Olympiades ENSAE - 1er S 2025
Exercice 1
Cet exercice est composé de parties $A$, $B$ et $C$ dans une large mesure indépendantes.
Partie A :
On définit par $A$ l'ensemble des fonctions $f\ :\ [0\;,1]\rightarrow \mathbb{R}$ vérifiant les conditions suivantes :
$\bullet\ $Pour tous réels $\alpha$ et $\beta\in[0\;,1]/\alpha <\beta$ si $f(\alpha)\times f(\beta)\leq 0$ alors il existe au moins $\overline{x}]\alpha\;,\beta[$ tel que $f\left(\overline{x}\right)=0$
$\bullet\ f(x)=f(1)=0$
$\bullet\ $Pour tout $x$ réel de l'intervalle $\left[0\;,\dfrac{7}{10}\right]\;,f\left(x+\dfrac{3}{10}\right)\neq f(x)$
Soit $f$ un élément de $A.$
On définit une fonction $h\ :\ \left[0\;,\dfrac{7}{10}\right]\rightarrow\;,\mathbb{R}$ donnée par : $h(x)=f\left(x+\dfrac{3}{10}\right)-f(x)$, pour tout $x\left[0\;,\dfrac{7}{10}\right]$
On suppose que h vérifie la condition $(1)$
$(1)$ Montrer que $h(x)$ est de signe constant sur $[0\;,\dfrac{7}{10}]$
$(2)$ Démontrer que l'équation $f(x)=0$ admet au moins sept solutions sur $[0\;,\dfrac{7}{10}]$
Partie B :
Les martiens sont les habitants, en nombre éventuellement infini, de la planète Mars.
Vis à vis d'eux-mêmes et de leurs semblables, les martiens sont capables de ressentir deux types d'émotions, qu'ils appellent amour et respect.
Il a été observé que :
$\bullet\ $Chaque martien aime un et un seul martien, et respecte un et un seul martien.
$\bullet\ $Si $A$ aime $B$, alors tout martien qui respecte $A$ aime également $B$
$\bullet\ $ Si $A$ respecte $B$, alors tout martien qui aime $A$ respecte également $B.$
$\bullet\ $Chaque martien est aimé d'au moins un martien.
On se propose de vérifier s'il est vrai que chaque martien respecte le martien qu'il aime.
Pour chaque martien $x$ , on désigne respectivement par $f(x)$ et $g(x)$ les martiens aimés et respectés par $x$
$(1)$ Montrer que les fonctions $f$ et $g$ sont bien définies de l'ensemble $X$ des martiens sur lui-même.
$(2)$ Montrer que $f[g(x)]=f(x)$ et $g[f(x)]=g(x)$ pour tout $x$ dans $X$
$(3)$ Montrer finalement que, pour tout $x$, on a $f(x)=g(x)=x$
$(4)$ Conclure !
Partie C :
Soit $n\in\mathbb{N}^{\ast}$, $m_{1}$, $m_{2}$, $\ldots$, $m_{n}$ des réels et $\mathrm{e}_{1}$, $\mathrm{e}_{2}$, $\ldots$, $\mathrm{e}_{n}$
des réels strictement, positifs on a :
$$\begin{array}{rcl}\dfrac{m_{1}^{2}}{\mathrm{e}_{1}}+\dfrac{m_{2}^{2}}{\mathrm{e}_{2}}+\ldots+\dfrac{m_{n}^{2}}{\mathrm{e}_{2}}\geq\dfrac{\left(m_{1}+m_{2}+\ldots+m_{n}\right)^{2}}{\mathrm{e}_{1}+\mathrm{2}+\ldots+\mathrm{e}_{n}}\end{array}$$
Cette inégalité est connue sous le nom de l'inégalité des Mauvais Élèves $(IME)$
En appliquant l'$IME$, montrer que :
$(1)$ Si $a_{1}$, $a_{2}$, $\ldots$, $a_{n}$ sont $n$ réels strictement positifs alors :
$\dfrac{1}{a_{1}}+\dfrac{1}{a_{2}}+\ldots+\dfrac{1}{a_{n}}\geq\dfrac{n^{2}}{a_{1}+a_{2}+\ldots+a_{n}}$
$(2)$ Si $a$, $b$ et $c$ sont $3$ réels strictement positifs alors :
$\dfrac{a}{a+2c}+\dfrac{b}{b+2a}+\dfrac{c}{c+2b}\geq 1$
$(3)$ Si $x$, $y$ et $z$ sont réels strictement positifs tels que : $\dfrac{1}{x+1}+\dfrac{1}{y+1}+\dfrac{1}{z+1}=1$ alors $xyz\geq 8$
On considère la figure suivante où $ABMN$ et $ARSC$ sont des carrés construits à partir du triangle $ABC$
On construit en outre le parallélogramme $ANA'R$
1. a. Démontrer que $\left(AA'\right)$ est une hauteur du triangle $ABC$
b. Démontrer que $AA'=BC$
2. On considère les parallélogramme $NARA'$, $QBMB'$ et $SCPC'$
Justifier que $\left(AA'\right)$, $\left(BB'\right)$ et $\left(CC'\right)$ sont concourantes.
b. Démontrer que dans un triangle $ABC$, si $M$ désigne le milieu de $[BC]$ alors : $AB^{2}+ac^{2}=2\left(BM^{2}+AM^{2}\right)$ (Théorème d'Apollonius).
c. En déduire que $NR^{2}+QM^{2}+SP^{2}=3\left(AB^{2}+AC^{2}+BC^{2}\right)$
Exercice 3
$\mathbb{R}$ désigne l'ensemble des nombres réels.
