper on Sales Promotion and Public Relations for you!
Online price wars do not typically lead to profitability. Repeat customers do. Companies wishing to establish a credible online presence should not typically focus on using temporarily low prices to attract customers without loyalty or a likelihood of repeat business. Rather, companies should to use e-commerce to acquire and retain customers who are likely to maintain long-term relationships with the company. Elements that have proved successful in promoting such customer retention include well-developed Web site design, liberal return policies, and targeted customer incentives based on records of customer activity.
Amazon was established in Seattle as a micro-enterprise in 1994. In 1995, Amazon opened its Web site, as a site with a modest discount for books, and quickly established a reputation for offering a larger selection of books than any bookstore, with a selection of 1.1 million titles. In 1998, it diversified into music and quickly became a leader in that category. It has since expanded into thirteen primary categories and an offering of 18 million items. Amazon also recognized quickly that simply being a distributor would subject it to online price wars and reduced margins. Its first expansion into other roles came in 1996, when it began the Amazon Associates program, which linked customers to Amazon through other content sites. Affiliates received commissions of 5 to 15 percent.
Another program is the Advantage program, which allows independent publishers to sell books on Amazon's site; Amazon pays the publisher 45 percent of list price. Another development was the zShops program, in which Amazon hosts small providers on its site, providing its distribution technology in exchange for a commission. Amazon also receives benefits from the additional traffic and the ability to cross-sell.
Finally, Amazon developed larger distribution partnerships. In August 2000, it created a strategic alliance with Toys 'R' Us to provide logistical support for a co-branded Web site. Amazon received a small percentage of revenue, per-unit payments, and fixed payments. Amazon handled site development, order fulfillment, and customer service, while Toys 'R' Us handled inventory. The deal boosted sales for both companies and forced a pure-play competitor, rival eToys, to fold.
In August 2001, Amazon took over operations for Borders.com, providing inventory, fulfillment, site content, and customer service. The Borders site adopted Amazon's one-click ordering and personalization. In teaming up with Borders, Amazon gained both customers and an offline presence. In 2002, the deal was enhanced to include the ability to check physical stores' inventory online and for Borders stores to accept returns from Amazon. It also took over operations for CDNow, a leader in online music sales owned by Bertelsmann, a major stakeholder in barnesandnoble.com.
Amazon has designed most of its own functions, including the search system, customer accounts system, and IT infrastructure. The design of Amazon's site contributes heavily to its high repeat customer rate. A key aspect of Amazon's site design is its personalization technology, which tracks customer preferences and informs customers, both on the site and through email, of products that might appeal to them. Amazon content is provided both by Amazon's staff and by users, who may submit reviews and other forms of feedback on products.
For customer service, Amazon offers dedicated email addresses that deal with specific customer topics, areas, and other functions. It also began offering free shipping on larger orders, an idea which it considered and scrapped in summer 2001. Later in 2002, it reduced considerably the purchase minimums for free shipping.
Another major advantage is Amazon's negative cash conversion cycle, because it collects sales payments from customers before it must pay distributors and vendors. By 2003 Amazon had 37 million customers. Though growth was strong, Amazon continued to lose money until January 2002, when Amazon reported its first quarter of profitability. Barnes and Noble's first reaction to Amazon was to design a store using America Online, which launched in 1997, nearly two years after the launch of Amazon. The site, however, was criticized as being slow and difficult to use. The site was also overloaded with orders at times, especially during the holiday season, without the technological capabilities to handle them. There were also no signs of integration with retail stores.
Barnes and Noble's offline business had always been centered around low prices, in contrast to its main offline competitor, Borders, which had competed on its wide assortment of titles. The core of the strategy was scale in distribution infrastructure and administration and in-store discounts. In 1998, Bertelsmann bought a 50 percent stake in the Web site for $200 million.
The new barnesandnoble.com was first designed as a separate unit, and eventually spun off as a stand-alone separate company. The Web site's headquarters was a colorful, open, and high-tech environment, designed to imitate the feel of a pure-play company. In 1999, its IPO raised $486 million, which was used primarily to improve the Web site and fulfillment operations. This relaunch of the Web site overhauled both front-end and back-end operations. The site itself was redesigned to be more like Amazon's, making ordering simpler and faster for customers. Amazon successfully sued Barnes and Noble, however, for too closely imitating its checkout technology.
In 2002, Barnes and Noble saw sales increase and net losses fall, leading to the company's first projections of profitability in 2003. In addition to higher revenue, the site benefited from cuts in operating expenses and more efficient shipping. But its slow move into e-commerce and poor integration with its bricks and mortar operation has kept it to a small fraction of the size of Amazon.
Remember, free research papers, sample research papers and research paper examples on Sales Promotion and Public Relations topics are traced by plagiarism detection systems. All samples online are plagiarized. Don't download them and submit them as your own research project for high school, college or university. Why not to get a 100% original research paper at PapersMart.net? Need a free quote?
If you need a custom research paper on Sales Promotion and Public Relations feel free to contact our online research paper writing company. Our professional academic writers who hold PhD and Master's degree will write a 100% non-plagiarized research paper, term paper, essay, research proposal or dissertation for you. Our custom research paper service produces high-quality custom papers on any topics and disciplines. On-time delivery and confidentiality guarantee!
Tags: essay on public relations, research paper on Amazon, research paper on public relations, sales promotion essays, sales promotion research paper, sales promotion term paper, term paper on public relations
Comment (RSS)	| Trackback
« Research Paper on My Experience in School
Hitler's Rise to Power Essay »
BEST WRITING SERVICE:
http://papersmart.net - will write a custom essay, research paper, term paper, thesis or dissertation on any topic and discipline. 100% non-plagiarized papers from professional writers. Affordable prices for everybody.
Sample research papers
Sample research proposals
A lot of students experience difficulties in getting good samples of essays, research papers, dissertations. Actually it's very difficult to find effective and professionally written academic papers online, especially for free. That's why we decided to provide college and university students with great sample essays, research paper samples, sample term papers, university dissertation samples and even sample Master's thesis papers on the best writing topics.
Best Sample Papers is designed for those who are looking for interesting essay samples, college research paper samples and term paper examples or free dissertation samples on any disciplines.
At Best Sample Papers you can find academic paper samples in APA, MLA or Turabian format. All free sample papers are sorted in categories, tag cloud and archives that makes navigation very convenient for any student who need professional paper writing help for free. Anyway, if students want to have their academic papers written they can contact the best custom writing services recommended by our specilaists and writers.
Powered by WordPress and plainscape theme.
Congratulations! You have successfully installed the Catfish Manager plugin!
Go to the administration panel to change this text, the options and to set custom CSS to change how the advert looks.


