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Elderly man saved after webcam viewer spies him floating in river
News by Press Association 21/03/2019, 5:26 pm Send us a story Sign up to our Daily newsletter A webcam viewer helped to save the life of an elderly man after spotting him floating in a river. According to the Hamburg Fire Brigade, police received a call in the early hours of Thursday morning from a man saying he had spotted a person in the River Elbe via a webcam. Boats and divers were deployed by the fire brigade, who quickly found an elderly man floating in the water. The 72-year-old, who was suffering from suspected hypothermia by the time fire crews reached him, was too weak to hold on to the flotation aid they threw for him but he was eventually pulled from the water. Paramedics then treated him and took him to a local hospital. It is not yet known how the man ended up in the water in the first place. Sign up to our Daily newsletter More from the Evening Express Man's body found in north-east river Man rescued by fire crews after falling into … [Read more...] about Elderly man saved after webcam viewer spies him floating in river
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Gardaí investigating assault on elderly man in Macroom
March 21, 2019 irishexaminer Leave a Comment
Gardaí are investigating a vicious assault on a 73-year-old man who was beaten around the head and body and left with a punctured lung when attacked in a van in which he was sleeping.The attack happened in Macroom town centre in the early hours of yesterday morning.The elderly man had been living in a white van for a number of years and it was parked in a public car park at Sleaveen East.The area is close to Fitzgerald's Funeral Home and the Dunnes Stores outlet.It is believed he chose the location because it was well-lit and he felt safe there.One local said the incident has shocked the community: "He's the kind of man who'd do no harm to anybody. He kept himself to himself."It is believed the pensioner was attacked by an intruder shortly after midnight.Gardaí were alerted by a passerby and were quickly on the scene.A short time later they arrested a man in his 30s close to the scene.In the meantime, an ambulance rushed the injured pensioner to Cork University Hospital.He … [Read more...] about Gardaí investigating assault on elderly man in Macroom
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Elderly man (73) hospitalised with 'serious injuries' after car park assault
March 21, 2019 independent Leave a Comment
Elderly man (73) hospitalised with 'serious injuries' after car park assault Independent.ie A PENSIONER is in serious condition in hospital after a vicious street assault in Cork. https://www.independent.ie/irish-news/news/elderly-man-73-hospitalised-with-serious-injuries-after-car-park-assault-37936820.html https://www.independent.ie/incoming/article37855589.ece/684b0/AUTOCROP/h342/GardaHQ-stock.jpg Email A PENSIONER is in serious condition in hospital after a vicious street assault in Cork. The 73-year-old man was attacked as he was walking home through a car park in Macroom, Co Cork around 10pm last night. The man suffered multiple injuries in the attack. He was discovered a short time later by a passerby and the alarm was raised. The man was rushed to Cork University Hospital (CUH) where he is now in a serious condition. It is understood he suffered multiple injuries to his head and torso. Gardaí arrested a man a short time after they began their investigation in the … [Read more...] about Elderly man (73) hospitalised with 'serious injuries' after car park assault
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Elderly man hurt and road closed after collision near Stockton pub
March 15, 2019 gazettelive Leave a Comment
An elderly man suffered suspected head injuries after a collision between a pedestrian and a car near the Tesco superstore in Stockton. Part of Durham Road was closed after the accident, which occurred just after midday on Friday outside the Horse and Jockey pub. A Cleveland Police spokeswoman told Teesside Live: "Police were contacted at 12.18pm by ambulance service colleagues reporting they were at the scene of a collision on Durham Road, Stockton near the large Tesco store - outside the Horse and Jockey pub. "The collision involved an elderly male pedestrian and a black Ford Fusion and the elderly man is believed to have suffered head injuries. "A road closure from Junction Road roundabout towards Tesco has been put in place and collision investigation team officers are attending." The road was reopened at around 1.30pm. Like the Teesside Live Facebook page to get the latest news in your feed and join our group dedicated to court and crime coverage . You can … [Read more...] about Elderly man hurt and road closed after collision near Stockton pub
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Elderly man waits over a hour and a half for ambulance after fall
March 14, 2019 grimsbytelegraph Leave a Comment
An elderly man who suffered head injuries after tripping over on St Peter's Avenue had to wait over an hour and a half for an ambulance to arrive. The incident happened at about 1pm on the busy Cleethorpes street, when the man, believed to be in his 80s or 90s, fell as he was walking near the Superdrug store and badly injured his head. People quickly rushed to the man's aid, after he was knocked unconscious by the fall, providing him with blankets and supporting his head after ringing the emergency services. Cleethorpes residents Ms Steele, spoke of her outrage at how long the man had to wait for an ambulance to arrive on the scene, saying that it took longer than a hour and a half for one to turn up. She said: "I have been down St Peter's Avenue shopping today, when I saw this very elderly gentleman trip over and smash his head on the ground. "He was knocked completely unconscious, and his head was left in a very bad way. "People quickly came to his aid, ringing an ambulance and … [Read more...] about Elderly man waits over a hour and a half for ambulance after fall
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It is almost the end of 2011. There have been department stores and shopping malls that had their grand opening in this year. You cannot miss large suburban outlet malls that offer full line of products at a bargain price as well as the shopping districts such as Yurakucho in Tokyo and Osaka that are going through a rapid change in recent years and Fukuoka that is celebrating the opening of the entire Kyushu Shinkansen line. On this page, we bring together information on newly opened stores across Japan. Check it out and find information useful for your travel!
LUMINE Yurakucho has opened on October 28, 2011 in Yurakucho, one of the Japan's biggest commercial districts near Ginza, with its concept "Yurakucho comfy breeze – comfortable air is there, to relaxing "Yurakucho." Centering on the floor for the fashionable clothing with individuality, LUMINE Yurakucho consist of a total of 107 shops including food shops convenient for lunch and for after work that are gathered on the same floor and shops for cosmetics, sundries, services, etc. In addition to the main stores found at LUMINE in other districts, a new category of business and hot stores that are opened in the district for the first time are found. The shops opened include the popular specialty store came from California "Ron Herman," a women's clothing store with sensitivity to the latest trends "PARIGOT" which entered the Kanto market for the first time, "WIRED CAFÉ<>FIT" whose new style of café and fitness club combined is much talked about. Each shop has special products or services offered only at LUMINE Yurakucho.
How about finding something that suits you at LUMINE Yurakucho where there are many brand stores that are popular also in overseas?
Hours:Shopping floor 11:00 a.m. – 9:00 p.m.
A department store exclusive for men with an unprecedented selection of products – Data on Hankyu MEN'S TOKYO.
On October 15, Hankyu MEN'S TOKYO, a department store exclusive for men was opened at a convenient location which is 3 minutes away from JR Yurakucho Station. Born from Yurakucho Hankyu, Hankyu MEN'S TOKYO is the first department store exclusive for men in Ginza area and the second one in Kanto. It gains attention also for having an unprecedented selection of products. Its feature is that each floor has different theme and brand stores or products relating to the theme are put together on the same floor making it easier to find what you are looking for. The huge department store with the total area of 11,000 square meters has everything from luxury brand name products to stationeries with style. Those who are fond of fashionable things will never get tired of spending time there all day. It is a Tokyo's new landmark.
The store information and the consumption tax exemption service are available in English and Chinese at the spacious information desk on the 1st floor which looks like a bar counter. And on the basement floor, you can relax reading English magazines at a cafe produced by the English informational magazine Monocle.
Hours:Monday – Saturday: 12:00 p.m. – 9:00 p.m.(Refresh court (8th floor): 11:00 a.m. -), Sunday & Holidays: 11:00 a.m. – 8:00 p.m.
JR Osaka Mitsukoshi Isetan had its grand opening in May in the JR Osaka Station terminal building. There are no super luxurious brand stores. 30% of the entire sales floor is occupied by organized zones which the department store collects and organize the floor of their own accord. This composition of sales floor is not common to all department stores. Organized zones such as "Re-style" and "Isetan Girl" for women's clothing and "Art Kaihoku" (liberated district for art) for art related products present the fashionability unique to Mitsukoshi Isetan. Many brands that entered the Kansai market for the first time are also found.
The featured services are the hands-on services such as free makeup products to try out on the spot (2 fl.), simulation golfing (8 fl.) and cigar tasting (8 fl.).
The large-scale renovation of Osaka Station started in 2004 and the station just had its grand-opening as Osaka Station City in May, 2011. JR Osaka Mitsukoshi Isetan was opened as the Japan's first department store that Isetan and Mitsukoshi merged together in the west side of North Gate Building in Osaka Station City. With this, the northern area of Osaka is getting more and more vibrant.
Having refurbished its image by changing the building appearance under the key words of "Tradition and Advancement, Conservation and Reproducing," Osaka Takashimaya had its grand opening in March 2011 of this year. It is one of the largest department stores in Kansai. Especially, the cosmetics floor on the 1st floor in the east zone is one of the largest in Kansai and has about 80 brands. It boasts divers brand lineup including Japanese brands such as SHISEIDO and ALBION, foreign brands such as CHANEL and Dior and the natural cosmetics brands that are assembled in the section called "Belle Naturelle." The luxurious zone on the 2nd floor in the east zone is also one of the biggest in Kansai and a wide selection of products, from brand stores such as Hermès and CHANEL to the section Takashimaya organizes of their own accord, is appealing. Men's clothing occupies four floors in the west zone and a variety of brand name products from luxurious to contemporary are found.
Attendant interpreter service in English and Chinese is available at the information desk on the 1st floor at all times to accompany customers for shopping. And the tax exemption service is offered at the customer service counter on the 7th floor.
Hankyu Hakata was opened on March 3 as an anchor tenant of the JR Hakata Station terminal building which was renovated for the opening of the entire Kyushu Shinkansen line. HAKATA SISTERS where popular young fashion brand stores are gathered has an unique selection of products not only clothes but also shoes, bags, sundries and cosmetics and this unique floor is much talked about.
Hakata Hankyu has 17 event spaces for limited-time brand stores and over 20 COTO COTO STAGE for seminar under the theme of "school of living." And events with various ideas are held day after day. It never loses the customers' attention. The world's first café produced in collaboration with a global trend leading magazine ELLE is on the 4th floor. You can enjoy what is on the menu that is conscious of beauty and health in the stylish space just like the one in a magazine. Magazines selected by ELLE are also sold at the cafe.
The consumption tax exemption service is available with the purchase of over 10,000 yen. And the attendant interpreter service in English, Chinese and Korean are available (but not all the time) at the information counter to accompany customers for shopping.
Hours:Basement floor – 4th floor: 10:00 a.m. – 9:00 p.m., 5th floor –8th floor: 10:00 a.m. – 8:00 p.m.
CANAL CITY HAKATA is a complex where there is a 180-meter long canal within its grounds. You can enjoy what is available in the facility as well as taking a walk. With the concept of "a theater in a city," CANAL CITY HAKATA is a place where visitors will be performing as an actor at one occasion and will be watching a show as an audience at another occasion.
The complex is packed with a wide variety of facilities such as shopping mall, movie theater, theater, amusement facility, hotel and showroom. At the Sun Plaza Stage on the basement floor, shows and live music performed by performers from all over the world are held. The famous ramen shops from across Japan are all assembled the Ramen Stadium where visitors can experience the food culture of Japan and Hakata. They are captivating the visitors.
In CANAL CITY HAKATA, the east building was newly opened in September of this year with the total floor area of 17,480 square meters. Many well-known brands that are very popular both at home and abroad such as H&M, the first store in the Kyushu region; ZARA, one of the largest store in Japan; COLLECT POINT and UNIQLO have opened up the stores in this building. CANAL CITY HAKATA is gaining more and more attentions as a shopping complex. Winter sale stars from January 1, 2012.
An outlet mall is a type of shopping mall where shops that sell samples; grade B products meaning products that are slightly damaged in production or in transit; or out of season products at a lower price than the regular price are assembled. The first outlet mall came into being in 1980's in the United States. The first outlet mall in Japan called RiSM was opened in Saitama Prefecture in 1993. Since then, the number of outlet malls is growing and now there are more than 30 of them across the nation. A new mall has come into being in 2011 too.
Lake Town OUTLET is an outlet mall that was newly opened on April 29 of this year in the complex where other two facilities are: Lake Town KAZE centered on clothing shops and restaurants and Lake Town MORI. The combined floor area of the entire Lake Town is 245,223 square meters. Lake Town is gaining attention as one of the largest shopping center in Asia. What is appealing is not only the huge scale but also the location which is less than one hour from the center of Tokyo and a 7-minute walk from the nearest JR station Koshigaya Lake Town Station.
Lake Town OUTLET features ecologically friendly facilities and events that are held more than other outlet malls. What is popular among foreign tourists is a workshop in which visitors can experience painting on a saucer or learn how to wrap things with a furoshiki, a traditional Japanese wrapping cloth. The workshops are held by an Arita ware shop Kouransha. The fountain show held in summer at the lake and BMX Flatland which determines the King of Ground winner as well as the BMX Flatland World Circuit ranking held in Autumn were well received. As an event is held every week at the complex, it is fun to go with friends or family.
MITSUI OUTLET PARK Kurashiki, which will open on December 1, is one of the largest outlet malls in the Chugoku region. Popular brand stores will be opened there. Total of 120 stores and a wide range of products from clothing to furniture as well as toys will be there. In the mall there is children's favorite tree house, a fountain show with music called POP JET and devices such as "power generating floor," that is, the picture on the monitor changes when power is generated by stepping on the floor. The entire family can have a good time there.
Located near the famous tourist attraction "the Kurashiki Bikan historical quarter" that offers the beautiful scenery of the streets with old Japanese architecture, it is convenient for sightseeing as well as shopping.


