Olympiades ENSAE - 1er S 2025

  • Posted on: 8 May 2025
  • By: sbana

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.

 

 

Niveau: 
Classe: 
Type: 
Série: 

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A bit random, but really cool for kitchen lovers

Just while browsing storage solutions I found a site https://kitchen-tips.chtonamstoit.site/.

It’s full of tools, guides, and little tricks that really work.

Some sections I liked most:
- Small kitchen organization

Also here’s <a href=https://kitchen-tips.chtonamstoit.site>this kitchen hacks hub</a> — definitely worth exploring!

What habits make your kitchen work better?

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1.
Хотите всегда иметь под рукой чистую питьевую воду? У нас — доставка воды в СПб в любое удобное время! Предлагаем заказ воды в бутылках 19 литров, быстро привозим как на дом, так и в офис. Свежесть и качество гарантированы!
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Quick share — this site is a gem

Just while checking ideas for small kitchens I came across a site https://kitchen-tips.chtonamstoit.site/.

It’s full of everything from fridge tips to spice storage.

Some sections I liked most:
- Storing spices and grains

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What else would you recommend about food storage?

Extreme heat is a killer. A recent heat wave shows how much more deadly it’s becoming
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Extreme heat is a killer and its impact is becoming far, far deadlier as the human-caused climate crisis supercharges temperatures, according to a new study, which estimates global warming tripled the number of deaths in the recent European heat wave.

For more than a week, temperatures in many parts of Europe spiked above 100 degrees Fahrenheit. Tourist attractions closed, wildfires ripped through several countries, and people struggled to cope on a continent where air conditioning is rare.
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трипскан
The outcome was deadly. Thousands of people are estimated to have lost their lives, according to a first-of-its-kind rapid analysis study published Wednesday.

A team of researchers, led by Imperial College London and the London School of Hygiene and Tropical Medicine, looked at 10 days of extreme heat between June 23 and July 2 across 12 European cities, including London, Paris, Athens, Madrid and Rome.

They used historical weather data to calculate how intense the heat would have been if humans had not burned fossil fuels and warmed the world by 1.3 degrees Celsius. They found climate change made Europe’s heat wave 1 to 4 degrees Celsius (1.8 to 7.2 Fahrenheit) hotter.

The scientists then used research on the relationship between heat and daily deaths to estimate how many people lost their lives.

They found approximately 2,300 people died during ten days of heat across the 12 cities, around 1,500 more than would have died in a world without climate change. In other words, global heating was responsible for 65% of the total death toll.

“The results show how relatively small increases in the hottest temperatures can trigger huge surges in death,” the study authors wrote.

Heat has a particularly pernicious impact on people with underlying health conditions, such as heart disease, diabetes and respiratory problems.

People over 65 years old were most affected, accounting for 88% of the excess deaths, according to the analysis. But heat can be deadly for anyone. Nearly 200 of the estimated deaths across the 12 cities were among those aged 20 to 65.

Climate change was responsible for the vast majority of heat deaths in some cities. In Madrid, it accounted for about 90% of estimated heat wave deaths, the analysis found.

The study’s focus on 12 cities makes it just a snapshot of the true heat wave death toll across the continent, which researchers estimate could be up to tens of thousands of people.
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“Heatwaves don’t leave a trail of destruction like wildfires or storms,” said Ben Clarke, a study author and a researcher at Imperial College London. “Their impacts are mostly invisible but quietly devastating — a change of just 2 or 3 degrees Celsius can mean the difference between life and death for thousands of people.”
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The world must stop burning fossil fuels to stop heat waves becoming hotter and deadlier and cities need to urgently adapt, said Friederike Otto, a climate scientist at Imperial College London. “Shifting to renewable energy, building cities that can withstand extreme heat, and protecting the poorest and most vulnerable is absolutely essential,” she said.

Akshay Deoras, a research scientist at the University of Reading who was not involved in the analysis, said “robust techniques used in this study leave no doubt that climate change is already a deadly force in Europe.”

Richard Allan, a professor of climate science at the University of Reading who was also not involved in the report, said the study added to huge amounts of evidence that climate change is making heat waves more intense, “meaning that moderate heat becomes dangerous and record heat becomes unprecedented.”