Son of Godzilla 1969 english dubbed Son of Godzilla 1969 english dubbed [267_19] - $19.99 : Monster Island Toys, The Godzilla Super Store!
English Dubbed Version!A team of scientists stationed on Sollgell Island attempts to perfect a weather control system. Their efforts are hampered by the presence of giant praying mantises and by the arrival of a nosy reporter. The first test of the weather control system goes awry when the remote control for a radioactive balloon is jammed by an unexplained signal coming from the center of the island. The balloon detonates prematurely, creating a radioactive storm that causes the giant mantises to grow to enormous sizes. Investigating the mantises, now called Kamacuras, the scientists find the creatures digging an egg out from under a pile of earth. The egg hatches, revealing a baby Godzilla. The scientists realize that the baby's cries for help were the cause of the interference that ruined their experiment. Soon Godzilla himself arrives on the island, incidentally stomping the scientist's base as he rushes to defend his son. Godzilla kills two Kamacuras during the battle, while one manages to fly away to safety. The baby quickly grows to about half the size of his father, and Godzilla instructs the child on the important monster skills of roaring and using his atomic breath. At first, the baby has difficulty producing anything more than atomic smoke rings, but Godzilla discovers that stressful conditions, such as stomping on the baby's tail, produce a true radioactive blast. Dubbed Minilla, the baby comes to the aid of Riko when she is attacked by a Kamacuras, but inadvertently awakens Kumonga, a giant spider. The spider attacks the caves where the scientists are hiding, and Minilla stumbles into the fray. Kumonga traps Minilla and the final Kamacuras with his webbing, but as Kumonga begins to feed on the deceased Kamacuras, Godzilla arrives to save the day. Godzilla saves his son and they both defeat Kumonga by using their atomic breaths on the giant spider. The scientists finally use their perfected weather altering device on the island and the once tropical island turns into an Arctic wasteland. Godzilla and Minilla begin to hibernate as they wait for the island to become tropical again. The scientists are saved by a submarine.
Mothra 3 Special Edition 2 Disc Dvd Uncut!


text:
import {
    createEvent,
    css,
    isNumeric,
    isString,
    on,
    startsWith,
    toFloat,
    trigger,
} from 'uikit-util';

export default {
    props: {
        media: Boolean,
    },

    data: {
        media: false,
    },

    connected() {
        const media = toMedia(this.media, this.$el);
        this.matchMedia = true;
        if (media) {
            this.mediaObj = window.matchMedia(media);
            const handler = () => {
                this.matchMedia = this.mediaObj.matches;
                trigger(this.$el, createEvent('mediachange', false, true, [this.mediaObj]));
            };
            this.offMediaObj = on(this.mediaObj, 'change', () => {
                handler();
                this.$emit('resize');
            });
            handler();
        }
    },

    disconnected() {
        this.offMediaObj?.();
    },
};

function toMedia(value, element) {
    if (isString(value)) {
        if (startsWith(value, '@')) {
            value = toFloat(css(element, `--uk-breakpoint-${value.substr(1)}`));
        } else if (isNaN(value)) {
            return value;
        }
    }

    return value && isNumeric(value) ? `(min-width: ${value}px)` : '';
}


I have a new set of templates for you ~ this is Fuss Free: Set Six ~ and they are based on my own layout creations. These are on sale for 20% for a limited time in The Digichick Shop. Image linked to the Shop.