Dans ce problème, on cherche à déterminer les applications $f$ définies sur $]0\ ;\ +\infty[$ et à valeurs dans $]0\ ;\ +\infty[$ vérifiant les deux propriétés suivantes :
$\bullet\ $pour tous nombres réels strictement positifs $x$ et $y$, $f[xf(y)]=yf(x)$ ;
$\bullet\ f$ est bornée sur $[1\ ;\ +\infty[$ il existe un nombre réel $A$ tel que pour tout nombre réel $x\geq 1$, $f|f(x)|\leq A$
Partie I
Soit $I$ un intervalle de $\mathbb{R}$ et soit $h$ une application définie sur $I$ et à valeurs dans $I$
On dit que est $h$ une involution de $I$ si pour tout nombre réel $x$ dans $I\;,h[h(x)]=x$
1. Donner un exemple d'involution de $\mathbb{R}$ dans R autre que l'identité.
2. Donner un exemple d'involution de $]0\ ;\ +\infty[$ dans $]0\ ;\ +\infty[$ autre que l'identité.
3. Montrer qu'une involution de $I$ dans $I$ est bijective.
Partie II
Soit $f$ une fonction vérifiant les deux conditions citées au début de l'énoncé.
1. Soit deux nombres réels $y_{1}$, $y_{2}$ strictement positifs tels que $f\left(y_{1}\right)=f\left(y_{2}\right).$
Montrer que $y_{1}f(1)=y_{2}f(1)$
2. Montrer que $f$ est injective.
3. Montrer que $f[f(1)]=f(1)$ puis $f(1)$ puis que $f(1)=1$
4. Montrer que $f$ est une involution de $]0\ ;\ +\infty[$
5. Soient $a$ et $b$ deux réels strictement positifs.
Montrer que $f(ab)=ff(a)f(b)$
Indication : on pourra poser $b=f(y)$
Partie III
On note $F$ l'ensemble des points fixes de $f$ : $F=\lbrace x\in]0\ ;\`+\infty\left[/f(x)=x\right\rbrace$
1) Montrer que pour tout $x\in]0\ ;\ +\infty[\;,xf(x)$ est un élément de $F.$
2. Montrer que $1$ est un élément de $F.$
3. Montrer que si $x$ et $y$ sont des éléments de $F$, alors $xy$ et $\dfrac{x}{y}$
sont également des éléments de $F.$
4. Montrer que si $x$ est un élément de $F$, alors pour tout entier naturel $n$, $xn$ est un élément de $F$
5. Montrer que si $x$ est un élément de $F$, alors $x=1$
Indication : on pourra considérer l'application : $\mathbb{N}\rightarrow \mathbb{N}$ définie par $x_{n}x^{n}$
6. Montrer que $F=\lbrace 1\rbrace$
7. En déduire $f.$
8. Donner enfin toutes les applications répondant au problème posé.
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A couple from the United Kingdom had to cut their vacation in Venice short after being caught swimming in the Grand Canal.
The 35-year-old British man and his 25-year-old Romanian girlfriend were forced to return to their home in the UK on Thursday, the same day they arrived in the city, after gondoliers reported them to local police for taking a dip in the canal.
The pair were fined €450 ($529) each and expelled from Venice for 48 hours, marking the 1,136th such sanction to be handed down to badly behaved tourists in the city so far this year, according to the Venice City Police.
The unnamed couple took the plunge near the Accademia bridge near St. Mark’s Square and gondoliers at the Rio San Vidal kiosk immediately called authorities, who removed them from the water.
“I thank the gondoliers for their cooperation and timely reporting,” said Venice Security Councillor Elisabetta Pesce in a statement published by city authorities on Friday.
https://trip-scan.co
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“Venice must be defended from those who disrespect it: protecting the city means ensuring decorum for residents and visitors who experience it with civility.”
Swimming in the Venice canals is prohibited for a variety of reasons, including the intense boat traffic and the cleanliness — or lack thereof — of the water, according to the city’s tourism ministry.
Of the 1,136 orders of expulsion from the city so far this year, about 10 were for swimming.