It’s not just heat that’s being supercharged in out hotter world, Allan added. “As one part of the globe bakes and burns, another region can suffer intense rainfall and catastrophic flooding.”

‘Hire back park staff’: Visitors feel the pinch of Trump’s layoffs at National Park Service
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The visitors who trek to America’s national parks are already noticing the changes, just months after President Donald Trump took office.

“I’ve been visiting national parks for 30 years and never has the presence of rangers been so absent,” one visitor to Zion National Park wrote in National Park Service public feedback obtained by CNN.

The visitor said they saw just one trail crew at the iconic Utah park. There were no educational programs offered at any of the five parks they visited on their trip.
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“Hire back park staff. We need them,” the visitor wrote.

At Yosemite, another visitor said there were no rangers at the Hetch Hetchy reservoir entrance station, preventing visitors from picking up wilderness permits.

“More staff would be a BIG and IMPORTANT improvement,” that visitor wrote.
America’s most treasured national parks are getting crunched by Trump’s government-shrinking layoffs just as the summer travel season gets into full swing.
Top officials vowed to hire thousands of seasonal employees to pick up the slack after the Trump administration fired around 1,000 NPS employees as part of wide-ranging federal firings known as the “Valentine’s Day Massacre.” Department of Interior officials said in a February memo they would aim to hire 7,700 seasonal workers at NPS, and post listings for 9,000 jobs.

But those numbers haven’t materialized ahead July 4th — the parks’ busiest time of the year. Internal National Park Service data provided to CNN by the National Parks Conservation Association shows that about 4,500 seasonal and temporary staff have been hired.

Santa Fe, New Mexico
AP — At least three people were missing in a mountain village in southern New Mexico that is a popular summer retreat after monsoon rains triggered flash flooding Tuesday that was so intense an entire house was swept downstream.
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Emergency crews carried out at least 85 swift water rescues in the Ruidoso area, including of people who were trapped in their homes and cars, said Danielle Silva of the New Mexico Department of Homeland Security and Emergency Management.

No deaths were immediately reported, but Silva said the extent of the destruction wouldn’t be known until the water recedes.
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“We knew that we were going to have floods … and this one hit us harder than what we were expecting,” Ruidoso Mayor Lynn D. Crawford said during a radio address Tuesday night.

Crawford said that some people were taken to the hospital, although the exact number was not immediately clear. He encouraged residents to call an emergency line if their loved ones or neighbors were missing.
The floods came just days after flash floods in Texas killed over 100 people and left more than 160 people missing.

In New Mexico, officials urged residents to seek higher ground Tuesday afternoon as the waters of the Rio Ruidoso rose nearly 19 feet in a matter of minutes amid heavy rainfall. The National Weather Service issued flood warnings in the area, which was stripped of vegetation by recent wildfires.

A weather service flood gauge and companion video camera showed churning waters of the Rio Ruidoso surge over the river’s banks into surrounding forest. Streets and bridges were closed in response.

Kaitlyn Carpenter, an artist in Ruidoso, was riding her motorcycle through town Tuesday afternoon when the storm started to pick up, and she sought shelter at the riverside Downshift Brewing Company with about 50 other people. She started to film debris rushing down the Rio Ruidoso when she spotted a house float by with a familiar turquoise door. It belonged to the family of one of her best friends.

Her friend’s family was not in the house and is safe, she said.

“I’ve been in that house and have memories in that house, so seeing it come down the river was just pretty heartbreaking,” Carpenter said. “I just couldn’t believe it.”

There were also reports of dead horses near the town’s horse racing track, the mayor said.

Two National Guard rescue teams and several local teams already were in the area when the flooding began, Silva said, and more Guard teams were expected.

The area has been especially vulnerable to flooding since the summer of 2024, when the South Fork and Salt fires raced across tinder-dry forest and destroyed an estimated 1,400 homes and structures. Residents were forced to flee a wall of flames, only to grapple with intense flooding later that summer.