Grey Geometric silkscreen linen wrapped cubestool. Perfect in a masculine or Industrial interior space with an air of grace and sophistication for a penthouse apartment in the city.
Handmade in England, these cube stools are perfect for comfortable, additional seating in any interior space or as a side table to sofas.


text:
An analysis of emergency department use by patients with minor illness
Robert Shesser, Thomas Kirsch, Jeff Smith, Robert Hirsch
Study objective: To describe the motivation for emergency department use by patients with minor illnesses and compare the demographics and social class characteristics of these patients with those of the general ED population. Design: Observational, case-control study. Setting: Urban ED. Type of participants: A sample group of 325 adult, nongeriatric patients with minor illnesses was selected by screening all patients registering in the ED between 9:00 am and 6:00 pm on 15 randomly selected weekdays. A patient was included in this study group if the chief complaint, method of arrival, and subsequent evaluation met predetermined criteria for minor illness. A comparison group (control) was composed of all ED patients (224) who presented during two randomly selected 24-hour periods that did not overlap with the times of study group enrollment. Interventions: Sample group patients were interviewed concerning their socioeconomic backgrounds, reasons for using the ED, and perceptions of the urgency of their conditions. Comparison group patients' interviews were confined to the collection of demographic and socioeconomic information. Measurements and main results: There were more men (P = .12), more self-pay patients (P = .017), and fewer Medicare patients (P <.001) in the study group. There also was a strong trend toward higher income (P = .059) in the study group. The racial, marital, employment, and educational backgrounds of the two groups were similar. Eighty-two percent of the study group had no chronic illness, and only 36% reported a problem of more than three days' duration. Patients chose to use the ED because of its convenience (23.7%), the absence of previous provider relationships (22.1%), and the inability to make a prompt appointment with their regular provider (19.0%). Major differences existed between the reasons for which different demographic and socioeconomic groups chose ED care. Study group patients believed that less than 24 hours should elapse between the onset of their problem and the time at which they receive medical care. Conclusion: There are no major differences in ED use for minor illness patients from different racial, educational, and economic backgrounds. These patients tend to have a low frequency of chronic illness and often have no established health care provider. They choose the ED for its ease of access and the wide scope of care that can be delivered.
Time and Motion Studies
Health Personnel
minor illness, emergency department use
Shesser, R., Kirsch, T., Smith, J., & Hirsch, R. (1991). An analysis of emergency department use by patients with minor illness. Annals of Emergency Medicine, 20(7), 743-748. https://doi.org/10.1016/S0196-0644(05)80835-2
An analysis of emergency department use by patients with minor illness. / Shesser, Robert; Kirsch, Thomas; Smith, Jeff; Hirsch, Robert.
In: Annals of Emergency Medicine, Vol. 20, No. 7, 1991, p. 743-748.
Shesser, R, Kirsch, T, Smith, J & Hirsch, R 1991, 'An analysis of emergency department use by patients with minor illness', Annals of Emergency Medicine, vol. 20, no. 7, pp. 743-748. https://doi.org/10.1016/S0196-0644(05)80835-2
Shesser R, Kirsch T, Smith J, Hirsch R. An analysis of emergency department use by patients with minor illness. Annals of Emergency Medicine. 1991;20(7):743-748. https://doi.org/10.1016/S0196-0644(05)80835-2
Shesser, Robert ; Kirsch, Thomas ; Smith, Jeff ; Hirsch, Robert. / An analysis of emergency department use by patients with minor illness. In: Annals of Emergency Medicine. 1991 ; Vol. 20, No. 7. pp. 743-748.
@article{a368b64150b04eec886adc844a99a60f,
title = "An analysis of emergency department use by patients with minor illness",
abstract = "Study objective: To describe the motivation for emergency department use by patients with minor illnesses and compare the demographics and social class characteristics of these patients with those of the general ED population. Design: Observational, case-control study. Setting: Urban ED. Type of participants: A sample group of 325 adult, nongeriatric patients with minor illnesses was selected by screening all patients registering in the ED between 9:00 am and 6:00 pm on 15 randomly selected weekdays. A patient was included in this study group if the chief complaint, method of arrival, and subsequent evaluation met predetermined criteria for minor illness. A comparison group (control) was composed of all ED patients (224) who presented during two randomly selected 24-hour periods that did not overlap with the times of study group enrollment. Interventions: Sample group patients were interviewed concerning their socioeconomic backgrounds, reasons for using the ED, and perceptions of the urgency of their conditions. Comparison group patients' interviews were confined to the collection of demographic and socioeconomic information. Measurements and main results: There were more men (P = .12), more self-pay patients (P = .017), and fewer Medicare patients (P <.001) in the study group. There also was a strong trend toward higher income (P = .059) in the study group. The racial, marital, employment, and educational backgrounds of the two groups were similar. Eighty-two percent of the study group had no chronic illness, and only 36{\%} reported a problem of more than three days' duration. Patients chose to use the ED because of its convenience (23.7{\%}), the absence of previous provider relationships (22.1{\%}), and the inability to make a prompt appointment with their regular provider (19.0{\%}). Major differences existed between the reasons for which different demographic and socioeconomic groups chose ED care. Study group patients believed that less than 24 hours should elapse between the onset of their problem and the time at which they receive medical care. Conclusion: There are no major differences in ED use for minor illness patients from different racial, educational, and economic backgrounds. These patients tend to have a low frequency of chronic illness and often have no established health care provider. They choose the ED for its ease of access and the wide scope of care that can be delivered.",