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Action/comedy | 1h48m | 2016
Based upon Marvel Comics' most unconventional anti-hero, DEADPOOL tells the origin story of former Special Forces operative turned mercenary Wade Wilson, who after being subjected to a rogue experiment that leaves him with accelerated healing powers, adopts the alter ego Deadpool. Armed with his new abilities and a dark, twisted sense of humor, Deadpool hunts down the man who nearly destroyed his life.
- 2 min 40 sec
Action/adventure | 2h24m | 2015
During a manned mission to Mars, Astronaut Mark Watney (Matt Damon) is presumed dead after a fierce storm and left behind by his crew. But Watney has survived and finds himself stranded and alone on the hostile planet. With only meager supplies, he must draw upon his ingenuity, wit and spirit to subsist and find a way to signal to Earth that he is alive.
"The Nice Guys" takes place in 1970s Los Angeles, when down-on-his-luck private eye Holland March (Gosling) and hired enforcer Jackson Healy (Crowe) must work together to solve the case of a missing girl and the seemingly unrelated death of a porn star. During their investigation, they uncover a shocking conspiracy that reaches up to the highest circles of power.
AMAZON PRIME VIDEO AND SXSW LAUNCH "PRIME VIDEO PRESENTS THE SXSW 2020 FILM FESTIVAL COLLECTION"
Fantasia 2018 Review: RONDO Appeals To The Baser Instincts (And I'm Done With That)
Fantasia 2018 Review: PLAYING HARD Hardly Plays As A Doc
Fantasia 2018 Review: NEOMANILLA Goes Ground Floor On Duterte's War on Drugs
Fantasia 2018 Review: THE MAN WHO KILLED HITLER AND THEN BIGFOOT Annihilates Its Target
SEA FEVER: Hermione Corfield Talks And Her Role In This Outbreak-At-Sea Film
TALES FROM THE LOOP: A Conversation With Composer Paul Leonard-Morgan
I AM PATRICK: John Rhys-Davies On St. Patrick, The Role of Christianity in Civilization, Slavery And Much More
THE CURRENT WAR: DIRECTOR'S CUT or What Happens When A Director Is Allowed To Take Back Back Creative Reins
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JUSTIN FURSTENFELD ON NEW MOVIE, NEW MUSIC, NEW TOUR, NEW LIFE
COMPOSER RAMIN DJAWADI WINS EMMY FOR WORK ON GAME OF THRONES
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JAMES MANGOLD TALKS ABOUT HUGH JACKMAN AND 'THE WOLVERINE'
August 11, 2013 By amfmstudios
Paul Salfen interviews James Mangold, director of "The Wolverine." Previously known for directing "Girl Interrupted," "Kate & Leopold," "Walk the Line,""3:10 to Yuma" and "Knight & Day". TOPICS: Why Hugh has such universal appeal, what it was like shooting in Japan and Australia, and what Mangold's "Hail Mary Moment" was for The Drew Pearson Show. … [Read more...]
THE WOLVERINE INTERVIEW WITH HIROYUKI SANADA, TAO OKAMOTO, AND RILA FUKUSHIMA
July 24, 2013 By amfmstudios
Paul Salfen interviews high-fashion-model-turned-actress Rila Fukushima, Tao Okamoto, former face of Ralph Lauren and Japanese top model, and Hiroyuki Sanada, one of the most talented actors in Japan for their roles in "The Wolverine," coming July 26th. THE INTERVIEW THE POSTER … [Read more...]
THE WOLVERINE: NEW TRAILER
March 27, 2013 By amfmstudios
Based on the celebrated comic book arc, this epic action-adventure takes Wolverine (Hugh Jackman), the most iconic character of the X-Men universe, to modern-day Japan. Out of his depth in an unknown world, he will face a host of unexpected and deadly opponents in a life-or-death battle that will leave him forever changed. Vulnerable for the first time and pushed to his … [Read more...]
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With Amelia Bedelia, anything can happen! Amelia Bedelia is going to get a puppy! When her parents ask her what kind of dog she'd like, Amelia Bedelia doesn't know what to say. There are hundreds of dogs in the world, maybe even millions! How will Amelia Bedelia ever find the perfect puppy? Look out! Here comes Amelia Bedelia, and she's got one thing on her mind - DOGS!


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Q: How can I get SE for smooth.spline()? I use smooth.spline() on two large numeric vectors, x and y. I now want to visualize it, showing confidence intervals (or standard errors).
Ideally, I would just use geom_smooth(method="spline"), but that doesn't exist. So I tried method = "loess", which is similar, but than it runs out of memory (unless I set se=F) and I already set it to the maximum capacity.
I than used base R function smooth.spline(), but that doesn't calculate standard errors or confidence intervals. I tried using the function predict(model, se = T), but it does not produce standard errors for smooth.spline models.
What can I do? please help, I am trying for days now, and even GPT couldn't do it

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Travel News: Colorado Hosts a Road-Trip-Worthy Winter Festival
Freeze the day at the 10th Annual Frozen Dead Guy Days in Nederland, Colorado next month.
By Bill Basore
Every so often you stumble upon an event so bizarre and strangely compelling, you just have to make a road trip out of it. So it is with the annual Frozen Dead Guy Days festival in Nederland, Colorado, population 1,500, a former mining town in the mountains west of Boulder.
If frozen turkey bowling, coffin races, and drinking to the eternal health of a Norwegian grandpa who's been in cryogenic suspension for more than 20 years sounds like your cup of tea, you'll want to be in Nederland the first weekend in March.
And you won't be alone. Last year's festival attracted 15,000 celebrants. The New York Times named the event to its "Top 10 Best Parties of the Winter" list last year, alongside New Or-leans Mardi Gras and Rio's Carnival.
Activities include a polar bear plunge, the frozen salmon toss, frozen turkey bowling, a frozen t-shirt contest, a brain-freeze competition, the Parade of Hearses, the Seventies-themed Fever Blue Ball (with a Stayin' Alive Grandpa costume contest)--even kids activities such as science experiments with liquid nitrogen!
Food is abundant at Frozen Dead Guy Days--including all-you-can-eat pancake breakfasts--as is music. Known for its music scene, Nederland's biggest party of the year includes live performances all weekend at restaurants and pubs around town.
When you're ready to thaw out, lodging in the Nederland area ranges from cabin rentals to historic B&Bs like the Goldminer Hotel. Closer to Boulder, you'll find more choices.
Residing in a Tuff Shed on private property in town, the man behind this celebration of all things frozen is tended to year round by Bo Shaffer, also known as the Ice Man.
Every month, Shaffer and a team of volunteers pack 1,600 pounds of dry ice around Bredo Morstoel in his sarcophagus--where he patiently awaits the day science can reanimate him and cure him of the heart disease that killed him in 1989.
Frozen Dead Guy loyalists traipse out to the Tuff Shed every March to have a drink with Grandpa Bredo. If you prefer your adult beverages surrounded by the living, you'll want to check out the microbrews from Avery and Left Hand brewing companies in the ReAnimate Yourself Beer Tent.