More than 200 firefighters are struggling to tackle an out-of-control wildfire on Crete — Greece’s largest island and a tourist hotspot — as authorities order mass evacuations.
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The fire broke out Wednesday afternoon near Ierapetra, a town on the island’s southeast coast, amid unusually high temperatures, 3 to 5 degrees Celsius (5.4 to 9 Fahrenheit) above average, and gale-force winds of around 50 miles an hour.

The conditions are creating “new outbreaks, making firefighting work very difficult,” the Fire Department’s press spokesperson, Chief Vasilios Vathrakoyannis, said in a statement Thursday.
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трипскан сайт
More than 230 firefighters, along with 46 vehicles and 10 helicopters have been deployed to fight the blaze, according to fire officials.

The flames have spread rapidly, reaching homes as well as hotels and other tourist accommodations.

Authorities asked residents of four settlements to evacuate and move toward Ierapetra. About 1,500 people have been evacuated so far, according to the Greek public broadcaster ERT.

The Ierapetra municipality has converted an indoor training center facility into a makeshift camp, where hundreds of tourists and residents who abandoned their homes spent the night Wednesday.
The police, medical services and the coast guard have all been called to the area.

“We are entering the third and most difficult month of the fire season,” Vathrakoyannis said. July is typically the hottest month in Greece and is often accompanied by strong winds. “These conditions favor the spread of fires and increase their danger,” he said.
Wildfires have ripped through other European countries this week as the continent endures a brutal heat wave.

Tens of thousands were evacuated in Turkey as blazes ripped through the western Izmir and Manisa provinces and southern Hatay province, damaging nearly 200 homes.

Blazes also broke out in France and in Spain, where two people died.

Europe experiences wildfires every year, but they are becoming more intense and frequent due to human-caused climate change, which fuels heat and drought, both helping set the stage for fierce, destructive fires.

High costs are still a big barrier to prospective customers, said Alan Gibson, principal at Maine-based builder GO Logic, where a shell for an ultra-efficient, two-story, 1,400 square foot home with three bedrooms can cost around $600,000.
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Homeowners also need to factor in additional costs, like buying and developing a suitable plot of land, and in some cases, getting access to water, electricity and septic, Gibson added.
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трипскан вход
The way to bring down costs, Gibson believes, is more panelized, multi-family housing.

“It can be done so much more efficiently,” Gibson said, “and there’s a lot more repetition” for the developer, making the process faster and less expensive than custom multi-family builds.
Goodson, the homeowner in Maine, was able to save big money with his engineering background and penchant for DIY. He installed a rooftop solar system and electrical improvements himself, saving hundreds of thousands of dollars in the process. He wound up spending around $500,000 in all, which he estimates was $200,000 less than he otherwise would have.
“It’s a big number to swallow, I’m not making light of that at all, but it’s not that far out of what’s reasonable,” Goodson told CNN. It’s also not considering the long-term savings he will experience with no utility bills.

He was also able to take advantage of federal tax credits that reduced the cost of his rooftop solar, which saved him more than $10,000 on his panels. Those tax credits are now endangered with House Republicans’ tax bill.

“That was huge,” he said. “It’s fairly unfortunate they’re looking at doing away with it.”

The latest Barbie slays in a chic blue polka-dot crop top, ruffled miniskirt, chunky heels and an insulin pump. She is the brand’s first doll with type 1 diabetes.
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Dollmaker Mattel worked with Breakthrough T1D, formerly known the Juvenile Diabetes Research Foundation, to design the doll, which aims to represent the roughly 304,000 kids and teens living with type 1 diabetes in the United States.
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The doll launched Tuesday at the Breakthrough T1D Children’s Congress, a three-day event in Washington that brings in kids and teens living with the condition to meet with lawmakers. This year, they’re asking Congress to renew funding for the Special Diabetes Program, which was first allocated by Congress in 1997. The program’s current funding ends after September.

The advocacy efforts have taken on new urgency this year. With so many deep cuts to federally funded projects in recent months, Breakthrough T1D said it’s anxiously watching to see if this funding will be reupped.

Type 1 diabetes is an autoimmune disease, meaning the body mistakenly attacks its own organs and tissues. In this case, rough antibodies go after cells in the pancreas that make insulin, an essential hormone that helps the body turn food into energy. As a result, the body doesn’t make enough of its own insulin, so people have to take insulin by injection or though a pump to survive.