keywords = "minor illness, emergency department use",
author = "Robert Shesser and Thomas Kirsch and Jeff Smith and Robert Hirsch",
journal = "Annals of Emergency Medicine",
T1 - An analysis of emergency department use by patients with minor illness
AU - Shesser, Robert
AU - Kirsch, Thomas
AU - Smith, Jeff
AU - Hirsch, Robert
N2 - Study objective: To describe the motivation for emergency department use by patients with minor illnesses and compare the demographics and social class characteristics of these patients with those of the general ED population. Design: Observational, case-control study. Setting: Urban ED. Type of participants: A sample group of 325 adult, nongeriatric patients with minor illnesses was selected by screening all patients registering in the ED between 9:00 am and 6:00 pm on 15 randomly selected weekdays. A patient was included in this study group if the chief complaint, method of arrival, and subsequent evaluation met predetermined criteria for minor illness. A comparison group (control) was composed of all ED patients (224) who presented during two randomly selected 24-hour periods that did not overlap with the times of study group enrollment. Interventions: Sample group patients were interviewed concerning their socioeconomic backgrounds, reasons for using the ED, and perceptions of the urgency of their conditions. Comparison group patients' interviews were confined to the collection of demographic and socioeconomic information. Measurements and main results: There were more men (P = .12), more self-pay patients (P = .017), and fewer Medicare patients (P <.001) in the study group. There also was a strong trend toward higher income (P = .059) in the study group. The racial, marital, employment, and educational backgrounds of the two groups were similar. Eighty-two percent of the study group had no chronic illness, and only 36% reported a problem of more than three days' duration. Patients chose to use the ED because of its convenience (23.7%), the absence of previous provider relationships (22.1%), and the inability to make a prompt appointment with their regular provider (19.0%). Major differences existed between the reasons for which different demographic and socioeconomic groups chose ED care. Study group patients believed that less than 24 hours should elapse between the onset of their problem and the time at which they receive medical care. Conclusion: There are no major differences in ED use for minor illness patients from different racial, educational, and economic backgrounds. These patients tend to have a low frequency of chronic illness and often have no established health care provider. They choose the ED for its ease of access and the wide scope of care that can be delivered.
AB - Study objective: To describe the motivation for emergency department use by patients with minor illnesses and compare the demographics and social class characteristics of these patients with those of the general ED population. Design: Observational, case-control study. Setting: Urban ED. Type of participants: A sample group of 325 adult, nongeriatric patients with minor illnesses was selected by screening all patients registering in the ED between 9:00 am and 6:00 pm on 15 randomly selected weekdays. A patient was included in this study group if the chief complaint, method of arrival, and subsequent evaluation met predetermined criteria for minor illness. A comparison group (control) was composed of all ED patients (224) who presented during two randomly selected 24-hour periods that did not overlap with the times of study group enrollment. Interventions: Sample group patients were interviewed concerning their socioeconomic backgrounds, reasons for using the ED, and perceptions of the urgency of their conditions. Comparison group patients' interviews were confined to the collection of demographic and socioeconomic information. Measurements and main results: There were more men (P = .12), more self-pay patients (P = .017), and fewer Medicare patients (P <.001) in the study group. There also was a strong trend toward higher income (P = .059) in the study group. The racial, marital, employment, and educational backgrounds of the two groups were similar. Eighty-two percent of the study group had no chronic illness, and only 36% reported a problem of more than three days' duration. Patients chose to use the ED because of its convenience (23.7%), the absence of previous provider relationships (22.1%), and the inability to make a prompt appointment with their regular provider (19.0%). Major differences existed between the reasons for which different demographic and socioeconomic groups chose ED care. Study group patients believed that less than 24 hours should elapse between the onset of their problem and the time at which they receive medical care. Conclusion: There are no major differences in ED use for minor illness patients from different racial, educational, and economic backgrounds. These patients tend to have a low frequency of chronic illness and often have no established health care provider. They choose the ED for its ease of access and the wide scope of care that can be delivered.
KW - minor illness, emergency department use
JO - Annals of Emergency Medicine
JF - Annals of Emergency Medicine