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High Performance, Intercity, M/W, News, Safety
NEC Commission identifies needs of $38 billion
Written by William C. Vantuono, Editor-in-Chief
The Northeast Corridor Commission on May 3 submitted to Congress two reports detailing short-and-long-term capital investment needs totaling some $38 billion for the 457-mile electrified rail line linking Boston, New York, Philadelphia and Washington D.C.
The Northeast Corridor Capital Investment Plan: Fiscal Years 2018 – 2022 and the Northeast Corridor Annual Report: Operations and Infrastructure, Fiscal Year 2016 are requirements of the FAST (Fixing America's Surface Transportation) Act. They "are critical elements of the Commission's policy framework, which balances cost sharing with improved collaboration, transparency and accountability," the Commission says. "The policy framework also calls for a federal-state funding partnership to restore the infrastructure of the most important passenger railroad [line] in the country," which serves four of the nation's ten largest metropolitan areas, supports more than 780,000 trips daily on eight commuter railroads and more than 40,000 trips on Amtrak's intercity services.
A 2014 Commission study found that a loss of all NEC services for a single day "could cost the economy $100 million in lost productivity, added congestion on the regional highway and aviation networks and other transportation-related costs."
The Capital Investment Plan identifies the Commission's top-ten NEC-wide unfunded priorities, "which are focused on addressing the Corridor's $38 billion backlog in state-of-good-repair needs. While the backlog would be addressed over many years, the Plan shows a five-year need, constrained by available resources, of $29 billion for a combination of investments that address the state-of-good-repair backlog as well as infrastructure and capacity enhancements to support the region's growth. Roughly $9 billion of that need is currently funded."
Many projects included in the Capital Investment Plan are eligible for funding from the Federal-State Partnership for State of Good Repair Program. "This competitive grant program is authorized to provide direct federal funding to supplement the large amounts of state and local dollars that are going to replace, rehabilitate or repair basic infrastructure assets," the Commission notes. "Congress will vote on the Fiscal Year 2017 omnibus bill this week to provide $25 million to the Federal-State Partnership Program, which is authorized at $175 million for FY18.
The Plan was completed "just as recent events (two derailments within a 10-day span) in the vicinity of Penn Station New York highlighted how infrastructure failures impact travelers across modes with serious consequences for the economy," the Commission said. "We will adjust these plans as necessary to redirect available resources where they are most needed."
"The states and Amtrak have stepped up to fund the Corridor's basic infrastructure and regular maintenance needs," said James Redeker, Commissioner of the Connecticut Department of Transportation and Co-Chair of the Northeast Corridor Commission. "With the Capital Investment Plan in place, we lay the foundation for the federal government to begin to help address the $38 billion state-of-good-repair backlog, infrastructure assets that, while safe, are operating beyond their useful lives, increasing maintenance costs and decreasing reliability."
In 2015, the Commission adopted the NEC Commuter and Intercity Rail Cost Allocation Policy, an agreement committing each passenger railroad using the Corridor to share approximately $1 billion annually in operating and normalized replacement capital costs based on use. "This policy does not, however, fully fund the Corridor's extensive capital needs, including the backlog," the Commission stresses.
"Reliable Amtrak and SEPTA service is essential to Delaware's economic growth," said Jennifer Cohan, Secretary of the Delaware Department of Transportation and Chair of the Commission's Planning Committee. "Failure to address the Corridor's significant investment needs identified in the Capital Investment Plan puts our future at risk."
The Northeast Corridor Annual Report: Operations and Infrastructure, Fiscal Year 2016 is the Commission's first annual report. It documents the operational performance of NEC trains in FY 2016, "allowing Commission stakeholders to identify and track performance trends over time, improving the understanding of the causes of delays and potential opportunities for performance improvement."
The Annual Report also addresses the implementation of the capital program for Fiscal Year 2016 and contains recommendations on improving capital planning and the annual One-Year Implementation Plan. Northeast Corridor stakeholders invested $1.06 billion in infrastructure in FY 2016. Some of these dollars were applied to the Cost Allocation Policy's Baseline Capital Charge (BCC) Program covering normalized replacement of basic infrastructure assets. Through this program, owners and operators contributed almost $460 million to replace more than 7,800 concrete ties, 43,000 wood ties, 348,000 feet of rail, and 51,000 feet of overhead catenary. The program also paid for more than two million feet of track surfacing and 107,000 feet of undercutting. The other $600 million funded Special Projects aimed at addressing the major bridges and tunnels in the state-of-good-repair backlog or improving the NEC.
"The funding committed by states and rail agencies through the cost allocation policy provides a critical lifeline to the aging NEC," said Stephen Gardner, Executive Vice President, Planning, Technology, & Public Affairs at Amtrak. "However, without significant new state and federal investment to address the Corridor's aging infrastructure, commuter and intercity rail service will continue to be at risk."
Both reports can be download at the links below.
The Northeast Corridor Commission was authorized by Congress in 2008 to improve coordination on the Corridor. It is comprised of one member from each of the NEC states and the District of Columbia; four members from Amtrak; and five members from the U.S. Department of Transportation. The Commission also includes non-voting representatives from NEC freight railroads, states with feeder corridors, and commuter rail authorities not directly represented by a Commission member.
Categories: High Performance, Intercity, M/W, News, Safety Tags: Amtrak, Maintenance of Way, Northeast Corridor, Northeast Corridor Commission, sustainability
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Wabtec Acquires RELCO Locomotives


text:
October 5, 2020 allisontedescoAmerican Anthropologist, BMC International Health and Human Rights, Colombia, criminalization, Criminology and Criminal Justice, Critical Asian Studies, dehumanize, Denmark, discrimination, discriminatory, diversity training, Finland, marginalization, minority, Northwestern University Law Review, Norway, police, police perceptions, police training, policing, Political and Legal Anthropology Review (PoLAR), Racialized Policing, racialized violence, racism, South Africa, stigmatization, Sweden, Transforming Anthropology, United States, victimhood, vulnerability, white supremacy Leave a comment
George Floyd protest signs at the Ottawa Courthouse by Janderson L. via wikimedia
Welcome back to In the Journals! This ongoing series aims to bridge conversations that are often siloed by discipline, geographical region, language, and race. One of our goals is to make sure that the diverse voices currently reporting their research on policing, crime, law, security, and punishment are presented here. We are continuing our catch-up to develop article collections around different questions and themes. This post brings together article from throughout 2019 and 2020 to identify experiences and impacts of police discrimination, as well as to understand police socialization and training which instills discriminatory and racialized biases in practice.
In "The Jungle Academy: Molding White Supremacy in American Police Recruits," included in American Anthropologist's March 2020 issue, Aisha M. Beliso-De Jesús uses ethnography in a police academy to argue that through militaristic training, officers mold recruits by inciting fear and teaching racist jungle metaphors of the streets and citizens they are patrolling, even in cultural diversity training. The training sculpts impressionable recruits to be uniform in action and mentality, forcing them to naturalize the jungle logic depiction of ghettos as urban jungles, and their inhabitants as animals, as well as the biases that logic entails. Beliso-De Jesús argues that these logics dehumanize and other Black, Indigenous, and people of colour while reinforcing narratives of white supremacy, and that their use is crucial in the creation of a "jungle academy" which reshapes young citizens into police officers that embody and maintain the white governance and supremacy of the state through racialized state violence. Beliso-De Jesús identifies the training program as idolizing and cultivating in every way possible the large and athletic white man who is docile yet commands respect, militant, and has an alpha male mentality, and operates on the basis of fear, control and submission when policing. This image and the article produce a clear understanding of the way in which the training of police officers creates racial discrimination and biases that uphold white superiority and non-white inferiority, and why donning a police uniform both allows and causes officers to act on that training.
Criminology and Criminal Justice included Mie Birk Haller et al.'s article, "Minor harassments: Ethnic minority youth in the Nordic countries and their perceptions of the police" in their February 2020 issue, which utilizes semi-structured interviews with ethnic minority youth in Sweden, Norway, Finland and Denmark, to understand their experiences with police. Haller et al. identify subtle provocations and intimidations by police on ethnic minority youth, arguing that these constant interactions negatively impact their experiences of procedural justice, as well as their compliance with law enforcement. Interviewees indicated that police attitudes were often negative when dealing with them, and police language was often discriminatory and patronizing, making them feel inferior, insecure and scared, and decreasing their trust in police. The authors argue that this racialization of ethnic minorities not only upholds existing discrimination and instills feelings of inadequacy, inferiority, discomfort, humiliation and lack of belonging amongst youth, but has also led to a lack of desire and willingness to comply with law enforcement, a distrust in police desire and ability to protect and keep them safe, and has encouraged them to engage in criminal activities and self-protective behaviour.
In April 2020, Transforming Anthropology published an article entitled, "Contentious Bodies: The Place, Race, and Gender of Victimhood in Colombia" by Dani R. Merriman. In this article, Merriman explores ethnographic accounts of police discrimination of Afro-Colombian rural farmers in María la Baja over sixty years of war and interspersed peacetime, but also how individuals use what she deems "contentious bodies" to resist state attempts at labelling them violent guerilla combatants. With violence of guerilla groups in the early 1960s claiming to be the voice of the landless peasant, Merriman identifies black farmers in María la Baja as being used as reasoning for insurgent movements claiming to protect them, yet also experiencing unprovoked, violent and torture-based killing by those same groups seeking to dehumanize and other them. Not only have black farmers experienced decades of violence because of guerillas claiming to act on their behalf, they have also been targets of racialization, police discrimination and state labelling of them as violent and guerillas. With no viable recourse or proof that they were not guerillas, black famers staved off police discrimination and racialization by using their contentious bodies, calloused and broken from farm work and not insurgent activity, to prove their innocence and victimization, not perpetration.
May 2020's issue of BMC International Health and Human Rights included the article, "'An ethnographic exploration of factors that drive policing of street-based female sex workers in a U.S. setting – identifying opportunities for intervention" by Katherine H. A. Footer et al. Using ethnography mixed with police observation and interviews involving 64 officers, Footer et al. identify factors at the individual, community, structural and organizational levels as key to shaping the harmful behaviour and practices of police officers towards cisgender female sex workers. They argue that police behaviour reinforces stigmatization and spatial limitations of sex workers while honouring community demands to police sex work, particularly in gentrifying neighbourhoods. Proximity to violent crime led to arrests of female sex workers as police searched for information, and community opposition to sex work caused the forced displacement of female sex workers to more marginalized areas with less complaints, policing and patrolling, even when it risked the health and safety of the sex workers. Officers used dehumanizing language to depict female sex workers, and painted an image of them as unworthy of police protection despite their acknowledged vulnerability to crime and assault. Footer et al. call for the decriminalization of sex work, policy reforms regarding police practices, as well as a shift in community and police cultural landscapes to improve the safety and health of female sex workers.
Northwestern University Law Review published I. India Thusi's "On Beauty and Policing" in March 2020, identifying the impact of police officers' perceptions of beauty on their policing of different classes of sex workers in Johannesburg, South Africa. Through ethnographic fieldwork, Thusi identifies that police officers' perceptions and policing of sex workers produces and reinforces a hierarchy of desirable and valuable bodies and preserves racial and gender subordination. Thusi asks critical questions regarding who the police are protecting and serving, as their intended function identifies, when they are not only neglecting but also harming the lives of already vulnerable and marginalized black female sex workers in their choices to surveil and protect white sex workers perceived as beautiful. Not only does the study indicate that blacker bodies are under-policed for protection reasons, it also identifies the police as more aggressive in those interactions than with whiter bodies. Their actions reinforce the white supremacy and black inferiority ideologies on which South Africa was previously based, as well as who is worthy and important to society based on perceived beauty by police officers. Police are not protecting and serving vulnerable communities and populations, Thusi argues, they are protecting and preserving society's biases by perpetuating them through their actions.
In May 2019, Jaime Amparo Alves's article on discriminatory policing practices and resistance strategies in Colombia, "Refusing to Be Governed: Urban Policing, Gang Violence, and the Politics of Evilness in an Afro-Colombian Shantytown," was featured in the Political and Legal Anthropology Review. Alves argues that policing in El Guayacán, Colombia is Foucauldian in its governing nature, as it enforces boundaries of space based on race through the targeting of black bodies and places, which both allows a spatial solution for national crime and security anxieties, and justifies a lack of governance, state divestment, social abandonment, and police aggression within those spaces. Based on fieldwork in El Guayacán from 2013 to 2018, Alves identifies the discourse utilized by police officers to depict black bodies as unruly and insecure, and black livelihoods as uncivilized and violence-ridden, causing what he terms 'social death', creating spatial limitations, and justifying a lack of state involvement. Despite this combination functioning to give "spatial form to racist imaginaries of crime and order," Alves indicates a simultaneous regaining of control and territorial autonomy of El Guayacán by residents (and largely gangs) as a result of that very lack of state governance in the area, as he seeks to understand their engagement with the state and a possibility for reinventing black life outside of it.
Rune Steenberg and Alessandro Rippa's article, "Development for all? State schemes, security, and marginalization in Kashgar, Xinjiang," published in Critical Asian Studies in February 2019 uses ethnography to identify reactions and strategies of Uyghurs to increased and discriminatory policing and securitization by the PRC. Steenberg and Rippa's article is based on research spanning 2009 to 2017, and focuses on the modernist, state-driven and economic growth-focused development between 2010 and 2014, which created wealth and income disparities and incited Uyghur-led violence often labelled acts of terror, and the subsequent development of increased policing and surveillance of Uyghurs, and securitization of Kashgar. The repressive security measures taken by the state and implemented by police led to detainment in "re-education" centers, with the state presence in Uyghur lives ever-increasing and entirely controlling, cutting off outside contact by late 2017. Steenberg and Rippa identify the use of state presence and surveillance through police officers to repress and marginalize Uyghurs in Kashgar, and they argue that the roots of this discrimination are based in China's economic development and policy, which created wealth and social disparities and incited the violence.
As always, we welcome your feedback. If you have any suggestions for journals we should be keeping tabs on for this feature, or if you want to call our attention to a specific issue or article, send an email to anthropoliteia@gmail.com with the words "In the Journals" in the subject line.
Times of Security: Ethnographies of Fear, Protest and the Future
May 26, 2016 wirnita9/11, Anja Kublitz, Brussels, civil society, Clifford Geertz, Cold War, Copenhagen University, Denmark, Islamic State, liberalism, Martin Holbraad, militarization, Morten Axel Pedersen, Nakba, North Korea, Ole Waever, Palestinians, Paris, Peru, police, political anthropology, Richard Kernaghan, secularization, Securitization Theory, security, Serbia, state sovereignty, Stine Krøijer, Syria, Times of Security: Ethnographies of Fear, Protest and the Future, Victor Turner Leave a comment
The editors of Anthropoliteia present to you the latest in our occasion series Interrogations, in which authors of recent volumes of interest to our readers discuss their work. In this post, Johanna Römer talks with Morten Axel Pedersen and Martin Holbraad on their edited volume, Times of Security: Ethnographies of Fear, Protest and the Future


LaMarcus Aldridge double-doubled in Thursday's 97-110 Game 3 loss to the Warriors with 18 points and 10 rebounds to go with four assists.
Aldridge went 6-for-10 from the floor which is a mark you like to see, except the field goal attempts are a bit low. The Spurs have no real shot creators outside of LMA and it's a bit concerning that he took fewer shots than Tony Parker, Patty Mills and Rudy Gay. It's a bit difficult to feed him the ball in the post as Draymond Green is all over him and pushing him out of the deep post area, but Aldridge has a strong high post game which could be utilized. It's all easier said than done as the Warriors have a DPOY candidate guarding him with Kevin Durant and Klay Thompson lurking on the wings to double and trap.