Type 1 diabetes is typically diagnosed in childhood but can be diagnosed in anyone at any age. It differs from type 2 diabetes, in which people are still able to make insulin but their cells stop responding to it.

In addition to the insulin pump that attaches to the new Barbie’s waist, the chestnut-haired beauty has a continuous glucose monitor on her arm – a button held on by a strip of heart-shaped Barbie-pink tape. Her cell phone displays an app that shows her glucose readings. She also has a light blue purse to hold her supplies and snacks to help her manage her blood sugar throughout the day. It matches her shoes, of course.

The levies are also likely to reduce America’s economic output, as has happened before. A 2020 study, based on data from 151 countries, including the US, between 1963-2014, found that tariffs have “persistent adverse effects on the size of the pie,” or the gross domestic product of the country imposing them.
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There are a number of possible explanations for this.

One is that, when tariffs are low or non-existent, the country in question can focus on the kind of economic activities where it has an edge and export those goods and services, Gimber told CNN.
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“If you raise tariffs, you’re not going to see that same level of specialization,” he said, noting that the result would be lower labor productivity. “The labor could be better used elsewhere in the economy, in areas where you have a greater competitive advantage.”
Another reason output falls when tariffs are raised lies in the higher cost of imported inputs, wrote the authors of the 2020 study, most of them International Monetary Fund economists.

Fatas at INSEAD suggested the same reason, providing an example: “So I’m a worker and work in a factory. To produce what we produce we need to import microchips from Taiwan. Those things are more expensive. Together, me and the company, we create less value per hour worked.”

Yet another way tariff hikes can hurt the economy is by disrupting the status quo and fueling uncertainty over the future levels of import taxes. That lack of clarity is particularly acute this year, given the erratic nature of Trump’s trade policy.

Surveys by the National Federation of Independent Business in the US suggest the uncertainty is already weighing on American companies’ willingness to invest. The share of small businesses planning a capital outlay within the next six months hit its lowest level in April since at least April 2020, when Covid was sweeping the globe.

“The economy will continue to stumble along until the major sources of uncertainty (including over tariffs) are resolved. It’s hard to steer a ship in the fog,” the federation said.

Whichever forces may be at work, the IMF, to cite just one example, thinks higher US tariffs will lower the country’s productivity and output.

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Rescuers are hailing as a “four-legged hero” a furry Chihuahua whose pacing atop an Alpine rock helped a helicopter crew find its owner, who had fallen into a crevasse on a Swiss glacier nearby.
<a href=https://tripscan.biz>трипскан вход</a>
The man, who was not identified, was exploring the Fee Glacier in southern Switzerland on Friday when he broke through a snow bridge and fell nearly 8 meters (about 26 feet), according to Air Zermatt, a rescue, training and transport company.

Equipped with a walkie-talkie, the man connected with a person nearby who relayed the accident to emergency services. But the exact location was unknown. After about a half-hour search, the pacing pooch caught the eye of a rescue team member.
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tripscan top
As the crew zeroed on the Chihuahua, the hole the man fell into became more visible. Rescuers rappelled down, rescued the man and flew him and his canine companion to a hospital.

“Imagine if the dog wasn’t there,” Air Zermatt spokesman Bruno Kalbermatten said by phone. “I have no idea what would happen to this guy. I think he wouldn’t survive this fall into the crevasse.”

On its website, the company was effusive: “The dog is a four-legged hero who may have saved his master’s life in a life-threatening situation.”

Extreme heat is a killer. A recent heat wave shows how much more deadly it’s becoming
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Extreme heat is a killer and its impact is becoming far, far deadlier as the human-caused climate crisis supercharges temperatures, according to a new study, which estimates global warming tripled the number of deaths in the recent European heat wave.

For more than a week, temperatures in many parts of Europe spiked above 100 degrees Fahrenheit. Tourist attractions closed, wildfires ripped through several countries, and people struggled to cope on a continent where air conditioning is rare.
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The outcome was deadly. Thousands of people are estimated to have lost their lives, according to a first-of-its-kind rapid analysis study published Wednesday.