After the 1980s tax reform the decline in savings and the increase in consumption caused domestic investment to fall, swamping any increase due to incentives from lower taxes on high incomes.
As corporate savings decreased (as a consequence of increasing the number of pass-through businesses), it was not replaced by personal savings but by personal consumption. Since the 1980s, consumption as a percent of GDP, went from around 60% to 68% mostly due to more money spent on services.
In the 1980s the effective top rate on pass-throughs (unearned) was dropped to match the corporate rate on profits, making pass-through businesses more desirable than in the past since with pass-throughs owners were not double taxed. As a consequence, these tax changes created an incentive to change the business structure from C corporation to pass-throughs. The double taxation of corporate profits had provided an incentive for corporations to retain earrings (to save) but a pass-through's profit is tax indifferent between saving and consumption (there is no incentive to either save it or spend it).
C corporation's share of net business income dropped from 1980 to 2012, 68% to 37%. The effect of fewer C corporations and more pass-through businesses was less savings since retained earnings by corporations was half of private savings (pdf). So, tax-induced decrease in number of corporations had a substantial effect on the level of private savings in the US.
Data Notes: Tax rates are from Internal Revenue Service; Tax Policy Center; Center for Tax Justice; Tax Foundation and more details on the tax rates available in Part 1 and Part 2 in the series.
Federal Reserve Economic Data is the source for net savings.
This is an intriguing graph showing the decline of companies listed in the United States on the stock exchange. (These companies would be corporations whose's stocks are freely traded on a stock exchange, not pass-throughs).
The tax changes in the 80s provided a tax incentive to change the business structure from C corporation to pass-throughs like LLCs. Originally, the IRS was very strict as to when a business could be treated a pass-through entity, however, that changed on January 1, 1997. That is when you see the ratio of listed companies the stock exchange drop dramatically.


We understand that life doesn't slow down when you accept a position. At Dickinson State, we offer many options to employees that need to take some time off in order to fulfill their civic duties, care for their loved ones, or to recover from an illness or injury.
or for the serious health condition of you, your spouse, child or parent.
After at least six months of continuous employment and exhausting all applicable paid time off, staff and faculty on 12-month appointments may receive donated leave. This leave can be donated by co-workers if the employee meets the criteria and is approved by the administration.
Upon employment, DSU provides paid time off for jury duty assignments.
Upon employment, DSU provides paid time off for the first 20 days of annual military duty.
Upon employment, DSU provides sick leave that accrues at a rate of 8 hours/month, 12 days/year with no limit. Up to 80 hours of leave per calendar year may be used for dependents.
Upon employment, DSU provides paid sick leave for occasional absences or for an extended illness.
Upon employment, DSU provides up to 24 hours of paid leave for a death in the employee or spouse's immediate family.
Upon employment, DSU provides 10 paid holidays including: New Year's Day, Martin Luther King Day, President's Day, Good Friday, Memorial Day, Independence Day, Labor Day, Veteran's Day, Thanksgiving and Christmas. In addition, offices close at noon on Christmas Eve day when it falls on Monday-Thursday.


Gary Smalley explains what motivates men and how women can use their natural attractive qualities to build a better marriage.
He helps women to understand not only the way men think, but also how to move a man's heart. Using case histories and biblical illustrations, he solves with empathy, humor and wisdom, every practical and emotional problem a woman can face in her marriage.


Un-Tie Tie-Up Relief 5 lbs.
Reduces muscle tie-up and soreness. Blood lactic acid remover, increases atamina and endurance.
Proprietary blend consisting of: Probiotic base with Calcium Lactate, Potassium Chloride, Sodium Chloride, Magnesium Hydrolide, Sodium BiCarbonate, Vitamin E, DMG, Calcium Propinate, Magnesium Citrate Powder, Zinc Chelate, Selenium, Amino Acid Chelate and flo agent.


3DS won't read it's SD card? Easy and efficient ways are offered here to fix 'Could not detect an SD card. The software on the SD Card could not be displayed' error in 3DS.
3DS won't read it's SD card? In this page, we focus on how to fix the issue in some easy and efficient ways.
"When I open my 3DS XL, it gives me a message says "Could not detect an SD Card. The software on the SD Card could not be displayed." Is there any fix?"
Follow the steps below to solve the issue correctly.
Whenever you get could not detect an SD card error message, please first try another SD card in your 3DS.
If another SD Card does not work, it might suggest that your 3DS should be sent in for repair.
If another SD Card works, it turns out to be a problem with your SD card. You can try to reformat 3DS SD card to FAT32 with EaseUS free partition software for repair. It is said to be helpful with a large number of users.
Here, before formatting, you can try EaseUS PC transfer software to transfer your 3DS Saved Data onto another SD card. It works if your card can be detected by your PC.
For some users who are still suffering could not detect an SD card error in 3DS after reformatting the card, replacing the old card with a new one is recommended.
Never remove or insert SD cards while the system is on.
Never remove a miniSD or microSD card while the adapter is still in the system.