Hi everyone! I'm so excited to be taking over 52 Quilters this week! I have a ton of fun quilt photos and blog posts for you this week. I am looking forward to getting to know you all and having great crafty conversations.
Let me officially introduce myself… I'm Michelle, a photographer & technical writer, turned obsessed quilter. I live in the Cascade mountains of the Washington State (USA) with my husband and our 16 month old little girl. We have a little cabin in the woods along with a tiny house that we built and lived in over the past few years. The nearest town is a little Bavarian style tourist town. It has a pretty great Oktoberfest and if you use a little imagination, it really feels like you're in another country.
I have been sewing & quilting off and on for a couple of years (a baby will do that!) and am self taught via the good ol' internet. Although I am a newer quilter, I've always has the desire to make and be artistic. I just hadn't found the right avenue to express that until I found quilting!!!
I'm drawn to simple, geometric quilt designs and solid fabrics, but have a hard time saying no to stripes, polka dots, and small florals as well. I sew on a vintage Kenmore machine and have a little quilting studio corner set up in our loft. This little collage is a good representation of some of the past projects I've worked on. I'll be sharing some more recent stuff with you this week over on instagram!
One of my favorite projects I've been working on lately is a modern quilting newsletter. I get to interview my favorite quilters and share inspiration each month. Along with that, I have just recently designed and launched my first quilt pattern called Starbelt for my newsletter subscribers. This week, the plan is to sew it from start to finish! I'm a pretty slow sewist, but I'm going to give it a shot! I would love to continue to design more patterns and it would be an absolute dream to design fabric. I love that quilting can incorporate so many different types of art and can be as high tech or as low tech as you want it to be.
-I use exclamation points a lot, but am trying to get that under control! But I'm excited a lot!
Thanks so much for taking some time out to meet me and I'm excited to spend the week with you!
Hi Michelle, I look forward to your posts this week. You live and quilt in a beautiful area.
Thanks Jennifer! I'm excited to have you following along!


I don't mind this because I don't think it's necessarily true that if someone pays X amount in taxes, they necessarily deserve X returned in services. If I never need an emergency room, should I stop paying for it? Of course not.
Tax collected must be spent efficiently and effectively wherever it's needed - in the long run, programs such as public health care, public education, and social services benefit everyone.
There are, however, certain segments of the population who incorrectly believe that Toronto and big cities receive too much in tax benefits and are an unfair tax burden - this dispels this myth.
It still holds true for me that services delivered elsewhere benefit everyone. In addition, the statistics clearly busted the myth that rural Canada ships its hard-earned tax dollars to the big cities.
The overall crime rate in small urban areas — home to at least 1,000 people — was 43 per cent higher than in large urban areas with a core of at least 100,000, indicates the Statistics Canada study of 2005 crime rates that was released Thursday. Only in Quebec were crime rates higher in bigger cities.
Now if you'll allow me to use the reference "certain segments of the population" once again; there are certain segments of the population who incorrectly believe that Toronto and big cities are unsafe and home to too much crime. This immediately dispels this myth.
What's more interesting, however, a lesser person, might for instance say, that small urban and rural areas are in a death spiral and that they need to "give their heads a shake" - clean up their act before they start coming back to us for more of our hard-earned tax dollars.
That would certainly be the case if the flow of taxes and the crime rate statistics were reversed.
Bottom line, crime is everybody's problem and support and help should go where it's needed.
Updated: Fixed the credit to the CBC story.


The first medical device to treat childhood attention deficit hyperactivity disorder, or ADHD, was OK'd Friday by the US Food and Drug Administration.
One of the benefits of being a billionaire is having money to burn on discretionary purchases. Colts owner Jim Irsay does precisely that from time to time.


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GH Group offers tailor-made induction heating solutions which suit the specific needs of your company, where quality is critical.


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With everyone wanting to attract maximum traffic to their internet pages copy writing services helps in this area especially when it comes to writing great SEO content. As an article writer you may be able to write great articles but you may not be familiar with SEO content. You may try to write this type of content but it may be blocked or black listed because it appears as spam to certain search engines.