Related article
Tourists take photographs on the Rialto Bridge in Venice, Italy, on Saturday, April 8, 2023. Italy's upcoming budget outlook will probably incorporate a higher growth forecast for 2023 followed by a worsened outlook for subsequent years, according to people familiar with the matter. Photographer: Andrea Merola/Bloomberg via Getty Images
Rising waters and overtourism are killing Venice. Now the fight is on to save its soul
“Since the beginning of the year, we have issued a total of 1,136 orders of expulsion for incidents of degradation and uncivilized behavior,” Venice local police deputy commander Gianni Franzoi said in a statement shared with CNN.
Poor visitor behavior is one of the worst byproducts of overtourism, Franzoi said, and incidents are on the rise.
In July 2024, an Australian man was fined and expelled for diving off the Rialto Bridge after his friends posted about it on social media.
The year before, two French tourists were fined and expelled for skinny dipping in the canal under the moonlight. In August 2022, a German man was fined and expelled for surfing in the canal.
Related article
Aerial view of the plagued ghost island of Poveglia in the Venetian lagoon
‘Haunted’ Venice island to become a locals-only haven where tourists are banned
Venice’s authorities have been trying to balance the need for visitor income with residents’ demands for a city that works for them.
Day trippers now pay a €10 entrance fee on summer weekends and during busy periods throughout the year.
The city has also banned tour groups of more than 25 people, loudspeakers and megaphones, and even standing on narrow streets to listen to tour guides.
“It was necessary to establish a system of penalties that would effectively deter potential violations,” Pesce said when the ordinance was passed in February.
“Our goal remains to combat all forms of irregularities related to overtourism in the historic lagoon city center,” she added.
“The new rules for groups accompanied by guides encourage a more sustainable form of tourism, while also ensuring greater protection and safety in the city and better balancing the needs of Venice residents and visitors.”
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Tourists fined and banned from Venice for swimming in canal
<a href=https://trip-scan.co>трипскан</a>
A couple from the United Kingdom had to cut their vacation in Venice short after being caught swimming in the Grand Canal.
The 35-year-old British man and his 25-year-old Romanian girlfriend were forced to return to their home in the UK on Thursday, the same day they arrived in the city, after gondoliers reported them to local police for taking a dip in the canal.
The pair were fined €450 ($529) each and expelled from Venice for 48 hours, marking the 1,136th such sanction to be handed down to badly behaved tourists in the city so far this year, according to the Venice City Police.
The unnamed couple took the plunge near the Accademia bridge near St. Mark’s Square and gondoliers at the Rio San Vidal kiosk immediately called authorities, who removed them from the water.
“I thank the gondoliers for their cooperation and timely reporting,” said Venice Security Councillor Elisabetta Pesce in a statement published by city authorities on Friday.
https://trip-scan.co
trip scan
“Venice must be defended from those who disrespect it: protecting the city means ensuring decorum for residents and visitors who experience it with civility.”
Swimming in the Venice canals is prohibited for a variety of reasons, including the intense boat traffic and the cleanliness — or lack thereof — of the water, according to the city’s tourism ministry.
Of the 1,136 orders of expulsion from the city so far this year, about 10 were for swimming.
Related article
Tourists take photographs on the Rialto Bridge in Venice, Italy, on Saturday, April 8, 2023. Italy's upcoming budget outlook will probably incorporate a higher growth forecast for 2023 followed by a worsened outlook for subsequent years, according to people familiar with the matter. Photographer: Andrea Merola/Bloomberg via Getty Images
Rising waters and overtourism are killing Venice. Now the fight is on to save its soul
“Since the beginning of the year, we have issued a total of 1,136 orders of expulsion for incidents of degradation and uncivilized behavior,” Venice local police deputy commander Gianni Franzoi said in a statement shared with CNN.
Poor visitor behavior is one of the worst byproducts of overtourism, Franzoi said, and incidents are on the rise.
In July 2024, an Australian man was fined and expelled for diving off the Rialto Bridge after his friends posted about it on social media.
The year before, two French tourists were fined and expelled for skinny dipping in the canal under the moonlight. In August 2022, a German man was fined and expelled for surfing in the canal.
Related article
Aerial view of the plagued ghost island of Poveglia in the Venetian lagoon
‘Haunted’ Venice island to become a locals-only haven where tourists are banned
Venice’s authorities have been trying to balance the need for visitor income with residents’ demands for a city that works for them.
Day trippers now pay a €10 entrance fee on summer weekends and during busy periods throughout the year.
The city has also banned tour groups of more than 25 people, loudspeakers and megaphones, and even standing on narrow streets to listen to tour guides.
“It was necessary to establish a system of penalties that would effectively deter potential violations,” Pesce said when the ordinance was passed in February.
“Our goal remains to combat all forms of irregularities related to overtourism in the historic lagoon city center,” she added.
“The new rules for groups accompanied by guides encourage a more sustainable form of tourism, while also ensuring greater protection and safety in the city and better balancing the needs of Venice residents and visitors.”