I THINK YOU SHOULD DISPLAY THE PASSWORDS IN YOUR AUTHOURES COMMENTS THOUGH.
This is a good game.The only thing that was wrong was that the levels are a bit to long, other than that it was a good game.
Very nice game, can't stop playing keet it up dude!


worth.200 (All User) Apply FreeCharge Add Money Coupon : rupay.20 cashback.20. Minimum Bill Payment Amount Of Rs 20 Is Required. All you need to do is enter using your Freecharge Login credentials and decide whether you want to recharge your phone or pay bills. Old Is Gold All of you old users might be thinking that theres nothing in it for you, but wait! Offer is valid for FreeCharge handled UPI transactions only. Freecharge is Offering Rs 25 Cashback on Mobile Recharges and Bill Payments of. View All Jabong Coupons Activate Offer Verified Coupon Description Description Upto. The code can be redeemed on Electricity Bill payments only before 30th June 2018. Rs 10 cashback on Rs 20 more On Recharge/Bill payments All Users code expired, show Description, verified Today. See All Paytm Offers, expired Coupons,.10 OFF. FreeCharge Recharge Cashback Coupons for Airtel, Vodafone, Idea, Reliance, Tata Docomo, Airtel, bsnl and others Recharge Bill Payments FreeCharge DTH Recharge Promo Code for Tata Sky, Airtel Digital TV, Reliance Big TV, Dish TV, Sun Direct and Videocon D2H Recharge FreeCharge electricity bills Offer and. FreeCharge Gag bill Payment Promo Code for Gas bill for Mahanagar Gas Limited FreeCharge Landline bill payments Promo Code for Airtel landline, bsnl landline and mtnl Delhi FreeCharge Data Card Recharge and Cashback for Datacard recharge for operators like Reliance Netconnect, Airtel, Tata Photon, Vodafone.
Rs.40 OFF Recharge Your Mobile Get Rs 40 Cashback On Electricity Bill Payments code expired Show Description Recharge your mobile through Freecharge get Rs 40 cashback on electricity bill payments. Follow the simple steps below to effectively maximize your savings on every online purchase. Apply FreeCharge CouponCode, first, get 7 cashback on eBay, use Promo Code. This is Not valid for Add Cash, Mobile Prepaid, Mobile Postpaid, Datacard, Landline, Electricity, Gas Metro transactions. They use secure payment gateways that are authenticated and mostly used in highly-secure transaction process. Not valid on prior purchases. Save your money on Recharge at FreeCharge Using Latest FreeCharge Promo Code Latest Update on Daily Basic. Use filters to find the coupons and deals for the category you want. This is Valid on credit/debit card/Net banking/FC Balance UPI transactions only. It works with all the service providers such as Airtel, Vodafone, Idea, Reliance Jio, Docomo, bsnl, Telenor, mtnl, Aircel, MTS, Virgin and Indicom Walky. This discount is valid for limited period. View All, amazon Coupons, activate Offer, verified Coupon.


This converter allows you to convert Length, Weight, Volume, Speed, Temperature, Fuel and Fraction.
Disclaimer - The currency converter may or may not be accurate and it is just for reference only. For more accurate exchange rates please check with your local bank or foreigner currency exchange agent.
For Feng Shui Ruler or Auspicious Measurement checks.