A team of researchers, led by Imperial College London and the London School of Hygiene and Tropical Medicine, looked at 10 days of extreme heat between June 23 and July 2 across 12 European cities, including London, Paris, Athens, Madrid and Rome.

They used historical weather data to calculate how intense the heat would have been if humans had not burned fossil fuels and warmed the world by 1.3 degrees Celsius. They found climate change made Europe’s heat wave 1 to 4 degrees Celsius (1.8 to 7.2 Fahrenheit) hotter.

The scientists then used research on the relationship between heat and daily deaths to estimate how many people lost their lives.

They found approximately 2,300 people died during ten days of heat across the 12 cities, around 1,500 more than would have died in a world without climate change. In other words, global heating was responsible for 65% of the total death toll.

“The results show how relatively small increases in the hottest temperatures can trigger huge surges in death,” the study authors wrote.

Heat has a particularly pernicious impact on people with underlying health conditions, such as heart disease, diabetes and respiratory problems.

People over 65 years old were most affected, accounting for 88% of the excess deaths, according to the analysis. But heat can be deadly for anyone. Nearly 200 of the estimated deaths across the 12 cities were among those aged 20 to 65.

Climate change was responsible for the vast majority of heat deaths in some cities. In Madrid, it accounted for about 90% of estimated heat wave deaths, the analysis found.

The study’s focus on 12 cities makes it just a snapshot of the true heat wave death toll across the continent, which researchers estimate could be up to tens of thousands of people.
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“Heatwaves don’t leave a trail of destruction like wildfires or storms,” said Ben Clarke, a study author and a researcher at Imperial College London. “Their impacts are mostly invisible but quietly devastating — a change of just 2 or 3 degrees Celsius can mean the difference between life and death for thousands of people.”
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The world must stop burning fossil fuels to stop heat waves becoming hotter and deadlier and cities need to urgently adapt, said Friederike Otto, a climate scientist at Imperial College London. “Shifting to renewable energy, building cities that can withstand extreme heat, and protecting the poorest and most vulnerable is absolutely essential,” she said.

Akshay Deoras, a research scientist at the University of Reading who was not involved in the analysis, said “robust techniques used in this study leave no doubt that climate change is already a deadly force in Europe.”

Richard Allan, a professor of climate science at the University of Reading who was also not involved in the report, said the study added to huge amounts of evidence that climate change is making heat waves more intense, “meaning that moderate heat becomes dangerous and record heat becomes unprecedented.”

It’s not just heat that’s being supercharged in out hotter world, Allan added. “As one part of the globe bakes and burns, another region can suffer intense rainfall and catastrophic flooding.”

‘Hire back park staff’: Visitors feel the pinch of Trump’s layoffs at National Park Service
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The visitors who trek to America’s national parks are already noticing the changes, just months after President Donald Trump took office.

“I’ve been visiting national parks for 30 years and never has the presence of rangers been so absent,” one visitor to Zion National Park wrote in National Park Service public feedback obtained by CNN.

The visitor said they saw just one trail crew at the iconic Utah park. There were no educational programs offered at any of the five parks they visited on their trip.
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“Hire back park staff. We need them,” the visitor wrote.

At Yosemite, another visitor said there were no rangers at the Hetch Hetchy reservoir entrance station, preventing visitors from picking up wilderness permits.

“More staff would be a BIG and IMPORTANT improvement,” that visitor wrote.
America’s most treasured national parks are getting crunched by Trump’s government-shrinking layoffs just as the summer travel season gets into full swing.
Top officials vowed to hire thousands of seasonal employees to pick up the slack after the Trump administration fired around 1,000 NPS employees as part of wide-ranging federal firings known as the “Valentine’s Day Massacre.” Department of Interior officials said in a February memo they would aim to hire 7,700 seasonal workers at NPS, and post listings for 9,000 jobs.

But those numbers haven’t materialized ahead July 4th — the parks’ busiest time of the year. Internal National Park Service data provided to CNN by the National Parks Conservation Association shows that about 4,500 seasonal and temporary staff have been hired.