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Tourists fined and banned from Venice for swimming in canal
<a href=https://trip-scan.co>трипскан вход</a>
A couple from the United Kingdom had to cut their vacation in Venice short after being caught swimming in the Grand Canal.
The 35-year-old British man and his 25-year-old Romanian girlfriend were forced to return to their home in the UK on Thursday, the same day they arrived in the city, after gondoliers reported them to local police for taking a dip in the canal.
The pair were fined €450 ($529) each and expelled from Venice for 48 hours, marking the 1,136th such sanction to be handed down to badly behaved tourists in the city so far this year, according to the Venice City Police.
The unnamed couple took the plunge near the Accademia bridge near St. Mark’s Square and gondoliers at the Rio San Vidal kiosk immediately called authorities, who removed them from the water.
“I thank the gondoliers for their cooperation and timely reporting,” said Venice Security Councillor Elisabetta Pesce in a statement published by city authorities on Friday.
https://trip-scan.co
trip scan
“Venice must be defended from those who disrespect it: protecting the city means ensuring decorum for residents and visitors who experience it with civility.”
Swimming in the Venice canals is prohibited for a variety of reasons, including the intense boat traffic and the cleanliness — or lack thereof — of the water, according to the city’s tourism ministry.
Of the 1,136 orders of expulsion from the city so far this year, about 10 were for swimming.
Related article
Tourists take photographs on the Rialto Bridge in Venice, Italy, on Saturday, April 8, 2023. Italy's upcoming budget outlook will probably incorporate a higher growth forecast for 2023 followed by a worsened outlook for subsequent years, according to people familiar with the matter. Photographer: Andrea Merola/Bloomberg via Getty Images
Rising waters and overtourism are killing Venice. Now the fight is on to save its soul
“Since the beginning of the year, we have issued a total of 1,136 orders of expulsion for incidents of degradation and uncivilized behavior,” Venice local police deputy commander Gianni Franzoi said in a statement shared with CNN.
Poor visitor behavior is one of the worst byproducts of overtourism, Franzoi said, and incidents are on the rise.
In July 2024, an Australian man was fined and expelled for diving off the Rialto Bridge after his friends posted about it on social media.
The year before, two French tourists were fined and expelled for skinny dipping in the canal under the moonlight. In August 2022, a German man was fined and expelled for surfing in the canal.
Related article
Aerial view of the plagued ghost island of Poveglia in the Venetian lagoon
‘Haunted’ Venice island to become a locals-only haven where tourists are banned
Venice’s authorities have been trying to balance the need for visitor income with residents’ demands for a city that works for them.
Day trippers now pay a €10 entrance fee on summer weekends and during busy periods throughout the year.
The city has also banned tour groups of more than 25 people, loudspeakers and megaphones, and even standing on narrow streets to listen to tour guides.
“It was necessary to establish a system of penalties that would effectively deter potential violations,” Pesce said when the ordinance was passed in February.
“Our goal remains to combat all forms of irregularities related to overtourism in the historic lagoon city center,” she added.
“The new rules for groups accompanied by guides encourage a more sustainable form of tourism, while also ensuring greater protection and safety in the city and better balancing the needs of Venice residents and visitors.”
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Tourists fined and banned from Venice for swimming in canal
<a href=https://trip-scan.co>трипскан сайт</a>
A couple from the United Kingdom had to cut their vacation in Venice short after being caught swimming in the Grand Canal.
The 35-year-old British man and his 25-year-old Romanian girlfriend were forced to return to their home in the UK on Thursday, the same day they arrived in the city, after gondoliers reported them to local police for taking a dip in the canal.
The pair were fined €450 ($529) each and expelled from Venice for 48 hours, marking the 1,136th such sanction to be handed down to badly behaved tourists in the city so far this year, according to the Venice City Police.
The unnamed couple took the plunge near the Accademia bridge near St. Mark’s Square and gondoliers at the Rio San Vidal kiosk immediately called authorities, who removed them from the water.
“I thank the gondoliers for their cooperation and timely reporting,” said Venice Security Councillor Elisabetta Pesce in a statement published by city authorities on Friday.
https://trip-scan.co
tripskan
“Venice must be defended from those who disrespect it: protecting the city means ensuring decorum for residents and visitors who experience it with civility.”
Swimming in the Venice canals is prohibited for a variety of reasons, including the intense boat traffic and the cleanliness — or lack thereof — of the water, according to the city’s tourism ministry.
Of the 1,136 orders of expulsion from the city so far this year, about 10 were for swimming.
Related article
Tourists take photographs on the Rialto Bridge in Venice, Italy, on Saturday, April 8, 2023. Italy's upcoming budget outlook will probably incorporate a higher growth forecast for 2023 followed by a worsened outlook for subsequent years, according to people familiar with the matter. Photographer: Andrea Merola/Bloomberg via Getty Images
Rising waters and overtourism are killing Venice. Now the fight is on to save its soul
“Since the beginning of the year, we have issued a total of 1,136 orders of expulsion for incidents of degradation and uncivilized behavior,” Venice local police deputy commander Gianni Franzoi said in a statement shared with CNN.