text:
\section{Introduction}
\par\quad
In this paper, we consider the following initial value problem.
\begin{equation}
\label{IVP}
\left\{
\begin{array}{l}
\displaystyle u_{tt}-\Delta u+\frac{\mu}{1+t}u_t=|u|^p
\quad \mbox{in}\ {\bf R}^n\times[0,\infty),\\
u(x,0)={\varepsilon} f(x),\ u_t(x,0)={\varepsilon} g(x), \quad  x\in{\bf R}^n,
\end{array}
\right.
\end{equation}
where $\mu>0,\ f,g\in C_0^{\infty}({\bf R}^n)$ and $n\in{\bf N}$.
We assume that ${\varepsilon}>0$ is a \lq\lq small" parameter.
\par
First, we shall outline a background of (\ref{IVP}) briefly
according to the classifications by Wirth in \cite{Wir1, Wir2, Wir3}
for the corresponding linear problem.
Let $u^0$ be a solution of the initial value problem
for the following linear damped wave equation.
\begin{equation}
\label{scale_eq}
\left\{
\begin{array}{l}
\displaystyle u^0_{tt}-\Delta u^0+\frac{\mu}{(1+t)^\beta}u^0_t=0,
\quad \mbox{in}\ {\bf R}^n \times[0,\infty),\\
u^0(x,0)=u_1(x),\ u^0_t(x,0)=u_2(x), \quad x\in{\bf R}^n,
\end{array}
\right.
\end{equation}
where $\mu>0$, $\beta\in{\bf R}$, $n\in{\bf N}$ and $u_1,u_2\in C^\infty_0({\bf R}^n)$.
When $\beta\in(-\infty,-1)$, we say that the damping term is \lq\lq overdamping"
in which case the solution does not decay to zero when $t\rightarrow\infty$.
When $\beta\in[-1,1)$, the solution behaves like that of the heat equation,
which means that the term $u^0_{tt}$ in (\ref{scale_eq}) has no influence
on the behavior of the solution.
In fact, $L^p$-$L^q$ decay estimates of the solution
which are almost the same as those of the heat equation are established.
In this case, we say that the damping term is \lq\lq effective."
In contrast, when $\beta\in(1,\infty)$,
it is known that the solution behaves like that of the wave equation,
which means that the damping term in (\ref{scale_eq}) has no influence
on the behavior of the solution.
In fact, in this case the solution scatters to that of the free wave equation
when $t\rightarrow\infty$,
and thus we say that we have \lq\lq scattering."
When $\beta=1$, the equation in (\ref{scale_eq}) is invariant under the following scaling
\[
\widetilde{u^0}(x,t):=u^0(\sigma x, \sigma(1+t)-1),\ \sigma>0,
\]
and hence we say that the damping term is \lq\lq scale invariant."
The remarkable fact in this case is that the behavior of the solution of (\ref{scale_eq})
is determined by the value of $\mu$.
Actually, for $\mu\in(0,1)$, it is known that the asymptotic behavior of the solution
is closely related to that of the free wave equation.
For this range of $\mu$,
we say that the damping term is \lq\lq non-effective."
However, the threshold of $\mu$ according to the behavior of the solution is still open.
We conjecture that it may be $\mu=1$ since we have the following $L^2$ estimates:
\[
\|u^0(\cdot,t)\|_{L^2}\lesssim
\|u_1\|_{L^2}+\|u_2\|_{H^{-1}}\times
\left\{
\begin{array}{ll}
(1+t)^{1-\mu}& \mbox{if}\ \mu \in(0,1),\\
\log (e+t) &  \mbox{if}\ \mu=1,\\
1 & \mbox{if}\ \mu>1.
\end{array}
\right.
\]
In this way, we may summarize all the classifications of the damping term in (\ref{scale_eq})
in the following table.
\begin{center}
\begin{tabular}{|c|c|}
\hline
$\beta\in(-\infty,-1)$ & overdamping\\
\hline
$\beta\in[-1,1)$ & effective\\
\hline
$\beta=1$ &
\begin{tabular}{c}
scaling invariant\\
$\mu\in(0,1)\Rightarrow$ non-effective
\end{tabular}
\\
 \hline
$\beta\in(1,\infty)$ & scattering\\
\hline
\end{tabular}
\end{center}
\par
Next, we consider the following initial value problem for semilinear damped wave equation.
\begin{equation}
\label{scale_eq_nonlinear}
\left\{
\begin{array}{l}
\displaystyle v_{tt}-\Delta v+\frac{\mu}{(1+t)^\beta}v_t=|v|^p, \quad \mbox{in}\ {\bf R}^n \times[0,\infty),\\
v(x,0)={\varepsilon} f(x),\ v_t(x,0)={\varepsilon} g(x), \quad x\in{\bf R}^n,
\end{array}
\right.
\end{equation}
where $\mu>0,\ \beta\ge-1,\ f,g\in C_0^{\infty}({\bf R}^n)$ and $n\in{\bf N}$.
We assume that ${\varepsilon}>0$ is a \lq\lq small" parameter.
\par
For the constant coefficient case, $\beta=0$,
Todorova and Yordanov \cite{TY} have shown that
the energy solution of (\ref{scale_eq_nonlinear}) exists globally-in-time
for \lq\lq small" initial data if $p>p_F(n)$, where
\begin{equation}
\label{fujita}
 p_F(n):=1+\frac{2}{n}
 \end{equation}
is the so-called Fujita exponent, the critical exponent for semilinear heat equations.
It has been also obtained in \cite{TY} that
the solution of (\ref{scale_eq_nonlinear})
blows-up in finite time for some positive data if $1<p<p_F(n)$.
The critical case $p=p_F(n)$ has been studied by Zhang \cite{Z}
by showing the blow-up result.
We note that Li and Zhou \cite{LZ}, or Nishihara \cite{N},
have obtained the sharp upper bound of the lifespan
which is the maximal existence time of solutions of (\ref{scale_eq_nonlinear})
in the case of $n=1,2$,  or $n=3$, respectively.
The sharpness of the upper bound has been studied by Li \cite{Li}
including the result for more general equations with all $n\ge1$,
but for smooth nonlinear terms.
The sharp lower bound has been obtained by Ikeda and Ogawa \cite{IO} for the critical case.
Recently,  Lai and Zhou \cite{LaZ} have obtained the sharp upper bound of the lifespan
in the critical case for $n\ge4$.
\par
For the variable coefficient case of the most part of the effective damping
with $-1<\beta<1$, Lin, Nishihara and Zhai \cite{LNZ12} have obtained
the blow-up result if $1<p\le p_F(n)$
and the global existence result if $p>p_F(n)$.
Later, D'Abbicco, Lucente and Reissig \cite{DLR13} have extended
the global existence result to more general equations.
For the precise estimates of the lifespan in this case,
see Introduction in Ikeda and Wakasugi \cite{IW}.
Recently, similar results on the remaining part of effective damping with $\beta=1$
have been obtained by Wakasugi \cite{WY17} for the global existence part,
and by Fujiwara, Ikeda and  Wakasugi \cite{FIW} for the blow-up part.
The sharp estimates of the lifespan are also obtained by \cite{FIW}
except for the upper bound in the critical case.
\par
Now, let us turn back to our problem (\ref{IVP}).
Wakasugi \cite{WY14_scale} has obtained the blow-up result
if $1<p\le p_F(n)$ and $\mu>1$, or $1<p\le 1+2/(n+\mu-1)$ and $0<\mu\le 1$.
He has also shown in \cite{WY14} that an upper bound of the lifespan is
\[
\left\{
\begin{array}{ll}
C{\varepsilon}^{-(p-1)/\{2-n(p-1)\}} & \mbox{if}\ 1<p<p_F(n)\ \mbox{and}\ \mu\ge1,\\
C{\varepsilon}^{-(p-1)/\{2-(n+\mu-1)(p-1)\}} & \mbox{if}\  \d1<p<1+\frac{2}{n+\mu-1}
\ \mbox{and}\ 0<\mu<1,
\end{array}
\right.
\]
where $C$ is a positive constant independent of ${\varepsilon}$.
We note that the both proofs in \cite{WY14} and \cite{WY14_scale}
are based on the so-called \lq\lq test function method" introduced by Zhang \cite{Z}.
On the other hand, D'Abbicco \cite{DABI} has obtained
the global existence result if $p>p_F(n)$,
but $\mu$ has to satisfy
\[
\mu\ge
\left\{
\begin{array}{cl}
 5/3 & \mbox{for}\  n=1,\\
 3 & \mbox{for}\ n=2,\\
n+2 & \mbox{for}\  n\ge3\ \left(\mbox{and}\ p\le1+2/(n-2)\right).
\end{array}
\right.
\]
It is remarkable that, by the so-called Liouville transform;
\[
w(x,t):=(1+t)^{\mu/2}u(x,t),
\]
(\ref{IVP}) can be rewritten as
\begin{equation}
\label{IVP_1}
\left\{
\begin{array}{l}
\displaystyle w_{tt}-\Delta w+\frac{\mu(2-\mu)}{4(1+t)^2}w=\frac{|w|^p}{(1+t)^{\mu(p-1)/2}}
\quad \mbox{in}\ {\bf R}^n \times[0,\infty),\\
w(x,0)={\varepsilon} f(x),\ w_t(x,0)={\varepsilon} \{(\mu/2)f(x)+g(x)\}, \quad x\in{\bf R}^n.
\end{array}
\right.
\end{equation}
When $\mu=2$, D'Abbicco, Lucente and Reissig \cite{DLR14} have obtained
the following result.
Let
\begin{equation}
\label{critical_value_IVP1}
p_c(n):=\max\left\{p_{F}(n),\ p_0(n+2)\right\},
\end{equation}
where
\begin{equation}
\label{strauss}
p_0(n):=\frac{n+1+\sqrt{n^2+10n-7}}{2(n-1)}
\quad(n\ge2)
\end{equation}
is the so-called Strauss exponent, the positive root of the quadratic equation,
\begin{equation}
\label{gamma}
\gamma(p,n):=2+(n+1)p-(n-1)p^2=0.
\end{equation}
We note that $p_0(n)$ is the critical exponent for semilinear wave equations,
$\mu=0$ in (\ref{IVP}).
They have shown in \cite{DLR14} that the problem (\ref{IVP}) admits a global-in-time solution
in the classical sense for \lq\lq small" ${\varepsilon}$ if $p>p_c(n)$ in the case of $n=2,3$
although the radial symmetry is assumed in $n=3$,
and that the classical solution of (\ref{IVP}) with positive data
blows-up in finite time if $1<p\le p_c(n)$ and $n\ge1$.
In the same year, with radial symmetric assumption,
D'Abbicco and Lucente \cite{D-L}
extended the global existence result for $p_0(n+2)<p<1+2/(\max\{2,(n-3)/2\})$
to odd higher dimensions ($n\geq 5$).
We remark that, in the case of $n=1$,
Wakasa \cite{wak16} has studied the estimates of the lifespan
and has shown that the critical exponent $p_c(1)=p_F(1)=3$
changes to $p_0(1+2)=1+\sqrt{2}$
when the nonlinearity is a sign-changing type, $|u|^{p-1}u$,
and the initial data is of odd functions.
Both results in \cite{DLR14} and \cite{wak16} heavily rely
on the special structure of the massless wave equations,
$\mu=2$ in (\ref{IVP_1}).
In view of them, $\mu=2$ may be an exceptional case.
Recalling Wirth' classification in the linear problem, (\ref{scale_eq}),
one may regard $\mu=1$ as a threshold also for the semilinear problem, (\ref{IVP}).
In this sense, the blow-up result in Wakasugi \cite{WY14_scale} says that
the solution may be \lq\lq heat-like" if $\mu>1$.
Here, \lq\lq heat-like" means that the critical exponent for (\ref{IVP}) is Fujita exponent.
\par
In this paper, we claim that the solution of (\ref{IVP}) is
\lq\lq wave-like" in some case even for $\mu>1$.
Here, \lq\lq wave-like" means that
the critical exponent for (\ref{IVP}) is bigger than Fujita exponent
and is related to Strauss exponent.
We also conjecture that such a threshold of $\mu$ depends on the space dimension $n$.
The main tool of our result is Kato's lemma in Kato \cite{Kato80}
on ordinary differential inequalities
which is improved to be applied to semilinear wave equations
by Takamura \cite{Takamura15}.
Together with Yordanov and Zhang's estimate in \cite{YZ06},
we can prove a new blow-up result for wave-like solutions
by means of some special transform for the time-derivative
of the spatial integral of unknown functions.
\par
This paper is organized as follows.
In the next section, we state our main result.
In the section 3, we estimate the spatial integral of unknown functions from below.
Making use of such an estimate, we prove the main result for $\mu\ge2$ in section 4,
and for $0<\mu<2$ in section 5.

\section{Main Result}
\label{section:lifespan}
\par\quad
First we define an energy solution of (\ref{IVP}).
\begin{Def}
We say that $u$ is an energy solution of (\ref{IVP}) on $[0,T)$
if
\begin{equation}
\label{reg}
u\in C([0,T),H^1({\bf R}^n))\cap C^1([0,T),L^2({\bf R}^n))\cap L_{\rm loc}
^p({\bf R}^n\times[0,T))
\end{equation}
satisfies
\begin{equation}
\label{sol}
\begin{array}{l}
\displaystyle\int_{{\bf R}^n}u_t(x,t)\phi(x,t)dx-\int_{{\bf R}^n}u_t(x,0)\phi(x,0)dx\\
\displaystyle+\int_0^tds\int_{{\bf R}^n}\left\{-u_t(x,s)\phi_t(x,s)+\nabla u(x,s)\cdot\nabla\phi(x,s)\right\}dx\\
\displaystyle+\int_0^tds\int_{{\bf R}^n}\frac{\mu u_t(x,s)}{1+s}\phi(x,s)dx
=\int_0^tds\int_{{\bf R}^n}|u(x,s)|^p\phi(x,s)dx
\end{array}
\end{equation}
with any $\phi\in C_0^{\infty}({\bf R}^n\times[0,T))$ and any $t\in[0,T)$.
\end{Def}

We note that, employing the integration by parts in (\ref{sol})
and letting $t\rightarrow T$, we have that
\[
\begin{array}{l}
\displaystyle\int_{{\bf R}^n\times[0,T)}
u(x,s)\left\{\phi_{tt}(x,s)-\Delta \phi(x,s)
-\left(\frac{\mu\phi(x,s)}{1+s}\right)_s \right\}dxds\\
\displaystyle=\int_{{\bf R}^n}\mu u(x,0)\phi(x,0)dx-\int_{{\bf R}^n}u(x,0)\phi_t(x,0)dx\\
\displaystyle\quad+\int_{{\bf R}^n}u_t(x,0)\phi(x,0)dx+\int_{{\bf R}^n\times[0,T)}|u(x,s)|^p\phi(x,s)dxds.
\end{array}
\]
This is exactly the definition of a weak solution of (\ref{IVP}).
\par
Our main result is the following theorem.

\begin{thm}
\label{thm:main}
Let $n\ge2$,
\begin{equation}
\label{mup}
0<\mu<\mu_0(n):=\frac{n^2+n+2}{2(n+2)}
\quad\mbox{and}\quad
p_F(n)\le p<p_0(n+2\mu).
\end{equation}
Assume that both $f\in H^1({\bf R}^n)$ and $g\in L^2({\bf R}^n)$
are non-negative and do not vanish identically.
Suppose that an energy solution $u$ of (\ref{IVP}) satisfies
\begin{equation}
\label{support}
\mbox{\rm supp}\ u\ \subset\{(x,t)\in{\bf R}^n\times[0,T)\ :\ |x|\le t+R\}
\end{equation}
with some $R\ge1$.
Then, there exists a constant ${\varepsilon}_0
={\varepsilon}_0(f,g,n,p,\mu,R)>0$ such that $T$ has to satisfy
\begin{equation}
\label{lifespan}
T\le C{\varepsilon}^{-2p(p-1)/\gamma(p,n+2\mu)}
\end{equation}
for $0<{\varepsilon}\le{\varepsilon}_0$, where $C$ is a positive constant independent of ${\varepsilon}$.
\end{thm}
\begin{rem}
Theorem \ref{thm:main} can be established also for $n=1$
if one define $\phi_1(x)=e^x+e^{-x}$ for $x\in{\bf R}$ in Section 3 below.
But the result is not new.
See the following two remarks.
\end{rem}
\begin{rem}
In view of (\ref{fujita}) and (\ref{gamma}),
one can see that
\[
\gamma\left(p_F(n),n+2\mu\right)
=\frac{2}{n^2}\left\{n^2+n+2-2(n+2)\mu\right\}.
\]
Therefore $0<\mu<\mu_0(n)$ is equivalent to
\[
p_F(n)<p_0(n+2\mu).
\]
We note that $\mu_0(2)=1$.
This means that Theorem \ref{thm:main} just covers
the non-effective range of $\mu$ for $n=2$.
Since $\mu_0(n)$ is increasing in $n$,
Theorem \ref{thm:main} gives us the blow-up result on super-Fujita exponent
even for $\mu$ in outside of the non-effective range for $n\ge3$.
We also note that
$\mu_0(n)<2$ for $n=2,3,4$ and
$\mu_0(n)>2$ for $n\ge5$.
\end{rem}