text:
About NSCA
NSCA Foundation
Assistantship
Volunteer Leadership Opportunities
Member Awards
Choosing the Right Certification
TSAC-F
NSCA-CPT
Stay Certified
Report CEUs
CEU Opportunities
NSCA TV
CASCE ACCREDITATION
Why CASCE
Apply for CASCE
About CASCE
State/Provincial & Regional Events
Researchers and Educators
TSAC Professionals
Strength and Conditioning Coaches
Store Overview
Become a member Create Account
Become a member | Create Account
Become a member Create an Account
Current: Quantifying Training and...
Quantifying Training and Competition Load
by NSCA's Essentials of Sport Science
Kinetic Select August 2021
Personal trainers TSAC Facilitators Coaches
Training Load Player Load RPE GPS
This excerpt from NSCA's Essentials of Sport Science highlights the importance of quantifying training load for both programming and monitoring an athlete's progression or regression over time.
The following is an exclusive excerpt from the book NSCA's Essentials of Sport Science, published by Human Kinetics. All text and images provided by Human Kinetics.
A key component for both programming and monitoring an athlete's progression or regression is the quantification of training load. This process is critical for assessing whether an athlete is adapting positively to a training program (14). As mentioned earlier, external load refers to what the athlete has done (e.g., distance and speed of running, kilograms lifted), while internal load refers to how the athlete has responded to a given external load (72, 73). This internal response can be both physiological (e.g., heart rate, blood lactate) and perceptual (e.g., rate of perceived exertion [RPE]) (73). Ultimately it is the internal response to a given external load that drives the training outcome (72, 73). Importantly, measures of external and internal load should be used in combination to provide a complete picture of the training process and response (14). Furthermore, as mentioned earlier, a comprehensive understanding of the external load of a sport allows the development of specific training programs aimed at targeting the relevant underlying physiological qualities (e.g., aerobic capacity, speed, strength).
External load can be measured in a variety of ways depending on the sport or training modality (14). Technological advances such as camera systems and microtechnology (local systems and Global Positioning Systems [GPS]), often in conjunction with other sensors such as accelerometers and power meters, have made the quantification of various activity metrics in teams and in sports such as running and cycling relatively simple. While this process has become common, some critical elements should be considered with regard to the measurement of external load, and these are explored next.
The measurement of speed and distance metrics using GPS is now commonplace, and the validity and reliability of these devices have been extensively examined (21, 36, 75, 77). In general, higher-sample-rate (e.g., 10 Hz versus 5 Hz) GPS chips have demonstrated superior validity and reliability to lower sample rates, particularly for the measurement of high-intensity running efforts and accelerations (21, 75, 77). The sampling rate of these systems continues to increase, which may assist in further improving validity and reliability for the measurement of high-intensity events. Furthermore, the use of indoor stadiums has necessitated the development of indoor tracking systems such as Local Positioning Systems (LPS), which can provide information similar to that with GPS (131). Additional detail on these systems is provided in chapter 9. Furthermore, determining thresholds for classification of high-speed running, sprinting, and accelerations is challenging for practitioners regardless of the tracking technology employed, and doing this includes consideration of whether these thresholds should be based on team or individual values and whether they should have a physiological basis (134). Work in this area has used a movement sequencing technique rather than arbitrary thresholds to classify velocity and accelerations performed by elite netball athletes, and similar approaches in other sports may yield valuable insights (133). A primary driver for practitioners in deciding whether to use relative or absolute speed and acceleration thresholds is likely related to whether comparisons are being made between or within individual athletes. Furthermore, sport scientists and coaches should be aware that values transmitted live by the units and those calculated after downloading data can be different, and this may have significant implications for training or competition decision making (6). The impact of data processing (e.g., smoothing techniques) on measured variables should also be considered (137). Finally, a highlighted factor in the quantification of team-sport activity profiles is the consideration of average intensity versus peak intensity (41). Peak running intensity is substantially higher in relatively short time windows (e.g., 1 min) compared to the average intensity in a half- or full-duration rugby league match (41). This has important implications for the design of training programs targeted at developing the underlying physical qualities important for being able to perform at the required intensity; and in practice, both peak and average intensity should be considered. These and other considerations are discussed in more detail in chapters 9 and 10 of this book.
Given the chaotic nature of team sports, it has been suggested that speed and distance metrics may not completely quantify the full external load (15, 114). The reason is that many movements that are energetically costly and taxing on the neuromuscular system (e.g., accelerations, decelerations, change of direction, and contact) can occur at low speed and accumulate relatively little distance (15, 114). These activities can be measured with a variety of sensors such as high-sample-rate (e.g., 100 Hz or greater) triaxial accelerometers, gyroscopes, and magnetometers, and these accelerometers in particular have demonstrated high reliability and ecological validity (15, 30, 34, 97, 114). Manufacturers have tended to create their own metrics for values obtained from triaxial accelerometers, similar to the Catapult PlayerLoad™ calculation shown, but they all essentially represent a combination of individual vector values (15):
Interestingly, changes to these metrics or the individual vector contributions to the overall value have shown promise in the ability to detect fatigue-induced changes in movement strategy (30, 97, 114). The use of this type of metric, in conjunction with traditional locomotor variables as measures of external load, may provide practitioners with additional insight.
Of particular interest is the fact that various manufacturers have developed algorithms to auto-detect specific sport events, such as fast bowling in cricket and tackles in contact sports, with reasonable accuracy (56, 71, 95). This may be useful in reducing the time and effort required for accurate measurement of external load, leading to more precise quantification and therefore assisting with both planning and monitoring of training and competition.
The frequent accelerations and decelerations performed in team sports can substantially increase the energy cost (42). In order to account for this, the concept of metabolic power was developed, which is based on the principle that the energy cost of acceleration is equivalent to running at a constant speed up an "equivalent slope" (42). As a result, numerous measures have been proposed; these include metabolic power (in categories from low [0-10 W/kg] to maximum [>55 W/kg]), total energy expenditure (kJ/kg), equivalent distance (representing the distance that would have been covered during steady-state running on a flat grass surface), and equivalent distance index (representing the ratio between equivalent distance and total distance) (108). While the use of metabolic power has undergone some investigation (37, 80) and has attractive practical aspects, its validity has been questioned for various reasons, including the innate error in measuring accelerations using positional systems (16, 19, 21).
In addition, work has focused on the detection of specific variables such as stride parameters and vertical stiffness from accelerometry (20, 49, 84, 101). This type of analysis may prove insightful for practitioners, although there is some conjecture regarding the impact of unit placement (i.e., scapular versus center of mass versus lower leg) on the ability to accurately measure specific variables (20, 46, 109).
Measurement of external load in endurance sports is also common (100). Sports such as running, cycling, and swimming lend themselves well to external load measurement via quantification of various combinations of speed, distance, and duration (100). In addition, the development of power meters has allowed easy measurement of power from pedal strokes in cycling (100). Readers are directed to part IV of this book for extensive coverage of this topic.
Because not all training occurs in the field, other training components also require quantification. For example, various indices of external load can be calculated from resistance training, including sets, repetitions, volume load, and device displacement velocity (124). An important reason for the quantification of resistance training load is the impact of volume and intensity of resistance training on muscular adaptation (110). These approaches can be used to both program and monitor resistance training load, although some methods arguably provide a more complete representation of external load than others (124). For example, the total number of repetitions performed (i.e., number of sets × number of repetitions) in a particular exercise provides a global representation of external load; however, it fails to account for the intensity (i.e., percent repetition maximum) (124). Accounting for the intensity in terms of load lifted by quantifying resistance training load as [number of sets × number of repetitions × weight lifted] somewhat overcomes the limitations mentioned earlier; however, it does not account for the intensity of the load relative to the maximum strength of the lifter (124). Therefore, quantification of resistance training load as [number of sets × number of repetitions × percent repetition maximum] may be most appropriate. Furthermore, the availability of measurement devices such as force plates, linear position transducers, and bar- and body-mounted accelerometers allows measurement of variables such as displacement, velocity, and power, which may also prove useful for both the programming and monitoring of resistance training (4, 9).
In addition to the measurement of external load, the quantification of internal load is a critical component of the training process. There are numerous approaches to this, including the use of both objective and subjective (often referred to as "perceptual") markers such as RPE, various heart rate indices, and biochemical markers. These measures are considered later in this chapter, and a detailed review of the assessment of internal load is provided in chapters 14, 16, and 17.
NSCA's Essentials of Sport Scienceprovides the most contemporary and comprehensive overview of the field of sport science and the role of the sport scientist. It is the primary preparation resource for the Certified Performance and Sport Scientist® (CPSS®) certification exam. The book is available in bookstores everywhere, as well as online at the NSCA Store.
Join the NSCA Today
Discover how NSCA Membership opens access to content and a community of professionals.
National Strength and Conditioning Association
1885 Bob Johnson Drive
The National Strength and Conditioning Association is proud to work with our outstanding partners and thank them for their continued support.
Retraction and Correction Policy
© 2023 National Strength and Conditioning Association
#everyonestronger #everyonestronger
has been added to your shopping cart!