Poor visitor behavior is one of the worst byproducts of overtourism, Franzoi said, and incidents are on the rise.
In July 2024, an Australian man was fined and expelled for diving off the Rialto Bridge after his friends posted about it on social media.
The year before, two French tourists were fined and expelled for skinny dipping in the canal under the moonlight. In August 2022, a German man was fined and expelled for surfing in the canal.
Related article
Aerial view of the plagued ghost island of Poveglia in the Venetian lagoon
‘Haunted’ Venice island to become a locals-only haven where tourists are banned
Venice’s authorities have been trying to balance the need for visitor income with residents’ demands for a city that works for them.
Day trippers now pay a €10 entrance fee on summer weekends and during busy periods throughout the year.
The city has also banned tour groups of more than 25 people, loudspeakers and megaphones, and even standing on narrow streets to listen to tour guides.
“It was necessary to establish a system of penalties that would effectively deter potential violations,” Pesce said when the ordinance was passed in February.
“Our goal remains to combat all forms of irregularities related to overtourism in the historic lagoon city center,” she added.
“The new rules for groups accompanied by guides encourage a more sustainable form of tourism, while also ensuring greater protection and safety in the city and better balancing the needs of Venice residents and visitors.”
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Permalien
трипскан сайт
Tourists fined and banned from Venice for swimming in canal
<a href=https://trip-scan.co>трипскан сайт</a>
A couple from the United Kingdom had to cut their vacation in Venice short after being caught swimming in the Grand Canal.
The 35-year-old British man and his 25-year-old Romanian girlfriend were forced to return to their home in the UK on Thursday, the same day they arrived in the city, after gondoliers reported them to local police for taking a dip in the canal.
The pair were fined €450 ($529) each and expelled from Venice for 48 hours, marking the 1,136th such sanction to be handed down to badly behaved tourists in the city so far this year, according to the Venice City Police.
The unnamed couple took the plunge near the Accademia bridge near St. Mark’s Square and gondoliers at the Rio San Vidal kiosk immediately called authorities, who removed them from the water.
“I thank the gondoliers for their cooperation and timely reporting,” said Venice Security Councillor Elisabetta Pesce in a statement published by city authorities on Friday.
https://trip-scan.co
tripskan
“Venice must be defended from those who disrespect it: protecting the city means ensuring decorum for residents and visitors who experience it with civility.”
Swimming in the Venice canals is prohibited for a variety of reasons, including the intense boat traffic and the cleanliness — or lack thereof — of the water, according to the city’s tourism ministry.
Of the 1,136 orders of expulsion from the city so far this year, about 10 were for swimming.
Related article
Tourists take photographs on the Rialto Bridge in Venice, Italy, on Saturday, April 8, 2023. Italy's upcoming budget outlook will probably incorporate a higher growth forecast for 2023 followed by a worsened outlook for subsequent years, according to people familiar with the matter. Photographer: Andrea Merola/Bloomberg via Getty Images
Rising waters and overtourism are killing Venice. Now the fight is on to save its soul
“Since the beginning of the year, we have issued a total of 1,136 orders of expulsion for incidents of degradation and uncivilized behavior,” Venice local police deputy commander Gianni Franzoi said in a statement shared with CNN.
Poor visitor behavior is one of the worst byproducts of overtourism, Franzoi said, and incidents are on the rise.
In July 2024, an Australian man was fined and expelled for diving off the Rialto Bridge after his friends posted about it on social media.
The year before, two French tourists were fined and expelled for skinny dipping in the canal under the moonlight. In August 2022, a German man was fined and expelled for surfing in the canal.
Related article
Aerial view of the plagued ghost island of Poveglia in the Venetian lagoon
‘Haunted’ Venice island to become a locals-only haven where tourists are banned
Venice’s authorities have been trying to balance the need for visitor income with residents’ demands for a city that works for them.
Day trippers now pay a €10 entrance fee on summer weekends and during busy periods throughout the year.
The city has also banned tour groups of more than 25 people, loudspeakers and megaphones, and even standing on narrow streets to listen to tour guides.
“It was necessary to establish a system of penalties that would effectively deter potential violations,” Pesce said when the ordinance was passed in February.
“Our goal remains to combat all forms of irregularities related to overtourism in the historic lagoon city center,” she added.
“The new rules for groups accompanied by guides encourage a more sustainable form of tourism, while also ensuring greater protection and safety in the city and better balancing the needs of Venice residents and visitors.”
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трипскан
Tourists fined and banned from Venice for swimming in canal
<a href=https://trip-scan.co>tripskan</a>
A couple from the United Kingdom had to cut their vacation in Venice short after being caught swimming in the Grand Canal.