Quick share — this site is a gem

Just recently I stumbled on a site https://kitchen-tips.chtonamstoit.site/.

It’s full of super clear advice on storage and cleaning.

Some sections I liked most:
- Storing spices and grains

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Any space-saving tricks to share?

Santa Fe, New Mexico
AP — At least three people were missing in a mountain village in southern New Mexico that is a popular summer retreat after monsoon rains triggered flash flooding Tuesday that was so intense an entire house was swept downstream.
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Emergency crews carried out at least 85 swift water rescues in the Ruidoso area, including of people who were trapped in their homes and cars, said Danielle Silva of the New Mexico Department of Homeland Security and Emergency Management.

No deaths were immediately reported, but Silva said the extent of the destruction wouldn’t be known until the water recedes.
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tripscan top
“We knew that we were going to have floods … and this one hit us harder than what we were expecting,” Ruidoso Mayor Lynn D. Crawford said during a radio address Tuesday night.

Crawford said that some people were taken to the hospital, although the exact number was not immediately clear. He encouraged residents to call an emergency line if their loved ones or neighbors were missing.
The floods came just days after flash floods in Texas killed over 100 people and left more than 160 people missing.

In New Mexico, officials urged residents to seek higher ground Tuesday afternoon as the waters of the Rio Ruidoso rose nearly 19 feet in a matter of minutes amid heavy rainfall. The National Weather Service issued flood warnings in the area, which was stripped of vegetation by recent wildfires.

A weather service flood gauge and companion video camera showed churning waters of the Rio Ruidoso surge over the river’s banks into surrounding forest. Streets and bridges were closed in response.

Kaitlyn Carpenter, an artist in Ruidoso, was riding her motorcycle through town Tuesday afternoon when the storm started to pick up, and she sought shelter at the riverside Downshift Brewing Company with about 50 other people. She started to film debris rushing down the Rio Ruidoso when she spotted a house float by with a familiar turquoise door. It belonged to the family of one of her best friends.

Her friend’s family was not in the house and is safe, she said.

“I’ve been in that house and have memories in that house, so seeing it come down the river was just pretty heartbreaking,” Carpenter said. “I just couldn’t believe it.”

There were also reports of dead horses near the town’s horse racing track, the mayor said.

Two National Guard rescue teams and several local teams already were in the area when the flooding began, Silva said, and more Guard teams were expected.

The area has been especially vulnerable to flooding since the summer of 2024, when the South Fork and Salt fires raced across tinder-dry forest and destroyed an estimated 1,400 homes and structures. Residents were forced to flee a wall of flames, only to grapple with intense flooding later that summer.

More than 200 firefighters are struggling to tackle an out-of-control wildfire on Crete — Greece’s largest island and a tourist hotspot — as authorities order mass evacuations.
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The fire broke out Wednesday afternoon near Ierapetra, a town on the island’s southeast coast, amid unusually high temperatures, 3 to 5 degrees Celsius (5.4 to 9 Fahrenheit) above average, and gale-force winds of around 50 miles an hour.

The conditions are creating “new outbreaks, making firefighting work very difficult,” the Fire Department’s press spokesperson, Chief Vasilios Vathrakoyannis, said in a statement Thursday.
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трипскан вход
More than 230 firefighters, along with 46 vehicles and 10 helicopters have been deployed to fight the blaze, according to fire officials.

The flames have spread rapidly, reaching homes as well as hotels and other tourist accommodations.

Authorities asked residents of four settlements to evacuate and move toward Ierapetra. About 1,500 people have been evacuated so far, according to the Greek public broadcaster ERT.

The Ierapetra municipality has converted an indoor training center facility into a makeshift camp, where hundreds of tourists and residents who abandoned their homes spent the night Wednesday.
The police, medical services and the coast guard have all been called to the area.

“We are entering the third and most difficult month of the fire season,” Vathrakoyannis said. July is typically the hottest month in Greece and is often accompanied by strong winds. “These conditions favor the spread of fires and increase their danger,” he said.
Wildfires have ripped through other European countries this week as the continent endures a brutal heat wave.

Tens of thousands were evacuated in Turkey as blazes ripped through the western Izmir and Manisa provinces and southern Hatay province, damaging nearly 200 homes.