text:
<?xml version = '1.0' encoding = 'UTF-8'?>
<DomainFile class="oracle.dbtools.crest.model.design.DomainFileWrapper" fileName="defaultdomains">
   <domains>
      <Domain class="oracle.dbtools.crest.model.design.Domain" name="Unknown" id="DOM3000004">
         <createdBy>bird</createdBy>
         <createdTime>2012-08-20 21:58:45 UTC</createdTime>
         <ownerDesignName>System</ownerDesignName>
         <avTSortOrder>0</avTSortOrder>
         <fileName>defaultdomains</fileName>
         <logicalDatatype>LOGDT017</logicalDatatype>
      </Domain>
   </domains>
</DomainFile>


text:
Salsola arbusculiformis är en amarantväxtart som beskrevs av Vasiliĭ Petrovich Drobow. Salsola arbusculiformis ingår i släktet sodaörter, och familjen amarantväxter. Inga underarter finns listade i Catalogue of Life.

Källor

Sodaörter
arbusculiformis


The then-Minister of Water and Environmental Affairs on 23 May 2014 established three new Catchment Management Agencies (CMA) under the National Water Act, No. 36 of 1998 (NWA). CMAs are responsible for the management of water resources within the defined catchment areas. The establishment of CMAs has the purpose of delegating water resource management to the regional or catchment level and to involve local communities within water management.
We are looking for master's and doctoral candidates who want to work with the M&G's science editor to have their writing published.


This multi-talented actor is just the entertainment you need you brighten up your corporate function, party, dinner, award night or special event.
Jack Dan can juggle, fall off a unicycle, stiltwalk. He can also snow and water ski, abseil, kayak and swim.
Amongst these extraordinary talents, Jack is also an accomplished musician. He plays the guitar, saxophone, and trumpet.
But the talent doesn't end here. Jack can also be a statue. He's no ordinary statue either. What gives him away is that no ordinary statue could ever demonstrate the range and diversity of emotions and attitudes that this piece of art does.
So if you need a roving act that can be a clown, musician, and statue, book Jack Dan for your special event to ensure a great and fun time.