The 35-year-old British man and his 25-year-old Romanian girlfriend were forced to return to their home in the UK on Thursday, the same day they arrived in the city, after gondoliers reported them to local police for taking a dip in the canal.
The pair were fined €450 ($529) each and expelled from Venice for 48 hours, marking the 1,136th such sanction to be handed down to badly behaved tourists in the city so far this year, according to the Venice City Police.
The unnamed couple took the plunge near the Accademia bridge near St. Mark’s Square and gondoliers at the Rio San Vidal kiosk immediately called authorities, who removed them from the water.
“I thank the gondoliers for their cooperation and timely reporting,” said Venice Security Councillor Elisabetta Pesce in a statement published by city authorities on Friday.
https://trip-scan.co
трипскан
“Venice must be defended from those who disrespect it: protecting the city means ensuring decorum for residents and visitors who experience it with civility.”
Swimming in the Venice canals is prohibited for a variety of reasons, including the intense boat traffic and the cleanliness — or lack thereof — of the water, according to the city’s tourism ministry.
Of the 1,136 orders of expulsion from the city so far this year, about 10 were for swimming.
Related article
Tourists take photographs on the Rialto Bridge in Venice, Italy, on Saturday, April 8, 2023. Italy's upcoming budget outlook will probably incorporate a higher growth forecast for 2023 followed by a worsened outlook for subsequent years, according to people familiar with the matter. Photographer: Andrea Merola/Bloomberg via Getty Images
Rising waters and overtourism are killing Venice. Now the fight is on to save its soul
“Since the beginning of the year, we have issued a total of 1,136 orders of expulsion for incidents of degradation and uncivilized behavior,” Venice local police deputy commander Gianni Franzoi said in a statement shared with CNN.
Poor visitor behavior is one of the worst byproducts of overtourism, Franzoi said, and incidents are on the rise.
In July 2024, an Australian man was fined and expelled for diving off the Rialto Bridge after his friends posted about it on social media.
The year before, two French tourists were fined and expelled for skinny dipping in the canal under the moonlight. In August 2022, a German man was fined and expelled for surfing in the canal.
Related article
Aerial view of the plagued ghost island of Poveglia in the Venetian lagoon
‘Haunted’ Venice island to become a locals-only haven where tourists are banned
Venice’s authorities have been trying to balance the need for visitor income with residents’ demands for a city that works for them.
Day trippers now pay a €10 entrance fee on summer weekends and during busy periods throughout the year.
The city has also banned tour groups of more than 25 people, loudspeakers and megaphones, and even standing on narrow streets to listen to tour guides.
“It was necessary to establish a system of penalties that would effectively deter potential violations,” Pesce said when the ordinance was passed in February.
“Our goal remains to combat all forms of irregularities related to overtourism in the historic lagoon city center,” she added.
“The new rules for groups accompanied by guides encourage a more sustainable form of tourism, while also ensuring greater protection and safety in the city and better balancing the needs of Venice residents and visitors.”
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трипскан вход
Tourists fined and banned from Venice for swimming in canal
<a href=https://trip-scan.co>tripscan top</a>
A couple from the United Kingdom had to cut their vacation in Venice short after being caught swimming in the Grand Canal.
The 35-year-old British man and his 25-year-old Romanian girlfriend were forced to return to their home in the UK on Thursday, the same day they arrived in the city, after gondoliers reported them to local police for taking a dip in the canal.
The pair were fined €450 ($529) each and expelled from Venice for 48 hours, marking the 1,136th such sanction to be handed down to badly behaved tourists in the city so far this year, according to the Venice City Police.
The unnamed couple took the plunge near the Accademia bridge near St. Mark’s Square and gondoliers at the Rio San Vidal kiosk immediately called authorities, who removed them from the water.
“I thank the gondoliers for their cooperation and timely reporting,” said Venice Security Councillor Elisabetta Pesce in a statement published by city authorities on Friday.
https://trip-scan.co
tripscan
“Venice must be defended from those who disrespect it: protecting the city means ensuring decorum for residents and visitors who experience it with civility.”
Swimming in the Venice canals is prohibited for a variety of reasons, including the intense boat traffic and the cleanliness — or lack thereof — of the water, according to the city’s tourism ministry.
Of the 1,136 orders of expulsion from the city so far this year, about 10 were for swimming.
Related article
Tourists take photographs on the Rialto Bridge in Venice, Italy, on Saturday, April 8, 2023. Italy's upcoming budget outlook will probably incorporate a higher growth forecast for 2023 followed by a worsened outlook for subsequent years, according to people familiar with the matter. Photographer: Andrea Merola/Bloomberg via Getty Images
Rising waters and overtourism are killing Venice. Now the fight is on to save its soul
“Since the beginning of the year, we have issued a total of 1,136 orders of expulsion for incidents of degradation and uncivilized behavior,” Venice local police deputy commander Gianni Franzoi said in a statement shared with CNN.
Poor visitor behavior is one of the worst byproducts of overtourism, Franzoi said, and incidents are on the rise.