\begin{rem}
One can see also that
\[
\gamma\left(1+\frac{2}{n+\mu-1},n+2\mu\right)\
=\frac{2\left\{(n-1)^2+(n-3)\mu\right\}}{(n+\mu-1)^2}.
\]
Therefore we have that
\[
1+\frac{2}{n+\mu-1}<p_0(n+2\mu)
\]
for $n=2$ and $0<\mu<1$, or $n\ge3$ and $\mu>0$.
This means that Theorem \ref{thm:main}
includes the blow-up result in Wakasugi \cite{WY14_scale}.
\end{rem}

\begin{rem}
If $\beta$ is in the scattering range, $(1,\infty)$, for the problem,
\[
u_{tt}-\Delta u+\frac{\mu}{(1+t)^\beta}u_t=|u|^p,
\]
the result will be
\[
T\le C{\varepsilon}^{-2p(p-1)/\gamma(p,n)}
\quad\mbox{for}\ 1<p<p_0(n)
\]
for all $\mu>0$.
This estimate coincides with the one for non-damped equation,
\[
u_{tt}-\Delta u=|u|^p
\]
except for the case of $\int_{{\bf R}^2}g(x)dx\neq0$ in $n=2$ and $1<p\le2$.
See Introduction of Takamura \cite{Takamura15} for its summary.
The proof of this fact will appear in our forthcoming paper.
\end{rem}
\section{Lower bound of the functional}
\par\quad
Let $u$ be an energy solution of (\ref{IVP}) on $[0,T)$.
We estimate
\[
F_0(t):=\int_{{\bf R}^n}u(x,t)dx
\]
from below in this section.
Choosing the test function $\phi=\phi(x,s)$ in (\ref{sol}) to satisfy
$\phi\equiv 1$ in $\{(x,s)\in {\bf R}^n\times[0,t]:|x|\le s+R\}$, we get
\[
\begin{array}{l}
\displaystyle\int_{{\bf R}^n}u_t(x,t)dx-\int_{{\bf R}^n}u_t(x,0)dx\\
\displaystyle+\int_0^tds\int_{{\bf R}^n}\frac{\mu u_t(x,s)}{1+s}dx
=\int_0^tds\int_{{\bf R}^n}|u(x,s)|^pdx,
\end{array}
\]
which means that
\[
F'_0(t)-F'_0(0)+\int_0^t\frac{\mu F'_0(s)}{1+s}dx
=\int_0^tds\int_{{\bf R}^n}|u(x,s)|^pdx.
\]
All the quantities in this equation except for $F'_0(t)$ are differentiable in $t$,
so that so is $F'_0(t)$.
Hence we have
\begin{equation}
\label{ode}
F''_0(t)+\frac{\mu F'_0(t)}{1+t}
=\int_{{\bf R}^n}|u(x,t)|^pdx.
\end{equation}
Integrating this equation with a multiplication by $(1+t)^\mu$, we obtain
\begin{equation}
\label{F'_0}
(1+t)^\mu F'_0(t)-F'_0(0)=\int_0^t(1+s)^{\mu}ds\int_{{\bf R}^n}|u(x,s)|^pdx.
\end{equation}
It follows from this equation and the assumption on the initial data that
\begin{equation}
\label{positive}
F'_0(t)\ge (1+t)^{-\mu}F'_0(0)>0
\quad\mbox{and}\quad
F_0(t)\ge F_0(0)>0
\quad\mbox{for}\quad
t\ge0.
\end{equation}
\par
From now on, we employ the modified argument of Yordanov and Zhang \cite{YZ06}.
Let us define
\[
F_1(t):=\int_{{\bf R}^n}u(x,t)\psi_1(x,t)dx,
\]
where
\[
\psi_1(x,t):=\phi_1(x)e^{-t},
\quad
\phi_1(x):=\int_{S^{n-1}}e^{x\cdot\omega}dS_\omega.
\]
In view of (\ref{F'_0}) and the argument of (2.4)-(2.5) in \cite{YZ06},
we know that there is a positive constant $C_1=C_1(n,p,R)$ such that
\begin{equation}
\label{YZ}
(1+t)^\mu F'_0(t)-F'_0(0)\ge C_1\int_0^t(1+s)^{\mu+(n-1)(1-p/2)}|F_1(s)|^pds.
\end{equation}
\par
In order to get a lower bound of $F_1(t)$,
we turn back to (\ref{sol}) and obtain that
\[
\begin{array}{l}
\displaystyle\frac{d}{dt}\int_{{\bf R}^n}u_t(x,t)\phi(x,t)dx\\
\displaystyle+\int_{{\bf R}^n}\left\{-u_t(x,t)\phi_t(x,t)-u(x,t)\Delta\phi(x,t)\right\}dx\\
\displaystyle+\int_{{\bf R}^n}\frac{\mu u_t(x,t)}{1+t}\phi(x,t)dx
=\int_{{\bf R}^n}|u(x,t)|^p\phi(x,t)dx.
\end{array}
\]
Multiplying the above equality by$(1+t)^{\mu}$, we have that
\[
\begin{array}{l}
\displaystyle\frac{d}{dt}\left\{(1+t)^\mu\int_{{\bf R}^n}u_t(x,t)\phi(x,t)dx\right\}\\
\displaystyle+(1+t)^\mu\int_{{\bf R}^n}\left\{-u_t(x,t)\phi_t(x,t)-u(x,t)\Delta\phi(x,t)\right\}dx\\
\displaystyle=(1+t)^\mu\int_{{\bf R}^n}|u(x,t)|^p\phi(x,t)dx.
\end{array}
\]
Integrating this equality over $[0,t]$, we get
\[
\begin{array}{l}
\displaystyle(1+t)^\mu\int_{{\bf R}^n}u_t(x,t)\phi(x,t)dx-{\varepsilon}\int_{{\bf R}^n}g(x)\phi(x,0)dx\\
\displaystyle-\int_0^tds\int_{{\bf R}^n}(1+s)^\mu u_t(x,s)\phi_t(x,s)dx\\
\displaystyle=\int_0^tds\int_{{\bf R}^n}\left\{(1+s)^\mu u(x,s)\Delta\phi(x,s)+(1+s)^\mu|u(x,s)|^p\phi(x,s)\right\}dx.
\end{array}
\]
It follows from this equation and
\[
\begin{array}{l}
\displaystyle\int_0^tds\int_{{\bf R}^n}(1+s)^\mu u_t(x,s)\phi_t(x,s)dx\\
\displaystyle=(1+t)^\mu\int_{{\bf R}^n}u(x,t)\phi_t(x,t)dx-\int_{{\bf R}^n}u(x,0)\phi_t(x,0)dx\\
\quad\displaystyle-\int_0^tds\int_{{\bf R}^n}\mu(1+s)^{\mu-1}u(x,s)\phi_t(x,s)dx\\
\quad\displaystyle-\int_0^tds\int_{{\bf R}^n}(1+s)^\mu u(x,s)\phi_{tt}(x,s)dx,
\end{array}
\]
which follows from integration by parts that
\[
\begin{array}{l}
\displaystyle(1+t)^\mu\int_{{\bf R}^n}\left\{u_t(x,t)\phi(x,t)-u(x,t)\phi_t(x,t)\right\}dx\\
\displaystyle-{\varepsilon}\int_{{\bf R}^n}g(x)\phi(x,0)dx+{\varepsilon}\int_{{\bf R}^n}f(x)\phi_t(x,0)dx\\
\displaystyle+\int_0^tds\int_{{\bf R}^n}\mu(1+s)^{\mu-1}u(x,s)\phi_t(x,s)dx\\
\displaystyle=\int_0^tds\int_{{\bf R}^n}(1+s)^\mu u(x,s)\{\Delta\phi(x,s)-\phi_{tt}(x,s)\}dx\\
\quad\displaystyle+\int_0^tds\int_{{\bf R}^n}(1+s)^\mu|u(x,s)|^p\phi(x,s)dx.
\end{array}
\]
\par
If we put
\[
\phi(x,t)=\psi_1(x,t)=e^{-t}\phi_1(x)
\quad\mbox{on}\quad \mbox{supp}\ u,
\]
we have
\[
\phi_t=-\phi,\ \phi_{tt}=\Delta\phi \quad\mbox{on}\quad \mbox{supp}\ u.
\]
Hence we obtain that
\[
\begin{array}{l}
\displaystyle(1+t)^\mu F_1'(t)+2(1+t)^\mu F_1(t)-{\varepsilon}\int_{{\bf R}^n}\left\{f(x)+g(x)\right\}\phi(x)dx\\
\displaystyle=\int_0^t\mu(1+s)^{\mu-1}F_1(s)ds
+\int_0^tds\int_{{\bf R}^n}(1+s)^\mu|u(x,s)|^p\phi(t, x)dx,
\end{array}
\]
which yields
\[
F_1'(t)+2F_1(t)\ge\frac{C_{f,g}{\varepsilon}}{(1+t)^\mu}+\frac{1}{(1+t)^\mu}\int_0^t\mu(1+s)^{\mu-1}F_1(s)ds,
\]
where
\[
C_{f,g}:=\int_{{\bf R}^n}\left\{f(x)+g(x)\right\}\phi_1(x)dx>0.
\]
Integrating this inequality over $[0,t]$ with a multiplication by $e^{2t}$, we get
\begin{equation}
\label{ineq:F1}
\begin{array}{ll}
e^{2t}F_1(t)\ge
&\displaystyle F_1(0)+C_{f,g}{\varepsilon}\int_0^t\frac{e^{2s}}{(1+s)^\mu}ds\\
&\displaystyle+\int_0^t\frac{e^{2s}}{(1+s)^\mu}ds\int_0^s\mu(1+r)^{\mu-1}F_1(r)dr.
\end{array}
\end{equation}
We note that the assumption on $f$ implies $F_1(0)>0$.
Hence we find that there is no zero point of $F_1(t)$ for $t>0$.
Because the continuity of $F_1$ implies $F_1(t)>0$ for small $t>0$.
If one assumes that there is a nearest zero point $t_0$ of $F_1$ to $0$,
then one has a contradiction in (\ref{ineq:F1});
\[
\begin{array}{ll}
e^{2t_0}F_1(t_0)=0\ge
&\displaystyle F_1(0)+C_{f,g}{\varepsilon}\int_0^{t_0}\frac{e^{2s}}{(1+s)^\mu}ds\\
&\displaystyle+\int_0^{t_0}\frac{e^{2s}}{(1+s)^\mu}ds\int_0^s\mu(1+r)^{\mu-1}F_1(r)dr.
\end{array}
\]
The last term in the right-hand side of this inequality is positive by $F_1(t)>0$ for $0<t<t_0$.
Turning back to (\ref{ineq:F1}), we obtain
\[
F_1(t)>\frac{C_{f,g}{\varepsilon}}{2(1+t)^\mu}(1-e^{-2t})+e^{-2t}F_1(0)
\ge\frac{C_{f,0}{\varepsilon}}{2(1+t)^\mu}\quad\mbox{for}\ t\ge0.
\]
Here we have used the fact that $C_{f,g}>C_{f,0}$.
\par
Plugging this estimate into (\ref{YZ}), we have
\[
(1+t)^\mu F'_0(t)-F'_0(0)>\frac{C_1C_{f,0}^p}{2^p}{\varepsilon}^p\int_0^t(1+s)^{\mu(1-p)+(n-1)(1-p/2)}ds.
\]
Since $F'_0(0)>0$ and it follows from $t\ge1$ that
\[
\begin{array}{l}
\displaystyle\int_0^t(1+s)^{\mu(1-p)+(n-1)(1-p/2)}ds
\ge(2t)^{\mu(1-p)}\int_{t/2}^ts^{(n-1)(1-p/2)}ds\\
\qquad\displaystyle\ge2^{\mu(1-p)-(n-1)(1-p/2)+1}t^{1+\mu(1-p)+(n-1)(1-p/2)},
\end{array}
\]
we obtain that
\[
F'_0(t)>C_2{\varepsilon}^pt^{1-\mu p+(n-1)(1-p/2)}
\quad\mbox{for}\ t\ge1,
\]
where
\[
C_2:=\frac{C_1C_{f,0}^p}{2^{(\mu+1)p+(n-1)(1-p/2)-1}}>0.
\]
Here we have used the fact that
\[
1+(n-1)\left(1-\frac{p}{2}\right)>0
\]
follows from
\[
p<p_0(n+2\mu)<
\left\{
\begin{array}{ll}
p_0(n)\le p_0(4)=2 & \mbox{for}\ n\ge4,\\
p_0(3)=1+\sqrt{2}<3 & \mbox{for}\ n=3,\\
p_0(2)=(3+\sqrt{17})/2<4 & \mbox{for}\ n=2.
\end{array}
\right.
\]
Integrating this inequality over $[1,t]$ and making use of $F_0(0)>0$ and
\[
\int_1^ts^{1-\mu p+(n-1)(1-p/2)}ds
\ge t^{-\mu p}\int_{t/2}^ts^{1+(n-1)(1-p/2)}ds
\quad\mbox{for}\ t\ge2,
\]
we get
\begin{equation}
\label{lower bound}
F_0(t)>C_3{\varepsilon}^pt^{2-\mu p+(n-1)(1-p/2)}
\quad\mbox{for}\ t\ge2,
\end{equation}
where
\[
C_3:=\frac{C_2}{2^{2+(n-1)(1-p/2)}}>0.
\]