Blazes also broke out in France and in Spain, where two people died.

Europe experiences wildfires every year, but they are becoming more intense and frequent due to human-caused climate change, which fuels heat and drought, both helping set the stage for fierce, destructive fires.

High costs are still a big barrier to prospective customers, said Alan Gibson, principal at Maine-based builder GO Logic, where a shell for an ultra-efficient, two-story, 1,400 square foot home with three bedrooms can cost around $600,000.
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Homeowners also need to factor in additional costs, like buying and developing a suitable plot of land, and in some cases, getting access to water, electricity and septic, Gibson added.
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The way to bring down costs, Gibson believes, is more panelized, multi-family housing.

“It can be done so much more efficiently,” Gibson said, “and there’s a lot more repetition” for the developer, making the process faster and less expensive than custom multi-family builds.
Goodson, the homeowner in Maine, was able to save big money with his engineering background and penchant for DIY. He installed a rooftop solar system and electrical improvements himself, saving hundreds of thousands of dollars in the process. He wound up spending around $500,000 in all, which he estimates was $200,000 less than he otherwise would have.
“It’s a big number to swallow, I’m not making light of that at all, but it’s not that far out of what’s reasonable,” Goodson told CNN. It’s also not considering the long-term savings he will experience with no utility bills.

He was also able to take advantage of federal tax credits that reduced the cost of his rooftop solar, which saved him more than $10,000 on his panels. Those tax credits are now endangered with House Republicans’ tax bill.

“That was huge,” he said. “It’s fairly unfortunate they’re looking at doing away with it.”

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Rescuers are hailing as a “four-legged hero” a furry Chihuahua whose pacing atop an Alpine rock helped a helicopter crew find its owner, who had fallen into a crevasse on a Swiss glacier nearby.
<a href=https://tripscan.biz>tripskan</a>
The man, who was not identified, was exploring the Fee Glacier in southern Switzerland on Friday when he broke through a snow bridge and fell nearly 8 meters (about 26 feet), according to Air Zermatt, a rescue, training and transport company.

Equipped with a walkie-talkie, the man connected with a person nearby who relayed the accident to emergency services. But the exact location was unknown. After about a half-hour search, the pacing pooch caught the eye of a rescue team member.
https://tripscan.biz
трип скан
As the crew zeroed on the Chihuahua, the hole the man fell into became more visible. Rescuers rappelled down, rescued the man and flew him and his canine companion to a hospital.

“Imagine if the dog wasn’t there,” Air Zermatt spokesman Bruno Kalbermatten said by phone. “I have no idea what would happen to this guy. I think he wouldn’t survive this fall into the crevasse.”

On its website, the company was effusive: “The dog is a four-legged hero who may have saved his master’s life in a life-threatening situation.”

The levies are also likely to reduce America’s economic output, as has happened before. A 2020 study, based on data from 151 countries, including the US, between 1963-2014, found that tariffs have “persistent adverse effects on the size of the pie,” or the gross domestic product of the country imposing them.
<a href=https://kra34g.cc>Кракен тор</a>
There are a number of possible explanations for this.

One is that, when tariffs are low or non-existent, the country in question can focus on the kind of economic activities where it has an edge and export those goods and services, Gimber told CNN.
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kra35.cc
“If you raise tariffs, you’re not going to see that same level of specialization,” he said, noting that the result would be lower labor productivity. “The labor could be better used elsewhere in the economy, in areas where you have a greater competitive advantage.”
Another reason output falls when tariffs are raised lies in the higher cost of imported inputs, wrote the authors of the 2020 study, most of them International Monetary Fund economists.

Fatas at INSEAD suggested the same reason, providing an example: “So I’m a worker and work in a factory. To produce what we produce we need to import microchips from Taiwan. Those things are more expensive. Together, me and the company, we create less value per hour worked.”

Yet another way tariff hikes can hurt the economy is by disrupting the status quo and fueling uncertainty over the future levels of import taxes. That lack of clarity is particularly acute this year, given the erratic nature of Trump’s trade policy.