In July 2024, an Australian man was fined and expelled for diving off the Rialto Bridge after his friends posted about it on social media.
The year before, two French tourists were fined and expelled for skinny dipping in the canal under the moonlight. In August 2022, a German man was fined and expelled for surfing in the canal.
Related article
Aerial view of the plagued ghost island of Poveglia in the Venetian lagoon
‘Haunted’ Venice island to become a locals-only haven where tourists are banned
Venice’s authorities have been trying to balance the need for visitor income with residents’ demands for a city that works for them.
Day trippers now pay a €10 entrance fee on summer weekends and during busy periods throughout the year.
The city has also banned tour groups of more than 25 people, loudspeakers and megaphones, and even standing on narrow streets to listen to tour guides.
“It was necessary to establish a system of penalties that would effectively deter potential violations,” Pesce said when the ordinance was passed in February.
“Our goal remains to combat all forms of irregularities related to overtourism in the historic lagoon city center,” she added.
“The new rules for groups accompanied by guides encourage a more sustainable form of tourism, while also ensuring greater protection and safety in the city and better balancing the needs of Venice residents and visitors.”
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tripscan
Tourists fined and banned from Venice for swimming in canal
<a href=https://trip-scan.co>трипскан вход</a>
A couple from the United Kingdom had to cut their vacation in Venice short after being caught swimming in the Grand Canal.
The 35-year-old British man and his 25-year-old Romanian girlfriend were forced to return to their home in the UK on Thursday, the same day they arrived in the city, after gondoliers reported them to local police for taking a dip in the canal.
The pair were fined €450 ($529) each and expelled from Venice for 48 hours, marking the 1,136th such sanction to be handed down to badly behaved tourists in the city so far this year, according to the Venice City Police.
The unnamed couple took the plunge near the Accademia bridge near St. Mark’s Square and gondoliers at the Rio San Vidal kiosk immediately called authorities, who removed them from the water.
“I thank the gondoliers for their cooperation and timely reporting,” said Venice Security Councillor Elisabetta Pesce in a statement published by city authorities on Friday.
https://trip-scan.co
трип скан
“Venice must be defended from those who disrespect it: protecting the city means ensuring decorum for residents and visitors who experience it with civility.”
Swimming in the Venice canals is prohibited for a variety of reasons, including the intense boat traffic and the cleanliness — or lack thereof — of the water, according to the city’s tourism ministry.
Of the 1,136 orders of expulsion from the city so far this year, about 10 were for swimming.
Related article
Tourists take photographs on the Rialto Bridge in Venice, Italy, on Saturday, April 8, 2023. Italy's upcoming budget outlook will probably incorporate a higher growth forecast for 2023 followed by a worsened outlook for subsequent years, according to people familiar with the matter. Photographer: Andrea Merola/Bloomberg via Getty Images
Rising waters and overtourism are killing Venice. Now the fight is on to save its soul
“Since the beginning of the year, we have issued a total of 1,136 orders of expulsion for incidents of degradation and uncivilized behavior,” Venice local police deputy commander Gianni Franzoi said in a statement shared with CNN.
Poor visitor behavior is one of the worst byproducts of overtourism, Franzoi said, and incidents are on the rise.
In July 2024, an Australian man was fined and expelled for diving off the Rialto Bridge after his friends posted about it on social media.
The year before, two French tourists were fined and expelled for skinny dipping in the canal under the moonlight. In August 2022, a German man was fined and expelled for surfing in the canal.
Related article
Aerial view of the plagued ghost island of Poveglia in the Venetian lagoon
‘Haunted’ Venice island to become a locals-only haven where tourists are banned
Venice’s authorities have been trying to balance the need for visitor income with residents’ demands for a city that works for them.
Day trippers now pay a €10 entrance fee on summer weekends and during busy periods throughout the year.
The city has also banned tour groups of more than 25 people, loudspeakers and megaphones, and even standing on narrow streets to listen to tour guides.
“It was necessary to establish a system of penalties that would effectively deter potential violations,” Pesce said when the ordinance was passed in February.
“Our goal remains to combat all forms of irregularities related to overtourism in the historic lagoon city center,” she added.
“The new rules for groups accompanied by guides encourage a more sustainable form of tourism, while also ensuring greater protection and safety in the city and better balancing the needs of Venice residents and visitors.”
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Выбор качественного металлического проката требует внимания к ряду параметров. В этой статье изложены основные критерии, которые помогут сделать правильный подбор при покупке прокатных изделий.
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Выбор качественного профилированного проката требует внимания к
Выбор качественного металлического проката требует внимания к ряду параметров. В этой статье изложены основные критерии, которые помогут сделать правильный подбор при покупке листового и профильного проката.
Качество материала
- Марка стали сталь и легирующие элементы — уточняйте нормативное обозначение (например, Ст3, 09Г2С, 12Х18Н10Т). Разные сорта подходят для разных задач.