\section{Proof of Theorem \ref{thm:main} for $\v{\mu\ge2}$}
\par\quad
Let us define
\[
F(t):=\int_{{\bf R}^n}w(x,t)dx=(1+t)^{\mu/2}F_0(t),
\]
where $w$ is the solution of (\ref{IVP_1}).
We note that (\ref{ode}) yields
\begin{equation}
\label{ineq_LG}
F''(t)+\frac{\mu(2-\mu)}{4(1+t)^2}F(t)
=(1+t)^{-\mu(p-1)/2}\int_{{\bf R}^n}|w(x,t)|^pdx.
\end{equation}
Then it follows from (\ref{support}) and H\"older's inequality that
\begin{equation}
\label{ineq_LF}
\int_{{\bf R}^n}|w(x,t)|^pdx\ge\{\mbox{vol}({\bf B}^n(0,1))\}^{1-p}(t+R)^{-n(p-1)}|F(t)|^p.
\end{equation}
By combining \eqref{ineq_LG} and \eqref{ineq_LF}, and noting the assumption $R\ge1$, we come to
\begin{equation}
\label{ineq_F}
F''(t)+\frac{\mu(2-\mu)}{4(1+t)^2}F(t)
\ge C_4(1+t)^{-(n+\mu/2)(p-1)}|F(t)|^p
\quad\mbox{for}\ t\ge0,
\end{equation}
where
\[
C_4:=\{\mbox{vol}({\bf B}^n(0,1))\}^{1-p}R^{-n(p-1)}>0.
\]
Due to (\ref{positive}), we have that
\begin{equation}
\label{positive_F}
\begin{array}{l}
F(t)=(1+t)^{\mu/2}F_0(t)>0,\\
\displaystyle F'(t)=\frac{\mu}{2}(1+t)^{\mu/2-1}F_0(t)+(1+t)^{\mu/2}F'_0(t)>0,
\end{array}
\end{equation}
which implies that
\begin{equation}
\label{data_Fat0}
\begin{array}{l}
F(0)=F_0(0)=\|f\|_{L^1({\bf R}^n)}{\varepsilon},\\
\displaystyle F'(0)=\frac{\mu}{2}F_0(0)+F'_0(0)
=\left(\frac{\mu}{2}\|f\|_{L^1({\bf R}^n)}+\|g\|_{L^1({\bf R}^n)}\right){\varepsilon}.
\end{array}
\end{equation}
\par
From now on, we focus on the case of $\mu\ge2$.
Then it follows from (\ref{ineq_F}) and (\ref{positive_F}) that
\begin{equation}
\label{ineq_F>2}
F''(t)\ge C_4(1+t)^{-(n+\mu/2)(p-1)}|F(t)|^p.
\end{equation}
We shall employ the following lemma now.
\begin{lem}[Takamura\cite{Takamura15}]
\label{lem:odi}Let $p>1,a>0,q>0$ satisfy
\begin{equation}
\label{condi:M}
M:=\frac{p-1}{2}a-\frac{q}{2}+1>0.
\end{equation}
 Assume that $F\in C^2([0,T))$ satisfies
\begin{eqnarray}
& F(t)\ge  At^a &  \mbox{for}\ t\ge T_0,\label{ineq:A}\\
& \displaystyle F''(t)\ge B(t+R)^{-q}|F(t)|^p& \mbox{for}\ t\ge0,\label{ineq:B}\\
& F(0)\ge0,\ F'(0)>0,\label{ineq:C}&
\end{eqnarray}
where $A,B,R,T_0$ are positive constants.
Then, there exists a positive constant $C_0=C_0(p,a,q,B)$ such that
\begin{equation}
\label{est:T1}
T<2^{2/M}T_1
\end{equation}
holds provided
\begin{equation}
\label{condi}
T_1:=\max\left\{T_0,\frac{F(0)}{F'(0)},R\right\}\ge C_0 A^{-(p-1)/(2M)}.
\end{equation}
\end{lem}

Due to the lower bound of $F_0$ in (\ref{lower bound}) and the definition of $F(t)$ in \eqref{positive_F},
we have
\begin{equation}
\label{lower bound_F}
F(t)>C_3{\varepsilon}^pt^{2-\mu p+(n-1)(1-p/2)+\mu/2}
\quad\mbox{for}\ t\ge2,
\end{equation}
which is (\ref{ineq:A}) in Lemma \ref{lem:odi} with
\[
A=C_3{\varepsilon}^p,
\quad a=2-\mu p+(n-1)\left(1-\frac{p}{2}\right)+\frac{\mu}{2},
\quad T_0=2.
\]
The inequality (\ref{ineq:B}) with
\[
B=C_4,
\quad q=\left(n+\frac{\mu}{2}\right)(p-1)
\]
follows from (\ref{ineq_F>2}), and
(\ref{ineq:C})  is already established by (\ref{data_Fat0}).
The final step to use Lemma \ref{lem:odi} is to check the sign of $M$. By the assumption that
$p<p_0(n+2\mu)$, we have
\[
M=\frac{\gamma(p,n+2\mu)}{4}>0.
\]

Set
\[
T_0=C_0A^{-(p-1)/(2M)}=C_0C_3^{-2(p-1)/\gamma(p,n+2\mu)}{\varepsilon}^{-2p(p-1)/\gamma(p,n+2\mu)}.
\]
Then, since $F(0)/F'(0)$ is independent of ${\varepsilon}$ by (\ref{data_Fat0}),
one can see that there is an ${\varepsilon}_0={\varepsilon}_0(f,g,n,p,\mu,R)>0$ such that
\[
T_0\ge\max\left\{2,\frac{F(0)}{F'(0)}\right\}\quad \mbox{for}\ 0<{\varepsilon}\le {\varepsilon}_0 .
\]
This means that $T_1=T_0$ in (\ref{condi}).
Therefore the conclusion of Lemma \ref{lem:odi} implies that the maximal existence
time $T$ of $F(t)$ has to satisfy
\[
T\le C_5{\varepsilon}^{-2p(p-1)/\gamma(p,n+2\mu)}\quad \mbox{for}\ 0<{\varepsilon} \le {\varepsilon}_0,
\]
where
\[
C_5:=2^{8/\gamma(p,n+2\mu)}C_0C_4^{-2(p-1)/\gamma(p,n+2\mu)}>0.
\]
This completes the proof in the case of $\mu\ge2$.
\hfill$\Box$

\section{Proof of Theorem \ref{thm:main} for $\v{0<\mu<2}$}
\par\quad
Before showing the proof of Theorem \ref{thm:main} for $0<\mu<2$, we first prepare the following
lemma:
\begin{lem}
\label{lem:treat-mass}
Suppose that the assumption in Theorem \ref{thm:main} is fulfilled.
Then it holds that
\begin{equation}
\label{F'}
F'(t)>\sqrt{\frac{C_4}{2(p+1)}}(1+t)^{-(n+\mu/2)(p-1)/2}F(t)^{(p+1)/2}
\end{equation}
for $t\ge C_6{\varepsilon}^{-2p(p-1)/\gamma(p,n+2\mu)}$, where we set
\[
C_6:=\left(\frac{\mu(2-\mu)(p+1)}{2C_3^{p-1}C_4}\right)^{1/X}>0
\]
and
\begin{equation}\nonumber
\begin{aligned}
X&:=2-\left(n+\frac{\mu}{2}\right)(p-1)
+(p-1)\left\{2-\mu p+(n-1)\left(1-\frac{p}{2}\right)+\frac{\mu}{2}\right\}\\
&=\frac{\gamma(p,n+2\mu)}{2}.
\end{aligned}
\end{equation}
$C_3$, $C_4$ are the one in (\ref{lower bound}), (\ref{ineq_F}), respectively,
\end{lem}
{\bf Proof.}
Multiplying the both sides of (\ref{ineq_F}) by $(1+t)^2F'(t)>0$ and noting that (\ref{positive_F}),
we get
\[
\begin{array}{l}
\displaystyle\frac{(1+t)^2}{2}\left\{\left(F'(t)\right)^2\right\}'
+\frac{\mu(2-\mu)}{8}\{F(t)^2\}'\\
\displaystyle\ge C_4(1+t)^{2-(n+\mu/2)(p-1)}F(t)^pF'(t)
\end{array}
\quad\mbox{for}\ t\ge0.
\]
Integration by parts yields that
\[
\begin{array}{l}
\displaystyle\frac{(1+t)^2}{2}\left(F'(t)\right)^2
+\frac{\mu(2-\mu)}{8}F(t)^2\\
\displaystyle>C_4\int_0^t(1+s)^{2-(n+\mu/2)(p-1)}F(s)^pF'(s)ds
\end{array}
\quad\mbox{for}\ t\ge0.
\]
Noting the assumption on $p$
\[
p\ge p_F(n)>1+\frac{2}{n+\displaystyle\frac{\mu}{2}}
\quad\mbox{for}\ \mu>0,
\]
it is easy to get that
\[
2-\left(n+\frac{\mu}{2}\right)(p-1)<0.
\]
And hence we have
\[
\begin{array}{l}
\displaystyle\int_0^t(1+s)^{2-(n+\mu/2)(p-1)}F(s)^pF'(s)ds\\
\displaystyle\ge(1+t)^{2-(n+\mu/2)(p-1)}\frac{F(t)^{p+1}-F(0)^{p+1}}{p+1}.
\end{array}
\]
Since
\[
p_F(n)=1+\frac{2}{n}>\frac{2}{n+1-\mu}\quad
\mbox{for $n\ge2$ and $0<\mu<2$},
\]
and hence
\[
p>\frac{2}{n+1-\mu}.
\]
This is equivalent to
\[
p\left(2-\mu p+(n-1)\left(1-\frac{p}{2}\right)+\frac{\mu}{2}\right)
>\frac{\gamma(p,n+2\mu)}{2}.
\]
Thus, for $t\ge C_6{\varepsilon}^{-2p(p-1)/\gamma(p,n+2\mu)}\ge 2$ (${\varepsilon}$ small enough), we have
\begin{equation}
\label{restriction2_new}
C_3{\varepsilon}^pt^{2-\mu p+(n-1)(1-p/2)+\mu/2}\ge2\|f\|_{L^1({\bf R}^n)}{\varepsilon},
\end{equation}
which implies
\begin{equation}
\label{restriction2}
F(t)\ge 2F(0).
\end{equation}
Hence, it follows from
\[
F(t)^{p+1}-F(0)^{p+1}\ge F(t)^p\left\{F(t)-F(0)\right\}\ge\frac{1}{2}F(t)^{p+1}
\]
that
\begin{equation}
\label{F'-final}
\frac{(1+t)^2}{2}\left(F'(t)\right)^2
+\frac{\mu(2-\mu)}{8}F(t)^2>\frac{C_4(1+t)^{2-(n+\mu/2)(p-1)}F(t)^{p+1}}{2(p+1)}
\end{equation}
for $t\ge C_6{\varepsilon}^{-2p(p-1)/\gamma(p,n+2\mu)}$.