Surveys by the National Federation of Independent Business in the US suggest the uncertainty is already weighing on American companies’ willingness to invest. The share of small businesses planning a capital outlay within the next six months hit its lowest level in April since at least April 2020, when Covid was sweeping the globe.

“The economy will continue to stumble along until the major sources of uncertainty (including over tariffs) are resolved. It’s hard to steer a ship in the fog,” the federation said.

Whichever forces may be at work, the IMF, to cite just one example, thinks higher US tariffs will lower the country’s productivity and output.

The latest Barbie slays in a chic blue polka-dot crop top, ruffled miniskirt, chunky heels and an insulin pump. She is the brand’s first doll with type 1 diabetes.
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Dollmaker Mattel worked with Breakthrough T1D, formerly known the Juvenile Diabetes Research Foundation, to design the doll, which aims to represent the roughly 304,000 kids and teens living with type 1 diabetes in the United States.
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The doll launched Tuesday at the Breakthrough T1D Children’s Congress, a three-day event in Washington that brings in kids and teens living with the condition to meet with lawmakers. This year, they’re asking Congress to renew funding for the Special Diabetes Program, which was first allocated by Congress in 1997. The program’s current funding ends after September.

The advocacy efforts have taken on new urgency this year. With so many deep cuts to federally funded projects in recent months, Breakthrough T1D said it’s anxiously watching to see if this funding will be reupped.

Type 1 diabetes is an autoimmune disease, meaning the body mistakenly attacks its own organs and tissues. In this case, rough antibodies go after cells in the pancreas that make insulin, an essential hormone that helps the body turn food into energy. As a result, the body doesn’t make enough of its own insulin, so people have to take insulin by injection or though a pump to survive.

Type 1 diabetes is typically diagnosed in childhood but can be diagnosed in anyone at any age. It differs from type 2 diabetes, in which people are still able to make insulin but their cells stop responding to it.

In addition to the insulin pump that attaches to the new Barbie’s waist, the chestnut-haired beauty has a continuous glucose monitor on her arm – a button held on by a strip of heart-shaped Barbie-pink tape. Her cell phone displays an app that shows her glucose readings. She also has a light blue purse to hold her supplies and snacks to help her manage her blood sugar throughout the day. It matches her shoes, of course.

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Extreme heat is a killer. A recent heat wave shows how much more deadly it’s becoming
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Extreme heat is a killer and its impact is becoming far, far deadlier as the human-caused climate crisis supercharges temperatures, according to a new study, which estimates global warming tripled the number of deaths in the recent European heat wave.

For more than a week, temperatures in many parts of Europe spiked above 100 degrees Fahrenheit. Tourist attractions closed, wildfires ripped through several countries, and people struggled to cope on a continent where air conditioning is rare.
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The outcome was deadly. Thousands of people are estimated to have lost their lives, according to a first-of-its-kind rapid analysis study published Wednesday.

A team of researchers, led by Imperial College London and the London School of Hygiene and Tropical Medicine, looked at 10 days of extreme heat between June 23 and July 2 across 12 European cities, including London, Paris, Athens, Madrid and Rome.

They used historical weather data to calculate how intense the heat would have been if humans had not burned fossil fuels and warmed the world by 1.3 degrees Celsius. They found climate change made Europe’s heat wave 1 to 4 degrees Celsius (1.8 to 7.2 Fahrenheit) hotter.

The scientists then used research on the relationship between heat and daily deaths to estimate how many people lost their lives.

They found approximately 2,300 people died during ten days of heat across the 12 cities, around 1,500 more than would have died in a world without climate change. In other words, global heating was responsible for 65% of the total death toll.

“The results show how relatively small increases in the hottest temperatures can trigger huge surges in death,” the study authors wrote.

Heat has a particularly pernicious impact on people with underlying health conditions, such as heart disease, diabetes and respiratory problems.

People over 65 years old were most affected, accounting for 88% of the excess deaths, according to the analysis. But heat can be deadly for anyone. Nearly 200 of the estimated deaths across the 12 cities were among those aged 20 to 65.

Climate change was responsible for the vast majority of heat deaths in some cities. In Madrid, it accounted for about 90% of estimated heat wave deaths, the analysis found.

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