- Сертификаты и бумажное подтверждение — требуйте сертификат качества (свидетельство о соответствии, сертификат испытаний).
- Химический состав и механические свойства — важны показатели прочности, пластичности, твердости и коррозионной стойкости.785412
Геометрические характеристики
- Точность размеров и допуски — для конструкционных узлов важна стабильная геометрия.
- Поверхность и состояние поверхности — отсутствие трещин, пор и ржавчины увеличивает срок службы.
- Форма изделия и профиль — квадратный, круглый, швеллер, уголок, лист — выбирайте по назначению.
Механические свойства
- Предел текучести и сопротивление разрушению — критично для несущих элементов.
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Условия эксплуатации
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- Гарантии и сервис — важно наличие технической поддержки.
- Логистика и сроки исполнения — уточняйте возможность срочных поставок и условия хранения.
Цена и экономическая целесообразность
- Стоимость и соотношение цена-качество — не всегда дорогой прокат оправдан.
- Общие затраты и эксплуатационные расходы — учитывайте не только цену за тонну, но и расходы на обработку и обслуживание.
- Скидки и льготные цены — для крупных заказов оговаривайте выгодные условия.
Контроль качества и приемка
- Методы контроля и проверочные процедуры — ультразвук, рентген, механические испытания.
- Визуальный контроль и инспекция — для подтверждения соответствия чертежам и спецификациям.
- Документальная приемка и акт приемки — сохраняйте все бумаги для гарантийных случаев.
Заключение
Правильный выбор металлопроката основывается на сочетании марки материала, механических свойств, геометрии, условий эксплуатации и надежности поставщика. Требуйте сертификаты и техпаспорт, проверяйте качество и сопоставляйте цены с реальной эксплуатационной выгодой.
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ven, 09/19/2025 - 02:01
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Tourists fined and banned from Venice for swimming in canal
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A couple from the United Kingdom had to cut their vacation in Venice short after being caught swimming in the Grand Canal.
The 35-year-old British man and his 25-year-old Romanian girlfriend were forced to return to their home in the UK on Thursday, the same day they arrived in the city, after gondoliers reported them to local police for taking a dip in the canal.
The pair were fined €450 ($529) each and expelled from Venice for 48 hours, marking the 1,136th such sanction to be handed down to badly behaved tourists in the city so far this year, according to the Venice City Police.
The unnamed couple took the plunge near the Accademia bridge near St. Mark’s Square and gondoliers at the Rio San Vidal kiosk immediately called authorities, who removed them from the water.
“I thank the gondoliers for their cooperation and timely reporting,” said Venice Security Councillor Elisabetta Pesce in a statement published by city authorities on Friday.
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“Venice must be defended from those who disrespect it: protecting the city means ensuring decorum for residents and visitors who experience it with civility.”
Swimming in the Venice canals is prohibited for a variety of reasons, including the intense boat traffic and the cleanliness — or lack thereof — of the water, according to the city’s tourism ministry.
Of the 1,136 orders of expulsion from the city so far this year, about 10 were for swimming.
Related article
Tourists take photographs on the Rialto Bridge in Venice, Italy, on Saturday, April 8, 2023. Italy's upcoming budget outlook will probably incorporate a higher growth forecast for 2023 followed by a worsened outlook for subsequent years, according to people familiar with the matter. Photographer: Andrea Merola/Bloomberg via Getty Images
Rising waters and overtourism are killing Venice. Now the fight is on to save its soul
“Since the beginning of the year, we have issued a total of 1,136 orders of expulsion for incidents of degradation and uncivilized behavior,” Venice local police deputy commander Gianni Franzoi said in a statement shared with CNN.
Poor visitor behavior is one of the worst byproducts of overtourism, Franzoi said, and incidents are on the rise.
In July 2024, an Australian man was fined and expelled for diving off the Rialto Bridge after his friends posted about it on social media.
The year before, two French tourists were fined and expelled for skinny dipping in the canal under the moonlight. In August 2022, a German man was fined and expelled for surfing in the canal.
Related article
Aerial view of the plagued ghost island of Poveglia in the Venetian lagoon
‘Haunted’ Venice island to become a locals-only haven where tourists are banned
Venice’s authorities have been trying to balance the need for visitor income with residents’ demands for a city that works for them.
Day trippers now pay a €10 entrance fee on summer weekends and during busy periods throughout the year.
The city has also banned tour groups of more than 25 people, loudspeakers and megaphones, and even standing on narrow streets to listen to tour guides.
“It was necessary to establish a system of penalties that would effectively deter potential violations,” Pesce said when the ordinance was passed in February.
“Our goal remains to combat all forms of irregularities related to overtourism in the historic lagoon city center,” she added.
“The new rules for groups accompanied by guides encourage a more sustainable form of tourism, while also ensuring greater protection and safety in the city and better balancing the needs of Venice residents and visitors.”
Simcealk (non vérifié)
ven, 09/19/2025 - 02:58
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