On the other hand, for $t\ge C_6{\varepsilon}^{-2p(p-1)/\gamma(p,n+2\mu)}$, we have
\[
\frac{C_4}{4(p+1)}(1+t)^{2-(n+\mu/2)(p-1)}\{C_3{\varepsilon}^pt^{2-\mu p+(n-1)(1-p/2)+\mu/2}\}^{p-1}
\ge \frac{\mu(2-\mu)}{8}
\]
which gives us
\begin{equation}
\label{restriction1}
\frac{C_4}{4(p+1)}(1+t)^{2-(n+\mu/2)(p-1)}F(t)^{p+1}
\ge\frac{\mu(2-\mu)}{8}F(t)^2
\end{equation}
 by combining \eqref{lower bound_F}.
Therefore, we get (\ref{F'}) from (\ref{F'-final}).

\hfill$\Box$
\par
By (\ref{F'}), it is easy to see that
there is a ${\varepsilon}_0={\varepsilon}_0(f,g,n,p,\mu,R)>0$ such that
\[
\frac{F'(t)}{F(t)^{1+\delta}}
>\sqrt{\frac{C_4}{2(p+1)}}(1+t)^{-(n+\mu/2)(p-1)/2}F(t)^{(p-1)/2-\delta}
\]
with $0<\delta<(p-1)/2$ holds for
\[
\ t\ge T_1:=C_6{\varepsilon}^{-2p(p-1)/\gamma(p,n+2\mu)}
\quad\mbox{and}\quad 0<{\varepsilon}\le{\varepsilon}_0.
\]
Here we use our lower bound of $F$ in (\ref{lower bound_F}) again to get
\begin{equation}
\label{contradict:F}
\frac{F'(t)}{F(t)^{1+\delta}}
>C_3^{(p-1)/2-\delta}\sqrt{\frac{C_4}{2(p+1)}}{\varepsilon}^{p\{(p-1)/2-\delta\}}t^Y
\quad\mbox{for}\ t\ge T_1,
\end{equation}
where
\[
\begin{array}{ll}
Y
&\displaystyle:=\left(\frac{p-1}{2}-\delta\right)
\left\{2-\mu p+(n-1)\left(1-\frac{p}{2}\right)+\frac{\mu}{2}\right\}
-\left(n+\frac{\mu}{2}\right)\frac{p-1}{2}\\
&\displaystyle=\frac{\gamma(p,n+2\mu)}{4}-1
-\left\{2-\mu p+(n-1)\left(1-\frac{p}{2}\right)+\frac{\mu}{2}\right\}\delta.
\end{array}
\]
Therefore, taking $\delta$ small enough such that $Y+1>0$, we then have by integrating
(\ref{contradict:F}) over $[T_1,t]$,
\[
\frac{F(T_1)^{-\delta}}{\delta}>\frac{C_3^{(p-1)/2-\delta}}{Y+1}
\sqrt{\frac{C_4}{2(p+1)}}{\varepsilon}^{p\{(p-1)/2-\delta\}}(t^{Y+1}-T_1^{Y+1})
\quad\mbox{for}\ t\ge T_1.
\]
Making use of (\ref{lower bound_F}) with $t=T_1$ in this inequality, we obtain that
\[
1>C_7{\varepsilon}^{p(p-1)/2}T_1^{\gamma(p,n+2\mu)/4-(Y+1)}
(t^{Y+1}-T_1^{Y+1})
\quad\mbox{for}\ t\ge T_1,
\]
where
\[
C_7:=\frac{\delta C_3^{(p-1)/2}}{Y+1}
\sqrt{\frac{C_4}{2(p+1)}}>0
\]
If one sets $t=kT_1$ with $k>1$, then, due to the definition of $T_1$, one has
\[
1>C_7C_6^{\gamma(p,n+2\mu)/4}(k^{Y+1}-1).
\]
Therefore the conclusion of the Theorem \ref{thm:main},
\[
T\le C_8{\varepsilon}^{-2p(p-1)/\gamma(p,n+2\mu)}
\quad\mbox{for}\ 0<{\varepsilon}\le{\varepsilon}_0,
\]
is now established, where
\[
C_8:=\left(1+C_7^{-1}C_6^{-\gamma(p,n+2\mu)/4}\right)^{1/(Y+1)}C_6>0.
\]
This completes the proof in the case of $0<\mu<2$.
\hfill$\Box$

\section*{Acknowledgment}
\par\quad
The first author is partially supported by NSFC(11501273), high level talent project
of Lishui City(2016RC25), the Scientific Research Foundation of the First-Class Discipline of Zhejiang Province(B)(201601), the key laboratory of Zhejiang Province(2016E10007).
The second author is partially supported by the Grant-in-Aid for Scientific Research (C)
(No.15K04964),
Japan Society for the Promotion of Science,
and Special Research Expenses in FY2016, General Topics (No.B21),
Future University Hakodate.
\par
Finally, all the authors are grateful to Prof.M.Reissig
(Technical University Bergakademie Freiberg, Germany)
for his great advice on the classification of the linear problem
for which our first manuscript of arXiv:1701.03232 was not appropriate.

\bibliographystyle{plain}

redpajama_set_name: RedPajamaArXiv


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By Meredith Mazzotta on October 21, 2010 .
This entry was posted in HIV/TB Co-infection, HIV/AIDS, IDSA 2010, U.S. Policy and Funding on October 21, 2010 .
By Staff Writer on October 21, 2010 .
Dr. Sten H. Vermund – a member of the Center's Scientific Advisory Board – released a new report in Current HIV/AIDS Reports this week on the significance, challenges and opportunities in combination HIV prevention strategies. He suggests that these "prevention packages" be scaled up and their effectiveness evaluated.
This week, the World Health Organization released its first report on neglected tropical diseases. Erin Hohlfelder at the ONE blog has a good post on the significance of this publication, saying it is the end of "report neglect" on NTDs.
This entry was posted in HIV/TB Co-infection, HIV/AIDS, TB, What we're reading on October 21, 2010 .


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> ES6 template string tag for multi-line blocks of text.

This template string tag allows you to create nicely formatted text blocks which are indented to match your code.

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Support for template strings exists in Node as of 4.0.0, but this module is not tied to that engine in `package.json` because Babel users should be able to use it on many other platforms (including the browser).

## Inspiration

If you didn't guess from the name, this module is inspired by Rod Vagg's [`tsml`](https://github.com/rvagg/tsml), which is similar except it takes a multi-line template string and returns a single line string. It's also very useful!

## License

`tsmlb` is Copyright (c) 2015 Pat O'Neill and licensed under the MIT license.

redpajama_set_name: RedPajamaGithub


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This entry was posted in Current Events, information security, Risk, Science, Security by mordaxus. Bookmark the permalink.
Disclosure: I play a peripheral role in quantum crypto commercialization efforts.
The discussion around the latest Makarov paper is somewhat misleading. The basic Makarov attack has been known for a couple of years (I heard him talk about it in Vienna in 2008), and the actual news in the current paper is that he managed to tune it so finely that the error rate no longer changes noticeably.
You say "quantum information science" needs to respond, but actual QI scientists don't care about this specific attack much since it's an implementation problem, so the onus is more or less on the experimentalists/engineers. Some QIS people try to solve a more general problem and produce a different security model where one can verify the confidentiality of the produced key under the heading of "device-independent QKD" (a bit of a misnomer in my lowly opinion), but I think this stuff is far out in theory-land at the moment.
Countermeasures are also not that hard to come up with, since the difference between "Makarov attack" and "no Makarov attack" is easy to recognize if you look for it – in one case, you have a continuous laser beam shining into your device, in the other you have dark fiber with the occasional single photon.
All that said, I'm aware that the QKD world needs more serious security engineering. Since the entire field is very much physicist-dominated, there are not that many considerations beyond "and then, you have the key on both sides with confidentiality guarantee epsilon and identity guarantee delta" and many of the higher-level designs of how to extend this to networks etc seem to lack sophistication compared to what I see in Internet work.
Thanks for writing, Thomas, and for your words.
For some time now, there's been tension between us classical security people and the QIS folks. Most of that comes from what we see as a lack of humility in the physics world. It's as if the QIS people think that because they're doing physics, they're immune to human frailties.
Most of us are science geeks. We're mathematicians, computer scientists, and engineers. We want to see QIS be successful. But because we're practitioners as much (well, more, really) than we're scientists, we have a very jaundiced eye that starts inward. If you look at the cryptographers with the most public successes and the ones with the most public failures, you'll find they're the same people. There's the old adage: How do you make good decisions? Through wisdom. How do you gain wisdom? Through bad decisions.
We'd love to help. It's nice that there have been quantum papers at the last couple of years of IACR conferences. It was pleasing to see a whole session in Santa Barbara a couple weeks ago. If there's anything you can do to help get security engineering with them, I'm sure you'll find people ready and willing to help.
A mere change in tone and language would help, too. If IDQ, MagiQ, and others said, "This is real. We take it seriously. We understand the issue and the fix will be deployed real soon now," the security people would say, "That's great. They have it under control." After all, we have our own long litany of things we were caught by.
Anyway, thanks for writing again, and thanks for reading, too.
Well maybe those actual QI scientists should find another field then.
Back in the 1950s a bunch of physicists decided they had found a method of making electricity that was practically free. Only thing was that they hadn't really thought about how to make it safe or what to do with the waste produced.
Instead they told us that the scheme they had thought up was absolutely safe and problem free. As a result the whole field of Nuclear power was discredited as serious problems occurred (Chernobyl, Three Mile Island) and the waste mounted up.
Now one of the big lies told by the nuclear industry is that Chernobyl was caused by Soviet reactor design techniques that were never used in the West. That is untrue. The Soviet reactor had a hidden flaw, a region of positive feedback that was not revealed using the limited 2D modeling simulations possible at the time. Western reactors were built using similar tools. Several of the UK Magnox reactors were shut down three years later in 1989.
The point I am making here is that if you are proposing a scheme for use in the real world then you had better learn to think like an engineer.
If nuclear power had been approached as an engineering problem rather than a science project we might have seen the type of designs that started to emerge in the 1990s that are genuinely 'fail-safe' designs. Rather than the fail-safe by assertion designs that were fobbed off as safe by scientists playing engineer.
Mordaxus is actually wrong with his title. The system was not quantum backdoored, the backdoor was in the classical physics. And this is what I suspect is going to prove the undoing of Quantum Cryptography.
Quantum cryptography looks very appealing as pure theory. But none of the systems that I have seen to date are implementable as a pure quantum system. So none of the systems are even theoretically quantum secure from an engineering point of view.


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